Energy Technology Data Exchange (ETDEWEB)
Lehnen, M.; Adbullaev, S.; Biel, W.; Bock, M. F. M.; Brezinsek, S.; Busch, C.; Classen, I.; Finken, K. H.; Hartin, D.; Hellermann, M. von; Jachmich, S.; Jakubowski, M.; Jaspers, R.; Koslowski, H. R.; Kramer-Flecken, A.; Kikuchi, Y.; Liang, Y.; Loozen, X.; Pospieszczyk, A.; Rompuy, T. van; Reiter, D.; Samm, U.; Schmitz, O.; Sergienko, G.; Tokar, M.; Unterberg, B.; Wolf, R.; Zimmermann, O.
2005-07-01
The concept of the Dynamic Ergodic Divertor (DED) is based on plasma edge ergodisation by a resonant perturbation. Such a divertor concept is closely related to helical or island divertors in stellarators. The base mode of the DED perturbation field can be m/n = 12 /4, 6/2 or 3/1. The 3/1 base mode with its deep penetration of the perturbation field provides the excitation of tearing modes. This topic was presented elsewhere. In this contribution we concentrate on the divertor properties of the DED. We report on the characterisation of the topology, transport properties in ergodic fields, divertor regimes, impurity transport and density limit behaviour. The 12/4 base mode where the perturbation is restricted to the plasma edge is suitable for divertor operation. With increasing perturbation field island chains are built up at the resonance layers. Overlapping islands lead to ergodisation. The plasma is guided in the laminar region via open field lines of short connection length to the divertor target. The magnetic topology is not only controlled by the coil current but especially by the edge safety factor. For appropriate edge safety factor we observe a strong temperature drop in the plasma edge, indicating an expanding laminar region, which is necessary to decouple the divertor plasma from the core plasma. This temperature drop is accompanied by a redistribution of the heat and particle flux on the divertor target which is measured by thermography, visible spectroscopy and Langmuir probes. The modifications of the magnetic topology by the DED are reflected in the distribution of the plasma edge density and temperature measured by atomic beams and can be directly seen for example from carbon emission lines. The magnetic structure is calculated by the ATLAS code and shows good agreement with the experimental findings. The particle and energy transport is modelled with the EMC3-EIRENE code package and is in qualitative agreement with the measured densities and
First results from the dynamic ergodic divertor at TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Lehnen, M. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, 52425 Juelich (Germany)]. E-mail: m.lehnen@fz-juelich.de; Abdullaev, S.S.; Biel, W.; Brezinsek, S.; Finken, K.H.; Harting, D.; Hellermann, M. von; Jakubowski, M.; Jaspers, R.; Kobayashi, M.; Koslowski, H.R.; Kraemer-Flecken, A.; Matsunaga, G.; Pospieszczyk, A.; Reiter, D.; Van Rompuy, T.; Samm, U.; Schmitz, O.; Sergienko, G.; Unterberg, B.; Wolf, R.; Zimmermann, O. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, 52425 Juelich (Germany)
2005-03-01
Experimental results from the dynamic ergodic divertor (DED) at TEXTOR are given, describing the complex structure of the edge plasma and the properties of the divertor as well as its influence on the plasma rotation.
Overview of experiments with the dynamic ergodic divertor on TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Finken, K.H.; Abdullaev, S.; Biel, W.; Brezinsek, S.; Busch, C.; Harting, D.; Jakubowski, M.; Koslowski, H.R.; Kraemer-Flecken, A.; Kikuchi, Y.; Lehnen, M.; Liang, Y.; Nicolai, A.; Pospieszczyk, A. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425 Juelich (Germany); Bock, M.F.M. de; Classen, I.; Hellermann, M. von; Jaspers, R. [FOM-Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box: 1207, NL-3430 BE Nieuwegein (Netherlands); Jachmich, S. [Laboratory for Plasma Physics, Association EURATOM - Belgian State, KMS - ERM, Trilateral Euregio Cluster, B-1000 Brussels (Belgium); Kobayashi, M. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki-shi 509-52 Toki (Japan); Reiter, D.; Rompuy, T. van; Samm, U.; Schmitz, O.; Sergienko, G.; Unterberg, B.; Westerhof, E.; Wolf, R.C.; Zimmermann, O.
2006-09-15
The Dynamic Ergodic Divertor (DED) has recently been taken into operation on TEXTOR. The device is rather flexible and allows the investigation of very different questions. In the present context we concentrate on the divertor aspect and on results of the m/n=12/4 base mode. The DED-field generates the proper ergodic zone and an area of open magnetic field lines, the laminar zone and the tangle structure. The properties of the laminar zone resemble the divertor region of a poloidal divertor. However, the distribution of the density and temperature is highly 3D and strongly related to the structure of the laminar and ergodic zones. The structures of the heat and particle fluxes to the wall agree well with the predicted patterns. A prominent feature of the ergodization is the creation of an edge electric field which results in a rotation of the plasma. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
The influence of the dynamic ergodic divertor on the radial electric field at the Tokamak TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Coenen, Jan Willem
2009-11-06
In this work the influence of external Resonant Magnetic Perturbations (RMPs) on the radial electric field Er in magnetically confined plasmas is investigated by Charge Exchange Recombination Spectroscopy (CXRS) at the Tokamak TEXTOR. Here, the RMPs are produced with the Dynamic Ergodic Divertor (DED), a set of 16 helical perturbation coils located at the high field side of TEXTOR. Within this work, the base mode number of perturbations has been m/n=6/2. We have first investigated the influence of external torque from neutral heating beams on plasma rotation and E{sub r}. The ergodic zone causes an electron loss, and subsequently a (vector)j x (vector)B force driven by the compensating ion return current. In addition, the DED changes the global confinement properties. Depending on the edge safety factor (''field line twist'') q{sub a}, either increased or decreased particle confinement is observed. In case of the increased particle confinement (IPC) the increase in density (40%) and particle confinement time {tau}{sub p} (30%) is correlated to the connection of field lines at the q=5/2 surface to the DED target, locally changing the transport properties and the E{sub r}. Transport is reduced and the E{sub r} shear is increased locally at q=5/2 up to 1.5 . 10{sup 5}s{sup -1}, while the E{sub r} becomes more positive. (orig.)
Tearing mode physics studies applying the dynamic ergodic divertor on TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Koslowski, H R [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Westerhof, E [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Bock, M de [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Classen, I [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Jaspers, R [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Kikuchi, Y [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Kraemer-Flecken, A [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Lazaros, A [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Liang, Y [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Loewenbrueck, K [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Varshney, S [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Hellermann, M von [FOM-Institute for Plasmaphysics ' Rijnhuizen' , Association EURATOM-FOM, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Wolf, R [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany); Zimmermann, O [Forschungszentrum Juelich GmbH, Institut fuer Plasmaphysik, Association EURATOM-FZ Juelich, D-52425 Juelich (Germany)
2006-12-15
The dynamic ergodic divertor (DED) on the TEXTOR tokamak allows for the reproducible destabilization of the m/n = 2/1 tearing mode which is phase locked to the external static or rotating perturbation field. In combination with its flexible heating systems (co- and counter-neutral beam injection, ion cyclotron resonance heating, electron cyclotron resonance heating (ECRH) with steerable launcher) dedicated experiments to study the mode onset, properties of large islands and mode stabilization can be performed. The dependence of the mode excitation threshold (field penetration) on the plasma rotation shows a resonance character, with minimum threshold when the external perturbation frequency matches the MHD frequency of the 2/1 mode. Mode stabilization by ECRH heating shows that for the TEXTOR plasma heating is more effective than the current drive in O-point. Extrapolation to ITER yields a significant contribution to the mode suppression originating from the temperature increase within the island. Alfven-like modes, which have been previously identified in the vicinity of large islands on FTU (Buratti et al 2005 Nuclear Fusion 45 1446), are found to be created already before island formation above a certain threshold of the externally applied perturbation field.
Study and simulation of carbon impurity dynamics near the ergodic divertor in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Giannella, R.; Cordier, J.J.; Corre, Y.; Ghendrih, P.; Guirlet, R.; Gunn, J. [Association Euratom-CEA, CEA/Cadarache, Dept. de Recherches sur la Fusion Controlee (DRFC), 13 - Saint-Paul-lez-Durance (France); Hogan, J. [Oak Ridge National Lab., TN (United States)
1999-10-15
In the past few years, effects induced by the ergodic dive such as impurity screening and transport modifications in the plasma edge have been used to achieve high radiation, low contamination regimes. A crucial issue in understanding these effects is that of impurity generation and propagation across the plasma edge, especially in the vicinity of the Ergodic Divertor (ED) neutralizer plates. A variety of diagnostic tools and techniques are used for this purpose. In the case of Tore Supra, interpretation of spectroscopic data is strongly complicated by the complex geometry of the ED, leading among other effects to the total lack of uniformity of the sources. Indeed, due to the specific pattern of impurity sources on the neutralizers and to their particular orientation with respect to the local magnetic field, densities of lowly ionised impurities are deeply modulated on the sub-centimeter scale in both directions perpendicular to the magnetic field. Because of this, accurate 3-D simulations are essential for the evaluation of experimental signals. (authors)
Turbulence during ergodic divertor experiments in Tore Supra
Energy Technology Data Exchange (ETDEWEB)
Payan, J.; Garbet, X.; Chatenet, J.H.; Clairet, F.; De Michelis, C.; Devynck, P.; Ghendrih, P.; Gil, C.; Grosman, A.; Guirlet, R. [and others
1994-12-01
The level of density fluctuations is shown to decrease during ergodic divertor operation in Tore Supra. This decrease of the turbulence is correlated with the onset of a temperature pedestal and a local improvement of the confinement. This pedestal is located close to the electric shear layer, i.e., within a narrow region between the plasma core and the ergodic layer. The onset of such a pedestal explains why the central electron temperature is not changed when the ergodic divertor is switched on, in spite of an ergodic zone where the temperature is low. (author). 30 refs., 14 figs.
The effect of the magnetic topology on particle recycling in the ergodic divertor of TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Lehnen, M. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany)]. E-mail: m.lehnen@fz-juelich.de; Abdullaev, S.S. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Brezinsek, S. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Finken, K.H. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Harting, D. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Hellermann, M. von [FOM-Rijnhuizen, Association EURATOM-FOM (Netherlands); Jakubowski, M.W. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Jaspers, R. [FOM-Rijnhuizen, Association EURATOM-FOM (Netherlands); Kirschner, A. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Pospieszczyk, A. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Reiter, D. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Samm, U. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Schmitz, O. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Sergienko, G. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Unterberg, B. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany); Wolf, R. [Institut fuer Plasmaphysik, Forschungszentrum Juelich, Association EURATOM-FZJ (Germany)
2007-06-15
The influence of the divertor geometry of the dynamic ergodic divertor (DED) in TEXTOR on particle recycling is discussed. The geometry can be varied by the choice of the base mode, the edge safety factor and the divertor coil current. The divertor volume is split into the upstream and the downstream area. Strong plasma flows in the downstream area, essential for high screening efficiency, are predicted. The source strength of deuterium and carbon in the downstream area is estimated by using the two-dimensional distribution of D{sub {alpha}} and CIII emission in front of the target. The results are compared to EMC3 and ERO-code calculations.
Ergodic theory and dynamical systems
Coudène, Yves
2016-01-01
This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of commen...
Edge turbulence and transport studies with ergodic divertor, on Tore Supra ohmic discharges
Energy Technology Data Exchange (ETDEWEB)
Payan, J.; Garbet, X.; Clairet, F.; Devynck, P.; Laviron, C.; Chatenet, J.H.; Ghendrih, P.N.; Grosman, A. [Association Euratom-CEA, Centre d`Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Gervais, F.; Hennequin, P.; Quemeneur, A.; Truc, A. [Ecole Polytechnique, 91 - Palaiseau (France). Lab. de Physique des Milieux Ionises
1995-12-31
Edge turbulence and transport studies have been performed when the ergodic divertor is applied on Tore Supra ohmic discharges. A modification of radial electric field profiles is expected. Such a change could influence edge transport and turbulence. A CO{sub 2} laser scattering diagnostic, ALTAIR, has been used to study the turbulence changes at the plasma edge. Reflectometry (used at fixed frequency) gives also access to localized turbulence measurements. Preliminary results from reflectometry are presented and compared to ALTAIR results. (K.A.) 6 refs.; 4 figs.
Energy Technology Data Exchange (ETDEWEB)
Costanzo, L
2001-10-01
The control of power deposition onto plasma facing components in tokamaks is a determining factor for future thermonuclear fusion reactors. Plasma surface interaction can be performed using limiters or divertors. The ergodic divertor installed on Tore Supra is an atypical example of a magnetic divertor. It consists in applying a magnetic perturbation which establishes a particular topology of the plasma in contact with the wall (edge plasma). We carried out dedicated experiments in order to study parallel heat flux which strike the divertor neutralizers. This quantitative and qualitative analysis of heat flux as a function of experimental conditions allows to determine the profiles of power deposition along the neutralizers. The influence of plasma electron density, additional heating, impurities and injected gas was established. An experimental study of the sheath heat transmission factor {gamma} was carried out by correlating measurements made with Langmuir probes and infrared imaging. This study gave rise to a major conclusion: for ohmic discharges with deuterium injection and most of the time with helium, it was experimentally confirmed that {gamma}=7 in agreement with classical sheath theory. However, an increase of this factor with additional power has been shown. Detached plasma, which is an attractive regime in order to reduce the power deposition, requires an optimized control. A new measurement of the detachment onset has been developed. It is based on the variation of heat flux onto the plates derived from infrared measurements. A detachment cartography with the determination of a new 2D 'IR' Degree of Detachment was carried out allowing to locate the zone where the detachment starts. We can apply this concept both to other tokamaks such as JET and ITER. A comparison between the axisymmetric divertor and the ergodic divertor is also presented concerning the power deposition in the two configurations. Low heat flux with the ergodic divertor is a
Ergodic Theory, Open Dynamics, and Coherent Structures
Bose, Christopher; Froyland, Gary
2014-01-01
This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, dynamical systems, numerical analysis, fluid dynamics, and networks. The volume will serve as a valuable reference for mathematicians, physicists, engineers, physical oceanographers, atmospheric scientists, biologists, and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open, coherent, or non-equilibrium behavior.
Energy Technology Data Exchange (ETDEWEB)
Owen, L.W. [Oak Ridge National Lab., TN (United States); Loarer, T. [Association CEA-Euratom, CEN/Cadarache, F-13108 St. Paul-les-Durance Cedex (France); Grosman, A. [Association CEA-Euratom, CEN/Cadarache, F-13108 St. Paul-les-Durance Cedex (France); Meslin, B. [Association CEA-Euratom, CEN/Cadarache, F-13108 St. Paul-les-Durance Cedex (France); Klepper, C.C. [Oak Ridge National Lab., TN (United States); Mioduszewski, P.K. [Oak Ridge National Lab., TN (United States); Uckan, T. [Oak Ridge National Lab., TN (United States)
1997-02-01
Active control of the core plasma density and partial depletion of the wall particle content have been achieved in experiments on Tore Supra with the plasma leaning on either the ergodic divertor (ED) or the pump limiters. Measurements of neutral pressures in the ED and outboard pump limiter (OPL) are modeled with 1D parallel transport equations (continuity and momentum balance) for the SOL plasma coupled to 2D neutral particle transport simulations. SOL density and temperature profiles from reciprocating Langmuir probe measurements for a range of volume-averaged densities are renormalized, where necessary, to agree with Langmuir probe measurements in the OPL throat and constitute the upstream boundary conditions for the 1D calculations. Good agreement with measured pressures and exhaust rates are obtained for both the ED and OPL in scans that span a factor of 2-3 in volume-averaged density. The importance of a self-consistent treatment of the plasma and neutral particle transport in the neighborhood of the neutralizer plate is demonstrated, particularly in the stronger recycling regimes characteristic of densities at the high end of the scans. Plasma flow reversal near the plasma/plenum interface is predicted to occur at the higher densities due to the large local ionization source. Predictions of pressure buildup in the plenum behind the prototype vented neutralizer plate agree with experiment if it is assumed that both the tops and partially the sides of the needles comprising the plate are wetted by the plasma. A discharge in which the ED pumps are active is analyzed; the calculated pressure and exhaust rate agree with experiment. The core fueling rate is the same as without pumping, suggesting, as is seen in the experiment, a small density decay rate and significant wall particle depletion. (orig.).
Energy Technology Data Exchange (ETDEWEB)
Meslin, B
1998-04-30
Plasma density control on the tokamak Tore Supra is important for the optimization of every experimental scenario dealing with the improvement of plasma performances. Specific conditions are required both in the plasma bulk and at the edge. Within the framework of the present study, a magnetic configuration is used in the e plasma edge of Tore Supra: the ergodic divertor configuration. A magnetic perturbation which is resonant with the permanent field destroys the plasma confinement locally, opening the field lines onto the material components. They aim of the study is the characterization of the edge density in every relevant scenario for Tore Supra. The first part of this work is dedicated to density and temperature measurements by a series of fixed Langmuir probes located at the very edge of the plasma. Thanks to them, density regimes have been put in evidence during experiments where the volume averaged density
Ergodicity convergence test suggests telomere motion obeys fractional dynamics
Kepten, E.; Bronshtein, I.; Garini, Y.
2011-04-01
Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested P-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.
Dynamics and ergodicity of the infinite harmonic crystal
van Hemmen, J. L.
1980-10-01
This is a comprehensive, relatively formal study of the a priori infinite harmonic crystal. A phase space is introduced and the equations of motion of a harmonic crystal, which need not be a primitive one, are explicitly solved by several methods. The crystal is taken infinite right at the beginni ng. Exploiting the fact that the dynamics is known we derive the thermal equilibrium state of the infinite system. In so doing we use the classical Kubo-Martin-Schwinger (KMS) condition. The thermal equilibrium state is a, so-called, gaussian measure on the phase space. The traditional procedure of the thermodynamic limit is considered as well. In both cases we exploit the advantages of the technique of Fourier transforms of measures. This technique is elucidated in a separate section, where the many connections with Euclidean quantum field theory are also indicated. Finally we settle the problem of the existence of a crystalline state in its appropriate setting: the infinite system. The system is a “crystal” only if it is three-dimensional. The three essential ingredients of the ergodic analysis are a phase space, a dynamics, and an invariant state, here the thermal equilibrium state. A system is ergodic when the time average of any observable equals its phase average. There are, however, stronger notions of ergodicity which are classified in an “ergodic hierarchy”. When a system is Bernoulli it is at the top of this hierarchy. A finite harmonic system is never ergodic. Here it is shown that, generally speaking, a perfect, infinite harmonic crystal in thermal equilibrium has to be Bernoulli. A detailed discussion of the physical relevance of this result has been included.
Energy Technology Data Exchange (ETDEWEB)
Azeroual, A
2000-04-04
In a thermonuclear reactor, one must continuously fuel the discharge and extract the ashes resulting from fusion reactions. To avoid the risk of discharge poisoning, {alpha}-particle concentration is limited to {approx} 10 %. To allow for steady-state conditions requires then to extract {>=}2 % of the helium out flux. In Tore Supra, the ergodic divertor is the main component managing the heat and particle fluxes at the edge. Its principle consists in generating a resonant perturbation able to destroy magnetic surfaces at the plasma periphery. In this region, the field lines are open and connected at both ends to neutralizers which are wetted by the major part of the heat and particle fluxes and are the structures through which a part of the plasma out flux is pumped for maintaining the discharge in steady-state conditions. This work describes the neutral recirculation around the ergodic divertor and is based on a data base of 56 discharges. One discuss the two processes allowing for particle exhaust: the ballistic collection of ions and that of neutrals backscattered by atomic reactions. These two processes are modelled accounting for a realistic description of the divertor geometry. A comparison between simulations and experiments is presented for measurements characterising the three main actors of plasma-wall interaction: the edge plasma, the D{sub {alpha}} light emission and the neutral pressure in the divertor plenum. Last, one question how such a system can be extrapolated to next step machines, for which one must account for technical constraints linked to the presence of the shield protecting the coils from the high neutron flux. (author)
Runaway losses in ergodized plasmas
Finken, K. H.; Abdullaev, S. S.; Jakubowski, M. W.; Jaspers, R.; Lehnen, M.; Schlickeiser, R.; Spatschek, K. H.; Wingen, A.; Wolf, R.; TEXTOR Team
2007-02-01
New results from the generation of runaways and the loss of runaway electrons in an ergodized magnetic field are presented. For the generation process, a clear difference between a 'normal' and a clean, freshly boronized wall condition has been found. Under clean wall conditions, one observes at low densities not only the runaway electrons with energies up to 30 MeV and at discharges with even lower electron density one finds more runaway electrons but at an energy in the low-MeV regime. The runaway electrons are utilized as test particles for revealing the ergodized magnetic field line structure. For the measurements the m/n = 6/2 base mode configuration of the dynamic ergodic divertor (DED), has been applied. One observes a clear modification of the radial runaway profile with preferential losses in the ergodized zone. From the loss rate of the runaway electrons due to ergodization and from the redistribution of the runaways after the DED phase, the diffusion rate is estimated to be of the order of 0.1 m2 s-1.
Losses of runaway electrons during ergodization
Finken, K. H.; Abdullaev, S. S.; Jakubowski, M.; Jaspers, R.; Lehnen, M.; Zimmermann, O.
2006-04-01
The dynamic ergodic divertor (DED) of TEXTOR has been applied to runaway discharges. The runaway electrons (ɛ < 30 MeV) are developed as probes for investigating the internal magnetic field line structure in the plasma. Complementary diagnostics are used, namely neutron measurements for the loss of the runaways and synchrotron radiation for the detection inside the plasma. During the DED phase, three features of the runaway electrons are found: a sudden loss from the just formed ergodic layer, an enhanced diffusive transport and very sudden loss events which may be related to field line reconnection processes.
Ergodic Dynamics by Design: A Route to Predictable Multi-Robot Systems
2005-03-01
in a principled fashion. We focus here on inter- robot dynamics , the roles played by those dynam- ics toward task achievement, and their implications...which the robot dynamics are essentially ergodic can be used to produce meaningful behavior, and allow automated synthesis techniques to focus on a small
Quantifying non-ergodic dynamics of force-free granular gases
Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf
2015-01-01
Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a...
Zhu, C. C.; Song, Y. T.; Peng, X. B.; Wei, Y. P.; Mao, X.; Li, W. X.; Qian, X. Y.
2016-02-01
In the divertor structure of ITER and EAST with mono-block module, tungsten plays not only a role of armor material but also a role of structural material, because electromagnetic (EM) impact will be exerted on tungsten components in VDEs or CQ. The EM loads can reach to 100 MN, which would cause high strain rates. In addition, directly exposed to high-temperature plasma, the temperature regime of divertor components is complex. Aiming at studying dynamical response of tungsten divertors under EM loads, an experiment on tungsten employed in EAST divertors was performed using a Kolsky bar system. The testing strain rates and temperatures is derived from actual working conditions, which makes the constitutive equation concluded by using John-Cook model and testing data very accurate and practical. The work would give a guidance to estimate the dynamical response, fatigue life and damage evolution of tungsten divertor components under EM impact loads.
Quantifying non-ergodic dynamics of force-free granular gases.
Bodrova, Anna; Chechkin, Aleksei V; Cherstvy, Andrey G; Metzler, Ralf
2015-09-14
Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient ε. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of ε on the impact velocity of particles.
Dynamical control of quantum systems in the context of mean ergodic theorems
Bernád, J. Z.
2017-02-01
Equidistant and non-equidistant single pulse ‘bang-bang’ dynamical controls are investigated in the context of mean ergodic theorems. We show the requirements in which the limit of infinite pulse control for both the equidistant and the non-equidistant dynamical control converges to the same unitary evolution. It is demonstrated that the generator of this evolution can be obtained by projecting the generator of the free evolution onto the commutant of the unitary operator representing the pulse. Inequalities are derived to prove this statement and in the case of non-equidistant approach these inequalities are optimised as a function of the time intervals.
Energy Technology Data Exchange (ETDEWEB)
Zhu, C.C. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Song, Y.T. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Peng, X.B., E-mail: pengxb@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Wei, Y.P. [Key Laboratory of Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); Mao, X. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Li, W.X.; Qian, X.Y. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China)
2016-02-15
In the divertor structure of ITER and EAST with mono-block module, tungsten plays not only a role of armor material but also a role of structural material, because electromagnetic (EM) impact will be exerted on tungsten components in VDEs or CQ. The EM loads can reach to 100 MN, which would cause high strain rates. In addition, directly exposed to high-temperature plasma, the temperature regime of divertor components is complex. Aiming at studying dynamical response of tungsten divertors under EM loads, an experiment on tungsten employed in EAST divertors was performed using a Kolsky bar system. The testing strain rates and temperatures is derived from actual working conditions, which makes the constitutive equation concluded by using John-Cook model and testing data very accurate and practical. The work would give a guidance to estimate the dynamical response, fatigue life and damage evolution of tungsten divertor components under EM impact loads. - Graphical abstract: From the comparison between the experimental curves and the predicted curves calculated by adopting the corrected m, it is very clear that the new model is of great capability to explain the deformation behavior of the tungsten material under dynamic compression at high temperatures. (EC, PC and PCM refers to experimental curve, predicted curve and predicted curve with a corrected m. Different colors represent different scenarios.). - Highlights: • Test research on dynamic properties of tungsten at working temperature range and strain rate range of divertors. • Constitutive equation descrbing strain hardening, strain rate hardening and temperature softening. • A guidance to estimate dynamical response and damage evolution of tungsten divertor components under impact.
Data-driven spectral decomposition and forecasting of ergodic dynamical systems
Giannakis, Dimitrios
2015-01-01
We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman group of unitary operators in a smooth orthonormal basis of the L2 space of the dynamical system, acquired from time-ordered data through the diffusion maps algorithm. Using this representation, we compute Koopman eigenfunctions through a regularized advection-diffusion operator, and employ these eigenfunctions in dimension reduction maps with projectible dynamics and high smoothness for the given observation modality. In systems with pure point spectra, we construct a decomposition of the generator of the Koopman group into mutually commuting vector fields, which we reconstruct in data space through a representation of the pushforward map in the Koopman eigenfunction basis. We also use a special property of this basis, namely that the basis elements evolve as simple harmonic oscillators, to build nonparamet...
Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids
McCowan, David D.
2015-08-01
Since the mid-1980s, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid state to the glassy state. MCT, however, is limited by the approximations used in its construction and lacks an unambiguous mechanism to institute corrections. We use recent results from a new theoretical framework—developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential—to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically arrested state. Unlike many previous numerical studies—and in stark contrast to experiment—we have access to the full time and wave-number range of the correlation function with great precision and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. We find complete qualitative agreement with known glassy behavior (e.g. power-law divergence of the α -relaxation time scale in the ergodic phase and square-root growth of the glass form factors in the nonergodic phase), as well as some limited quantitative agreement [e.g. the transition at packing fraction η*=0.60149761 (10 ) ] , consistent with previous static solutions under this theory and with comparable colloidal suspension experiments. However, most importantly, we establish that this new theory is able to reproduce the salient features seen in other theories, experiments, and simulations but has the advantages of being
Level sets of multiple ergodic averages
Ai-Hua, Fan; Ma, Ji-Hua
2011-01-01
We propose to study multiple ergodic averages from multifractal analysis point of view. In some special cases in the symbolic dynamics, Hausdorff dimensions of the level sets of multiple ergodic average limit are determined by using Riesz products.
Energy Technology Data Exchange (ETDEWEB)
Groth, M., E-mail: mathias.groth@aalto.fi [Aalto University, Association EURATOM-Tekes, Otakaari 4, Espoo (Finland); Brezinsek, S. [Forschungszentrum Jülich, IEK4 – Plasma Physik, Jülich (Germany); Belo, P. [Institute of Plasmas and Nuclear Fusion, Association EURATOM/IST, Lisbon (Portugal); Culham Centre for Fusion Energy, Association EURATOM-CCFE, Abingdon (United Kingdom); Brix, M. [Culham Centre for Fusion Energy, Association EURATOM-CCFE, Abingdon (United Kingdom); Calabro, G. [Association EURATOM-ENEA, Frascati (Italy); Chankin, A. [Max-Planck Institute for Plasma Physics, EURATOM Association, Garching (Germany); Clever, M.; Coenen, J.W. [Forschungszentrum Jülich, IEK4 – Plasma Physik, Jülich (Germany); Corrigan, G. [Culham Centre for Fusion Energy, Association EURATOM-CCFE, Abingdon (United Kingdom); Drewelow, P. [Max-Planck-Institute for Plasma Physics, EURATOM Association, Greifswald (Germany); Guillemaut, C. [Association EURATOM CEA, CEA/DSM/IRFM, Cadarache (France); Harting, D. [Culham Centre for Fusion Energy, Association EURATOM-CCFE, Abingdon (United Kingdom); Huber, A. [Forschungszentrum Jülich, IEK4 – Plasma Physik, Jülich (Germany); Jachmich, S. [Association ‘Euratom-Belgian state’, Ecole Royale Militaire, Brussels (Belgium); Järvinen, A. [Aalto University, Association EURATOM-Tekes, Otakaari 4, Espoo (Finland); Kruezi, U.; Lawson, K.D. [Culham Centre for Fusion Energy, Association EURATOM-CCFE, Abingdon (United Kingdom); Lehnen, M. [Forschungszentrum Jülich, IEK4 – Plasma Physik, Jülich (Germany); ITER Organisation, 13115 Saint-Paul-Lez-Durance (France); and others
2015-08-15
Measurements of the plasma conditions at the low field side target plate in JET ITER-like wall ohmic and low confinement mode plasmas show minor differences in divertor plasma configurations with horizontally and vertically inclined targets. Both the reduction of the electron temperature in the vicinity of the strike points and the rollover of the ion current to the plates follow the same functional dependence on the density at the low field side midplane. Configurations with vertically inclined target plates, however, produce twice as high sub-divertor pressures for the same upstream density. Simulations with the EDGE2D-EIRENE code package predict significantly lower plasma temperatures at the low field side target in vertical than in horizontal target configurations. Including cross-field drifts and imposing a pumping by-pass leak at the low-field side plate can still not recover the experimental observations.
Nadkarni, M G
2013-01-01
This is an introductory book on Ergodic Theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics around the Glimm-Effros theorem are discussed. In the third edition a chapter entitled 'Additional Topics' has been added. It gives Liouville's Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden's theorem on arithmetical progressions.
The large deviations theorem and ergodicity
Energy Technology Data Exchange (ETDEWEB)
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2007-12-15
In this paper, some relationships between stochastic and topological properties of dynamical systems are studied. For a continuous map f from a compact metric space X into itself, we show that if f satisfies the large deviations theorem then it is topologically ergodic. Moreover, we introduce the topologically strong ergodicity, and prove that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is sensitively dependent on initial conditions.
Operator theoretic aspects of ergodic theory
Eisner, Tanja; Haase, Markus; Nagel, Rainer
2015-01-01
Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: •an intuitive introduction to ergodic theory •an introduction to the basic notions, constructions, and standard examples of topological dynamical systems •Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem •m...
Dynamics and stability of divertor detachment in H-mode plasmas on JET
Field, A. R.; Balboa, I.; Drewelow, P.; Flanagan, J.; Guillemaut, C.; Harrison, J. R.; Huber, A.; Huber, V.; Lipschultz, B.; Matthews, G.; Meigs, A.; Schmitz, J.; Stamp, M.; Walkden, N.; contributors, JET
2017-09-01
The dynamics and stability of divertor detachment in {{{N}}}2 seeded, type-I, ELMy H-mode plasmas with dominant NBI heating in the JET ITER-like wall device is studied by means of an integrated analysis of diagnostic data from several systems, classifying data relative to the ELM times. It is thereby possible to study the response of the detachment evolution to the control parameters (SOL input power, upstream density and impurity fraction) prevailing during the inter-ELM periods and the effect of ELMs on the detached divertor. A relatively comprehensive overview is achieved, including the interaction with the targets at various stages of the ELM cycle, the role of ELMs in affecting the detachment process and the overall performance of the scenario. The results are consistent with previous studies in devices with an ITER-like, metal wall, with the important advance of distinguishing data from intra- and inter-ELM periods. Operation without significant degradation of the core confinement can be sustained in the presence of strong radiation from the x-point region (MARFE).
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
Krasheninnikov, Sergei
2015-11-01
The heat exhaust is one of the main conceptual issues of magnetic fusion reactor. In a standard operational regime the large heat flux onto divertor target reaches unacceptable level in any foreseeable reactor design. However, about two decades ago so-called ``detached divertor'' regimes were found. They are characterized by reduced power and plasma flux on divertor targets and look as a promising solution for heat exhaust in future reactors. In particular, it is envisioned that ITER will operate in a partly detached divertor regime. However, even though divertor detachment was studied extensively for two decades, still there are some issues requiring a new look. Among them is the compatibility of detached divertor regime with a good core confinement. For example, ELMy H-mode exhibits a very good core confinement, but large ELMs can ``burn through'' detached divertor and release large amounts of energy on the targets. In addition, detached divertor regimes can be subject to thermal instabilities resulting in the MARFE formation, which, potentially, can cause disruption of the discharge. Finally, often inner and outer divertors detach at different plasma conditions, which can lead to core confinement degradation. Here we discuss basic physics of divertor detachment including different mechanisms of power and momentum loss (ionization, impurity and hydrogen radiation loss, ion-neutral collisions, recombination, and their synergistic effects) and evaluate the roles of different plasma processes in the reduction of the plasma flux; detachment stability; and an impact of ELMs on detachment. We also evaluate an impact of different magnetic and divertor geometries on detachment onset, stability, in- out- asymmetry, and tolerance to the ELMs. Supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under Award Number DE-DE-FG02-04ER54739 at UCSD.
Kaplan, L
1998-01-01
We examine the consequences of classical ergodicity for the localization properties of individual quantum eigenstates in the classical limit. We note that the well known Schnirelman result is a weaker form of quantum ergodicity than the one implied by random matrix theory. This suggests the possibility of systems with non-gaussian random eigenstates which are nonetheless ergodic in the sense of Schnirelman and lead to ergodic transport in the classical limit. These we call "weakly quantum ergodic.'' Indeed for a class of "slow ergodic" classical systems, it is found that each eigenstate becomes localized to an ever decreasing fraction of the available state space, in the semiclassical limit. Nevertheless, each eigenstate in this limit covers phase space evenly on any classical scale, and long-time transport properties betwen individual quantum states remain ergodic due to the diffractive effects which dominate quantum phase space exploration.
Directory of Open Access Journals (Sweden)
Akio Matsumoto
1997-01-01
Full Text Available This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output constraints and the dynamics of the modified model. Due to the upper and lower bounds, a transitional function takes on a tilted z-profile having three piecewise segments with two turning points. It prevents the price (or quantity dynamics from explosive oscillations. This study demonstrates, by presenting numerical examples, that the modified cobweb model can generate various dynamics ranging from stable periodic cycles to ergodic chaos if a product of the marginal propensity to consume and the marginal product is greater than unity.
Ergodicity of the generalized lemon billiards
Chen, Jingyu; Mohr, Luke; Zhang, Hong-Kun; Zhang, Pengfei
2013-12-01
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Ergodicity of the generalized lemon billiards
Energy Technology Data Exchange (ETDEWEB)
Chen, Jingyu [Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-2302 (United States); Mohr, Luke; Zhang, Hong-Kun, E-mail: hongkun@math.umass.edu; Zhang, Pengfei [Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003 (United States)
2013-12-15
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Ergodic theory independence and dichotomies
Kerr, David
2016-01-01
This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems
Everest, B.; Marcuzzi, M.; Garrahan, J. P.; Lesanovsky, I.
2016-11-01
Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.
Ergodicity of a single particle confined in a nanopore
DEFF Research Database (Denmark)
Bernardi, S.; Hansen, Jesper Schmidt; Frascolli, F.;
2012-01-01
We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall at...
Impact of ELM filaments on divertor heat flux dynamics in NSTX
Energy Technology Data Exchange (ETDEWEB)
Ahn, J.-W., E-mail: jahn@pppl.gov [Oak Ridge National Laboratory, Oak Ridge (United States); Maingi, R. [Princeton Plasma Physics Laboratory, Princeton (United States); Canik, J.M. [Oak Ridge National Laboratory, Oak Ridge (United States); Gan, K.F. [Institute of Plasma Physics, Chinese Academy of Science, Hefei (China); Gray, T.K. [Oak Ridge National Laboratory, Oak Ridge (United States); McLean, A.G. [Lawrence Livermore National Laboratory, Livermore (United States)
2015-08-15
The ELM induced change in wetted area (A{sub wet}) and peak heat flux (q{sub peak}) of divertor heat flux is investigated as a function of the number of striations, which represent ELM filaments, observed in the heat flux profile in NSTX. More striations are found to lead to larger A{sub wet} and lower q{sub peak}. The typical number of striations observed in NSTX is 0–9, while 10–15 striations are normally observed in other machines such as JET, and the ELM contracts heat flux profile when the number of striations is less than 3–4 but broadens it with more of them. The smaller number of striations in NSTX is attributed to the fact that NSTX ELMs are against kink/peeling boundary with lower toroidal mode number (n = 1–5), while typical peeling–ballooning ELMs have higher mode number of n = 10–20. For ELMs with smaller number of striations, relative A{sub wet} change is rather constant and q{sub peak} change rapidly increases with increasing ELM size, while A{sub wet} change slightly increases leading to a weaker increase of q{sub peak} change for ELMs with larger number of striations, both of which are unfavourable trend for the material integrity of divertor tiles.
Are there ergodic limits to evolution? Ergodic exploration of genome space and convergence.
McLeish, Tom C B
2015-12-06
We examine the analogy between evolutionary dynamics and statistical mechanics to include the fundamental question of ergodicity-the representative exploration of the space of possible states (in the case of evolution this is genome space). Several properties of evolutionary dynamics are identified that allow a generalization of the ergodic dynamics, familiar in dynamical systems theory, to evolution. Two classes of evolved biological structure then arise, differentiated by the qualitative duration of their evolutionary time scales. The first class has an ergodicity time scale (the time required for representative genome exploration) longer than available evolutionary time, and has incompletely explored the genotypic and phenotypic space of its possibilities. This case generates no expectation of convergence to an optimal phenotype or possibility of its prediction. The second, more interesting, class exhibits an evolutionary form of ergodicity-essentially all of the structural space within the constraints of slower evolutionary variables have been sampled; the ergodicity time scale for the system evolution is less than the evolutionary time. In this case, some convergence towards similar optima may be expected for equivalent systems in different species where both possess ergodic evolutionary dynamics. When the fitness maximum is set by physical, rather than co-evolved, constraints, it is additionally possible to make predictions of some properties of the evolved structures and systems. We propose four structures that emerge from evolution within genotypes whose fitness is induced from their phenotypes. Together, these result in an exponential speeding up of evolution, when compared with complete exploration of genomic space. We illustrate a possible case of application and a prediction of convergence together with attaining a physical fitness optimum in the case of invertebrate compound eye resolution.
Smooth ergodic theory for endomorphisms
Qian, Min; Zhu, Shu
2009-01-01
This volume presents a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms, mainly concerning the relations between entropy, Lyapunov exponents and dimensions. The authors make extensive use of the combination of the inverse limit space technique and the techniques developed to tackle random dynamical systems. The most interesting results in this book are (1) the equivalence between the SRB property and Pesin’s entropy formula; (2) the generalized Ledrappier-Young entropy formula; (3) exact-dimensionality for weakly hyperbolic diffeomorphisms and for expanding maps. The proof of the exact-dimensionality for weakly hyperbolic diffeomorphisms seems more accessible than that of Barreira et al. It also inspires the authors to argue to what extent the famous Eckmann-Ruelle conjecture and many other classical results for diffeomorphisms and for flows hold true. After a careful reading of the book, one can systematically learn the Pesin theory for endomorphis...
Theory of Advanced Magnetic Divertors
Kotschenreuther, Michael; Valanju, Prashant; Mahajan, Swadesh; Covele, Brent
2013-10-01
The magnetic field structure in the SOL is the most important determinant of divertor physics. A comprehensive analytical and numerical methodology is developed to investigate SOL magnetic fields in the backdrop of two advanced divertor geometries- the X-divertor (XD) proposed and discussed in 2004, and the snowflake divertor (SFD) of 2007-2010. The analysis shows that XD and SFD represent very distinct and readily distinguishable magnetic geometries, epitomized through a differentiating metric, the Divertor Index (DI). In terms of this simple metric, the XD (DI > 1) and the SFD (DI XD flux surfaces are less convergent, in fact, divergent (flaring). These different SOL magnetics imply different physics, particularly with respect to detachment dynamics. It is also shown that some experiments on NSTX and DIII-D match both the prescription and the predictions of the 2004 XD paper. Work supported under US-DOE projects DE-FG02-04ER54742 and DE-FG02-04ER54754.
Quantization Ambiguity, Ergodicity and Semiclassics
Kaplan, L
1999-01-01
A simple argument shows that eigenstates of a classically ergodic system are individually ergodic on coarse-grained scales. This has implications for the quantization ambiguity in ergodic systems: the difference between alternative quantizations is suppressed compared with the $O(\\hbar^2)$ ambiguity in the integrable case. For two-dimensional ergodic systems in the high-energy regime, individual eigenstates are independent of the choice of quantization procedure, in contrast with the regular case, where even the ordering of eigenlevels is ambiguous. Surprisingly, semiclassical methods are shown to be much more precise for chaotic than for integrable systems.
Quantization ambiguity, ergodicity and semiclassics
Energy Technology Data Exchange (ETDEWEB)
Kaplan, Lev [Institute for Nuclear Theory, University of Washington, Seattle, WA (United States)
2002-11-01
It is well known that almost all eigenstates of a classically ergodic system are individually ergodic on coarse-grained scales. This has important implications for the quantization ambiguity in ergodic systems: the difference between alternative quantizations is suppressed compared with the O( h-bar {sup 2}) ambiguity in the integrable or regular case. For two-dimensional ergodic systems in the high-energy regime, individual eigenstates are independent of the choice of quantization procedure, in contrast with the regular case, where even the ordering of eigenlevels is ambiguous. Surprisingly, semiclassical methods are shown to be much more precise in any dimension for chaotic than for integrable systems.
Mixing, ergodicity and slow relaxation phenomena
Costa, I. V. L.; Vainstein, M. H.; Lapas, L. C.; Batista, A. A.; Oliveira, F. A.
2006-11-01
Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.
Bassily, Raef
2010-01-01
In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MAC-WT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together with the time varying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling based alignment (SBA)), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme (ergodic secret alignment (ESA)). For each scheme, we obtain the resulting achievable secrecy rate region. We show that the secrecy rates achieved by both schemes scale with SNR as 1/2log(SNR...
On reducibility and ergodicity of population projection matrix models
DEFF Research Database (Denmark)
Stott, Iain; Townley, Stuart; Carslake, David
2010-01-01
1. Population projection matrices (PPMs) are probably the most commonly used empirical population models. To be useful for predictive or prospective analyses, PPM models should generally be irreducible (the associated life cycle graph contains the necessary transition rates to facilitate pathways...... structure used in the population projection). In our sample of published PPMs, 15·6% are non-ergodic. 3. This presents a problem: reducible–ergodic models often defy biological rationale in their description of the life cycle but may or may not prove problematic for analysis as they often behave similarly...... to irreducible models. Reducible–non-ergodic models will usually defy biological rationale in their description of the both the life cycle and population dynamics, hence contravening most analytical methods. 4. We provide simple methods to evaluate reducibility and ergodicity of PPM models, present illustrative...
Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence
Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor
2010-01-01
We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.
Levnajić, Zoran; Mezić, Igor
2010-09-01
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed by Mezić (Ph.D. thesis, Caltech, 1994) and Mezić and Wiggins [Chaos 9, 213 (1999)]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation--based on time averages of observables--a mesochronic plot (from Greek: meso--mean, chronos--time). The method is useful for identifying low-dimensional projections (e.g., two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the mesochronic scatter plot. We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froéschle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional extended standard map for which we study the conjecture on its ergodicity [I. Mezić, Physica D 154, 51 (2001)]. We extend the study in our next paper [Z. Levnajić and I. Mezić, e-print arXiv:0808.2182] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)].
Elemental methods in ergodic Ramsey theory
McCutcheon, Randall
1999-01-01
This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerédi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look.
Ergodic theory and the duality principle on homogeneous spaces
Gorodnik, Alexander
2012-01-01
We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are quantitative, namely we establish rates of convergence in the mean and pointwise ergodic theorems, which can be estimated explicitly. Our results give a precise and in most cases optimal quantitative form to the duality principle governing dynamics on homogeneous spaces. We illustrate their scope in a variety of equidistribution problems.
Ergodic optimization in the expanding case concepts, tools and applications
Garibaldi, Eduardo
2017-01-01
This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study of optimizing probability measures. This work presents and discusses the fundamental concepts of the theory, including the use and relevance of Sub-actions as analogues to subsolutions of the Hamilton-Jacobi equation. Further, it provides evidence for the impressively broad applicability of the tools inspired by the weak KAM theory.
Weak ergodicity breaking induced by global memory effects
Budini, Adrián A.
2016-08-01
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, sets the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the residence time in each state may have a divergent mean value, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, we conclude that global memory effects are an alternative mechanism able to induce ergodicity breaking without involving power-law statistics. Analytical and numerical calculations support these results.
International Conference on Ergodic Theory and Related Topics
Richter, Karin; Warstat, Volker
1992-01-01
The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schult...
Ergodic averages via dominating processes
DEFF Research Database (Denmark)
Møller, Jesper; Mengersen, Kerrie
2006-01-01
We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary ...
Ergodicity of polygonal slap maps
Del Magno, Gianluigi; Lopes Dias, João; Duarte, Pedro; Gaivão, José Pedro
2014-08-01
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflection laws. We study the absolutely continuous invariant probabilities (acips) of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps with more than one ergodic acip.
Pointwise ergodic theorems beyond amenable groups
Bowen, Lewis
2011-01-01
We prove pointwise and maximal ergodic theorems for probability measure preserving actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type III_r for some r >0. Our approach is based on the following two principles. First, it is possible to generalize the ergodic theory of measure-preserving actions of amenable groups to include probability-measure-preserving amenable equivalence relations. Second, it is possible to reduce the proof of ergodic theorems for actions of a general group to the proof of ergodic theorems in an associated measure-preserving amenable equivalence relation, provided the group admits an amenable action with the properties stated above. The general ergodic theorems established here are used in a sequel paper to prove mean and pointwise ergodic theorems for arbitrary Gromov-hyperbolic groups.
The ergodic theory of lattice subgroups
Gorodnik, Alexander
2010-01-01
The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean
Oseledec multiplicative ergodic theorem for laminations
Nguyên, Viêt-Anh
2017-01-01
Given a n-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained...
ergodicity and chaos in geomorphology
Aadel, S.; Gaiumi, M.
2009-04-01
The past three dicades can be considered as a period in which the fundamentals of scientific epistemology have been subjected to drastic revision.The dissemination of the general theory of systems in 1972 , one year after the death of ludwing von Berthalanfi , the proposition of fuzzy logic by Zade, and the foemulation of chaos theory in 1986 by Harison and Biswas allserved to explode the myth that scientific thought was invulnerable. This paper , which has resulted from the theoretical investigation of project based on the paraglicial sediment and glacial evidence on the Zagros-pishkoh to explain the elements of chaos theory and their compatibility with ergodic geomorphology
Eigenvalues, inequalities and ergodic theory
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper surveys the main results obtained during the period 1992-1999 on three aspects mentioned in the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e. the first non-trivial eigenvalue) of elliptic operators in Euclidean space, Laplacian on Riemannian manifolds or Markov chains (§1). Here, a probabilistic method -coupling method is adopted. The new formula is a dual of the classical variational formula. The last formula is actually equivalent to Poincaré inequality. To which, there are closely related logarithmic Sobolev inequality, Nash inequality, Liggett inequality and so on. These inequalities are treated in a unified way by using Cheeger's method which comes from Riemannian geometry. This consists of §2. The results on these two aspects are mainly completed by the author joint with F. Y. Wang. Furthermore, a diagram of the inequalities and the traditional three types of ergodicity is presented (§3). The diagram extends the ergodic theory of Markov processes. The details of the methods used in the paper will be explained in a subsequent paper under the same title.
Characterizing self-organization and coevolution by ergodic invariants
Mendes, R V
1999-01-01
In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified for this purpose, which is computed in several examples, namely a Bernoulli network with either global or nearest-neighbor coupling, a generalized Bak-Sneppen model and a continuous minority model.
Ergodicity breakdown and scaling from single sequences
Energy Technology Data Exchange (ETDEWEB)
Kalashyan, Armen K. [Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427 (United States); Buiatti, Marco [Laboratoire de Neurophysique et Physiologie, CNRS UMR 8119 Universite Rene Descartes - Paris 5 45, rue des Saints Peres, 75270 Paris Cedex 06 (France); Cognitive Neuroimaging Unit - INSERM U562, Service Hospitalier Frederic Joliot, CEA/DRM/DSV, 4 Place du general Leclerc, 91401 Orsay Cedex (France); Grigolini, Paolo [Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427 (United States); Dipartimento di Fisica ' E.Fermi' - Universita di Pisa and INFM, Largo Pontecorvo 3, 56127 Pisa (Italy); Istituto dei Processi Chimico, Fisici del CNR Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124 Pisa (Italy)], E-mail: grigo@df.unipi.it
2009-01-30
In the ergodic regime, several methods efficiently estimate the temporal scaling of time series characterized by long-range power-law correlations by converting them into diffusion processes. However, in the condition of ergodicity breakdown, the same methods give ambiguous results. We show that in such regime, two different scaling behaviors emerge depending on the age of the windows used for the estimation. We explain the ambiguity of the estimation methods by the different influence of the two scaling behaviors on each method. Our results suggest that aging drastically alters the scaling properties of non-ergodic processes.
Classical Ergodicity and Modern Portfolio Theory
Directory of Open Access Journals (Sweden)
Geoffrey Poitras
2015-01-01
Full Text Available What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.
Advanced divertor configurations with large flux expansion
Soukhanovskii, V. A.; R.E. Bell,; Diallo, A.; S. Gerhardt,; S. Kaye,; E. Kolemen,; B.P. LeBlanc,; McLean, A.; Menard, J. E.; S.F. Paul,; Podesta, M.; Raman, R.; D.D. Ryutov,; F. Scotti,; Kaita, R.; Maingi, R.; D.M. Mueller,; Roquemore, A. L.; Reimerdes, H.; G.P. Canal,; Labit, B.; Vijvers, W.; Coda, S.; Duval, B. P.; Morgan, T.; Zielinski, J.; De Temmerman, G.; Tal, B.
2013-01-01
Experimental studies of the novel snowflake divertor concept (D. Ryutov, Phys. Plasmas 14 (2007) 064502) performed in the NSTX and TCV tokamaks are reviewed in this paper. The snowflake divertor enables power sharing between divertor strike points, as well as the divertor plasma-wetted area, effecti
ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
Institute of Scientific and Technical Information of China (English)
O Hyong-chol; Ro Yong-hwa; Kil Won-gun
2005-01-01
A set of contraction maps of a metric space is called an iterated function systems.Iterated function systems with condensation can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.
Contribution to the ergodic theory of piecewise monotone continuous maps
Faller, Bastien
2008-01-01
This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Ré...
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
CHEN; Jinwen(
2001-01-01
［1］Liggett, T. M., Interacting Particle Systems, New York: Springer-Verlag, 1985.［2］Andjel, E. D., Ergodic and mixing properties of equilibrium measures for Markov processes, Trans. of the AMS, 1990, 318:601－614.［3］Franchi, J., Asymptotic windings of ergodic diffusion, Stoch. Processes Appl., 1996, 62: 277－298.［4］Golden, K. , Goldstein, S., Lebowitz, J. L., Nash estimates and the asymptotic behavior of diffusion, Ann. Prob., 1988,16: 1127－1146.［5］Gordin. M. I., Lifsic, B. A. , The central limit theorem for stationary ergodic Markov process, Dokl, Akad. Nauk SSSR,1978, 19: 392－393.［6］Orey, S., Large deviations in ergodic theory, Seminar on Stochastic Processes, 1985, 12: 195－249.［7］Veretenikov, A. Y., On large deviations for ergodic process empirical measures, Adv. Sov. Math., 1992, 12: 125－133.［8］Deuschel, J. D., Stroock, D. W., Large Deviations, San Diego, CA: Academic Press, 1989.［9］Rosenblatt, M., Markov Processes, Structure and Asymptotic Behavior, Berlin: Springer-Verlag, 1971.［10］Liggett, T. M., Stochastic Interacting Systems: Contact, Voter, and Exclusion Processes, Berlin: Springer-Verlag, 1999.［11］Albevrio, S., Kondratiev, Y. G., Rockner, M., Ergodicity of L2-semigroups and extremality of Gibbs states, J. Funct.Anal. , 1997, 144: 293－423.［12］Liverani, C. , Olla, S. , Ergodicity in infinite Hamiltonian systems with conservative noise, Probab. Th. Rel. Fields, 1996,106: 401－445.［13］Varadhan, S. P. S., Large Deviations and Applications, Philadelphia: SIAM, 1984.［14］Chen, J. W. , A variational principle for Markov processes, J. Stat. Phys. , 1999, 96: 1359－1364.
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
东金文
2001-01-01
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
Structure of Quantum Chaotic Wavefunctions Ergodicity, Localization, and Transport
Kaplan, L
1999-01-01
We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are absent from the long-time classical motion. These imprints can lead to quantum behavior on single-wavelength or single-channel scales which are very different from random matrix theory expectations. Robust and quantitative predictions are obtained using semiclassical methods. Applications to wavefunction intensity statistics and to resonances in open systems are discussed.
Topology, ergodic theory, real algebraic geometry Rokhlin's memorial
Turaev, V
2001-01-01
This book is dedicated to the memory of the outstanding Russian mathematician, V. A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmüller
The Non-Ergodic Nature of Internal Conversion
DEFF Research Database (Denmark)
Kuhlman, Thomas Scheby
The absorption of light by molecules can induce ultrafast dynamics of coupled electronic and nuclear vibrational motion. The ultrafast nature in many cases rests on the importance of several potential energy surfaces in guiding the nuclear dynamics – a concept of central importance in many aspects...... of chemical reaction dynamics. In this thesis, we focus on the non-ergodic nature of internal conversion, i.e. the concept that the nuclear dynamics only sample a reduced phase space potentially resulting in localization of the dynamics in real space. In essence, this is a consequence of vibrational energy...... of primarily two parameters: the vibrational frequency and the energy difference between the Franck-Condon and equilibrium geometries of the upper electronic state. In the cyclopentadienes, the twisting of a single double bond is essential in reaching the conical intersection seam connecting the lowest excited...
Ergodicity of Quasi-birth and Death Processes (Ⅰ)
Institute of Scientific and Technical Information of China (English)
Zhen Ting HOU; Xiao Hua LI
2007-01-01
Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for l-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic.
Upgraded divertor Thomson scattering system on DIII-D
Glass, F.; Carlstrom, T. N.; Du, D.; McLean, A. G.; Taussig, D. A.; Boivin, R. L.
2016-11-01
A design to extend the unique divertor Thomson scattering system on DIII-D to allow measurements of electron temperature and density in high triangularity plasmas is presented. Access to this region is selectable on a shot-by-shot basis by redirecting the laser beam of the existing divertor Thomson system inboard — beneath the lower floor using a moveable, high-damage threshold, in-vacuum mirror — and then redirecting again vertically. The currently measured divertor region remains available with this mirror retracted. Scattered light is collected from viewchords near the divertor floor using in-vacuum, high temperature optical elements and relayed through the port window, before being coupled into optical fiber bundles. At higher elevations from the floor, measurements are made by dynamically re-focusing the existing divertor system collection optics. Nd:YAG laser timing, analysis of the scattered light spectrum via polychromators, data acquisition, and calibration are all handled by existing systems or methods of the current multi-pulse Thomson scattering system. Existing filtered polychromators with 7 spectral channels are employed to provide maximum measurement breadth (Te in the range of 0.5 eV-2 keV, ne in the range of 5 × 1018-1 × 1021 m3) for both low Te in detachment and high Te measurement up beyond the separatrix.
Upgraded divertor Thomson scattering system on DIII-D
Energy Technology Data Exchange (ETDEWEB)
Glass, F., E-mail: glassf@fusion.gat.com; Carlstrom, T. N.; Du, D.; Taussig, D. A.; Boivin, R. L. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); McLean, A. G. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)
2016-11-15
A design to extend the unique divertor Thomson scattering system on DIII-D to allow measurements of electron temperature and density in high triangularity plasmas is presented. Access to this region is selectable on a shot-by-shot basis by redirecting the laser beam of the existing divertor Thomson system inboard — beneath the lower floor using a moveable, high-damage threshold, in-vacuum mirror — and then redirecting again vertically. The currently measured divertor region remains available with this mirror retracted. Scattered light is collected from viewchords near the divertor floor using in-vacuum, high temperature optical elements and relayed through the port window, before being coupled into optical fiber bundles. At higher elevations from the floor, measurements are made by dynamically re-focusing the existing divertor system collection optics. Nd:YAG laser timing, analysis of the scattered light spectrum via polychromators, data acquisition, and calibration are all handled by existing systems or methods of the current multi-pulse Thomson scattering system. Existing filtered polychromators with 7 spectral channels are employed to provide maximum measurement breadth (T{sub e} in the range of 0.5 eV–2 keV, n{sub e} in the range of 5 × 10{sup 18}–1 × 10{sup 21} m{sup 3}) for both low T{sub e} in detachment and high T{sub e} measurement up beyond the separatrix.
Smooth Rényi Entropy of Ergodic Quantum Information Sources
Schoenmakers, Berry; Tjoelker, Jilles; Tuyls, Pim; Verbitskiy, Evgeny
2007-01-01
We investigate the recently introduced notion of smooth Rényi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical
Smooth Rényi Entropy of Ergodic Quantum Information Sources
Schoenmakers, Berry; Tjoelker, Jilles; Tuyls, Pim; Verbitskiy, Evgeny
2007-01-01
We investigate the recently introduced notion of smooth Rényi entropy for the case of ergodic information sources, thereby generalizing previous work which concentrated mainly on i.i.d. information sources. We will actually consider ergodic quantum information sources, of which ergodic classical inf
Directory of Open Access Journals (Sweden)
Bernard Wong
2009-01-01
martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
Extended application of constructive criteria for ergodicity of interacting particle systems
DeJong, H; Maes, C
1996-01-01
We discuss computational aspects of verifying constructive criteria for ergodicity of interacting particle systems. Both discrete time (probabilistic cellular automata) and continuous time spin flip dynamics are considered. We also investigate how the criteria have to be adapted if stirring is added
Design method of divertor in tokamak reactors
Energy Technology Data Exchange (ETDEWEB)
Ueda, Noriaki (Mitsubishi Atomic Power Industries, Inc., Tokyo (Japan)); Itoh, Sanae; Tanaka, Masaaki; Itoh, Kimitaka
1991-03-01
Computational method to design the efficient divertor configuration in tokamak reactor is presented. The two-dimensional code has been developed to analyze the distributions of the plasma and neutral particles for realistic configurations. Using this code, a method to design the efficient divertor configuration is developed. An example of new divertor, which consists of the baffle and fin plates, is analyzed. (author).
Ergodicity test of the eddy correlation method
Chen, J.; Hu, Y.; Yu, Y.; Lü, S.
2014-07-01
The turbulent flux observation in the near-surface layer is a scientific issue which researchers in the fields of atmospheric science, ecology, geography science, etc. are commonly interested in. For eddy correlation measurement in the atmospheric surface layer, the ergodicity of turbulence is a basic assumption of the Monin-Obukhov (M-O) similarity theory, which is confined to steady turbulent flow and homogenous surface; this conflicts with turbulent flow under the conditions of complex terrain and unsteady, long observational period, which the study of modern turbulent flux tends to focus on. In this paper, two sets of data from the Nagqu Station of Plateau Climate and Environment (NaPlaCE) and the cooperative atmosphere-surface exchange study 1999 (CASE99) were used to analyze and verify the ergodicity of turbulence measured by the eddy covariance system. Through verification by observational data, the vortex of atmospheric turbulence, which is smaller than the scale of the atmospheric boundary layer (i.e., its spatial scale is less than 1000 m and temporal scale is shorter than 10 min) can effectively meet the conditions of the average ergodic theorem, and belong to a wide sense stationary random processes. Meanwhile, the vortex, of which the spatial scale is larger than the scale of the boundary layer, cannot meet the conditions of the average ergodic theorem, and thus it involves non-ergodic stationary random processes. Therefore, if the finite time average is used to substitute for the ensemble average to calculate the average random variable of the atmospheric turbulence, then the stationary random process of the vortex, of which spatial scale was less than 1000 m and thus below the scale of the boundary layer, was possibly captured. However, the non-ergodic random process of the vortex, of which the spatial scale was larger than that of the boundary layer, could not be completely captured. Consequently, when the finite time average was used to substitute
Detached divertor plasmas in JET
Energy Technology Data Exchange (ETDEWEB)
Horton, L.D.; Borrass, K.; Corrigan, G.; Gottardi, N.; Lingertat, J.; Loarte, A.; Simonini, R.; Stamp, M.F.; Taroni, A. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking; Stangeby, P.C. [Toronto Univ., ON (Canada). Inst. for Aerospace Studies
1994-07-01
In simulations with high radiated power fractions, it is possible to produce the drop in ion current to the divertor targets typical of detached plasmas. Despite the fact that these experiments are performed on beryllium target tiles, radiation from deuterium and beryllium cannot account for the measured power losses. The neutral deuterium levels in the SOL in these plasmas are higher than the model predicts. This may be due to leakage from the divertor or to additional wall sources related to the non-steady nature of these plasmas. In contrast, a surprisingly high level of carbon is present in these discharges; higher even than would be predicted are the divertor target tiles pure carbon. This level may well be large enough to produce the measured radiation. (authors). 6 refs., 2 figs., 1 tab.
Actively convected liquid metal divertor
Shimada, Michiya; Hirooka, Yoshi
2014-12-01
The use of actively convected liquid metals with j × B force is proposed to facilitate heat handling by the divertor, a challenging issue associated with magnetic fusion experiments such as ITER. This issue will be aggravated even more for DEMO and power reactors because the divertor heat load will be significantly higher and yet the use of copper would not be allowed as the heat sink material. Instead, reduced activation ferritic/martensitic steel alloys with heat conductivities substantially lower than that of copper, will be used as the structural materials. The present proposal is to fill the lower part of the vacuum vessel with liquid metals with relatively low melting points and low chemical activities including Ga and Sn. The divertor modules, equipped with electrodes and cooling tubes, are immersed in the liquid metal. The electrode, placed in the middle of the liquid metal, can be biased positively or negatively with respect to the module. The j × B force due to the current between the electrode and the module provides a rotating motion for the liquid metal around the electrodes. The rise in liquid temperature at the separatrix hit point can be maintained at acceptable levels from the operation point of view. As the rotation speed increases, the current in the liquid metal is expected to decrease due to the v × B electromotive force. This rotating motion in the poloidal plane will reduce the divertor heat load significantly. Another important benefit of the convected liquid metal divertor is the fast recovery from unmitigated disruptions. Also, the liquid metal divertor concept eliminates the erosion problem.
Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
Budini, Adrián A.
2016-11-01
We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.
Advanced divertor configurations with large flux expansion
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V.A., E-mail: vlad@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA (United States); Bell, R.E.; Diallo, A.; Gerhardt, S.; Kaye, S.; Kolemen, E.; LeBlanc, B.P. [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); McLean, A. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Menard, J.E.; Paul, S.F.; Podesta, M. [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); Raman, R. [University of Washington, Seattle, WA (United States); Ryutov, D.D. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Scotti, F.; Kaita, R. [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); Maingi, R. [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Mueller, D.M.; Roquemore, A.L. [Princeton Plasma Physics Laboratory, Princeton, NJ (United States); Reimerdes, H.; Canal, G.P. [Ecole Polytechnique Fédérale de Lausanne, Centre de Recherches en Physique des Plasmas, Association Euratom Confédération Suisse, Lausanne (Switzerland); and others
2013-07-15
Experimental studies of the novel snowflake divertor concept (D. Ryutov, Phys. Plasmas 14 (2007) 064502) performed in the NSTX and TCV tokamaks are reviewed in this paper. The snowflake divertor enables power sharing between divertor strike points, as well as the divertor plasma-wetted area, effective connection length and divertor volumetric power loss to increase beyond those in the standard divertor, potentially reducing heat flux and plasma temperature at the target. It also enables higher magnetic shear inside the separatrix, potentially affecting pedestal MHD stability. Experimental results from NSTX and TCV confirm the predicted properties of the snowflake divertor. In the NSTX, a large spherical tokamak with a compact divertor and lithium-coated graphite plasma-facing components (PFCs), the snowflake divertor operation led to reduced core and pedestal impurity concentration, as well as re-appearance of Type I ELMs that were suppressed in standard divertor H-mode discharges. In the divertor, an otherwise inaccessible partial detachment of the outer strike point with an up to 50% increase in divertor radiation and a peak divertor heat flux reduction from 3–7 MW/m{sup 2} to 0.5–1 MW/m{sup 2} was achieved. Impulsive heat fluxes due to Type-I ELMs were significantly dissipated in the high magnetic flux expansion region. In the TCV, a medium-size tokamak with graphite PFCs, several advantageous snowflake divertor features (cf. the standard divertor) have been demonstrated: an unchanged L–H power threshold, enhanced stability of the peeling–ballooning modes in the pedestal region (and generally an extended second stability region), as well as an H-mode pedestal regime with reduced (×2–3) Type I ELM frequency and slightly increased (20–30%) normalized ELM energy, resulting in a favorable average energy loss comparison to the standard divertor. In the divertor, ELM power partitioning between snowflake divertor strike points was demonstrated. The NSTX
An ergodic configurational thermostat using selective control of higher order temperatures.
Patra, Puneet Kumar; Bhattacharya, Baidurya
2015-05-21
The conventional Nosé-Hoover type deterministic thermostat scheme for controlling temperature by configurational variables (Braga-Travis (BT) thermostat) is non-ergodic for systems with a few degrees of freedom. While for the original Nosé-Hoover kinetic thermostat ergodicity has been achieved by controlling the higher order moments of kinetic energy, the issues of nonergodicity of BT thermostat persists. In this paper, we introduce two new measures of configurational temperature (second and third order) based on the generalized temperature-curvature relationship and obtain a family of deterministic thermostatting schemes by selectively (and simultaneously) controlling the different orders of temperatures through pseudo-friction terms. The ergodic characteristics of the proposed thermostats are tested using a single harmonic oscillator through statistical (normality of joint distributions at different Poincare sections) as well as dynamical tests (difference of the minimum and maximum largest Lyapunov exponent). Our results indicate that simultaneously controlling the first and the second order configurational temperatures (C(1,2) thermostat) is sufficient to make the dynamics ergodic. A 2000 particle Lennard-Jones system is subjected to (i) equilibrium and (ii) sudden temperature change under BT and C(1,2) thermostatting schemes. The C(1,2) thermostat is found to be more robust than the BT thermostat without increasing computational costs.
Pietracaprina, F.; Gogolin, C.; Goold, J.
2017-03-01
The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics in systems without degeneracies. In analogy to the time average of a classical phase-space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper bound on the multipartite entanglement, it quantifies the combination of both classical and quantum correlations in a mixed state. We generalize the total correlations of the diagonal ensemble to more general α -Renyi entropies and focus on the cases α =1 and α =2 with further numerical extensions in mind. Here we show that the total correlations of the diagonal ensemble is a generic indicator of ergodicity breaking, displaying a subextensive behavior when the system is ergodic. We demonstrate this by investigating its scaling in a range of spin chain models focusing not only on the cases of integrability breaking but also emphasize its role in understanding the transition from an ergodic to a many-body localized phase in systems with disorder or quasiperiodicity.
Oscillation and the mean ergodic theorem
Avigad, Jeremy
2012-01-01
Let B be a uniformly convex Banach space, let T be a nonexpansive linear operator, and let A_n x denote the ergodic average (1/n) sum_{i 0, the sequence has only finitely many fluctuations greater than epsilon. Drawing on calculations by Kohlenbach and Leustean, we provide a uniform bound on the number of fluctuations that depends only on rho := || x || / epsilon and a modulus, eta, of uniform convexity for B. Specifically, we show that the sequence of averages (A_n x) has O(rho^2 log rho * eta(1/(8 rho))^{-1})-many epsilon-fluctuations, and if B is a Hilbert space, the sequence has O(rho^3 log rho)-many epsilon-fluctuations. The proof is fully explicit, providing a remarkably uniform, quantitative, and constructive formulation of the mean ergodic theorem.
Ergodic Capacity for the SIMO Nakagami- Channel
Directory of Open Access Journals (Sweden)
Vagenas EfstathiosD
2009-01-01
Full Text Available This paper presents closed-form expressions for the ergodic channel capacity of SIMO (single-input and multiple output wireless systems operating in a Nakagami- fading channel. As the performance of SIMO channel is closely related to the diversity combining techniques, we present closed-form expressions for the capacity of maximal ratio combining (MRC, equal gain combining (EGC, selection combining (SC, and switch and stay (SSC diversity systems operating in Nakagami- fading channels. Also, the ergodic capacity of a SIMO system in a Nakagami- fading channel without any diversity technique is derived. The latter scenario is further investigated for a large amount of receive antennas. Finally, numerical results are presented for illustration.
Schroedinger difference equation with deterministic ergodic potentials
Suto, Andras
2012-01-01
We review the recent developments in the theory of the one-dimensional tight-binding Schr\\"odinger equation for a class of deterministic ergodic potentials. In the typical examples the potentials are generated by substitutional sequences, like the Fibonacci or the Thue-Morse sequence. We concentrate on rigorous results which will be explained rather than proved. The necessary mathematical background is provided in the text.
Probability, random processes, and ergodic properties
Gray, Robert M
1988-01-01
This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split...
Algebraic convergence for discrete-time ergodic Markov chains
Institute of Scientific and Technical Information of China (English)
MAO; Yonghua(毛永华)
2003-01-01
This paper studies the e-ergodicity for discrete-time recurrent Markov chains. It proves that thee-order deviation matrix exists and is finite if and only if the chain is (e + 2)-ergodic, and then the algebraicdecay rates of the n-step transition probability to the stationary distribution are obtained. The criteria fore-ergodicity are given in terms of existence of solution to an equation. The main results are illustrated by some examples.
Pietracaprina, Francesca; Gogolin, Christian; Goold, John
2016-01-01
The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics. In analogy to the time average of a classical phase space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper-bound on the multipartite entang...
Divertor Plasma Parameters During Radiative Divertor Operation on DIII--D
Allen, S. L.; Fenstermacher, M. E.; Hill, D. N.; Lasnier, C. J.; Meyer, W. H.; Porter, G. D.; Wood, R. D.; Leonard, A. W.; Mahdavi, M. A.; Petrie, T. W.; West, W. P.; Maingi, R.; Wade, M. R.; Whyte, D. G.
1996-11-01
A large array of divertor diagnostics has been used to characterize the DIII--D divertor conditions during radiative divertor operation. We have used both D2 and impurities to reduce the divertor heat flux. Several discharge conditions have been obtained, including attached and detached ELMing H-modes. The multi-chord Divertor Thomson Scattering (DTS) system has been used with divertor sweeping to obtain 2-D measurements of ne and Te in the divertor. The Te drops to <= 2 eV with D2 puffing, ne increases, and the electron pressure Pe decreases. The radiation zone, measured by multi-chord bolometry, moves from the inside leg of the divertor to the outside. Comparisons of the 2-D distribution of ne and Te and the radiation distribution will be presented.
Magnetic Geometry and Physics of Advanced Divertors: The X-Divertor and the Snowflake
Kotschenreuther, Mike; Covele, Brent; Mahajan, Swadesh
2013-01-01
Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust - the Scrape-Off Layer (SOL). A primary result of our analysis is the emergence of a physical "metric", the Divertor Index DI, that quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics - the Standard Divertor (SD, DI = 1), and two advanced geometries: the X-Divertor (XD, DI > 1) and the Snowflake (SFD, DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent NSTX and DIIID experiments are X-Divertors, not Snowflakes.
Geometric covering arguments and ergodic theorems for free groups
Bowen, Lewis
2009-01-01
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering and asymptotic invariance arguments used in the ergodic theory of amenable groups. We use this approach to generalize the existing maximal and pointwise ergodic theorems for free group actions to a large class of geometric averages which were not accessible by previous techniques. Some applications of our approach to other groups and other problems in ergodic theory are also briefly discussed.
Development of divertor remote maintenance system
Energy Technology Data Exchange (ETDEWEB)
Takeda, Nobukazu; Oka, Kiyoshi; Akou, Kentaro; Takiguchi, Yuji [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-04-01
The ITER divertor is categorized as a scheduled maintenance component because of extreme heat and particle loads it is exposed to by plasma. It is also highly activated by 14 MeV neutrons. Reliable remote handling equipment and tools are required for divertor maintenance under intense gamma radiation. To facilitate remote maintenance, the divertor is segmented into 60 cassettes, and each cassette weighing about 25 tons and maintained and replaced through four maintenance ports each 90 degrees. Divertor cassettes must be transported toroidally and radially for replacement through maintenance ports. Remote handling involving cassette movers and carriers for toroidal and radial transport has been developed. Under the ITER R and D program, technology critical to divertor cassette maintenance is being developed jointly by Japan, E.U., and U.S. home teams. This paper summarizes divertor remote maintenance design and the status of technology development by the Japan Home Team. (author)
Periodically driven ergodic and many-body localized quantum systems
Energy Technology Data Exchange (ETDEWEB)
Ponte, Pedro [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1 (Canada); Chandran, Anushya [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Papić, Z., E-mail: zpapic@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Institute for Quantum Computing, Waterloo, ON N2L 3G1 (Canada); Abanin, Dmitry A. [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Institute for Quantum Computing, Waterloo, ON N2L 3G1 (Canada)
2015-02-15
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.
Anomalous Thermalization in Ergodic Systems
Luitz, David J.; Bar Lev, Yevgeny
2016-10-01
It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry's conjecture.
Simulation Analysis of Divertor Performance in EAST
Institute of Scientific and Technical Information of China (English)
Zhu Sizheng; Zha Xuejun
2005-01-01
A detailed study of the divertor performance in the EAST has been conducted for both its double null and single null configurations. The results of the application of the SOLPS (B2/Eirene) code package to the analysis of the EAST divertor are summarized. Here we concentrate on the effects of the increased geometrical closure and variation in the magnetic topology on the behavior of divertor plasmas. The results of numerical predictions for the EAST divertor's operational window are also described in this paper.
Energy Technology Data Exchange (ETDEWEB)
Ohno, N. [Nagoya Univ. (Japan). Dept. of Energy Eng. and Sci.; Mori, S. [Nagoya Univ. (Japan). Dept. of Energy Eng. and Sci.; Ezumi, N. [Nagoya Univ. (Japan). Dept. of Energy Eng. and Sci.; Takagi, M. [Nagoya Univ. (Japan). Dept. of Energy Eng. and Sci.; Takamura, S. [Nagoya Univ. (Japan). Dept. of Energy Eng. and Sci.; Suzuki, H. [National Inst. for Fusion Science, Nagoya (Japan)
1996-08-01
It is one of the most critical requirements to reduce the heat load to the divertor plate in the next generation fusion devices such as ITER, intended to have a long pulse or a steady state operation. Dynamic gas target divertor as well as high recycling divertor is one of the most important candidates for ITER. Recently a detached plasma has been observed in experimental fusion devices. Knowledge of the basic physics of the plasma detachment is required for any application of the gas target and high recycling divertor to the next generation experimental reactors. Linear plasma divertor simulators with high heat flux plasmas are used to investigate the plasma detachment because its good accessibility for comprehensive measurements and simple geometry leads a deeper understanding of the plasma detachment by comparing between simulation predictions and the experimental results. (orig.)
Ergodicity and Gaussianity for Spherical Random Fields
Marinucci, Domenico
2009-01-01
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
Engineering conceptual design of CFETR divertor
Energy Technology Data Exchange (ETDEWEB)
Peng, Xuebing, E-mail: pengxb@ipp.cas.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Shushanhu Road 350, 230031 Hefei Anhui (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, Jinzhai Road 96, 230026 Hefei Anhui (China); Institute of Plasma Physics, Chinese Academy of Sciences, Shushanhu Road 350, 230031 Hefei Anhui (China); Song, Yuntao [Institute of Plasma Physics, Chinese Academy of Sciences, Shushanhu Road 350, 230031 Hefei Anhui (China); School of Nuclear Science and Technology, University of Science and Technology of China, Jinzhai Road 96, 230026 Hefei Anhui (China); Mao, Xin [Institute of Plasma Physics, Chinese Academy of Sciences, Shushanhu Road 350, 230031 Hefei Anhui (China); Chen, Peiming; Qian, Xinyuan [School of Nuclear Science and Technology, University of Science and Technology of China, Jinzhai Road 96, 230026 Hefei Anhui (China)
2015-10-15
Highlights: • Three divertor structures for two plasma configurations, ITER-like and snowflake. • Property of enlarging wet area for all three divertors is analyzed. • The divertor accommodating with both the plasma configurations is unfeasible. • Divertor cooling system is developed. - Abstract: The China Fusion Engineering Test Reactor (CFETR), which is in conceptual design phase, aims at producing fusion power of 50–200 MW with tritium breeding ratio of ∼1.2 and duty cycle time of 0.3–0.5. Its designed main parameters are major/minor radii of 5.7 m/1.6 m and plasma current of 10 MA. Although the fusion power is lower than the one of ITER, the relative smaller machine dimensions and planed much higher auxiliary heating power of 100–140 MW make that the power exhausting for the CFETR divertor is a very critical issue. To solve this issue, the divertor should be better designed with advanced physical operation mode, advanced configuration/geometry or high efficient cooling structure. In the paper, much effort was put on the divertor configuration and geometry. With designed magnet system, three divertor configurations can be realized, ITER-like, snowflake and super-X. However, considering structural design feasibility and remote handling compatibility, only the first two configurations were selected for the first step of engineering design. Three divertors were designed. They have different first wall geometries to accommodate with different plasma configurations, one for the ITER-like, one for the snowflake and the third one for both the configurations. All three divertors employ the same cassette body as the support and the cooling water manifold for the first wall. This feature simplifies the interface of the divertor to other components in the vacuum vessel. Besides, the cooling structure and the remote maintenance concept are also introduced in the paper.
A large divertor manipulator for ASDEX Upgrade
Energy Technology Data Exchange (ETDEWEB)
Herrmann, Albrecht, E-mail: albrecht.herrmann@ipp.mpg.de; Jaksic, Nikola; Leitenstern, Peter; Greuner, Henri; Krieger, Karl; Marné, Pascal de; Oberkofler, Martin; Rohde, Volker; Schall, Gerd
2015-10-15
Highlights: • A large divertor manipulator for ASDEX Upgrade is developed and tested. • It allows replacing a relevant part of the divertor by dedicated targets and probes. • Modified solid standard targets. • Electrical and mechanical probes for dedicated investigations. • Test of actively cooled component. - Abstract: In 2013 a new bulk tungsten divertor, Div-III, was installed in ASDEX Upgrade (AUG). During the concept and design phase of Div-III the option of adaptable divertor instrumentation and divertor modification as contribution for divertor investigations in preparation of ITER was given a high priority. To gain flexibility for the test of divertor modifications without affecting the operational space of AUG, the large divertor manipulator, DIM-II, was designed and installed. DIM-II allows to retract 2 out of 128 outer divertor target tiles including the water cooled support structure into a target exchange box and to replace these targets without breaking the vacuum of the AUG vessel. DIM-II is based on a carriage-rail system with a driving rod pushing a front-end with the target module into the divertor position for plasma operation. Three types of front-ends are foreseen for physics investigations: (i) modified standard targets clamped to the standard cooling structure, (ii) dedicated front-ends making use of the whole available volume of about 230 × 160 × 80 mm{sup 3} and (iii) actively cooled/heated targets for cooling water temperatures up to 230 °C. This paper presents the DIM-II design including the FEM calculations for the modified divertor support structure and the front-end options, as well as the test procedure and operation mode.
On the rate of quantum ergodicity in Euclidean billiards
Bäcker, A; Stifter, P
1998-01-01
For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdière and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we first give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions like bouncing ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a sim...
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Moving Divertor Plates in a Tokamak
Energy Technology Data Exchange (ETDEWEB)
S.J. Zweben, H. Zhang
2009-02-12
Moving divertor plates could help solve some of the problems of the tokamak divertor through mechanical ingenuity rather than plasma physics. These plates would be passively heated on each pass through the tokamak and cooled and reprocessed outside the tokamak. There are many design options using varying plate shapes, orientations, motions, coatings, and compositions.
Rapidly Moving Divertor Plates In A Tokamak
Energy Technology Data Exchange (ETDEWEB)
S. Zweben
2011-05-16
It may be possible to replace conventional actively cooled tokamak divertor plates with a set of rapidly moving, passively cooled divertor plates on rails. These plates would absorb the plasma heat flux with their thermal inertia for ~10-30 sec, and would then be removed from the vessel for processing. When outside the tokamak, these plates could be cooled, cleaned, recoated, inspected, and then returned to the vessel in an automated loop. This scheme could provide nearoptimal divertor surfaces at all times, and avoid the need to stop machine operation for repair of damaged or eroded plates. We describe various possible divertor plate designs and access geometries, and discuss an initial design for a movable and removable divertor module for NSTX-U.
Septum assessment of the JET gas box divertor
Rapp, J.; Fundamenski, W.; Ingesson, L. C.; Jachmich, S.; Huber, A.; Matthews, G. F.; Morgan, P.; Stamp, M. F.
2008-01-01
The influence of the physical isolation of inner and outer divertor volumes by a septum plate of the Mk-II gas box divertor, thus increasing divertor closure and neutral compression, on the plasma and divertor performance has been studied at the Joint European Torus (JET). The septum plate was insta
Ergodic theory of expanding thurston maps
Li, Zhiqiang
2017-01-01
Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general eq...
An Ergodic Dilation of Completely Positive Maps
Pandiscia, Carlo
2011-01-01
We shall prove the following Stinespring-type theorem: there exists a triple $(\\pi,\\mathcal{H},\\mathbf{V})$ associated with an unital completely positive map $\\Phi:\\mathfrak{A}\\rightarrow \\mathfrak{A}$ on C* algebra $\\mathfrak{A}$ with unit, where $\\mathcal{H}$ is a Hilbert space, $\\pi:\\mathfrak{A\\rightarrow B}(\\mathcal{H})$ is a faithful representation and $\\mathbf{V}$ is a linear isometry on $\\mathcal{H}$ such that $\\pi(\\Phi(a)=\\mathbf{V}^*\\pi(a)\\mathbf{V}$ for all $a$ belong to $\\mathfrak{A}$. The Nagy dilation theorem, applied to isometry $\\mathbf{V}$, allows to construct a dilation of ucp-map, $\\Phi$, in the sense of Arveson, that satisfies ergodic properties of a $\\Phi $-invariante state $\\phi$ on $\\mathfrak{A}$, if $\\Phi$ admit a $\\phi $-adjoint.
Ergodic directional switching in mobile insect groups
Escudero, Carlos
2010-07-29
We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group\\'s direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation. © 2010 The American Physical Society.
First Divertor Operation on the HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
YANG Qing-Wei; CAO Zeng; LI Xiao-Dong; MAO Wei-Cheng; ZHOU Cai-Pin; WANG En-Yao; YAN Jian-Cheng; LIU Yong; HL-2A team; DING Xuan-Tong; YAN Long-Wen; XUAN Wei-Min; LIU De-Quan; CHEN Liao-Yuan; SONG Xian-Ming; YUAN Bao-Shan; ZHANG Jin-Hua
2004-01-01
@@ HL-2A device is the first divertor tokamak in China. One of its main subjects is to study the features of the divertor plasma. In the last campaign, the first divertor configuration has been achieved and sustained on the HL-2A tokamak. Here we give a brief description about the HL-2A tokamak, diagnostics arrangements, and the equilibrium analysis results on divertor configuration. The main results of divertor experiments are also presented.
From infinite ergodic theory to number theory (and possibly back)
Energy Technology Data Exchange (ETDEWEB)
Isola, Stefano, E-mail: stefano.isola@unicam.it [Dipartimento di Matematica e Informatica, Universita di Camerino, via Madonna delle Carceri, I-62032 Camerino (Italy)
2011-07-15
Highlights: > Systems preserving an infinite measure need new indicators such as the wandering rate. > Coping wild behaviour of the ergodic sums with very good sets and universal sequences. > Applications to Farey map and slow convergents in continued fractions theory. - Abstract: Some basic facts of infinite ergodic theory are reviewed in a form suitable to be applied to interval maps with number theoretic significance such as the Farey map. This is an enlarged version of the lecture notes accompanying a short course on Infinite Ergodic Theory at the First meeting of the (mostly) young italian hyperbolicians (Corinaldo, Italy, June 8-12, 2009).
Dust divertor for a tokamak fusion reactor
Energy Technology Data Exchange (ETDEWEB)
Tang, X Z [Los Alamos National Laboratory; Delzanno, G L [Los Alamos National Laboratory
2009-01-01
Micron-size tungsten particulates find equilibrium position in the magnetized plasma sheath in the normal direction of the divertor surface, but are convected poloidally and toroidally by the sonic-ion-flow drag parallel to the divertor surface. The natural circulation of dust particles in the magnetized plasma sheath can be used to set up a flowing dust shield that absorbs and exhausts most of the tokamak heat flux to the divertor. The size of the particulates and the choice of materials offer substantial room for optimization.
MAST-Upgrade Divertor Facility and Assessing Performance of Long-Legged Divertors
Fishpool, G; Cunningham, G; Harrison, J; Katramados, I; Kirk, A; Kovari, M; Meyer, H; Scannell, R
2013-01-01
A potentially important feature in a divertor design for a high-power tokamak is an extended and expanded divertor leg. The upgrade to MAST will allow a wide range of such divertor leg geometries to be produced, and hence will allow the roles of greatly increased connection length and flux expansion to be experimentally tested. This will include testing the potential of the Super-X configuration [1]. The design process for the upgrade has required analysis of producing and controlling the magnetic configurations, and has included consideration of the roles that divertor closure and increasing magnetic connection length will play.
The average-shadowing property and topological ergodicity for flows
Energy Technology Data Exchange (ETDEWEB)
Gu Rongbao [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)]. E-mail: rbgu@njue.edu.cn; Guo Wenjing [School of Finance, Nanjing University of Finance and Economics, Nanjing 210046 (China)
2005-07-01
In this paper, the transitive property for a flow without sensitive dependence on initial conditions is studied and it is shown that a Lyapunov stable flow with the average-shadowing property on a compact metric space is topologically ergodic.
Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence
Shebalin, John V.
2010-01-01
Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures
ARIES-III divertor engineering design
Energy Technology Data Exchange (ETDEWEB)
Wong, C.P.C.; Schultz, K.R. [General Atomics, San Diego, CA (United States); Cheng, E.T. [TSI Research, Solana Beach, CA (United States); Grotz, S.; Hasan, M.A.; Najmabadi, F.; Sharafat, S. [California Univ., Los Angeles, CA (United States). Dept. of Mechanical, Aerospace and Nuclear Engineering; Brooks, J.N.; Ehst, D.A.; Sze, D.K. [Argonne National Lab., IL (United States); Herring, J.S. [EG and G Idaho, Inc., Idaho Falls, ID (United States); Valenti, M.; Steiner, D. [Rensselaer Polytechnic Inst., Troy, NY (United States). Plasma Dynamics Lab.
1992-01-01
This paper reports the engineering design of the ARIES-III double- null divertor. The divertor coolant tubes are made from W-3Re alloy and cooled by subcooled flow boiling of organic coolant. A coating of 4 mm thick tungsten is plasma sprayed onto the divertor surface. This W layer can withstand the thermal deposition of a few disruptions. At a maximum surface heat flux of 5.4 MW/m{sup 2}, a conventional divertor design can be used. The divertor surface is contoured to have a constant heat flux of 5.4 MW/m{sup 2}. The net erosion of the W-surface was found to be negligible at about 0.1 mm/year. After 3 years of operation, the W-3Re alloy ARIES-III divertor can be disposed of as Class A waste. In order to control the prompt dose release at site boundary to less than 200 Rem, isotopic tailoring of the W-alloy will be needed.
Application of the radiating divertor approach to innovative tokamak divertor concepts
Energy Technology Data Exchange (ETDEWEB)
Petrie, T.W., E-mail: petrie@fusion.gat.com [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Allen, S.L.; Fenstermacher, M.E. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Groebner, R.J. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Holcomb, C.T. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Kolemen, E. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, NJ 08543-0451 (United States); La Haye, R.J. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Lasnier, C.J. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Leonard, A.W.; Luce, T.C. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); McLean, A.G. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Maingi, R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, NJ 08543-0451 (United States); Moyer, R.A. [University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0417 (United States); Solomon, W.M. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, NJ 08543-0451 (United States); Soukhanovskii, V.A. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Turco, F. [Columbia University, 2960 Broadway, New York, NY 10027 (United States); Watkins, J.G. [Sandia National Laboratory, PO Box 5800, Albuquerque, NM 87185 (United States)
2015-08-15
We survey the results of recent DIII-D experiments that tested the effectiveness of three innovative tokamak divertor concepts in reducing divertor heat flux while still maintaining acceptable energy confinement under neon/deuterium-based radiating divertor (RD) conditions: (1) magnetically unbalanced high performance double-null divertor (DND) plasmas, (2) high performance double-null “Snowflake” (SF-DN) plasmas, and (3) single-null H-mode plasmas having different isolation from their divertor targets. In general, all three concepts adapt well to RD conditions, achieving significant reduction in divertor heat flux (q{sub ⊥p}) and maintaining high performance metrics, e.g., 50–70% reduction in peak divertor heat flux for DND and SF-DN plasmas that are characterized by β{sub N} ≅ 3.0 and H{sub 98(y,2)} ≈ 1.35. It is also demonstrated that q{sub ⊥p} could be reduced ≈50% by extending the parallel connection length (L{sub ||-XPT}) in the scrape-off layer between the X-point and divertor targets over a variety of the RD and non-RD environments tested.
Secrecy Capacity over Correlated Ergodic Fading Channel
Jeon, Hyoungsuk; Kim, Minki; Lee, Hyuckjae; Ha, Jeongseok
2008-01-01
We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss of the secrecy capacity due to the correlation. In addition, we study the asymptotic behavior of the secrecy capacity as Signal-to-Noise Ratio (SNR) tends to infinity. The capacity of an ordinary fading channel logarithmically increases with SNR. On the contrary, the secrecy capacity converges into a limit which can be an upper bound on the secrecy capacity over the fading wiretap channel. We find a closed form of the upper bound for the correlated Rayleigh wiretap channel which also includes the independent case as a special one. Our work shows that the upper bound is determined by only two channel parameters; the correlation coefficient an...
Fractional Feynman-Kac equation for weak ergodicity breaking.
Carmi, Shai; Barkai, Eli
2011-12-01
The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, ψ(τ) ~ τ(-(1+α)), leads to subdiffusion (x(2) ~ t(α)) for 0 Feynman-Kac equation if the motion is Brownian. Here, we derive forward and backward fractional Feynman-Kac equations for functionals of CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for t → ∞ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for α = 1, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.
High-speed Flight in an Ergodic Forest
Karaman, Sertac
2012-01-01
Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of a novel motion planning problem: high-speed navigation through a randomly-generated obstacle field when only the statistics of the obstacle generating process are known a priori. Resembling a planar forest environment, the obstacle generating process is assumed to determine the locations and sizes of disk-shaped obstacles. When this process is ergodic, and under mild technical conditions on the dynamics of the bird, it is shown that the existence of an infinite collision-free trajectory through the forest exhibits a phase transition. On one hand, if the bird flies faster than a certain critical speed, then, with probability one, there is no infinite collision-free trajectory, i.e., the bird will eventually collide with some tree, almost surely, regardless of the planning algorithm governing the bird's motion. On the other hand, if the bird flies slower than this critical speed, then...
Atomic and molecular processes in JT-60U divertor plasmas
Energy Technology Data Exchange (ETDEWEB)
Takenaga, H.; Shimizu, K.; Itami, K. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment] [and others
1997-01-01
Atomic and molecular data are indispensable for the understanding of the divertor characteristics, because behavior of particles in the divertor plasma is closely related to the atomic and molecular processes. In the divertor configuration, heat and particles escaping from the main plasma flow onto the divertor plate along the magnetic field lines. In the divertor region, helium ash must be effectively exhausted, and radiation must be enhanced for the reduction of the heat load onto the divertor plate. In order to exhaust helium ash effectively, the difference between behavior of neutral hydrogen (including deuterium and tritium) and helium in the divertor plasma should be understood. Radiation from the divertor plasma generally caused by the impurities which produced by the erosion of the divertor plate and/or injected by gas-puffing. Therefore, it is important to understand impurity behavior in the divertor plasma. The ions hitting the divertor plate recycle through the processes of neutralization, reflection, absorption and desorption at the divertor plates and molecular dissociation, charge-exchange reaction and ionization in the divertor plasma. Behavior of hydrogen, helium and impurities in the divertor plasmas can not be understood without the atomic and molecular data. In this report, recent results of the divertor study related to the atomic and molecular processes in JT-60U were summarized. Behavior of neural deuterium and helium was discussed in section 2. In section 3, the comparisons between the modelling of the carbon impurity transport and the measurements of C II and C IV were discussed. In section 4, characteristics of the radiative divertor using Ne puffing were reported. The new diagnostic method for the electron density and temperature in the divertor plasmas using the intensity ratios of He I lines was described in section 5. (author)
Snowflake divertor configuration studies in National Spherical Torus Experiment
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V. A.; McLean, A. G.; Rognlien, T. D.; Ryutov, D. D.; Umansky, M. V. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Bell, R. E.; Diallo, A.; Gerhardt, S.; Kaye, S.; Kolemen, E.; LeBlanc, B. P.; Menard, J. E.; Paul, S. F.; Podesta, M.; Roquemore, A. L.; Scotti, F.; Battaglia, D.; Bell, M. G.; Gates, D. A.; Kaita, R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); and others
2012-08-15
Experimental results from NSTX indicate that the snowflake divertor (D. Ryutov, Phys. Plasmas 14, 064502 (2007)) may be a viable solution for outstanding tokamak plasma-material interface issues. Steady-state handling of divertor heat flux and divertor plate erosion remains to be critical issues for ITER and future concept devices based on conventional and spherical tokamak geometry with high power density divertors. Experiments conducted in 4-6 MW NBI-heated H-mode plasmas in NSTX demonstrated that the snowflake divertor is compatible with high-confinement core plasma operation, while being very effective in steady-state divertor heat flux mitigation and impurity reduction. A steady-state snowflake divertor was obtained in recent NSTX experiments for up to 600 ms using three divertor magnetic coils. The high magnetic flux expansion region of the scrape-off layer (SOL) spanning up to 50% of the SOL width {lambda}{sub q} was partially detached in the snowflake divertor. In the detached zone, the heat flux profile flattened and decreased to 0.5-1 MW/m{sup 2} (from 4-7 MW/m{sup 2} in the standard divertor) indicative of radiative heating. An up to 50% increase in divertor, P{sub rad} in the snowflake divertor was accompanied by broadening of the intrinsic C III and C IV radiation zones, and a nearly order of magnitude increase in divertor high-n Balmer line emission indicative of volumetric recombination onset. Magnetic reconstructions showed that the x-point connection length, divertor plasma-wetted area and divertor volume, all critical parameters for geometric reduction of deposited heat flux, and increased volumetric divertor losses were significantly increased in the snowflake divertor, as expected from theory.
Snowflake divertor configuration studies for NSTX-Upgrade
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V A
2011-11-12
Snowflake divertor experiments in NSTX provide basis for PMI development toward NSTX-Upgrade. Snowflake configuration formation was followed by radiative detachment. Significant reduction of steady-state divertor heat flux observed in snowflake divertor. Impulsive heat loads due to Type I ELMs are partially mitigated in snowflake divertor. Magnetic control of snowflake divertor configuration is being developed. Plasma material interface development is critical for NSTX-U success. Four divertor coils should enable flexibility in boundary shaping and control in NSTX-U. Snowflake divertor experiments in NSTX provide good basis for PMI development in NSTX-Upgrade. FY 2009-2010 snowflake divertor experiments in NSTX: (1) Helped understand control of magnetic properties; (2) Core H-mode confinement unchanged; (3) Core and edge carbon concentration reduced; and (4) Divertor heat flux significantly reduced - (a) Steady-state reduction due to geometry and radiative detachment, (b) Encouraging results for transient heat flux handling, (c) Combined with impurity-seeded radiative divertor. Outlook for snowflake divertor in NSTX-Upgrade: (1) 2D fluid modeling of snowflake divertor properties scaling - (a) Edge and divertor transport, radiation, detachment threshold, (b) Compatibility with cryo-pump and lithium conditioning; (2) Magnetic control development; and (3) PFC development - PFC alignment and PFC material choice.
Impurity-induced divertor plasma oscillations
Energy Technology Data Exchange (ETDEWEB)
Smirnov, R. D., E-mail: rsmirnov@ucsd.edu; Krasheninnikov, S. I.; Pigarov, A. Yu. [University of California, San Diego, La Jolla, California 92093 (United States); Kukushkin, A. S. [NRC “Kurchatov Institute”, Moscow 123182 (Russian Federation); National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation); Rognlien, T. D. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
2016-01-15
Two different oscillatory plasma regimes induced by seeding the plasma with high- and low-Z impurities are found for ITER-like divertor plasmas, using computer modeling with the DUSTT/UEDGE and SOLPS4.3 plasma-impurity transport codes. The oscillations are characterized by significant variations of the impurity-radiated power and of the peak heat load on the divertor targets. Qualitative analysis of the divertor plasma oscillations reveals different mechanisms driving the oscillations in the cases of high- and low-Z impurity seeding. The oscillations caused by the high-Z impurities are excited near the X-point by an impurity-related instability of the radiation-condensation type, accompanied by parallel impurity ion transport affected by the thermal and plasma friction forces. The driving mechanism of the oscillations induced by the low-Z impurities is related to the cross-field transport of the impurity atoms, causing alteration between the high and low plasma temperature regimes in the plasma recycling region near the divertor targets. The implications of the impurity-induced plasma oscillations for divertor operation in the next generation tokamaks are also discussed.
Impurity-induced divertor plasma oscillations
Smirnov, R. D.; Kukushkin, A. S.; Krasheninnikov, S. I.; Pigarov, A. Yu.; Rognlien, T. D.
2016-01-01
Two different oscillatory plasma regimes induced by seeding the plasma with high- and low-Z impurities are found for ITER-like divertor plasmas, using computer modeling with the DUSTT/UEDGE and SOLPS4.3 plasma-impurity transport codes. The oscillations are characterized by significant variations of the impurity-radiated power and of the peak heat load on the divertor targets. Qualitative analysis of the divertor plasma oscillations reveals different mechanisms driving the oscillations in the cases of high- and low-Z impurity seeding. The oscillations caused by the high-Z impurities are excited near the X-point by an impurity-related instability of the radiation-condensation type, accompanied by parallel impurity ion transport affected by the thermal and plasma friction forces. The driving mechanism of the oscillations induced by the low-Z impurities is related to the cross-field transport of the impurity atoms, causing alteration between the high and low plasma temperature regimes in the plasma recycling region near the divertor targets. The implications of the impurity-induced plasma oscillations for divertor operation in the next generation tokamaks are also discussed.
A semigroup approach to the strong ergodic theorem of the multistate stable population process.
Inaba, H
1988-01-01
"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE)
Localization to ergodic transitions: is Rosenzweig-Porter ensemble the hidden skeleton?
Shukla, Pragya
2016-02-01
The presence of local interactions and wave-localization phenomena is quite generic to a wide range of complex systems. Based on the evidence of two transitions similar to those in many body states as well as single particle states, the work by Kravtsov et al (2015 New J. Phys. 17 122002) indicates the strong prospect of Rosenzweig-Porter ensemble to serve as the good model for many particle localization as well as that of single particle. With already well-known statistical universality of ergodic dynamics, this also reveals the next level in the hierarchy of the universality of statistical fluctuations.
Impact of divertor geometry on radiative divertor performance in JET H-mode plasmas
Jaervinen, A. E.; Brezinsek, S.; Giroud, C.; Groth, M.; Guillemaut, C.; Belo, P.; Brix, M.; Corrigan, G.; Drewelow, P.; Harting, D.; Huber, A.; Lawson, K. D.; Lipschultz, B.; Maggi, C. F.; Matthews, G. F.; Meigs, A. G.; Moulton, D.; Stamp, M. F.; Wiesen, S.; Contributors, JET
2016-04-01
Radiative divertor operation in JET high confinement mode plasmas with the ITER-like wall has been experimentally investigated and simulated with EDGE2D-EIRENE in horizontal and vertical low field side (LFS) divertor configurations. The simulations show that the LFS divertor heat fluxes are reduced with N2-injection in similar fashion in both configurations, qualitatively consistent with experimental observations. The simulations show no substantial difference between the two configurations in the reduction of the peak LFS heat flux as a function of divertor radiation, nitrogen concentration, or pedestal Zeff. Consistently, experiments show similar divertor radiation and nitrogen injection levels for similar LFS peak heat flux reduction in both configurations. Nevertheless, the LFS strike point is predicted to detach at 20% lower separatrix density in the vertical than in the horizontal configuration. However, since the peak LFS heat flux in partial detachment in the vertical configurations is shifted towards the far scrape-off layer (SOL), the simulations predict no benefit in the reduction of LFS peak heat flux for a given upstream density in the vertical configuration relative to a horizontal one. A factor of 2 reduction of deuterium ionization source inside the separatrix is observed in the simulations when changing to the vertical configuration. The simulations capture the experimentally observed particle and heat flux reduction at the LFS divertor plate in both configurations, when adjusting the impurity injection rate to reproduce the measured divertor radiation. However, the divertor D α -emissions are underestimated by a factor of 2-5, indicating a short-fall in radiation by the fuel species. In the vertical configuration, detachment is experimentally measured and predicted to start next to the strike point, extending towards the far SOL with increasing degree of detachment. In contrast, in the horizontal configuration, the entire divertor particle flux
Weak ergodicity breaking, irreproducibility, and ageing in anomalous diffusion processes
Energy Technology Data Exchange (ETDEWEB)
Metzler, Ralf [Institute for Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Tampere University of Technology, FI-33101 Tampere (Finland)
2014-01-14
Single particle traces are standardly evaluated in terms of time averages of the second moment of the position time series r(t). For ergodic processes, one can interpret such results in terms of the known theories for the corresponding ensemble averaged quantities. In anomalous diffusion processes, that are widely observed in nature over many orders of magnitude, the equivalence between (long) time and ensemble averages may be broken (weak ergodicity breaking), and these time averages may no longer be interpreted in terms of ensemble theories. Here we detail some recent results on weakly non-ergodic systems with respect to the time averaged mean squared displacement, the inherent irreproducibility of individual measurements, and methods to determine the exact underlying stochastic process. We also address the phenomenon of ageing, the dependence of physical observables on the time span between initial preparation of the system and the start of the measurement.
Ergodicity in randomly forced Rayleigh-Bénard convection
Földes, J.; Glatt-Holtz, N. E.; Richards, G.; Whitehead, J. P.
2016-11-01
We consider the Boussinesq approximation for Rayleigh-Bénard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two space dimensions, with sufficient stochastic forcing in the temperature component and large Prandtl number Pr > 0, we establish the existence of a unique ergodic invariant measure. In three space dimensions, we prove the existence of a statistically invariant state, and establish unique ergodicity for the infinite Prandtl Boussinesq system. Throughout this work we provide streamlined proofs of unique ergodicity which invoke an asymptotic coupling argument, a delicate usage of the maximum principle, and exponential martingale inequalities. Lastly, we show that the background method of Constantin and Doering (1996 Nonlinearity 9 1049-60) can be applied in our stochastic setting, and prove bounds on the Nusselt number relative to the unique invariant measure.
Uniform convergence of Vapnik--Chervonenkis classes under ergodic sampling
Adams, Terrence M; 10.1214/09-AOP511
2010-01-01
We show that if $\\mathcal{X}$ is a complete separable metric space and $\\mathcal{C}$ is a countable family of Borel subsets of $\\mathcal{X}$ with finite VC dimension, then, for every stationary ergodic process with values in $\\mathcal{X}$, the relative frequencies of sets $C\\in\\mathcal{C}$ converge uniformly to their limiting probabilities. Beyond ergodicity, no assumptions are imposed on the sampling process, and no regularity conditions are imposed on the elements of $\\mathcal{C}$. The result extends existing work of Vapnik and Chervonenkis, among others, who have studied uniform convergence for i.i.d. and strongly mixing processes. Our method of proof is new and direct: it does not rely on symmetrization techniques, probability inequalities or mixing conditions. The uniform convergence of relative frequencies for VC-major and VC-graph classes of functions under ergodic sampling is established as a corollary of the basic result for sets.
Designing divertor targets for uniform power load
Dekeyser, W.; Reiter, D.; Baelmans, M.
2015-08-01
Divertor design for next step fusion reactors heavily relies on 2D edge plasma modeling with codes as e.g. B2-EIRENE. While these codes are typically used in a design-by-analysis approach, in previous work we have shown that divertor design can alternatively be posed as a mathematical optimization problem, and solved very efficiently using adjoint methods adapted from computational aerodynamics. This approach has been applied successfully to divertor target shape design for more uniform power load. In this paper, the concept is further extended to include all contributions to the target power load, with particular focus on radiation. In a simplified test problem, we show the potential benefits of fully including the radiation load in the design cycle as compared to only assessing this load in a post-processing step.
DEFF Research Database (Denmark)
Liu, S. C.; Guo, H. Y.; Xu, Guandong
2012-01-01
Divertor asymmetry and its dependence on the ion del B direction has been investigated in the Experimental Advanced Superconducting Tokamak by changing the divertor configuration from lower single null (LSN), via double null (DN), to upper single null (USN) during one single discharge. Divertor p...
Universally Typical Sets for Ergodic Sources of Multidimensional Data
Krüger, Tyll; Seiler, Ruedi; Siegmund-Schultze, Rainer
2011-01-01
We lift important results of the theory of samples of discrete ergodic information sources to the multidimensional setting. We use the technique of packings and coverings with multidimensional windows in entropy estimation and universal lossless compression. In particular, we construct sequences of multidimensional array sets which, in the limit, build the generated samples of any ergodic source of entropy rate below an $h_{0}$ with probability 1 and whose cardinality grows at most at exponential rate $h_{0}$. Thereby we extrapolate mathematical framework relevant for universal source coding of multi-dimensionally correlated data.
Characteristics of divertor detachment for ITER conditions
Energy Technology Data Exchange (ETDEWEB)
Kukushkin, A.S., E-mail: andre.kukushkin@iter.org [ITER Organization, St Paul Lez Durance (France); Pacher, H.D. [INRS-EMT, Varennes, Québec (Canada); Pitts, R.A. [ITER Organization, St Paul Lez Durance (France)
2015-08-15
The relative role of particle balance vs. momentum balance in the phenomenon of divertor plasma detachment in tokamaks is re-assessed. Ion removal from the plasma flow by volumetric recombination and/or cross-field transport is identified as the key element in the formation of the rollover of the ion saturation current on the targets, whereas “momentum removal” (friction) is responsible for maintaining high plasma pressure upstream. The deterioration of neutral particle confinement in the divertor as particle throughput increases is the primary cause of the solution collapse typically seen when deep detachment is modelled for present day experiments.
An ergodic approach to eruption hazard scaling
De la Cruz-Reyna, Servando; Mendoza-Rosas, Ana Teresa
2014-05-01
The complexity and indeterminacy of volcanic processes demand the use of statistical methods to analyze the expectations of the occurrence and size of future eruptions. The probability of a volcano producing potentially destructive eruptions in a given time interval may be estimated analyzing the sequence of past eruptions assuming a physically plausible process. Since the threat posed by eruptions depends on their mass or energy release (magnitude) and on their emission rate (intensity), the Volcanic Explosivity Index is a suitable measure to quantify the eruptive events, particularly considering that the largest available global catalogues use that measure. The definition of volcanic hazard is thus posed here in terms of the expected annual release of energy by eruptions in each VEI category. This concept is based on the ergodic property of a large set of volcanoes to release about the same amount of energy in each VEI category over a sufficiently large time interval. This property is however constrained to the VEI range of eruptions that constitute complete catalogues (VEI >2) in the lower end, and to the extreme eruptions that may destroy or significantly alter a volcanic system, such as the large caldera-forming eruptions (VEI < 7). In such conditions, a simple power law for eruptions at the global level relating the global rate of energy release to the eruption magnitude has been proposed as a statistical basis for eruptive event model development. Following the above mentioned arguments, we assume that a similar scaling law rules the annual rate at which energy is released by eruptions at individual volcanoes as log(EmRm)=bM+a, where Em is the energy released by eruptions in the VEI magnitude class M, and Rm is the occurrence rate of such eruptions over times ranges in which catalogues may be considered complete. The parameters b and a depend on the eruptive history of individual volcanoes, the former determining the preferred mode of the volcano to release
Simulation of divertor targets shielding during transients in ITER
Energy Technology Data Exchange (ETDEWEB)
Pestchanyi, Sergey, E-mail: serguei.pestchanyi@kit.edu [KIT, Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen (Germany); Pitts, Richard; Lehnen, Michael [ITER Organization,Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France)
2016-11-01
Highlights: • We simulated plasma shielding effect during disruption in ITER using the TOKES code. • It has been found that vaporization is unavoidable under action of ITER transients, but plasma shielding drastically reduces the divertor target damage: the melt pool and the vaporization region widths reduced 10–15 times. • A simplified 1D model describing the melt pool depth and the shielded heat flux to the divertor targets have been developed. • The results of the TOKES simulations have been compared with the analytic model when the model is valid. - Abstract: Direct extrapolation of the disruptive heat flux on ITER conditions predicts severe melting and vaporization of the divertor targets causing their intolerable damage. However, tungsten vaporized from the target at initial stage of the disruption can create plasma shield in front of the target, which effectively protects the target surface from the rest of the heat flux. Estimation of this shielding efficiency has been performed using the TOKES code. The shielding effect under ITER conditions is found to be very strong: the maximal depth of the melt layer reduced 4 times, the melt layer width—more than 10 times and vaporization region shrinks 10–15 times due to shielding for unmitigated disruption of 350 MJ discharge. The simulation results show complex, 2D plasma dynamics of the shield under ITER conditions. However, a simplified analytic model, valid for rough estimation of the maximum value for the shielded flux to the target and for the melt depth at the target surface has been developed.
Conceptual design of CFETR divertor remote handling compatible structure
Energy Technology Data Exchange (ETDEWEB)
Dai, Huaichu, E-mail: yaodm@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); University of Science and Technology of China, Hefei (China); Yao, Damao; Cao, Lei; Zhou, Zibo; Li, Lei [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2016-11-15
Highlights: • Conceptual design for the CFETR divertor have been proposed, especially the divertor remote handling compatible structure. • The degrees of freedom of the divertor are analyzed in order to validate the design the divertor supports structure. • Besides the ITER-like scheme, a new scheme for the divertor remote handling compatible supports is proposed, that is the rack and pinion mechanism. • The installation/removel process is verified through simulation in Delmia in order to check design quality for remote handling requirements. - Abstract: Divertor is one of key components of tokamak fusion reactor. The CFETR is China Fusion Engineering Test Reactor. Its divertor will expose to tritium environment and neutron radiation. Materials of the divertor will be radioactived, and cannot be handled by personnel directly. To develop structure which compatible with robots handle for installation, maintenance and removing is required. This paper introduces a conceptual design of CFETR divertor module which compatible with remote handling end-effectors. The divertor module is confined by inner and outer support. The inner support is only confined divertor module radial, toroidal and vertical moving freedom degrees, but not confined rotating freedom degrees. The outer support is the structure that can confine rotating freedom degrees and should also be compatible with remote handling end-effectors.
Small angle slot divertor concept for long pulse advanced tokamaks
Guo, H. Y.; Sang, C. F.; Stangeby, P. C.; Lao, L. L.; Taylor, T. S.; Thomas, D. M.
2017-04-01
SOLPS-EIRENE edge code analysis shows that a gas-tight slot divertor geometry with a small-angle (glancing-incidence) target, named the small angle slot (SAS) divertor, can achieve cold, dissipative/detached divertor conditions at relatively low values of plasma density at the outside midplane separatrix. SAS exhibits the following key features: (1) strong enhancement of the buildup of neutral density in a localized region near the plasma strike point on the divertor target; (2) spreading of the cooling front across the divertor target with the slot gradually flaring out from the strike point, thus effectively reducing both heat flux and erosion on the entire divertor target surface. Such a divertor may potentially provide a power and particle handling solution for long pulse advanced tokamaks.
Efficient estimation for ergodic diffusions sampled at high frequency
DEFF Research Database (Denmark)
Sørensen, Michael
A general theory of efficient estimation for ergodic diffusions sampled at high fre- quency is presented. High frequency sampling is now possible in many applications, in particular in finance. The theory is formulated in term of approximate martingale estimating functions and covers a large class...
Mean ergodic operators and reflexive Fréchet lattices
Bonet, J.; De Pagter, B.; Ricker, W.J.
2011-01-01
Connections between (positive) mean ergodic operators acting in Banach lattices and properties of the underlying lattice itself are well understood (see the works of Emel'yanov, Wolff and Zaharopol). For Fréchet lattices (or more general locally convex solid Riesz spaces) there is virtually no infor
The quantum unique ergodicity conjecture for thin sets
Young, Matthew P
2013-01-01
We consider some analogs of the quantum unique ergodicity conjecture for geodesics, horocycles, or ``shrinking'' families of sets. In particular, we prove the analog of the QUE conjecture for Eisenstein series restricted to the infinite geodesic connecting 0 and infinity inside the modular surface.
Ergodicity of unipotent flows and geometrically finite Kleinian groups
Mohammadi, Amir
2011-01-01
Let M be a non-elementary convex cocompact hyperbolic 3 manifold and delta the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure if and only if delta>1.
Public Key Cryptography Based on Ergodic Matrices over Finite Field
Institute of Scientific and Technical Information of China (English)
PEI Shihui; ZHAO Hongwei; ZHAO Yongzhe
2006-01-01
A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem: multivariate quadratic equations over finite fields. This problem has been shown to be NP-complete and can' be solved with polynomial time algorithm.
Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
Saeidi Shahram
2010-01-01
Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.
Joshi, Nidhi; Rawat, Kamla; Bohidar, H B
2016-01-20
In order to customize the viscoelastic properties of pectin gels, it is necessary to work on a composite platform. Herein, the gelation kinetics, and viscoelastic characterization of anionic polysaccharide pectin dispersion prepared in presence of nanoclay laponite are reported using dynamic light scattering and rheology measurements. The ratio Rg/Rh (Rg and Rh are radius of gyration and hydrodynamic radius respectively) determined from light scattering data revealed the presence of random coils of pectin chains inside the gel matrix. When nanoclay laponite was added to the pectin chains solution, two-phase separation was noticed instantaneously. Therefore, the surfactant cetyltrimethylammonium bromide [CTAB] was added to exfoliate the clay platelets in the dispersion, and also in its gel phase. The exfoliating agent cetyltrimethylammonium bromide ([CTAB]≈ cmc/10) helped to enhance the homogeneity and stability of the pectin-clay sols and gels. The storage and loss moduli (G' and G") of the composite gel changed significantly as function of nanoclay laponite content for concentration up to 0.03% (w/v) causing the softening of the gels (gel strength reduced by close to 50%) compared to pectin-calcium gel. However, as the concentration of nanoclay laponite was maintained between 0.01% and 0.03% (w/v), the gel rigidity (G') recovered by 30% (35-45 Pa). The transition from ergodic to non-ergodic state occurred during sol-gel transition owing to the presence of the nanoclay laponite. The gelation time was not too different from the ergodicity breaking time. Thus, the presence of nanoclay laponite in such minute concentration is shown to cause considerable change in the thermo-physical property of the composite gels. This material property modulation will facilitate designing of soft gels having storage modulus continuously varying in the wide range of 10-70 Pa while keeping the gelation temperature mostly unaltered.
Upstream Density for Plasma Detachment with Conventional and Lithium Vapor-Box Divertors
Goldston, Rj; Schwartz, Ja
2016-10-01
Fusion power plants are likely to require detachment of the divertor plasma from material targets. The lithium vapor box divertor is designed to achieve this, while limiting the flux of lithium vapor to the main plasma. We develop a simple model of near-detachment to evaluate the required upstream plasma density, for both conventional and lithium vapor-box divertors, based on particle and dynamic pressure balance between up- and down-stream, at near-detachment conditions. A remarkable general result is found, not just for lithium-induced detachment, that the upstream density divided by the Greenwald-limit density scales as (P 5 / 8 /B 3 / 8) Tdet1 / 2 / (ɛcool + γTdet) , with no explicit size scaling. Tdet is the temperature just before strong pressure loss, 1/2 of the ionization potential of the dominant recycling species, ɛcool is the average plasma energy lost per injected hydrogenic and impurity atom, and γ is the sheath heat transmission factor. A recent 1-D calculation agrees well with this scaling. The implication is that the plasma exhaust problem cannot be solved by increasing R. Instead significant innovation, such as the lithium vapor box divertor, will be required. This work supported by DOE Contract No. DE-AC02-09CH11466.
Development of the NSTX-U Advanced Divertor Control
Vail, Patrick; Kolemen, Egemen
2016-10-01
Advanced magnetic divertor configurations such as the snowflake (SF) divertor are being investigated at NSTX-U for reducing the peak heat flux onto plasma-facing components. Initial efforts include development of plasma scenarios incorporating SF configurations using an upgraded set of divertor coils as well as implementation of a feedback control system for real-time detection and manipulation of two closely-spaced magnetic null points. Closed-loop plasma simulations are performed to demonstrate precise control of various SF configurations. The simulations are then used to demonstrate that the controller can be enhanced to regulate additional parameters such as strike point location and divertor flux expansion. The advanced divertor control will be used in the coming years to enable experiments investigating the physics of advanced divertors at NSTX-U. Supported by the US DOE under DE-AC02-09CH11466.
ITER tungsten divertor design development and qualification program
Energy Technology Data Exchange (ETDEWEB)
Hirai, T., E-mail: takeshi.hirai@iter.org [ITER Organization, Route de Vinon sur Verdon, F-13115 Saint Paul lez Durance (France); Escourbiac, F.; Carpentier-Chouchana, S.; Fedosov, A.; Ferrand, L.; Jokinen, T.; Komarov, V.; Kukushkin, A.; Merola, M.; Mitteau, R.; Pitts, R.A.; Shu, W.; Sugihara, M. [ITER Organization, Route de Vinon sur Verdon, F-13115 Saint Paul lez Durance (France); Riccardi, B. [F4E, c/ Josep Pla, n.2, Torres Diagonal Litoral, Edificio B3, E-08019 Barcelona (Spain); Suzuki, S. [JAEA, Fusion Research and Development Directorate JAEA, 801-1 Mukouyama, Naka, Ibaragi 311-0193 (Japan); Villari, R. [Associazione EURATOM-ENEA sulla Fusione, Via Enrico Fermi 45, I-00044 Frascati, Rome (Italy)
2013-10-15
Highlights: • Detailed design development plan for the ITER tungsten divertor. • Latest status of the ITER tungsten divertor design. • Brief overview of qualification program for the ITER tungsten divertor and status of R and D activity. -- Abstract: In November 2011, the ITER Council has endorsed the recommendation that a period of up to 2 years be set to develop a full-tungsten divertor design and accelerate technology qualification in view of a possible decision to start operation with a divertor having a full-tungsten plasma-facing surface. To ensure a solid foundation for such a decision, a full tungsten divertor design, together with a demonstration of the necessary high performance tungsten monoblock technology should be completed within the required timescale. The status of both the design and technology R and D activity is summarized in this paper.
Examining Innovative Divertor and Main Chamber Options for a National Divertor Test Tokamak
Labombard, B.; Umansky, M.; Brunner, D.; Kuang, A. Q.; Marmar, E.; Wallace, G.; Whyte, D.; Wukitch, S.
2016-10-01
The US fusion community has identified a compelling need for a National Divertor Test Tokamak. The 2015 Community Planning Workshop on PMI called for a national working group to develop options. Important elements of a NDTT, adopted from the ADX concept, include the ability to explore long-leg divertor `solutions for power exhaust and particle control' (Priority Research Direction B) and to employ inside-launch RF actuators combined with double-null topologies as `plasma solution for main chamber wall components, including tools for controllable sustained operation' (PRD-C). Here we examine new information on these ideas. The projected performance of super-X and X-point target long-leg divertors is looking very promising; a stable fully-detached divertor condition handling an order-of-magnitude increase in power handling over conventional divertors may be possible. New experiments on Alcator C-Mod are addressing issues of high-field side versus low-field side heat flux sharing in double-null topologies and the screening of impurities that might originate from RF actuators placed in the high-field side - both with favorable results. Supported by USDoE Awards DE-FC02-99ER54512 and DE-AC52-07NA27344.
Neutral recirculation—the key to control of divertor operation
Kukushkin, A. S.; Pacher, H. D.
2016-12-01
Interaction of the plasma with neutral gas in the divertor affects virtually all aspects of divertor functionality (power loading of the targets, pumping and fuelling, sustaining the operational conditions of the core plasma). In the course of ITER design development, this interaction has been the subject of intense modelling analysis, supported by experiments on various tokamaks. Neutral gas puffing is found to be the most effective means of divertor control. The results of those studies are summarized and assessed in the paper.
NSTX Plasma Response to Lithium Coated Divertor
Energy Technology Data Exchange (ETDEWEB)
H.W. Kugel, M.G. Bell, J.P. Allain, R.E. Bell, S. Ding, S.P. Gerhardt, M.A. Jaworski, R. Kaita, J. Kallman, S.M. Kaye, B.P. LeBlanc, R. Maingi, R. Majeski, R. Maqueda, D.K. Mansfield, D. Mueller, R. Nygren, S.F. Paul, R. Raman, A.L. Roquemore, S.A. Sabbagh, H. Schneider, C.H. Skinner, V.A. Soukhanovskii, C.N. Taylor, J.R. Timberlak, W.R. Wampler, L.E. Zakharov, S.J. Zweben, and the NSTX Research Team
2011-01-21
NSTX experiments have explored lithium evaporated on a graphite divertor and other plasma facing components in both L- and H- mode confinement regimes heated by high-power neutral beams. Improvements in plasma performance have followed these lithium depositions, including a reduction and eventual elimination of the HeGDC time between discharges, reduced edge neutral density, reduced plasma density, particularly in the edge and the SOL, increased pedestal electron and ion temperature, improved energy confinement and the suppression of ELMs in the H-mode. However, with improvements in confinement and suppression of ELMs, there was a significant secular increase in the effective ion charge Zeff and the radiated power in H-mode plasmas as a result of increases in the carbon and medium-Z metallic impurities. Lithium itself remained at a very low level in the plasma core, <0.1%. Initial results are reported from operation with a Liquid Lithium Divertor (LLD) recently installed.
Module of lithium divertor for KTM tokamak
Energy Technology Data Exchange (ETDEWEB)
Lyublinski, I., E-mail: yublinski@yandex.ru [FSUE ' Red Star' , Moscow (Russian Federation); Vertkov, A.; Evtikhin, V.; Balakirev, V.; Ionov, D.; Zharkov, M. [FSUE ' Red Star' , Moscow (Russian Federation); Tazhibayeva, I. [IAE NNC RK, Kurchatov (Kazakhstan); Mirnov, S. [TRINITI, Troitsk, Moscow Region (Russian Federation); Khomiakov, S.; Mitin, D. [OJSC Dollezhal Institute, Moscow (Russian Federation); Mazzitelli, G. [ENEA RC Frascati (Italy); Agostini, P. [ENEA RC Brasimone (Italy)
2012-10-15
Highlights: Black-Right-Pointing-Pointer Problems of PFE degradation, tritium accumulation and plasma pollution can be overcome by the use of liquid lithium-metal with low Z. Black-Right-Pointing-Pointer Capillary-porous system (CPS) - new material in which liquid lithium fill a solid matrix from porous material. Black-Right-Pointing-Pointer Lithium divertor module for KTM tokamak is under development. Black-Right-Pointing-Pointer Lithium filled tungsten felt is offered as the base plasma facing material of divertor. Black-Right-Pointing-Pointer Results of this project addresses to the progress in the field of fusion neutrons source and fusion energy source creation. - Abstract: Activity on projects of ITER and DEMO reactors has shown that solution of problems of divertor target plates and other plasma facing elements (PFEs) based on the solid plasma facing materials cause serious difficulties. Problems of PFE degradation, tritium accumulation and plasma pollution can be overcome by the use of liquid lithium-metal with low Z. Application of lithium will allow to create a self-renewal and MHD stable liquid metal surface of the in-vessel devices possessing practically unlimited service life; to reduce power flux due to intensive re-irradiation on lithium atoms in plasma periphery that will essentially facilitate a problem of heat removal from PFE; to reduce Z{sub eff} of plasma to minimally possible level close to 1; to exclude tritium accumulation, that is provided with absence of dust products and an opportunity of the active control of the tritium contents in liquid lithium. Realization of these advantages is based on use of so-called lithium capillary-porous system (CPS) - new material in which liquid lithium fill a solid matrix from porous material. The progress in development of lithium technology and also activity in lithium experiments in the tokamaks TFTR, T-11M, T-10, FTU, NSTX, HT-7 and stellarator TJ II permits of solving the problems in development of
Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.
Levnajić, Zoran; Mezić, Igor
2015-05-01
We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.
Ergodic Capacity of Cognitive Radio under Imperfect Channel State Information
Rezk, Zouheir
2012-01-01
A spectrum-sharing communication system where the secondary user is aware of the instantaneous channel state information (CSI) of the secondary link, but knows only the statistics and an estimated version of the secondary transmitter-primary receiver (ST-PR) link, is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels (with continuous probability density function) under average and peak transmit-power constraints and with respect to two different interference constraints: an interference outage constraint and a signal-to-interference outage constraint. When applied to Rayleigh fading channels, our results show, for instance, that the interference constraint is harmful at high-power regime in the sense that the capacity does not increase with the power, whereas at low-power regime, it has a marginal impact and no-interference performance corresponding to the ergodic capacity under average or peak transmit power constraint in absence of ...
Ergodic Capacity for the SIMO Nakagami-m Channel
Directory of Open Access Journals (Sweden)
Efstathios D. Vagenas
2009-01-01
Full Text Available This paper presents closed-form expressions for the ergodic channel capacity of SIMO (single-input and multiple output wireless systems operating in a Nakagami-m fading channel. As the performance of SIMO channel is closely related to the diversity combining techniques, we present closed-form expressions for the capacity of maximal ratio combining (MRC, equal gain combining (EGC, selection combining (SC, and switch and stay (SSC diversity systems operating in Nakagami-m fading channels. Also, the ergodic capacity of a SIMO system in a Nakagami-m fading channel without any diversity technique is derived. The latter scenario is further investigated for a large amount of receive antennas. Finally, numerical results are presented for illustration.
On the ergodicity of perpendicular cosmic ray transport
Tautz, R C
2016-01-01
Aims. The random walk of energetic charged particles in turbulent magnetic fields is investigated. Special focus is placed on transport across the mean magnetic field, which had been found to be subdiffusive on many occasions. Therefore, a characterization using the concept of ergodicity is attempted by noting the connection to the time evolution of the mean-square displacement. Methods. Based on the test-particle approach, a numerical Monte-Carlo simulation code is used to integrate the equation of motion for particles that are scattered by magnetic turbulence. The turbulent fields are generated by superposing plane waves with a Kolmogorov-type power spectrum. The individual particle trajectories are then used to calculate a variety of statistical quantities. Results. The simulation results clearly demonstrate how the heterogeneity of the particle ensemble causes the system to be weakly non-ergodic. In addition, it is shown how the step length distribution varies with the particle energy. In conclusion, cros...
Energy Technology Data Exchange (ETDEWEB)
Sastry, M D [Department of Physics and Measurement Technology, Linkoeping University, S-581 83 Linkoeping (Sweden); Gustafsson, H [Department of Medicine and Care, Radiation Physics, Faculty of Health Sciences, Linkoeping University, S-581 85 Linkoeping (Sweden); Danilczuk, M [Department of Physics and Measurement Technology, Linkoeping University, S-581 83 Linkoeping (Sweden); Institute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw (Poland); Lund, A [Department of Physics and Measurement Technology, Linkoeping University, S-581 83 Linkoeping (Sweden)
2006-05-03
Three-pulse electron spin echo envelope modulation (ESEEM), hyperfine sublevel correlation spectroscopy (HYSCORE) investigations and two-pulse electron spin echo (ESE) measurements of phase memory time T{sub M}, were carried out, in the 20-200 K temperature range, on an AsO{sub 4}{sup 4-} paramagnetic probe stabilized in RbH{sub 2}PO{sub 4} (RDP), NH{sub 4}H{sub 2}PO{sub 4} (ADP), and dipolar glass Rb{sub 0.5}(NH{sub 4}){sub 0.5}H{sub 2}PO{sub 4} (RADP). The results obtained on ADP revealed hyperfine interaction of the probe ion with the {sup 14}N of the ammonium ion, the coupling constant satisfying the condition of 'cancellation' at a field of 480 mT. The ammonium ion was found to be in two different sites in ADP, which became indistinguishable on the formation of dipolar glass RADP. These results were confirmed by HYSCORE spectral measurements. The fast Fourier transform (FFT) spectra of three-pulse ESEEM decays have clearly revealed the interaction with protons in the O-H----O bond both in ADP and RDP; and in RADP with an averaged coupling constant. The phase memory times in RADP exhibited strong temperature dependence and were found to be dependent on the nuclear spin quantum number m{sub I} of {sup 75}As. The temperature dependence of T{sub M} exhibited a well-defined maximum around 90 K, coinciding with the temperature of onset of 'freezing' in Rb{sub 0.5}(NH{sub 4}){sub 0.5}H{sub 2}PO{sub 4}. This is symptomatic of dynamic fluctuations in the dipolar glass phase, with onset around 150 K, going through a maximum around 90 K and slowing down on further cooling. These results suggest that in RADP, a dynamical mechanism with progressive slowing down below 90 K is operative in the glass formation. This implies that the RADP system, with x = 0.5, exists in an ergodic relaxor (R)-state in the 20-200 K temperature range wherein every fluctuating monodomain can be viewed as statistically representative of the whole sample.
Divertor Heat Flux Mitigation in the National Spherical Torus Experiment
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V A; Maingi, R; Gates, D A; Menard, J E; Paul, S F; Raman, R; Roquemore, A L; Bell, M G; Bell, R E; Boedo, J A; Bush, C E; Kaita, R; Kugel, H W; LeBlanc, B P; Mueller, D
2008-08-04
Steady-state handling of divertor heat flux is a critical issue for both ITER and spherical torus-based devices with compact high power density divertors. Significant reduction of heat flux to the divertor plate has been achieved simultaneously with favorable core and pedestal confinement and stability properties in a highly-shaped lower single null configuration in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 2000] using high magnetic flux expansion at the divertor strike point and the radiative divertor technique. A partial detachment of the outer strike point was achieved with divertor deuterium injection leading to peak flux reduction from 4-6 MW m{sup -2} to 0.5-2 MW m{sup -2} in small-ELM 0.8-1.0 MA, 4-6 MW neutral beam injection-heated H-mode discharges. A self-consistent picture of outer strike point partial detachment was evident from divertor heat flux profiles and recombination, particle flux and neutral pressure measurements. Analytic scrape-off layer parallel transport models were used for interpretation of NSTX detachment experiments. The modeling showed that the observed peak heat flux reduction and detachment are possible with high radiated power and momentum loss fractions, achievable with divertor gas injection, and nearly impossible to achieve with main electron density, divertor neutral density or recombination increases alone.
Divertor E X B Plasma Convection in DIII-D
Energy Technology Data Exchange (ETDEWEB)
Boedo, J.A.; Schaffer, M.J.; Maingi, M.; Lasnier, C.J.; Watkins, J.G.
1999-07-01
Extensive two-dimensional measurements of plasma potential in the DIII-D tokamak divertor region are reported for standard (ion VB{sub T} drift toward divertor X-point) and reversed B{sub T} directions; for low (L) and high (H) confinement modes; and for partially detached divertor mode. The data are consistent with recent computational modeling identifying E x B{sub T} circulation, due to potentials sustained by plasma gradients, as the main cause of divertor plasma sensitivity to B{sub T} direction.
Magnetic geometry and particle source drive of supersonic divertor regimes
Bufferand, H.; Ciraolo, G.; Dif-Pradalier, G.; Ghendrih, P.; Tamain, Ph; Marandet, Y.; Serre, E.
2014-12-01
We present a comprehensive picture of the mechanisms driving the transition from subsonic to supersonic flows in tokamak plasmas. We demonstrate that supersonic parallel flows into the divertor volume are ubiquitous at low density and governed by the divertor magnetic geometry. As the density is increased, subsonic divertor plasmas are recovered. On detachment, we show the change in particle source can also drive the transition to a supersonic regime. The comprehensive theoretical analysis is completed by simulations in ITER geometry. Such results are essential in assessing the divertor performance and when interpreting measurements and experimental evidence.
ADX - Advanced Divertor and RF Tokamak Experiment
Greenwald, Martin; Labombard, Brian; Bonoli, Paul; Irby, Jim; Terry, Jim; Wallace, Greg; Vieira, Rui; Whyte, Dennis; Wolfe, Steve; Wukitch, Steve; Marmar, Earl
2015-11-01
The Advanced Divertor and RF Tokamak Experiment (ADX) is a design concept for a compact high-field tokamak that would address boundary plasma and plasma-material interaction physics challenges whose solution is critical for the viability of magnetic fusion energy. This device would have two crucial missions. First, it would serve as a Divertor Test Tokamak, developing divertor geometries, materials and operational scenarios that could meet the stringent requirements imposed in a fusion power plant. By operating at high field, ADX would address this problem at a level of power loading and other plasma conditions that are essentially identical to those expected in a future reactor. Secondly, ADX would investigate the physics and engineering of high-field-side launch of RF waves for current drive and heating. Efficient current drive is an essential element for achieving steady-state in a practical, power producing fusion device and high-field launch offers the prospect of higher efficiency, better control of the current profile and survivability of the launching structures. ADX would carry out this research in integrated scenarios that simultaneously demonstrate the required boundary regimes consistent with efficient current drive and core performance.
Resilient non-resonant divertors for stellarators
Bader, A.; Boozer, A. H.; Hegna, C. C.; Lazerson, S. A.
2016-10-01
In this work, we investigate whether resilient non-resonant divertor solutions exist for optimized stellarators. Resiliency is measured by the consistency of performance over a broad range of operational states, such as through bootstrap current and modified plasma pressures. A non-resonant configuration is one where the crucial topological feature is the existence and sharpness of ridges along the last closed flux surface. We develop a modified field-line following method for testing the resiliency of stellarator divertors and apply it to altered HSX configurations generated by varying external coil currents, wall positioning, and internal plasma currents. We compare a magnetic diffusion calculation with a ``zero-diffusion'' calculation that endeavors to measure the first escaping flux tubes. The results from these calculations are corroborated with a more complete edge simulation with EMC3-EIRENE. The EMC3-EIRENE simulations show resilient helical stripes that are consistent with the simpler field line following methods. The goal of the study is to find a metric for edge/divertor optimization of stellarators, a crucial piece that is missing from current optimization schemes. Work supported by DE-SC0006103 and DE-FG02-93ER54222,.
Analysis of the Emergent Properties: Stationarity and Ergodicity
Jakob Grazzini
2012-01-01
This paper illustrates the use of the nonparametric Wald-Wolfowitz test to detect stationarity and ergodicity in agent-based models. A nonparametric test is needed due to the practical impossibility to understand how the random component influences the emergent properties of the model in many agent-based models. Nonparametric tests on real data often lack power and this problem is addressed by applying the Wald-Wolfowitz test to the simulated data. The performance of the tests is evaluated us...
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Logical entropy of quantum dynamical systems
Directory of Open Access Journals (Sweden)
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
Ergodic time-reversible chaos for Gibbs' canonical oscillator
Energy Technology Data Exchange (ETDEWEB)
Hoover, William Graham, E-mail: hooverwilliam@yahoo.com [Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, NV 89833 (United States); Sprott, Julien Clinton [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Patra, Puneet Kumar [Advanced Technology Development Center, Department of Civil Engineering, Indian Institute of Technology, Kharagpur, West Bengal, 721302 (India)
2015-12-04
Nosé's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical distribution for the one-dimensional harmonic oscillator. A 2001 doubly-thermostated model, claimed to be ergodic, has a singly-thermostated version. Though neither of these models is ergodic this work has suggested a successful route toward singly-thermostated ergodicity. We illustrate both ergodicity and its lack for these models using phase-space cross sections and Lyapunov instability as diagnostic tools. - Highlights: • We develop cross-section and Lyapunov methods for diagnosing ergodicity. • We apply these methods to several thermostatted-oscillator problems. • We demonstrate the nonergodicity of previous work. • We find a novel family of ergodic thermostatted-oscillator problems.
Ergodic capacity of switch-and-examine combining under flat Rayleigh fading channels
Institute of Scientific and Technical Information of China (English)
ZHAO Shuang; YAO Wen-bin; YANG Hong-wen; WANG Ya-feng
2009-01-01
Switch-and-examine combining (SEC) is an interesting diversity technique that is simpler than selection combining (SC), whereas its performances is similar in terms of bit error rate (BER) and diversity order. As ergodic capacity is also a key performance index in modern wireless systems, this article analyzes the ergodic capacity of the SEC system. The numerical results show that the ergodic capacity of SEC with optimal threshold is similar to that of SC for arbitrary number of diversity branches.
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
Directory of Open Access Journals (Sweden)
Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
Power distribution in the snowflake divertor in TCV
Reimerdes, H.; G.P. Canal,; Duval, B. P.; Labit, B.; Lunt, T.; Vijvers, W. A. J.; Coda, S.; De Temmerman, G.; Morgan, T. W.; Nespoli, F.; Tal, B.; the TCV Team,
2013-01-01
TCV experiments demonstrate the basic power exhaust properties of the snowflake (SF) plus and SF minus divertor configurations by measuring the heat fluxes at each of their four divertor legs. The measurements indicate an enhanced transport into the private flux region and a reduction of peak heat f
Divertor plasma physics experiments on the DIII-D tokamak
Energy Technology Data Exchange (ETDEWEB)
Mahdavi, M.A.; Allen, S.L.; Evans, T.E. [and others
1996-10-01
In this paper we present an overview of the results and conclusions of our most recent divertor physics and development work. Using an array of new divertor diagnostics we have measured the plasma parameters over the entire divertor volume and gained new insights into several divertor physics issues. We present direct experimental evidence for momentum loss along the field lines, large heat convection, and copious volume recombination during detachment. These observations are supported by improved UEDGE modeling incorporating impurity radiation. We have demonstrated divertor exhaust enrichment of neon and argon by action of a forced scrape off layer (SOL) flow and demonstrated divertor pumping as a substitute for conventional wall conditioning. We have observed a divertor radiation zone with a parallel extent that is an order of magnitude larger than that estimated from a 1-D conduction limited model of plasma at coronal equilibrium. Using density profile control by divertor pumping and pellet injection we have attained H-mode confinement at densities above the Greenwald limit. Erosion rates of several candidate ITER plasma facing materials are measured and compared with predictions of a numerical model.
Comparison of ELM heat loads in snowflake and standard divertors
Energy Technology Data Exchange (ETDEWEB)
Rognlien, T D; Cohen, R H; Ryutov, D D; Umansky, M V
2012-05-08
An analysis is given of the impact of the tokamak divertor magnetic structure on the temporal and spatial divertor heat flux from edge localized modes (ELMs). Two configurations are studied: the standard divertor where the poloidal magnetic field (B{sub p}) varies linearly with distance (r) from the magnetic null and the snowflake where B{sub p} varies quadratrically with r. Both one and two-dimensional models are used to analyze the effect of the longer magnetic field length between the midplane and the divertor plate for the snowflake that causes a temporal dilation of the ELM divertor heat flux. A second effect discussed is the appearance of a broad region near the null point where the poloidal plasma beta can substantially exceed unity, especially for the snowflake configuration during the ELM; such a condition is likely to drive additional radial ELM transport.
RELAP5 MODEL OF THE DIVERTOR PRIMARY HEAT TRANSFER SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Popov, Emilian L [ORNL; Yoder Jr, Graydon L [ORNL; Kim, Seokho H [ORNL
2010-08-01
This report describes the RELAP5 model that has been developed for the divertor primary heat transfer system (PHTS). The model is intended to be used to examine the transient performance of the divertor PHTS and evaluate control schemes necessary to maintain parameters within acceptable limits during transients. Some preliminary results are presented to show the maturity of the model and examine general divertor PHTS transient behavior. The model can be used as a starting point for developing transient modeling capability, including control system modeling, safety evaluations, etc., and is not intended to represent the final divertor PHTS design. Preliminary calculations using the models indicate that during normal pulsed operation, present pressurizer controls may not be sufficient to keep system pressures within their desired range. Additional divertor PHTS and control system design efforts may be required to ensure system pressure fluctuation during normal operation remains within specified limits.
Nonlinear Dynamics and Ergodic Theory Methods in Control
2005-12-31
area preserving maps of R2 to itself. We focused on the standard map and a discrete Duffing oscillator as specific examples. We related the level 9 Wk...mixing. We have pursued an investigation of a system of coupled oscillators that exhibits conformational transitions upon targeted, small external...and numerical studies of mixing in a laminar, weakly 3D, weakly time-periodic vortex flow. An oscillating horizontal vortex chain is generated
Ergodic properties of diffusion-type quantum dynamical semigroups
Energy Technology Data Exchange (ETDEWEB)
Lugiewicz, P; Olkiewicz, R [Institute of Theoretical Physics, University of Wroclaw, Wroclaw (Poland); Zegarlinski, B, E-mail: piol@ift.uni.wroc.p, E-mail: rolek@ift.uni.wroc.p, E-mail: b.zegarlinski@imperial.ac.u [CNRS Toulouse and Department of Mathematics, Imperial College, London (United Kingdom)
2010-10-22
We develop a framework for investigation of asymptotic behavior of quantum Markov semigroups on C*-algebras associated with noncommutative elliptic generators. An exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and, in a particular case of the semigroup selecting rotationally invariant states of a three-dimensional quantum system, the time factor of such a convergence has been estimated.
Researches on the Neutral Gas Pressure in the Divertor Chamber of the HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
WANGMingxu; LIBo; YANGZhigang; YANLongwen; HONGWenyu; YUANBaoshan; LIULi; CAOZeng; CUIChenghe; LIUYong; WANGEnyao; ZHANGNianman
2003-01-01
The neutral gas pressure in divertor chamber is a very basic and important physics parameter because it determines the temperature of charged particles, the thermal flux density onto divertor plates, the erosion of divertor plates, impurity retaining and exhausting, particle transportation and confinement performance of plasma in tokamaks. Therefore, the pressure measurement in divertor chamber is taken into account in many large tokamaks.
Absolute regularity and ergodicity of Poisson count processes
Neumann, Michael H
2012-01-01
We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that a stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables, we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.
Ergodic channel capacity of the spatial correlated rayleigh MIMO channel
Institute of Scientific and Technical Information of China (English)
ZHANG Hui-ping; WU Ping; LIU Ai-jun
2007-01-01
The theoretical capacity of the spatial correlated Rayleigh multiple input multiple output (MIMO) channel is an important issue in MIMO technology. In this article, an ergodic channel capacity formula of the spatial correlated rayleigh MIMO channel is provided, which is deduced when two antennas exist at either the transmitter or the receiver. The multi-dimensional least-squares fit algorithm is employed to narrow the difference between the theoretical formula capacity and the practical capacity. Simulation results show that the theoretical capacity approaches the practical one closely.
Asymptotic Ergodic Capacity Analysis of Composite Lognormal Shadowed Channels
Ansari, Imran Shafique
2015-05-01
Capacity analysis of composite lognormal (LN) shadowed links, such as Rician-LN, Gamma-LN, and Weibull-LN, is addressed in this work. More specifically, an exact closed-form expression for the moments of the end-to-end signal-to-noise ratio (SNR) of a single composite link transmission system is presented in terms of well- known elementary functions. Capitalizing on these new moments expressions, we present asymptotically tight lower bounds for the ergodic capacity at high SNR. All the presented results are verified via computer-based Monte-Carlo simulations. © 2015 IEEE.
On the Ergodic Secrecy Capacity with Full Duplex Communication
DEFF Research Database (Denmark)
Mahmood, Nurul Huda; Shafique Ansari, Imran; Mogensen, Preben Elgaard
2017-01-01
Full duplex communication promises performance gains in terms of the throughput and the delay. Generally, it has been shown that the throughput and delay gains of full duplex communication are somewhat limited in realistic network settings, leading researchers to study other possible applications...... capacity for a pair of nodes with full duplex communication. The ergodic secrecy rate with full duplex communication is found to grow linearly with the log of the direct channel SNR as opposed to the flattened out secrecy rate with conventional half duplex communication, irrespective of the eavesdropper...
Energy Technology Data Exchange (ETDEWEB)
Rimza, Sandeep, E-mail: sandeepr@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Satpathy, Kamalakanta, E-mail: satpathy@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Khirwadkar, Samir, E-mail: sameer@ipr.res.in [Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat (India); Velusamy, Karupanna, E-mail: kvelu@igcar.gov.in [Mechanics and Hydraulics Division, Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102 (India)
2015-11-15
Highlights: • Effect of design variables in enhancing heat removal potential with pumping power assessed. • The optimization objective is to minimize the thimble temperature. • Investigation of optimum design parameters for various Reynolds number. • Practicability of the optimum designs is verified through structural analysis. • Benchmark validation of divertor finger mock-up against in-house experiment and good agreement is achieved. - Abstract: Cooling of fusion reactor divertor by helium is widely accepted due to its chemical and neutronic inertness and superior safety aspect. However, its poor thermo physical characteristics need high pressure to remove large heat flux encountered in fusion power plant (DEMO). In the perspective of DEMO, it is desirable to explore efficient cooling technology for divertor that can handle high heat flux. Toward this, a novel sectorial extended surface (SES) was proposed by the authors Rimza et al. (2014) [2]. The present work focuses on design optimization of divertor finger mock-up with SES to enhance the thermal hydraulic performance. The maximum thimble temperature is considered as the vital design constraint. Various non-dimensional design variables, viz., relative pitch, thickness, jet diameter, the ratio of height of SES to jet diameter and circumferential position of the SES are considered for the present optimization study. The effects of design variables on thermal performance of the divertor are evaluated in the Reynolds number (Re) range of 7.5 × 10{sup 4}–1.2 × 10{sup 5}. The analysis reveals that, the heat transfer performance of divertor finger mock-up with SES is improved for two optimum designs having relative pitch and thickness of 0.30 and 0.56, respectively. Also, it is observed that finger mock-up heat sink with SES performs better, when the ratio of SES height to jet diameter, reduces to 0.75 at the cost of marginally higher pumping power. The effects of jet diameter and circumferential
Feller property and exponential ergodicity of diffusion processes with state-dependent switching
Institute of Scientific and Technical Information of China (English)
XI FuBao
2008-01-01
In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with State-dependent switching. We prove their Feller continuity by means of intro-ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.
Feller property and exponential ergodicity of diffusion processes with state-dependent switching
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.
Ergodicity of the IPP +M=M=c Queue%IPP+M/M/C排队的遍历性
Institute of Scientific and Technical Information of China (English)
李晓花; 侯振挺
2011-01-01
The IPP + M/M/c queueing system has been extensively used in the modern communication system. The existence and uniqueness of stationary distribution of the queue length L(t) for IPP + M/M/1 queue has been proved in [10]. In this paper, we shall give the su±cient and necessary conditions of l-ergodicity, geometric ergodicity, and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.
Photon trapping effects in DEMO divertor plasma
Energy Technology Data Exchange (ETDEWEB)
Hoshino, K.; Tokunaga, S.; Asakura, N. [Japan Atomic Energy Agency, Rokkasho, Aomori (Japan); Sawada, K.; Idei, R. [Faculty of Engineering, Shinshu Univ., Nagano (Japan); Shimizu, K. [Japan Atomic Energy Agency, Naka, Ibaraki (Japan); Ohno, N. [Graduate School of Engineering, Nagoya Univ, Aichi (Japan)
2016-08-15
In the DEMO divertor, the neutral density becomes high to produce the full detachment and therefore the photon trapping can become important. In this paper, effects of the photon trapping on the DEMO divertor plasma has been studied. The pre-evaluation of the photon trapping effects on the fixed background plasma profile was carried out by using an iterative self-consistent collisional radiative model. The recombining plasma near the inner target and the private region changed to the ionizing plasma by the photon-excitation. Based on the preevaluation result, the database of the effective ionization rate coefficient including the photon transport inside a 2 mm sphere. Advantage of the 2 mm sphere approximation is that the extra calculation cost is not necessary. Iterative calculation of the SONIC including the photon trapping effects was carried out. While the electron density increased and the neutral density decreased in the wide region, the electron density decreases close to the inner strike point. This may be due to decrease in the ionization rate by decrease in the neutral density. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Extinguishing ELMs in detached radiative divertor plasmas
Pigarov, Alexander; Krasheninnikov, Sergei; Rognlien, Thomas
2016-10-01
In order to avoid deleterious effects of ELMs on PFCs in next-step fusion devices it has been suggested to operate with small-sized ELMs naturally extinguishing in the divertor. Our modeling effort is focusing at extinguishing type-I ELMs: conditions for expelled plasma dissipation; efficiency of ELM power handling by detached radiative divertors; and the ELM impact on detachment state. Here time-dependent modeling of a sequence of many ELMs was performed with 2-D edge plasma transport code UEDGE-MB-W which incorporates the Macro-Blob (MB) approach to simulate non-diffusive filamentary transport and various ``Wall'' (W) models for time-dependent hydrogen wall inventory and recycling. Three cases were modeled, in which extinguishing ELMs are achieved due to: (i) intrinsic impurities via graphite sputtering, (ii) extrinsic impurity gas puff (Ne), and (iii) =(i) +(ii). For each case, we performed a series of UEDGE-MB-W runs scanning the deuterium and impurity inventories, pedestal losses and ELM frequency. Temporal variations of the degree of detachment, ionization front shape, recombination sink strength, radiated fraction, peak power loads, OSP, impurity charge states, and in/out asymmetries were analyzed. We discuss the onset of extinguishing ELMs, conditions for not burning through and enhanced plasma recombination as functions of scanned parameters. Efficiencies of intrinsic and extrinsic impurities in ELM extinguishing are compared.
Norm convergence of continuous-time polynomial multiple ergodic averages
Austin, Tim
2011-01-01
For a jointly measurable probability-preserving action \\tau:\\bbR^D\\curvearrowright (X,\\mu) and a tuple of polynomial maps p_i:\\bbR\\to \\bbR^D, i=1,2,...,k, the multiple ergodic averages \\frac{1}{T}\\int_0^T (f_1\\circ \\tau^{p_1(t)})(f_2\\circ\\tau^{p_2(t)})... (f_k\\circ\\tau^{p_k(t)})\\,\\d t converge in L^2(\\mu) as T \\to \\infty for any f_1,f_2,...,f_k \\in L^\\infty(\\mu). This confirms the continuous-time analog of the conjectured norm convergence of discrete polynomial multiple ergodic averages, which in is its original formulation remains open in most cases. A proof of convergence can be given based on the idea of passing up to a sated extension of (X,\\mu,\\tau) in order to find simple characteristic factors, similarly to the recent development of this idea for the study of related discrete-time averages, together with a new inductive scheme on tuples of polynomials. The new induction scheme becomes available upon changing the time variable in the above integral by some fractional power, and provides an alternative t...
Numerical studies on divertor plasmas in helical systems
Energy Technology Data Exchange (ETDEWEB)
Ueda, Noriaki (Mitsubishi Atomic Power Industries, Inc., Tokyo (Japan)); Itoh, Kimitaka; Itoh, Sanae
1989-12-01
Scrape-off layer and divertor plasmas in helical systems are studied by using the two-dimensional (2D) numerical simulation code. Unified edge divertor analysis code (UEDA code) is applied to the straight helical model of torsatron/helical heliotron configurations. 2D profiles of plasma parameter, neutrals and impurities are obtained. Erosion rate and neutral back flow rate to the core plasma are also evaluated. Various shapes of the buffle plate are examined from the view point of the establishment of 'dense-cold divertor plasma' by which we can avoid the damage of the target plate. (author).
Coupled Kinetic-MHD Simulations of Divertor Heat Load with ELM Perturbations
Cummings, Julian; Chang, C. S.; Park, Gunyoung; Sugiyama, Linda; Pankin, Alexei; Klasky, Scott; Podhorszki, Norbert; Docan, Ciprian; Parashar, Manish
2010-11-01
The effect of Type-I ELM activity on divertor plate heat load is a key component of the DOE OFES Joint Research Target milestones for this year. In this talk, we present simulations of kinetic edge physics, ELM activity, and the associated divertor heat loads in which we couple the discrete guiding-center neoclassical transport code XGC0 with the nonlinear extended MHD code M3D using the End-to-end Framework for Fusion Integrated Simulations, or EFFIS. In these coupled simulations, the kinetic code and the MHD code run concurrently on the same massively parallel platform and periodic data exchanges are performed using a memory-to-memory coupling technology provided by EFFIS. The M3D code models the fast ELM event and sends frequent updates of the magnetic field perturbations and electrostatic potential to XGC0, which in turn tracks particle dynamics under the influence of these perturbations and collects divertor particle and energy flux statistics. We describe here how EFFIS technologies facilitate these coupled simulations and discuss results for DIII-D, NSTX and Alcator C-Mod tokamak discharges.
A review of ELMs in divertor tokamaks
Energy Technology Data Exchange (ETDEWEB)
Hill, D.N.
1996-05-23
This paper reviews what is known about edge localized modes (ELMs), with an emphasis on their effect on the scrape-off layer and divertor plasmas. ELM effects have been measured in the ASDEX-U, C-Mod, COMPASS-D, DIII-D, JET, JFT-2M,JT-60U, and TCV tokamaks and are reported here. At least three types of ELMs have been identified and their salient features determined. Type-1 giant ELMs can cause the sudden loss of up to 10-15% of the plasma stored energy but their amplitude ({Delta}W/W) does not increase with increasing power. Type- 3 ELMs are observed near the H-mode power threshold and produce small energy dumps (1-3% of the stored energy). All ELMs increase the scrape- off layer plasma and produce particle fluxes on the divertor targets which are as much as ten times larger that the quiescent phase between ELMs. The divertor heat pulse is largest on the inner target, unlike that of L-Mode or quiescent H-mode; some tokamaks report radial structure in the heat flux profile which is suggestive of islands or helical structures. The power scaling of Type-1 ELM amplitude and frequency have been measured in several tokamaks and has recently been applied to predictions of the ELM Size in ITER. Concern over the expected ELM amplitude has led to a number of experiments aimed at demonstrating active control of ELMs. Impurity gas injection with feedback control on the radiation loss in ASDEX-U suggests that a promising mode of operation (the CDH-mode) with a very small type-3 ELMs can be maintained with heating power sell above the H-mode threshold, where giant type-1 ELMs can be maintained with heating power well above the H-mode threshold, where Giant type-1 ELMs are normally observed. While ELMs have many potential negative effects, the beneficial effect of ELMs in providing density control and limiting the core plasma impurity content in high confinement H- mode discharges should not be overlooked.
Neutral particle dynamics in the Alcator C-Mod tokamak
Energy Technology Data Exchange (ETDEWEB)
Niemczewski, A.P.
1995-08-01
This thesis presents an experimental study of neutral particle dynamics in the Alcator C-Mod tokamak. The primary diagnostic used is a set of six neutral pressure gauges, including special-purpose gauges built for in situ tokamak operation. While a low main chamber neutral pressure coincides with high plasma confinement regimes, high divertor pressure is required for heat and particle flux dispersion in future devices such as ITER. Thus we examine conditions that optimize divertor compression, defined here as a divertor-to-midplane pressure ratio. We find both pressures depend primarily on the edge plasma regimes defined by the scrape-off-layer heat transport. While the maximum divertor pressure is achieved at high core plasma densities corresponding to the detached divertor state, the maximum compression is achieved in the high-recycling regime. Variations in the divertor geometry have a weaker effect on the neutral pressures. For otherwise similar plasmas the divertor pressure and compression are maximum when the strike point is at the bottom of the vertical target plate. We introduce a simple flux balance model, which allows us to explain the divertor neutral pressure across a wide range of plasma densities. In particular, high pressure sustained in the detached divertor (despite a considerable drop in the recycling source) can be explained by scattering of neutrals off the cold plasma plugging the divertor throat. Because neutrals are confined in the divertor through scattering and ionization processes (provided the mean-free-paths are much shorter than a typical escape distance) tight mechanical baffling is unnecessary. The analysis suggests that two simple structural modifications may increase the divertor compression in Alcator C-Mod by a factor of about 5. Widening the divertor throat would increase the divertor recycling source, while closing leaks in the divertor structure would eliminate a significant neutral loss mechanism. 146 refs., 82 figs., 14 tabs.
Compatibility of detached divertor operation with robust edge pedestal performance
Energy Technology Data Exchange (ETDEWEB)
Leonard, A.W., E-mail: leonard@fusion.gat.com [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Makowski, M.A.; McLean, A.G. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Osborne, T.H.; Snyder, P.B. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States)
2015-08-15
The compatibility of detached radiative divertor operation with a robust H-mode pedestal is examined in DIII-D. A density scan produced low temperature plasmas at the divertor target, T{sub e} ⩽ 2 eV, with high radiation leading to a factor of ⩾4 drop in peak divertor heat flux. The cold radiative plasma was confined to the divertor and did not extend across the separatrix in X-point region. A robust H-mode pedestal was maintained with a small degradation in pedestal pressure at the highest densities. The response of the pedestal pressure to increasing density is reproduced by the EPED pedestal model. However, agreement of the EPED model with experiment at high density requires an assumption of reduced diamagnetic stabilization of edge Peeling–Ballooning modes.
Thermal Fatigue Study on the Divertor Plate Materials
Institute of Scientific and Technical Information of China (English)
吴继红; 张斧; 许增裕; 严建成
2002-01-01
Thermal fatigue property of the divertor plate is one of the key issues that governs the lifetime of the divertor plate. Taking tungsten as surface material, a small-mock-up divertor plate was made by hot isostatic press welding (HIP). A thermal cycling experiment for divertor mock-up was carried out in the vacuum, where a high-heat-flux electronic gun was used as the thermal source. A cyclic heat flux of 9 MW/m2 was loaded onto the mock-up, a heating duration of 20 s was selected, the cooling water flow rate was 80 ml/s. After 1000 cycles, the surface and the W/Cu joint of the mock-up did not show any damage. The SEM was used to analyze the microstructure of the welding joint, where no cracks were found also.
Numerical analysis of divertor plasma for demo-CREST
Energy Technology Data Exchange (ETDEWEB)
Ishida, M.; Maeki, K.; Hatayama, A. [Graduate School of Fundamental Science and Technology, Keio University, Yokohama (Japan); Hiwatari, R. [Central Research Institute of Electric Power Industry (CRIEPI), Tokyo (Japan); Bonnin, X. [LIMHP-CNRS, Universite Paris 13, Villetaneuse (France); Zhu, S. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); Schneider, R. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Greifswald (Germany); Coster, D. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany)
2010-05-15
The numerical analysis of the demonstration fusion reactor Demo-CREST has been carried out; this analysis focuses on impurity seeding. Several design activities for DEMO have been carried out; however, its detailed divertor plasma analysis remains to be carried out. Therefore, in this study, we discuss the possibility of neon puffing in demo-CREST to decrease the power load to the divertor plate by using the B2-EIRENE code. It has been shown that the radiation power loss by neon increases with upstream plasma density and that the peak power load to the divertor plate comes close to the allowable level by using the preliminary divertor configuration (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Plasma detachment with molecular processes in divertor plasmas
Energy Technology Data Exchange (ETDEWEB)
Ohno, N.; Ezumi, N.; Nishijima, D.; Takamura, S. [Dept. of Energy Engineering and Science, Graduate School of Engineering, Nagoya Univ., Nagoya, Aichi (Japan); Krasheninnikov, S.I.; Pigarov, A.Yu. [MIT Plasma Science and Fusion Center, Cambridge, MA (United States)
2000-01-01
Molecular processes in detached recombining plasmas are briefly reviewed. Several reactions with vibrationally excited hydrogen molecule related to recombination processes are described. Experimental evidence of molecular activated recombination observed in a linear divertor plasma simulator is also shown. (author)
Divertor IR thermography on Alcator C-Mod.
Terry, J L; LaBombard, B; Brunner, D; Payne, J; Wurden, G A
2010-10-01
Alcator C-Mod is a particularly challenging environment for thermography. It presents issues that will similarly face ITER, including low-emissivity metal targets, low-Z surface films, and closed divertor geometry. In order to make measurements of the incident divertor heat flux using IR thermography, the C-Mod divertor has been modified and instrumented. A 6° toroidal sector has been given a 2° toroidal ramp in order to eliminate magnetic field-line shadowing by imperfectly aligned divertor tiles. This sector is viewed from above by a toroidally displaced IR camera and is instrumented with thermocouples and calorimeters. The camera provides time histories of surface temperatures that are used to compute incident heat-flux profiles. The camera sensitivity is calibrated in situ using the embedded thermocouples, thus correcting for changes and nonuniformities in surface emissivity due to surface coatings.
Divertor IR thermography on Alcator C-Moda)
Terry, J. L.; LaBombard, B.; Brunner, D.; Payne, J.; Wurden, G. A.
2010-10-01
Alcator C-Mod is a particularly challenging environment for thermography. It presents issues that will similarly face ITER, including low-emissivity metal targets, low-Z surface films, and closed divertor geometry. In order to make measurements of the incident divertor heat flux using IR thermography, the C-Mod divertor has been modified and instrumented. A 6° toroidal sector has been given a 2° toroidal ramp in order to eliminate magnetic field-line shadowing by imperfectly aligned divertor tiles. This sector is viewed from above by a toroidally displaced IR camera and is instrumented with thermocouples and calorimeters. The camera provides time histories of surface temperatures that are used to compute incident heat-flux profiles. The camera sensitivity is calibrated in situ using the embedded thermocouples, thus correcting for changes and nonuniformities in surface emissivity due to surface coatings.
Evaluation of helium cooling for fusion divertors
Energy Technology Data Exchange (ETDEWEB)
Baxi, C.B.
1993-09-01
The divertors of future fusion reactors will have a power throughput of several hundred MW. The peak heat flux on the diverter surface is estimated to be 5 to 15 MW/m{sup 2} at an average heat flux of 2 MW/m{sup 2}. The divertors have a requirement of both minimum temperature (100{degrees}C) and maximum temperature. The minimum temperature is dictated by the requirement to reduce the absorption of plasma, and the maximum temperature is determined by the thermo-mechanical properties of the plasma facing materials. Coolants that have been considered for fusion reactors are water, liquid metals and helium. Helium cooling has been shown to be very attractive from safety and other considerations. Helium is chemically and neutronically inert and is suitable for power conversion. The challenges associated with helium cooling are: (1) Manifold sizes; (2) Pumping power; and (3) Leak prevention. In this paper the first two of the above design issues are addressed. A variety of heat transfer enhancement techniques are considered to demonstrate that the manifold sizes and the pumping power can be reduced to acceptable levels. A helium-cooled diverter module was designed and fabricated by GA for steady-state heat flux of 10 MW/m{sup 2}. This module was recently tested at Sandia National Laboratories. At an inlet pressure of 4 MPa, the module was tested at a steady-state heat flux of 10 MW/m{sup 2}. The pumping power required was less than 1% of the power removed. These results verified the design prediction.
Beryllium flux distribution and layer deposition in the ITER divertor
Schmid, K.
2008-10-01
The deposition of Be eroded from the main chamber wall on the W surfaces in the ITER divertor could result in the formation of Be rich Be/W mixed layers with a low melting temperature compared with pure W. To predict whether or not these layers form the Be flux distribution in the ITER divertor is required. This paper presents the results of a combination of plasma transport with erosion/deposition simulations that allow one to calculate both the Be flux distribution and the Be layer deposition in the ITER divertor. This model includes the Be source due to Be erosion in the main chamber and the deposition, re-erosion and re-deposition of Be in the ITER divertor. The calculations show that the fraction of Be in the incident particle flux in the divertor ranges from ≈10-3 to ≈5% with a pronounced inner-outer divertor asymmetry. The flux fractions in the inner divertor are on average ten times higher than in the outer divertor. Thick Be layers only form at the inner strike point and the dome baffles. The highest Be layer growth rate is found to be 1.0 nm s-1. Despite the Be deposition the formation of Be rich Be/W mixed layers is not to be expected in ITER. The expected surface temperature at these locations during steady-state operation is too low as to result in Be diffusion into W and thus Be/W mixed layers cannot form. The paper also discusses the influence of off normal events such as ELMs or VDEs on the formation of Be/W mixed layers.
Characterizing the Outer Divertor Leg Transition to Full Detachment
McLean, A. G.; Allen, S. L.; Fenstermacher, M. E.; Lasnier, C. J.; Meyer, W. H.; Porter, G. D.; Soukhanovskii, V. A.; Bray, B. D.; Carlstrom, T. N.; Leonard, A. W.; Liu, C.; Eldon, D.; Groth, M.; Stangeby, P. C.; Tsui, C. K.
2013-10-01
Experiments at DIII-D have explored the transition from an attached to fully detached divertor condition in L- and H-mode with an unprecedented level of detail. Improved divertor Thomson scattering capturing Te operation in future devices. This work supported in part by the US Department of Energy under DE-AC52-07NA27344 and DE-FC02-04ER54698.
Turbulent Simulations of Divertor Detachment Based On BOUT + + Framework
Chen, Bin; Xu, Xueqiao; Xia, Tianyang; Ye, Minyou
2015-11-01
China Fusion Engineering Testing Reactor is under conceptual design, acting as a bridge between ITER and DEMO. The detached divertor operation offers great promise for a reduction of heat flux onto divertor target plates for acceptable erosion. Therefore, a density scan is performed via an increase of D2 gas puffing rates in the range of 0 . 0 ~ 5 . 0 ×1023s-1 by using the B2-Eirene/SOLPS 5.0 code package to study the heat flux control and impurity screening property. As the density increases, it shows a gradually change of the divertor operation status, from low-recycling regime to high-recycling regime and finally to detachment. Significant radiation loss inside the confined plasma in the divertor region during detachment leads to strong parallel density and temperature gradients. Based on the SOLPS simulations, BOUT + + simulations will be presented to investigate the stability and turbulent transport under divertor plasma detachment, particularly the strong parallel gradient driven instabilities and enhanced plasma turbulence to spread heat flux over larger surface areas. The correlation between outer mid-plane and divertor turbulence and the related transport will be analyzed. Prepared by LLNL under Contract DE-AC52-07NA27344. LLNL-ABS-675075.
X-Divertors on ITER - with no hardware changes
Valanju, Prashant; Covele, Brent; Kotschenreuther, Mike; Mahajan, Swadesh; Kessel, Charles
2014-10-01
Using CORSICA, we have discovered that X-Divertor (XD) equilibria are possible on ITER - without any extra PF coils inside the TF coils, and with no changes to ITER's poloidal field (PF) coil set, divertor cassette, strike points, or first wall. Starting from the Standard Divertor (SD), a sequence of XD configurations (with increasing flux expansions at the divertor plate) can be made by reprogramming ITER PF coil currents while keeping them all under their design limits (Lackner and Zohm have shown this to be impossible for Snowflakes). The strike point is held fixed, so no changes in the divertor or pumping hardware will be needed. The main plasma shape is kept very close to the SD case, so no hardware changes to the main chamber will be needed. Time-dependent ITER-XD operational scenarios are being checked using TSC. This opens the possibility that many XDs could be tested and used to assist in high-power operation on ITER. Because of the toroidally segmented ITER divertor plates, strongly detached operation may be critical for making use of the largest XD flux expansion possible. The flux flaring in XDs is expected to increase the stability of detachment, so that H-mode confinement is not affected. Detachment stability is being examined with SOLPS. This work supported by US DOE Grants DE-FG02-04ER54742 and DE-FG02-04ER54754 and by TACC at UT Austin.
Johnson, Joseph F
2011-01-01
We give Sir James Jeans's notion of 'normal state' a mathematically precise definition. We prove that normal cells of trajectories exist in the Hamiltonian heat-bath model of an assembly of linearly coupled oscillators that generates the Ornstein--Uhlenbeck process in the limit of an infinite number of degrees of freedom. This, in some special cases, verifies some far-reaching conjectures of Khintchine on the weak ergodicity of a dynamical system with a large number of degrees of freedom. In order to estimate the theoretical auto-correlation function of a time series from the sample auto-correlation function of one of its realisations, it is usually assumed without justification that the time series is ergodic. Khintchine's conjectures about dynamical systems with large numbers of degrees of freedom justifies, even in the absence of ergodicity, approximately the same conclusions. Para emplear el correlograma de los valores muestrales de un proceso estoc\\'astico para estimar su funci\\'on te\\'orica de autocorre...
Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient
Chestnut, Stephen
2010-01-01
We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.
The onset of magnetic stochasticity for an ergodic limiter
Energy Technology Data Exchange (ETDEWEB)
Vasconcelos, D.B. [Centro Federal de Educacao Tecnologica do Parana, GO (Brazil); Viana, R.L. [Parana Univ., Curitiba, PR (Brazil). Dept. de Fisica
1995-12-31
In a previous communication we have reported on a Hamiltonian formulation for the Martin-Taylor model of a tokamak with an Ergodic Magnetic Limiter. This is a device designed to create a cold boundary layer of chaotic magnetic field lines in the peripheral region of a tokamak, in order to reduce plasma-wall interactions. The equilibrium field is modelled bay a cylindrical plasma column, conducting a total current I{sub p}. The details of the current density profile are not taken into account, because we are intending to describe de peripheral region of the torus only, The limiter field is supposed to be of an impulsive character, i.e., a periodic delta function modulating the magnetic field created by 2 m very long wires. (author). 7 refs., 2 figs.
Random Sequences and Pointwise Convergence of Multiple Ergodic Averages
Frantzikinakis, Nikos; Wierdl, Mate
2010-01-01
We prove pointwise convergence, as $N\\to \\infty$, for the multiple ergodic averages $\\frac{1}{N}\\sum_{n=1}^N f(T^nx)\\cdot g(S^{a_n}x)$, where $T$ and $S$ are commuting measure preserving transformations, and $a_n$ is a random version of the sequence $[n^c]$ for some appropriate $c>1$. We also prove similar mean convergence results for averages of the form $\\frac{1}{N}\\sum_{n=1}^N f(T^{a_n}x)\\cdot g(S^{a_n}x)$, as well as pointwise results when $T$ and $S$ are powers of the same transformation. The deterministic versions of these results, where one replaces $a_n$ with $[n^c]$, remain open, and we hope that our method will indicate a fruitful way to approach these problems as well.
Quantile estimation for a non-geometric ergodic Markov chain
Ramirez-Nafarrate, Adrian; Muñoz, David F.
2013-10-01
Simulation has been successfully used for estimating performance measures (e.g. mean, variance and quantiles) of complex systems, such as queueing and inventory systems. However, parameter estimation using simulation may be a difficult task under some conditions. In this paper, we present a counterexample for which traditional simulation methods do not allow us to estimate the accuracy of the point estimators for the mean and risk performance measures for steady-state. The counterexample is based on a Markov chain with continuous state space and non-geometric ergodicity. The simulation of this Markov chain shows that neither multiple replications nor batch-based methodologies can produce asymptotically valid confidence intervals for the point estimators.
On Ergodic Secrecy Capacity for Gaussian MISO Wiretap Channels
Li, Jiangyuan
2010-01-01
A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that achieves ergodic secrecy capacity subject to a power constraint where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero-mean and unit-variance, i.e., the channels have trivial covariances. This paper addresses the general case where eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framew...
Logistic Growth and Ergodic Properties of Urban Forms
Masucci, A Paolo; Wang, Jiaqiu; Hatna, Erez; Stanilov, Kiril; Batty, Michael
2015-01-01
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and allometries have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying percolation theory to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the allometries that are present in cities, thus casting light on the concept of ergodicity as relat...
Criteria for Super- and Weak-Poincaré Inequalities of Ergodic Birth-Death Processes
Institute of Scientific and Technical Information of China (English)
Jian WANG
2012-01-01
Criteria for the super-Poincaré inequality and the weak-Poincaré inequality about ergodic birth-death processes are presented.Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p.15) of Prof.Mu-Fa Chen's book “Eigenvalues,Inequalities and Ergodic Theory” (Springer,London,2005).As a byproduct,we conclude that only ergodic birth-death processes on finite state space satisfy the Nash inequality with index 0 ＜ V ≤ 2.
Servidio, S; Matthaeus, W H; Carbone, V
2008-10-01
We explore the problem of the ergodicity of magnetohydrodynamics and Hall magnetohydrodynamics in three-dimensional, ideal Galerkin systems that are truncated to a finite number of Fourier modes. We show how single Fourier modes follow the Gibbs ensemble prediction, and how the ergodicity of the phase space is restored for long-time Galerkin solutions. Running time averages and two-time correlation functions show, at long times, a convergence towards zero of time averaged single Fourier modes. This suggests a delayed approach to, rather than a breaking of, ergodicity. Finally, we present some preliminary ideas concerning the origin of the associated time scales.
Tokamak edge Er studies by turbulence and divertor simulations
Nishimura, Y.; Coster, D.; Scott, B.
2002-11-01
Numerical coupling of the divertor code B2(B. J. Braams, Next European Torus Technical Report 68 (1987).) and the turbulence code DALF(B. D. Scott, Phys. Fluids B 4), 2468 (1992). is pursued. Within this model, space and time dependent transport coefficients (D and i) respond to the dynamics of drift wave turbulence. The Braginskii transport model of the B2 code incorporates guiding-center plasma drifts self-consistently and generate Er shear in the presence of steep pressure gradients. This Braginskii type Er can enter the turbulence model as a background E × B shear flow which suppresses the radial flux together with Reynolds stress induced electric fields. As an example of L-H transition, influx at the core boundary is controlled to produce steepening of the edge gradients. ( Y.Hamada et al.), in Proceedings of the 17th IAEA Fusion Energy Conference (IAEA-F1-CN-69/PD, 1998) reveals heat pulse induced L-H transitions after sawtooth events.
Nille, Dirk; Eich, Thomas
2016-01-01
Topic is the divertor broadening $S$, being a result of perpendicular transport in the scrape-off layer and resulting in a better distribution of the power load onto the divertor target. Recent studies show a scaling of the divertor broadening with an inverse power law to the target temperature $T_t$, promising its reduction to be a way of distributing the power entering the divertor volume onto a large surface area. It is shown that for pure conductive transport in the divertor region the suggested inverse power law scaling to $T_t$ is only valid for high target electron temperatures. For decreasing target temperatures ($T_t < 20\\,$eV) the increase of $S$ stagnates and the conductive model results in a finite value of $S$ even for zero target temperature. It is concluded that the target temperature is no valid parameter for a power law scaling, as it is not representative for the entire divertor volume. This is shown in simulations solving the 2D heat diffusion equation, which is used as reference for an ...
Sun, Hailing; Wu, Xiao; Peng, Deng Feng; Kwok, K W
2017-10-04
Ferroelectric oxides with luminescent ions hold great promise in future optoelectronic devices because of their unique photoluminescence and inherent ferroelectric properties. Intriguingly, the photoluminescence performance of ferroelectric ceramics could be modulated by an external electric field. However, researchers face a current challenge of the diminutive extent and degree of reversibility of the field-driven modification that hinder their use in room-temperature practical applications. Within the scope of current contribution in rare-earth-doped bismuth sodium titanate relaxors, the most important information to be noted is the shifting of the depolarization temperature toward room temperature and the resulting considerable enhancement in ergodicity, as evidenced by the dielectric properties, polarization, and strain hysteresis, as well as the in situ Raman/X-ray diffraction studies. After the introduction of 1 mol % Eu, the induced composition and charge disorders disrupt the original long-range ferroelectric macrodomains into randomly dynamic and weakly correlated polar nanoregions, which facilitates a reversible transformation between polar nanoregions and unstable ferroelectric state under an electric field, engendering a large strain. By virtue of this, both the extent and degree of reversibility of photoluminescence modulation are enhanced (∼60%) considerably, and room-temperature in situ tunable photoluminescence response is then achieved under electric field. These should be helpful for the realization of regulating the physical couplings (photoluminescent-ferroelectrics) in multifunctional inorganic ferroelectrics with a high ergodic state by reversibly tuning the structural symmetry.
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
Gong, FuZhou; Liu, Yuan
2015-06-01
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
Directory of Open Access Journals (Sweden)
Miguel Carvalhais
2015-11-01
Full Text Available Procedural systems allow unique modes of authorship and singular aesthetic experiences. As creators and users of these systems, we need to be aware that their aesthetic potential is not solely defined by interaction but that interpretation, and the capacity to understand and simulate the processes taking place within these artefacts is highly significant. This paper argues that although direct interaction is usually the most discernible component in the relationship between ergodic artefacts and their users, ergodicity does not necessarily imply interaction. Non-interactive procedural artefacts may allow the development of ergodic experiences through interpretation, and the probing of the system by its reader through simulations. We try to set the grounds for designing towards virtuosic interpretation, an activity that we may describe as the ergodic experience developed by means of mental simulation through the development of theories of systems.
On the Robustness of the Twin-Peaked Ergodic Distribution of Income Across Countries
Gisele Hites
2000-01-01
In the literature on convergence, the simple Markov chain model indicates evolution towards a twin-peaked world. Although cleansing the ergodic distribution of income across countries of short-run noise reinforces its twin-peaked shape, these twin peaks are not statistically significant. Moreover, the specific type high immobility reflected by the data on income renders the estimated transition matrix particularly prone to the generation of twin-peaked ergodic distributions.
Reducing quasi-ergodicity in a double well potential by Tsallis Monte Carlo simulation
Iwamatsu, Masao; Okabe, Yutaka
2000-01-01
A new Monte Carlo scheme based on the system of Tsallis's generalized statistical mechanics is applied to a simple double well potential to calculate the canonical thermal average of potential energy. Although we observed serious quasi-ergodicity when using the standard Metropolis Monte Carlo algorithm, this problem is largely reduced by the use of the new Monte Carlo algorithm. Therefore the ergodicity is guaranteed even for short Monte Carlo steps if we use this new canonical Monte Carlo sc...
Spectroscopic investigations of divertor detachment in TCV
Verhaegh, K; Duval, B P; Harrison, J R; Reimerdes, H; Theiler, C; Labit, B; Maurizio, R; Marini, C; Nespoli, F; Sheikh, U; Tsui, C K; Vianello, N; Vijvers, W A J
2016-01-01
The aim of this work is to provide an understanding of detachment at TCV with emphasis on analysis of the Balmer line emission. A new Divertor Spectroscopy System has been developed for this purpose. Further development of Balmer line analysis techniques has allowed detailed information to be extracted on free-free and three-body recombination. During density ramps, the plasma at the target detaches as inferred from a drop in density at, and ion current to, the target. At the same time the Balmer $6\\rightarrow2$ and $7\\rightarrow2$ line emission near the target is dominated by recombination, indicating that the ionization region has also detached from the target to be replaced by a recombining region with densities more than a factor 2 higher than at the target. As the core density increases further, the density and recombination rate are rising all along the outer leg to the x-point while remaining highest at the target. Even at the highest core densities accessed (Greenwald fraction 0.7) the peaks in recomb...
Efficiency of water coolant for DEMO divertor
Energy Technology Data Exchange (ETDEWEB)
Fetzer, Renate, E-mail: renate.fetzer@kit.edu; Igitkhanov, Yuri; Bazylev, Boris
2015-10-15
Up to now, water-cooled divertor concepts have been developed for limited incident fluxes without taking into account transient power loadings. In this paper we analyzed the efficiency of water as a coolant for the particular PFC tungsten monoblock shield with a cooling tube made from Cu alloy (Cu OFHC) as a laminate adjacent to W and a low activation martensitic steel (Eurofer) as inner tube contacting the coolant. Thermal analysis is carried out by using the code MEMOS, which simulates W armour damage under the repetitive ELM heat loads. We consider cooling conditions which allow one to keep relatively high material temperatures (in the range 300–600 °C) thus minimizing Eurofer embrittlement under neutron irradiation. Expected DEMO I and DEMO II heat loads including type I ELMs are found to cause melting of the W surface during unmitigated ELMs. By mitigation of the ELMs melting of W is avoided. DEMO I operation under these conditions is save for cooling at water pressure 15.5 MPa and temperature 325 °C, while for DEMO II with mitigated ELMs the critical heat flux is exceeded and safe operation is not provided.
Initial Development of the NSTX-U Snowflake Divertor Control
Vail, Patrick; Kolemen, Egemen; Welander, Anders; Lanctot, Matthew
2015-11-01
A feedback control system has been implemented at NSTX-U for real-time detection and manipulation of snowflake divertor (SFD) magnetic configurations. The SFD is an alternative magnetic divertor concept that is characterized by a second-order null formed by two x-points in close proximity. The SFD is an attractive option for heat flux mitigation for NSTX-U in which unmitigated peak heat fluxes in standard divertor operation near 20 MW/m2 may compromise plasma-facing components. The real-time control system at NSTX-U is capable of simultaneous control of multiple SFD parameters, such as the separation between the two x-points in the divertor region and their orientation. Control of SFD configurations in NSTX-U has been simulated in TOKSYS using the upgraded sets of poloidal field coils in both the upper and lower divertor regions. Performance of the real-time control system and its effect on plasma performance will be assessed experimentally as an initial step toward the development of the SFD concept at NSTX-U. Supported by the US DOE under DE-AC02-09CH11466.
Large deviations of ergodic counting processes: a statistical mechanics approach.
Budini, Adrián A
2011-07-01
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations. Here we study this formalism through a statistical mechanics approach, that is, with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential. We show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones, providing is this way an alternative measurement interpretation of the thermodynamic approach. General results are obtained for renewal counting processes, that is, those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution. The underlying statistical mechanics is controlled by the same waiting time distribution, rescaled by an exponential decay measured by the free energy function. A scale invariance, shift closure, and intermittence phenomena are obtained and interpreted in this context. Similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution.
Anderson localization and ergodicity on random regular graphs
Tikhonov, K. Â. S.; Mirlin, A. Â. D.; Skvortsov, M. Â. A.
2016-12-01
A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In a certain sense, the RRG ensemble can be seen as an infinite-dimensional (d →∞ ) cousin of the Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from a small (N ≪Nc ) to a large (N ≫Nc ) system, where Nc is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wave-function statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly nontrivial. Our results support an analytical prediction that states in the delocalized phase (and at N ≫Nc ) are ergodic in the sense that their inverse participation ratio scales as 1 /N .
Non-ergodicity for $C^{1}$ Expanding Maps
Quas, A N
1993-01-01
In this paper, we consider the question of existence and uniqueness of absolutely continuous invariant measures for expanding $C^1$ maps of the circle. This is a question which arises naturally from results which are known in the case of expanding $C^k$ maps of the circle where $k\\geq 2$, or even $C^{1+\\epsilon}$ expanding maps of the circle. In these cases, it is known that there exists a unique absolutely continuous invariant probability measure by the so-called `Folklore Theorem'. It follows that this measure is ergodic. It has been shown however that for $C^1$ maps there need not be any such measure. However, this leaves the question of whether there can be more than one such measure for $C^1$ expanding maps of the circle. This is the subject of this paper, and in it, we show that there exists a $C^1$ expanding map of the circle which has more than one absolutely continuous invariant probability measure.
Hydrogen recycling and transport in the helical divertor of TEXTOR
Energy Technology Data Exchange (ETDEWEB)
Clever, Meike
2010-07-01
The aim of this thesis was to investigate the hydrogen recycling at the target plates of the helical divertor in TEXTOR and by this the capability of this divertor configuration to access such favourable operational regimes. In order to study the different divertor density regimes in TEXTOR, discharges were performed in which the total plasma density was increased continuously up to the density limit. The recycling was investigated in a fixed helical divertor structure where four helical strike points with a poloidal width of about 8-10 cm are created at the divertor target plates. The experimental investigation of the hydrogen recycling was carried out using mainly spectroscopic methods supplemented by Langmuir probe, interferometric and atomic beam measurements. In the framework of this thesis a spectroscopic multi camera system has been built that facilitates the simultaneous observation of four different spectral lines, recording images of the divertor target plates and the plasma volume close to the target. The system facilitates the simultaneous measurement of the poloidal and toroidal pattern of the recycling flux at the divertor target without the need for sweeping the plasma structure. The simultaneous observation of different spectral lines reduces the uncertainty in the analysis based on several lines, as the contribution from uncertainties in the reproducibility of plasma parameters in different discharges are eliminated and only the uncertainty of the measurement method limits the accuracy. The spatial resolution of the system in poloidal and toroidal direction (0.8 mm{+-}0.01 mm) is small compared to the separation of the helical strike points, the capability of the measurement method to resolve these structures is therefore limited by the line-of-sight integration and the penetration depth of the light emitting species. The measurements showed that the recycling flux increases linearly with increasing plasma density, a high recycling regime is not
Plasma transport in a simulated magnetic-divertor configuration
Energy Technology Data Exchange (ETDEWEB)
Strawitch, C. M.
1981-03-01
The transport properties of plasma on magnetic field lines that intersect a conducting plate are studied experimentally in the Wisconsin internal ring D.C. machine. The magnetic geometry is intended to simulate certain aspects of plasma phenomena that may take place in a tokamak divertor. It is found by a variety of measurements that the cross field transport is non-ambipolar; this may have important implications in heat loading considerations in tokamak divertors. The undesirable effects of nonambipolar flow make it preferable to be able to eliminate it. However, we find that though the non-ambipolarity may be reduced, it is difficult to eliminate entirely. The plasma flow velocity parallel to the magnetic field is found to be near the ion acoustic velocity in all cases. The experimental density and electron temperature profiles are compared to the solutions to a one dimensional transport model that is commonly used in divertor theory.
Radiative divertor plasmas with convection in DIII-D
Energy Technology Data Exchange (ETDEWEB)
Leornard, A.W. [General Atomics, San Diego, CA (United States); Porter, G.D.; Wood, R.D. [Lawrence Livermore National Lab., CA (United States)] [and others
1998-01-01
The radiation of divertor heat flux on DIII-D is shown to greatly exceed the limits imposed by assumptions of energy transport dominated by electron thermal conduction parallel to the magnetic field. Approximately 90% of the power flowing into the divertor is dissipated through low Z radiation and plasma recombination. The dissipation is made possible by an extended region of low electron temperature in the divertor. A one-dimensional analysis of the parallel heat flux finds that the electron temperature profile is incompatible with conduction dominated parallel transport. Plasma flow at up to the ion acoustic speed, produced by upstream ionization, can account for the parallel heat flux. Modeling with the two-dimensional fluid code UEDGE has reproduced many of the observed experimental features.
A novel approach to magnetic divertor configuration design
Blommaert, M.; Baelmans, M.; Dekeyser, W.; Gauger, N. R.; Reiter, D.
2015-08-01
Divertor exhaust system design and analysis tools are crucial to evolve from experimental fusion reactors towards commercial power plants. In addition to material research and dedicated vessel geometry design, improved magnetic configurations can contribute to sustaining the diverted heat loads. Yet, computational design of the magnetic divertor is a challenging process involving a magnetic equilibrium solver, a plasma edge grid generator and a computationally demanding plasma edge simulation. In this paper, an integrated approach to efficient sensitivity calculations is discussed and applied to a set of slightly reduced divertor models. Sensitivities of target heat load performance to the shaping coil currents are directly evaluated. Using adjoint methods, the cost for a sensitivity evaluation is reduced to about two times the simulation cost of one specific configuration. Further, the use of these sensitivities in an optimal design framework is illustrated by a case with realistic Joint European Torus (JET) configurational parameters.
TECXY study of a liquid lithium divertor for DEMO
Energy Technology Data Exchange (ETDEWEB)
Pelka, G.; Chmielewski, P.; Zagorski, R. [Institute of Plasma Physics and Laser Microfusion, Warsaw (Poland); Pericoli-Ridolfini, V.; Viola, B. [ENEA C.R. Frascati, Roma (Italy)
2016-08-15
Divertor targets made out of a capillary porous system (CPS) filled with liquid lithium, have been proposed as an alternative to standard, solid state plates. In the current work we simulate the DEMO edge plasma in either a standard single-null or snowflake divertor configuration. Our tool is the 2D code TECXY. Lithium ablated from the target plate surface and released into the plasma is shown here to partially screen the incoming heat flux. Lithium's moderate SOL radiation levels suggest additional seeding to be beneficial. Very high heat fluxes to the divertor need to be avoided, as intensive lithium evaporation might unacceptably pollute the plasma. (copyright 2016 The Authors. Contributions to Plasma Physics published by Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)
Resonant magnetic perturbations and divertor footprints in poloidally diverted tokamaks
Cahyna, Pavel
2010-01-01
General formula describing both the divertor strike point splitting and width of magnetic islands created by resonant magnetic perturbations (RMPs) in a poloidally diverted tokamak equilibrium is derived. Under the assumption that the RMP is produced by coils at the low-field side such as those used to control edge localized modes (ELMs) it is demonstrated that the width of islands on different magnetic surfaces at the edge and the amount of divertor splitting are related to each other. Explanation is provided of aligned maxima of the perturbation spectra with the safety factor profile - an effect empirically observed in models of many perturbation coil designs.
Thermal Analysis of the Divertor Primary Heat Transfer System Piping During the Gas Baking Process
Energy Technology Data Exchange (ETDEWEB)
Yoder Jr, Graydon L [ORNL; Harvey, Karen [ORNL; Ferrada, Juan J [ORNL
2011-02-01
A preliminary analysis has been performed examining the temperature distribution in the Divertor Primary Heat Transfer System (PHTS) piping and the divertor itself during the gas baking process. During gas baking, it is required that the divertor reach a temperature of 350 C. Thermal losses in the piping and from the divertor itself require that the gas supply temperature be maintained above that temperature in order to ensure that all of the divertor components reach the required temperature. The analysis described in this report was conducted in order to estimate the required supply temperature from the gas heater.
Invariance of divertor retention on external particle flow in detached ASDEX upgrade discharges
Energy Technology Data Exchange (ETDEWEB)
Bosch, H.; Dux, R.; Haas, G.; Kallenbach, A.; Kaufmann, M.; Lackner, K.; Mertens, V.; Murmann, H.; Poschenrieder, W.; Salzmann, H.; Schweinzer, J.; Suttrop, W.; Weinlich, M. [Max-Planck-Institut fuer Plasmaphysik, IPP-EURATOM Association, D-85748 Garching (Germany); ASDEX Upgrade team% NI team
1996-04-01
Divertor plasmas with strong external gas puffing in ASDEX Upgrade have shown very efficient impurity retention, increasing with the divertor neutral gas density. The experiments presented here use feedback-controlled gas puffs in discharges with different pumping speed to keep the divertor neutral gas flux density the same. This allows for the first time a decoupling of the divertor neutral gas flux density and the external gas flow. The resulting plasmas are almost identical and show identical impurity retention, clearly demonstrating the importance of the divertor neutral gas density over the externally induced flow. {copyright} {ital 1996 The American Physical Society.}
Energy Technology Data Exchange (ETDEWEB)
Tanchuk, Victor, E-mail: Victor.Tanchuk@sintez.niiefa.spb.su [Scientific Technical Center SINTEZ, D.V. Efremov Institute, 196641 St. Petersburg (Russian Federation); Grigoriev, Sergey; Makhankov, Alexey; Senik, Konstantin; Yablokov, Nikolay [Scientific Technical Center SINTEZ, D.V. Efremov Institute, 196641 St. Petersburg (Russian Federation); Belenky, Mikhail; Blinov, Mikhail; Lebedev, Mikhail; Fokin, Boris [I.I. Polzunov Scientific and Development Association on Research and Design of Power Equipment, 191167 St. Petersburg (Russian Federation)
2014-10-15
Highlights: • The experiments on the assembly of the ¼ ITER divertor dome consisting of three groups of hypervapotrons with aim to prove applicability of the thermography method for detection of defective channels are performed. • Numerical simulation of the FAT procedure on the calculation model of ½ dome is carried out. • It is not only the flow rate difference in parallel channels caused by defective hypervapotrons but also the flow history that affects essentially the dynamics of the temperature field of the dome surface. - Abstract: The divertor dome (DO), being part of the ITER divertor, is designed to extract the major part of the plasma thermal energy. As a plasma-facing component (PFC), the DO experiences high heat fluxes (up to 5.0 MW/m{sup 2}). Such severe operation conditions of the DO imply stringent requirements for the DO design and its cooling system to ensure the required temperature operation regime of the dome. Hence, Final Acceptance Tests (FAT) shall be performed on each DO final assembled component with the aim to demonstrate that none of parallel coolant channels are completely or partially blocked. The paper presents the results of the analytical and experimental testing of the thermography method capability to perform the FAT. The aim is to determine defective hypervapotrons of the divertor dome. The method consists in contactless measurement of the dynamic temperature field of the PFC surface at a step-like increase (from zero to constant value) in the coolant flow rate with a temperature higher than that of the hypervapotron.
Taming the plasma-material interface with the snowflake divertor.
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V A
2015-04-24
Experiments in several tokamaks have provided increasing support for the snowflake configuration as a viable tokamak heat exhaust concept. This white paper summarizes the snowflake properties predicted theoretically and studied experimentally, and identifies outstanding issues to be resolved in existing and future facilities before the snowflake divertor can qualify for the reactor interface.
Enhancing the DEMO divertor target by interlayer engineering
Energy Technology Data Exchange (ETDEWEB)
Barrett, T.R., E-mail: tom.barrett@ccfe.ac.uk [CCFE, Culham Science Centre, Oxfordshire OX14 3DB (United Kingdom); McIntosh, S.C.; Fursdon, M.; Hancock, D.; Timmis, W.; Coleman, M. [CCFE, Culham Science Centre, Oxfordshire OX14 3DB (United Kingdom); Rieth, M.; Reiser, J. [Karlsruhe Institute for Technology, IMF-I, D-7602 Karlsruhe (Germany)
2015-10-15
Highlights: • The European ‘near-term’ DEMO forsees a water-cooled divertor. • Divertor targets typically use an interlayer between the armour and structure. • Engineering the properties of the interlayer can yield large gains in performance. • A response surface based design search and optimisation method is used. • A new design passes linear-elastic code rules up to applied heat flux of 18 MW/m{sup 2}. - Abstract: A robust water-cooled divertor target plate solution for DEMO has to date remained elusive. Common to all contemporary concepts is an interlayer at the boundary between the tungsten armour and the cooling structure. In this paper we show by design optimisation that an effectively designed interlayer can produce dramatic gains in power handling. By engineering the interlayer as part of the design study, it is found that divertor performance is enhanced by either a low conductivity ‘Thermal Break’ interlayer or an ‘Ultra-Compliant’ interlayer. For a 10 MW/m{sup 2} surface heat flux we find that a thermal conductivity of 15 W/mK and elastic modulus of 1 GPa are effective. A design is proposed which passes linear-elastic code rules up to an applied heat flux of 18 MW/m{sup 2}.
Divertor performance on carbon and beryllium targets in JET
Energy Technology Data Exchange (ETDEWEB)
Janeschitz, G.; Koenig, R.; Lauro-Taroni, L.; Lingertat, J.; Matthews, G.; Stamp, M.; Vlases, G.; Campbell, D.; Clement, S.; De Kock, L.; Ehrenberg, J.; Gottardi, N.; Harbour, P.; Horton, L.; Jaeckel, H.; Lesourd, M.; Loarte, A.; Lowry, C.; Saibene, G.; Summers, D.; Tagle, J.A.; Thomas, P.R.; Von Hellerman, M. (JET Joint Undertaking, Abingdon (United Kingdom)); Eckstein, W.; Roth, J. (Max Planck Inst. fuer Plasmaphysik, Garching (Germany))
1992-12-01
The dependence of impurity production and retention on the divertor density, on the power flow into this region as well as on the X-point to target distance are investigated. Model predictions suggest a good impurity retention above a certain divertor (scrape-off) density threshold, which is dependent on heating power. In our experiments pre-programmed midplane or X-point gas puffs were used to scan the density, as well as to avoid the depletion of particles from the divertor and the scrape-off during H-models. The gas puffs reduce T[sub e] and increase N[sub e] in particular at the outer strike zone. In general the Be as well as the C influx increases with density, which is understood from the T[sub e] (T[sub i]) dependence of the sputtering yields. The impurity retention shows the expected improvement with increasing scrape-off (divertor) density as well as with increasing X-point to target distance (connection length). (orig.).
On the Ergodic Capacity of Dual-Branch Correlated Log-Normal Fading Channels with Applications
Al-Quwaiee, Hessa
2015-05-01
Closed-form expressions of the ergodic capacity of independent or correlated diversity branches over Log-Normal fading channels are not available in the literature. Thus, it is become of an interest to investigate the behavior of such metric at high signal-to-noise (SNR). In this work, we propose simple closed-form asymptotic expressions of the ergodic capacity of dual-branch correlated Log- Normal corresponding to selection combining, and switch-and-stay combining. Furthermore, we capitalize on these new results to find new asymptotic ergodic capacity of correlated dual- branch free-space optical communication system under the impact of pointing error with both heterodyne and intensity modulation/direct detection. © 2015 IEEE.
Ergodicity for a Class of Markov Operators%一类Markov算子的遍历性
Institute of Scientific and Technical Information of China (English)
郭新伟; 喻建华; 齐海涛
2013-01-01
利用遍历理论研究了完备可分距离空间上其对偶算子的算术平均具有等度连续性的Markov-Feller算子的遍历性质,得到此类算子的Yosida型遍历分解定理,并简洁证明了Markov-Feller算子具有唯一不变测度的一个结果.%Ergodicity of a class of Markov-Feller operators with equicontinuous average dual operators is studied by the ergodic theory.As an application,a Yosida type ergodic decomposition theorem for such operators is proved and a simple proof on the uniqueness of invariant measures for Markov-Feller operators is given.
Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
Gomez, Ignacio; Castagnino, Mario
2014-01-01
In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8].
A constructive version of Birkhoff's ergodic theorem for Martin-L\\"of random points
Bienvenu, Laurent; Hoyrup, Mathieu; Mezhirov, Ilya; Shen, Alexander
2010-01-01
A theorem of Ku\\v{c}era states that given a Martin-L\\"of random infinite binary sequence {\\omega} and an effectively open set A of measure less than 1, some tail of {\\omega} is not in A. We first prove several results in the same spirit and generalize them via an effective version of a weak form of Birkhoff's ergodic theorem. We then use this result to get a stronger form of it, namely a very general effective version of Birkhoff's ergodic theorem, which improves all the results previously obtained in this direction, in particular those of V'Yugin, Nandakumar and Hoyrup, Rojas.
Development and application of ergodicity model with FRCM and FLAR for hydrological process
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.
Development and application of ergodicity model with FRCM and FLAR for hydrological process
Institute of Scientific and Technical Information of China (English)
WANG HongRui; FENG QiLei; LIN Xin; ZENG WenYi
2009-01-01
In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951--2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.
Can future systemic financial risks be quantified?: ergodic vs nonergodic stochastic processes
Directory of Open Access Journals (Sweden)
Paul Davidson
2009-12-01
Full Text Available Different axioms underlie efficient market theory and Keynes's liquidity preference theory. Efficient market theory assumes the ergodic axiom. Consequently, today's decision makers can calculate with actuarial precision the future value of all possible outcomes resulting from today's decisions. Since in an efficient market world decision makers "know" their intertemporal budget constraints, decision makers never default on a loan, i.e., systemic defaults, insolvencies, and bankruptcies are impossible. Keynes liquidity preference theory rejects the ergodic axiom. The future is ontologically uncertain. Accordingly systemic defaults and insolvencies can occur but can never be predicted in advance.
Ergodic Properties of Local Spectral Density for a Conservative System of Coupled Quantum States
Starovoitov, V S
2002-01-01
The shape and the inverse participation ratio (IPR) of local spectral density (LSD) are studied for a generic isolated system of coupled quantum states, the Hamiltonian of which is represented by a band random matrix with the disordered leading diagonal. We find for the matrices with arbitrary small band that the lack of ergodicity for LSD can be associated with an exponential increase in IPR with the ratio $v/\\Delta_c$ ($v$ - the root of mean square for off-diagonal matrix elements, $\\Delta_c$ - the energy spacing between directly coupled basis states). Criterions specifying transition to localization and ergodicity for LSD are considered.
Ergodic and chaotic hypotheses nonequilibrium ensembles in statistical mechanics and turbulence
Gallavotti, G
1999-01-01
The ergodic hypothesis outgrew from the ancient conception of motion as periodic or quasi periodic. It did cause a revision of our views of motion, particularly through Boltzmann and Poincaré: we discuss how Boltmann's conception of motion is still very modern and how it can provide ideas and methods to study the problem of nonequilibrium in mechanics and in fluids. This leads to the chaotic hypothesis, a recent interpretation of a very ambitious principle conceived by D. Ruelle: it is a possible extension of the ergodic hypothesis and it implies general parameterless relations. Together with further ideas, it appears to be consistent with some recent experiments as we discuss here.
Strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in multi-Banach space
Indian Academy of Sciences (India)
M AZHINI; H M KENARI; R SAADATI
2017-09-01
Let $C$ be a bounded closed convex subset of a uniformly convex multi-Banach space $X$ and let $\\Im_{j}$ = ${T_{j} (t) : t \\in G}$ be a commutative semigroup of asymptotically nonexpansive in the intermediate mapping from $C$ into itself. In this paper, we prove the strong mean ergodic convergence theorem for the almost-orbit of $\\Im$. Our results extend and unify many previously known results especially (Dong et al. On the strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in Banach space, preprint).
Diagnostic options for radiative divertor feedback control on NSTX-U.
Soukhanovskii, V A; Gerhardt, S P; Kaita, R; McLean, A G; Raman, R
2012-10-01
A radiative divertor technique is used in present tokamak experiments and planned for ITER to mitigate high heat loads on divertor plasma-facing components (PFCs) to prevent excessive material erosion and thermal damage. In NSTX, a large spherical tokamak with lithium-coated graphite PFCs and high divertor heat flux (q(peak) ≤ 15 MW/m(2)), radiative divertor experiments have demonstrated a significant reduction of divertor peak heat flux simultaneously with good core H-mode confinement using pre-programmed D(2) or CD(4) gas injections. In this work diagnostic options for a new real-time feedback control system for active radiative divertor detachment control in NSTX-U, where steady-state peak divertor heat fluxes are projected to reach 20-30 MW/m(2), are discussed. Based on the NSTX divertor detachment measurements and analysis, the control diagnostic signals available for NSTX-U include divertor radiated power, neutral pressure, spectroscopic deuterium recombination signatures, infrared thermography of PFC surfaces, and thermoelectric scrape-off layer current. In addition, spectroscopic "security" monitoring of possible confinement or pedestal degradation is recommended. These signals would be implemented in a digital plasma control system to manage the divertor detachment process via an actuator (impurity gas seeding rate).
Divertor remote handling for DEMO: Concept design and preliminary FMECA studies
Energy Technology Data Exchange (ETDEWEB)
Carfora, D., E-mail: dario.carfora@gmail.com [VTT Technical Research Centre of Finland, P.O. Box 1300, FI-33101 Tampere (Finland); Tampere University of Technology, Korkeakoulunkatu 6, 33720 Tampere (Finland); ENEA/CREATE/Università degli studi Napoli Federico II, 80125 Napoli (Italy); Di Gironimo, G. [ENEA/CREATE/Università degli studi Napoli Federico II, 80125 Napoli (Italy); Järvenpää, J. [VTT Technical Research Centre of Finland, P.O. Box 1300, FI-33101 Tampere (Finland); Huhtala, K. [Tampere University of Technology, Korkeakoulunkatu 6, 33720 Tampere (Finland); Määttä, T.; Siuko, M. [VTT Technical Research Centre of Finland, P.O. Box 1300, FI-33101 Tampere (Finland)
2015-10-15
Highlights: • Concept design of the RH system for the DEMO fusion power plant. • Divertor mover: hydraulic telescopic boom concept design. • An alternative solution to ITER rack and pinion divertor mover (CMM). • Divertor cassettes end effector studies. • FMECA studies started on the DEMO divertor mover. - Abstract: The paper describes a concept design of a remote handling (RH) system for replacing divertor cassettes and cooling pipes in future DEMO fusion power plant. In DEMO reactor design important considerations are the reactor availability and reliable maintenance operations. The proposed divertor mover is a hydraulic telescopic boom driven from the transportation cask through the maintenance tunnel of the reactor. The boom is divided in three sections and it is driving an end-effector in order to perform the scheduled operations of maintenance inside the vacuum vessel. Two alternative designs of the end effector to grip and manipulate the divertor cassette are presented in this work. Both concepts are hydraulically actuated, based on ITER previous studies. The divertor cassette end-effector consists of a lifting arm linked to the divertor mover, a tilting plate, a cantilever arm and a hook-plate. Taking advantage of the ITER RH background and experience, the proposed hydraulic RH system is compared with the rack and pinion system currently designed for ITER and is an object of simulations at Divertor Test Platform (DTP2) in VTT's Labs of Tampere, Finland. Pros and cons will be put in evidence.
Diagnostic options for radiative divertor feedback control on NSTX-U
Energy Technology Data Exchange (ETDEWEB)
Soukhanovskii, V. A.; Gerhardt, S. P.; Kaita, R.; McLean, A. G.; Raman, R.
2012-10-01
A radiative divertor technique is used in present tokamak experiments and planned for ITER to mitigate high heat loads on divertor plasma-facing components (PFCs) to prevent excessive material erosion and thermal damage. In NSTX, a large spherical tokamak with lithium-coated graphite PFCs and high divertor heat flux (qpeak ≤ 15 MW/m2), radiative divertor experiments have demonstrated a significant reduction of divertor peak heat flux simultaneously with good core H-mode confinement using pre-programmed D2 or CD4 gas injections. In this work diagnostic options for a new real-time feedback control system for active radiative divertor detachment control in NSTX-U, where steady-state peak divertor heat fluxes are projected to reach 20–30 MW/m^{2}, are discussed. Based on the NSTX divertor detachment measurements and analysis, the control diagnostic signals available for NSTX-U include divertor radiated power, neutral pressure, spectroscopic deuterium recombination signatures, infrared thermography of PFC surfaces, and thermoelectric scrape-off layer current. In addition, spectroscopic “security” monitoring of possible confinement or pedestal degradation is recommended. These signals would be implemented in a digital plasma control system to manage the divertor detachment process via an actuator (impurity gas seeding rate).
Estimation of peak heat flux onto the targets for CFETR with extended divertor leg
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chuanjia; Chen, Bin [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026 (China); Xing, Zhe [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Wu, Haosheng [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026 (China); Mao, Shifeng, E-mail: sfmao@ustc.edu.cn [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026 (China); Luo, Zhengping; Peng, Xuebing [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China)
2016-11-01
Highlights: • A hypothetical geometry is assumed to extend the outer divertor leg in CFETR. • Density scan SOLPS simulation is done to study the peak heat flux onto target. • Attached–detached regime transition in out divertor occurs at lower puffing rate. • Unexpected delay of attached–detached regime transition occurs in inner divertor. - Abstract: China Fusion Engineering Test Reactor (CFETR) is now in conceptual design phase. CFETR is proposed as a good complement to ITER for demonstrating of fusion energy. Divertor is a crucial component which faces the plasmas and handles huge heat power for CFETR and future fusion reactor. To explore an effective way for heat exhaust, various methods to reduce the heat flux to divertor target should be considered for CFETR. In this work, the effect of extended out divertor leg on the peak heat flux is studied. The magnetic configuration of the long leg divertor is obtained by EFIT and Tokamak Simulation Code (TSC), while a hypothetical geometry is assumed to extend the out divertor leg as long as possible inside vacuum vessel. A SOLPS simulation is performed to study peak heat flux of the long leg divertor for CFETR. D{sub 2} gas puffing is used and increasing of the puffing rate means increase of plasma density. Both peak heat flux onto inner and outer targets are below 10 MW/m{sup 2} is achieved. A comparison between the peak heat flux between long leg and conventional divertor shows that an attached–detached regime transition of out divertor occurs at lower gas puffing gas puffing rate for long leg divertor. While for the inner divertor, even the configuration is almost the same, the situation is opposite.
Divertor heat and particle control experiments on the DIII-D tokamak
Energy Technology Data Exchange (ETDEWEB)
Mahdavi, M.A; Baker, D.R. [General Atomics, San Diego, CA (United States); Allen, S.L. [Lawrence Livermore National Lab., CA (United States)] [and others
1994-05-01
In this paper we present a summary of recent DIII-D divertor physics activity and plans for future divertor upgrades. During the past year, DIII-D experimental effort was focused on areas of active heat and particle control and divertor target erosion studies. Using the DIII-D Advanced Divertor system we have succeeded for the first time to control the plasma density and demonstrate helium exhaust in H-mode plasmas. Divertor heat flux control by means of D{sub 2} gas puffing and impurity injection were studied separately and in, both cases up to a factor of five reduction of the divertor peak heat flux was observed. Using the DiMES sample transfer system we have obtained erosion data on various material samples in well diagnosed plasmas and compared the results with predictions of numerical models.
The control of convection by fuelling and pumping in the JET pumped divertor
Energy Technology Data Exchange (ETDEWEB)
Harbour, P.J.; Andrew, P.; Campbell, D.; Clement, S.; Davies, S.; Ehrenberg, J.; Erents, S.K.; Gondhalekar, A.; Gadeberg, M.; Gottardi, N.; Von Hellermann, M.; Horton, L.; Loarte, A.; Lowry, C.; Maggi, C.; McCormick, K.; O`Brien, D.; Reichle, R.; Saibene, G.; Simonini, R.; Spence, J.; Stamp, M.; Stork, D.; Taroni, A.; Vlases, G. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking
1994-07-01
Convection from the scrape-off layer (SOL) to the divertor will control core impurities, if it retains them in a cold, dense, divertor plasma. This implies a high impurity concentration in the divertor, low at its entrance. Particle flux into the divertor entrance can be varied systematically in JET, using the new fuelling and pumping systems. The convection ratio has been estimated for various conditions of operation. Particle convection into the divertor should increase thermal convection, decreasing thermal conduction, and temperature and density gradients along the magnetic field, hence increasing the frictional force and decreasing the thermal force on impurities. Changes in convection in the SOL, caused by gaseous fuelling, have been studied, both experimentally in the JET Mk I divertor and with EDGE2/NIMBUS. 1 ref., 4 figs., 1 tab.
Kinetic effects in edge plasma: kinetic modeling for edge plasma and detached divertor
Takizuka, T.
2017-03-01
Detached divertor is considered a solution for the heat control in magnetic-confinement fusion reactors. Numerical simulations using the comprehensive divertor codes based on the plasma fluid modeling are indispensable for the design of the detached divertor in future reactors. Since the agreement in the results between detached-divertor experiments and simulations has been rather fair but not satisfactory, further improvement of the modeling is required. The kinetic effect is one of key issues for improving the modeling. Complete kinetic behaviors are able to be simulated by the kinetic modeling. In this paper at first, major kinetic effects in edge plasma and detached divertor are listed. One of the most powerful kinetic models, particle-in-cell (PIC) model, is described in detail. Several results of PIC simulations of edge-plasma kinetic natures are presented. Future works on PIC modeling and simulation for the deeper understanding of edge plasma and detached divertor are discussed.
Self-averaging and weak ergodicity breaking of diffusion in heterogeneous media
Russian, Anna; Dentz, Marco; Gouze, Philippe
2017-08-01
Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q ≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.
Non-ergodic Z-periodic billiards and infinite translation surfaces
Frączek, Krzysztof
2011-01-01
We give a criterion which allows to prove non-ergodicity for certain infinite periodic billiards and directional flows on Z-periodic translation surfaces. Our criterion applies in particular to a billiard in an infinite band with periodically spaced vertical barriers and to the Ehrenfest wind-tree model, which is a planar billiard with a $Z^2$-periodic array of rectangular obstacles. We prove that, in these two examples, both for a full measure set of parameters of the billiard tables and for tables with rational parameters, for almost every direction the corresponding billiard flow is not ergodic and has uncountably many ergodic components. As another application, we show that for any recurrent Z-cover of a square tiled surface of genus two the directional flow is not ergodic and has no invariant sets of finite measure for a full measure set of directions. In the language of essential values, we prove that the skew-products which arise as Poincare' maps of the above systems are associated to non-regular Z-va...
Exponential and Strong Ergodicity for Markov Processes with an Application to Queues
Institute of Scientific and Technical Information of China (English)
Yuanyuan LIU; Zhenting HOU
2008-01-01
For an ergodic continuous-time Markov process with a particular state in its space, the authors provide the necessary and sufficient conditions for exponential and strongerg odicity in terms of the moments of the first hitting time on the state. An application to the queue length process of M/G/1 queue with multiple vacations is given.
Ruin probability with claims modeled by a stationary ergodic stable process
Mikosch, T; Samorodnitsky, G
2000-01-01
For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin
In vivo Anomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules
DEFF Research Database (Denmark)
Jeon, J.-H.; Tejedor, V.; Burov, S.;
2011-01-01
Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion accord...
Strong laws for generalized absolute Lorenz curves when data are stationary and ergodic sequences
Helmers, R.; Zitikis, R.
2004-01-01
We consider generalized absolute Lorenz curves that include, as special cases, classical and generalized L - statistics as well as absolute or, in other words, generalized Lorenz curves. The curves are based on strictly stationary and ergodic sequences of random variables. Most of the previous resul
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, usi...
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
2011-01-01
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, )\\. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on , where is the ring of integers in...
Directory of Open Access Journals (Sweden)
Chunyan Ji
2010-01-01
Full Text Available We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property.
An automated approach to magnetic divertor configuration design
Blommaert, M.; Dekeyser, W.; Baelmans, M.; Gauger, N. R.; Reiter, D.
2015-01-01
Automated methods based on optimization can greatly assist computational engineering design in many areas. In this paper an optimization approach to the magnetic design of a nuclear fusion reactor divertor is proposed and applied to a tokamak edge magnetic configuration in a first feasibility study. The approach is based on reduced models for magnetic field and plasma edge, which are integrated with a grid generator into one sensitivity code. The design objective chosen here for demonstrative purposes is to spread the divertor target heat load as much as possible over the entire target area. Constraints on the separatrix position are introduced to eliminate physically irrelevant magnetic field configurations during the optimization cycle. A gradient projection method is used to ensure stable cost function evaluations during optimization. The concept is applied to a configuration with typical Joint European Torus (JET) parameters and it automatically provides plausible configurations with reduced heat load.
Preparation of the liquid lithium divertor plates for NSTX
Nygren, R. E.; McKee, G. R.; Fordham, J. A.; Lewis, S. A.; Kugel, H.; Ellis, R. A.; Viola, M. E.; O'Dell, J. S.
2011-10-01
Each of the four toroidal panels of the liquid lithium divertor being installed in NSTX for operation in the 2010 campaign is a conical section inclined at 22° like the previous graphite divertor tiles. Each panel is a copper plate clad with stainless steel and a surface layer of porous plasma sprayed molybdenum (Mo) that will host lithium deposited from an evaporator. This paper describes the processes in fabrication; these include cutting to rough shape, die pressing into conical sections, machining to near final shape with holes for electrical heaters, thermocouples and a groove for a cooling tube, brazing of the 0.25-mm cladding and vacuum plasma spraying of the Mo coating.
Spectroscopic Characterizations of the DIII--D Divertor
Isler, R. C.; Klepper, C. C.; Wood, R. D.; Fenstermacher, M. E.; Leonard, A. W.
1996-11-01
Radiative losses from the DIII--D divertor have been characterized for various types of discharges by making extensive use of vacuum ultraviolet spectral lines in conjunction with a collisional-radiative model. Carbon and hydrogen account for essentially all the emission with the carbon fraction usually between 50% and 80% of the total. Ion densities are estimated from a simplified approach to modeling using a one-dimensional transport code. The concentrations range from 2%--6% of the electron density in partially detached plasmas, but it appears that carbon may supply most of the electrons in the divertor in attached plasmas. Ion temperatures are measured from Doppler broadening of spectral lines after accounting precisely for the Zeeman/Paschen-Back effect. In general, the ion temperatures agree well with the electron temperatures at the location of the radiating ions as deduced from spectral line ratio measurements and from the modeling.
Metzler, Ralf; Jeon, Jae-Hyung; Cherstvy, Andrey G; Barkai, Eli
2014-11-28
Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.
Progress of ITER full tungsten divertor technology qualification in Japan
Energy Technology Data Exchange (ETDEWEB)
Ezato, K., E-mail: ezato.koichiro@jaea.go.jp [Japan Atomic Energy Agency, 801-1, Mukoyma, Naka-shi, Ibaraki (Japan); Suzuki, S.; Seki, Y.; Mohri, K.; Yokoyama, K. [Japan Atomic Energy Agency, 801-1, Mukoyma, Naka-shi, Ibaraki (Japan); Escourbiac, F.; Hirai, T. [ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France); Kuznetcov, V. [NIIEFA, 3 doroga na Metallostroy, Metallostroy, St. Petersburg 196641 (Russian Federation)
2015-10-15
Highlights: • JAEA has demonstrated tungsten monoblock technology for ITER divertor that needs to withstand the repetitive heat load as high as 20 MW/m{sup 2}. This includes as follows; • Bonding technologies between W and Cu interlayer, and between Cu interlayer and CuCrZr tube. • Non-destructive examination techniques, especially, ultrasonic testing method, and. • Load carrying capability of W monoblock attachment to support structure of ITER divertor. - Abstract: Japan Atomic Energy Agency (JAEA) is in progress for technology qualification toward full-tungsten (W) ITER divertor outer vertical target (OVT), especially, tungsten monoblock technology that needs to withstand the repetitive heat load as high as 20 MW/m{sup 2}. To demonstrate the armor heat sink bonding technology and heat removal capability, 6 small-scale W monoblock mock-ups manufactured by different bonding technologies using different W materials in addition to 4 full-scale prototype plasma-facing units (PFUs). After non-destructive test, the W components were tested under high heat flux (HHF) in ITER Divertor Test Facility (IDTF) at NIIEFA. Consequently, all of the W monoblocks endured the repetitive heat load at 20 MW/m{sup 2} for 1000 cycles (requirements 20 MW/m{sup 2} for 300 cycles) without any failure. In addition to the armor to heat sink joints, the load carrying capability test on the W monoblock with a leg attachment was carried out. In uniaxial tensile test, all of the W monoblock attachments with different bonding technologies such as brazing and HIPping withstand the tensile load exceeding 20 kN that is the value more than twice the design value. The failures occurred at the leg attachments or the W monoblocks, rather than the bonding interface of the W monoblocks to the leg attachment.
Comparative studies of inner and outer divertor discharges and a fueling study in QUEST
Energy Technology Data Exchange (ETDEWEB)
Mitarai, O., E-mail: omitarai@ktmail.tokai-u.jp [Kumamoto Liberal Arts Education Center, Tokai University, 9-1-1 Toroku, Higashi-ku, Kumamoto 862-8652 (Japan); Nakamura, K.; Hasegawa, M.; Onchi, T.; Idei, H.; Fujisawa, A.; Hanada, K.; Zushi, H.; Higashijima, A.; Nakashima, H.; Kawasaki, S. [Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasugakoen, Kasuga 816-8580 Japan (Japan); Matsuoka, K. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292 (Japan); Koike, S.; Takahashi, T. [Division of Electronics and Informatics, Faculty of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515 (Japan); Tsutsui, H. [Research Laboratory for Nuclear Reactors, Tokyo Inst. Tech, 2-12-1 Ookayama, Tokyo 152-8550 (Japan)
2016-11-01
Highlights: • Central solenoid has a small flux in QUEST. • Large plasma current is obtained when the position is shifted to the inboard side. • Two types of divertor operation are compared. • Novel merging fueling methods are proposed. • Coaxial helicity injection (CHI) fueling was examined in QUEST divertor configuration. - Abstract: As QUEST has a small central solenoid (CS), a larger Ohmic discharge current has been obtained when the plasma shifts to the inboard side. This tendency restricts a divertor operation to the smaller plasma current regime. As the inner divertor coil has a smaller mutual inductance, it would be expected that its utilization seems to be better for easier plasma current ramp-up for a divertor operation. In this work, we made comparative studies on the plasma current ramp-up for two divertor coils. It is found that while the inner divertor coil with smaller mutual inductance needs a larger coil current, the outer divertor coil with larger mutual inductance needs a smaller coil current for divertor operation. Thus we have found that the plasma current ramp-up characteristics are almost similar for both configurations. We also propose a new fueling method for spherical tokamak (ST) using the coaxial helicity injection (CHI). The main plasma current would be generated at first, and then the CHI plasma current is created between bottom two electrode plates and merged into the main plasma current for fueling.
Influence of helium puff on divertor asymmetry in experimental advanced superconducting tokamak
DEFF Research Database (Denmark)
Liu, S. C.; Guo, H. Y.; Xu, G. S.
2014-01-01
Divertor asymmetries with helium puffing are investigated in various divertor configurations on Experimental Advanced Superconducting Tokamak (EAST). The outer divertor electron temperature decreases significantly during the gas injection at the outer midplane. As soon as the gas is injected......; the power deposition increases slightly at the outer targets while shows no obvious variation at the inner targets in double null configuration. The radiated power measured by the extreme ultraviolet arrays increases significantly due to helium gas injection, especially in the outer divertor. The edge...
L-H power threshold studies with tungsten/carbon divertor on the EAST tokamak
DEFF Research Database (Denmark)
Chen, L.; Xu, G. S.; Gao, W.
2016-01-01
The power threshold for low (L) to high (H) confinement mode transition achieved by radio-frequency heating and molybdenum first wall with lithium coating has been experimentally investigated on the EAST tokamak for two sets of divertor geometries and materials: tungsten/carbon divertor and full...... configuration, with the ion grad-B drift direction away from the primary X-point, a lower normalized power threshold is observed in EAST with the tungsten/carbon divertor, compared to the carbon divertor after intensive lithium wall coating. A newly installed cryopump increasing the pumping efficiency also...
Hybrid formulation of radiation transport in optically thick divertor plasmas
Energy Technology Data Exchange (ETDEWEB)
Rosato, J.; Marandet, Y.; Bufferand, H.; Stamm, R. [PIIM, UMR 7345 Aix-Marseille Universite / CNRS, Centre de St-Jerome, Marseille (France); Reiter, D. [IEK-4 Plasmaphysik, Forschungszentrum Juelich GmbH, Juelich (Germany)
2016-08-15
Kinetic Monte Carlo simulations of coupled atom-radiation transport in optically thick divertor plasmas can be computationally very demanding, in particular in ITER relevant conditions or even larger devices, e.g. for power plant divertor studies. At high (∝ 10{sup 15} cm{sup -3}) atomic densities, it can be shown that sufficiently large divertors behave in certain areas like a black body near the first resonance line of hydrogen (Lyman α). This suggests that, at least in part, the use of continuum model (radiation hydrodynamics) can be sufficiently accurate, while being less time consuming. In this work, we report on the development of a hybrid model devoted to switch automatically between a kinetic and a continuum description according to the plasma conditions. Calculations of the photo-excitation rate in a homogeneous slab are performed as an illustration. The outlined hybrid concept might be also applicable to neutral atom transport, due to mathematical analogy of transport equations for neutrals and radiation. (copyright 2016 The Authors. Contributions to Plasma Physics published by Wiley-VCH Verlag GmbH and Co. KGaA Weinheim. This)
An Exploration of Advanced X-Divertors on ITER
Covele, Brent; Kotschenreuther, Mike; Mahajan, Swadesh
2013-01-01
It is found that the X-Divertor (XD) configuration [1-3] can be made with the conventional PF coil set on ITER[4], where all PF coils are outside the TF coils. Desirable configurations are possible where the PF currents are below the present maximum design limits on ITER, and where the baseline divertor cassette is used. It is possible that the XD could be used to assist in high-power operation on ITER, but some further issues need examination. Note that the increased major radius of the Super X-Divertor (SXD) [5-8] is not a feature of the XD geometry. In addition, we present an XD configuration for K-DEMO [9], to demonstrate that it is also possible to attain the XD configuration in advanced tokamak reactors with all PF coils outside the TF coils. The results given here for the XD are far more encouraging than recent calculations by Lackner and Zohm [10] for the Snowflake [11,12], where the required high PF currents represent a major technological challenge. The magnetic field structure in the outboard diver...
Automated magnetic divertor design for optimal power exhaust
Energy Technology Data Exchange (ETDEWEB)
Blommaert, Maarten
2017-07-01
The so-called divertor is the standard particle and power exhaust system of nuclear fusion tokamaks. In essence, the magnetic configuration hereby 'diverts' the plasma to a specific divertor structure. The design of this divertor is still a key issue to be resolved to evolve from experimental fusion tokamaks to commercial power plants. The focus of this dissertation is on one particular design requirement: avoiding excessive heat loads on the divertor structure. The divertor design process is assisted by plasma edge transport codes that simulate the plasma and neutral particle transport in the edge of the reactor. These codes are computationally extremely demanding, not in the least due to the complex collisional processes between plasma and neutrals that lead to strong radiation sinks and macroscopic heat convection near the vessel walls. One way of improving the heat exhaust is by modifying the magnetic confinement that governs the plasma flow. In this dissertation, automated design of the magnetic configuration is pursued using adjoint based optimization methods. A simple and fast perturbation model is used to compute the magnetic field in the vacuum vessel. A stable optimal design method of the nested type is then elaborated that strictly accounts for several nonlinear design constraints and code limitations. Using appropriate cost function definitions, the heat is spread more uniformly over the high-heat load plasma-facing components in a practical design example. Furthermore, practical in-parts adjoint sensitivity calculations are presented that provide a way to an efficient optimization procedure. Results are elaborated for a fictituous JET (Joint European Torus) case. The heat load is strongly reduced by exploiting an expansion of the magnetic flux towards the solid divertor structure. Subsequently, shortcomings of the perturbation model for magnetic field calculations are discussed in comparison to a free boundary equilibrium (FBE) simulation
Investigations on the heat flux and impurity for the HL-2M divertor
Zheng, G. Y.; Cai, L. Z.; Duan, X. R.; Xu, X. Q.; Ryutov, D. D.; Cai, L. J.; Liu, X.; Li, J. X.; Pan, Y. D.
2016-12-01
The controllability of the heat load and impurity in the divertor is very important, which could be one of the critical problems to be solved in order to ensure the success for a steady state tokamak. HL-2M has the advantage of the poloidal field (PF) coils placed inside the demountable toroidal field (TF) coils and close to the main plasma. As a result, it is possible to make highly accurate configuration control of the advanced divertor for HL-2M. The divertor target geometry of HL-2M has been designed to be compatible with different divertor configurations to study the divertor physics and support the high performance plasma operations. In this paper, the heat loads and impurities with different divertor configurations, including the standard X-point divertor, the snowflake-minus divertor and two tripod divertor configurations for HL-2M, are investigated by numerical simulations with the SOLPS5.0 code under the current design of the HL-2M divertor geometry. The plasmas with different conditions, such as the low discharge parameters with {{I}\\text{p}} = 0.5 MA at the first stage of HL-2M and the high parameters with {{I}\\text{p}} = 2.0 MA during the normal operations, are simulated. The heat load profiles and the impurity distributions are obtained, and the control of the peak heat load and the effect of impurity on the core plasma are discussed. The compatibility of different divertor configurations for HL-2M is also evaluated. It is seen that the excellent compatibility of different divertor configurations with the current divertor geometry has been verified. The results show that the snowflake-minus divertor and the tripod divertor with {{d}x}=30 \\text{cm} present good performance in terms of the heat load profiles and the impurity distributions under different conditions, which may not have a big effect on the core plasma. In addition, it is possible to optimize the distance between the two X-points, {{d}x} , to achieve a better
Jennings, Robert C; Zucchelli, Giuseppe
2014-01-01
We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero.
Design study of JT-60SA divertor for high heat and particle controllability
Energy Technology Data Exchange (ETDEWEB)
Kawashima, H. [Japan Atomic Energy Agency, 801-1, Mukoyama, Naka-shi, Ibaraki-ken 311-0193 (Japan)], E-mail: kawashima.hisato@jaea.go.jp; Shimizu, K.; Takizuka, T.; Asakura, N.; Sakurai, S.; Matsukawa, M.; Fujita, T. [Japan Atomic Energy Agency, 801-1, Mukoyama, Naka-shi, Ibaraki-ken 311-0193 (Japan)
2008-12-15
The modification of JT-60 to a fully superconducting coil tokamak, JT-60SA (JT-60 Super Advanced) device, has been programmed to contribute and supplement ITER toward to DEMO. Lower divertor design with the ITER-like lower single null divertor configuration is studied to obtain high heat and particle controllability using SOLDOR/NEUT2D code. With anticipated total power flux into SOL of 37 MW (90% of input power), the peak heat load on outer divertor target can be reduced to 5.8 MW/m{sup 2} at the detached condition by gas puffing in the vertical divertor target with the 'V-shaped corner'. It is {approx}2/5 of the allowable level of 15 MW/m{sup 2}. On the other hand, particle controllability such as control of detached to attached condition by divertor pumping is improved by increase the strike point distance from 20 to 120 mm with above divertor geometry, suggesting that recover from severe detachment at the small distance case can be achieving by elevation of the strike point locations. Optimization of upper divertor design is in progress for high {beta} steady-state operation using upper single null divertor configuration.
Investigation of scrape-off layer and divertor heat transport in ASDEX Upgrade L-mode
Sieglin, B.; Eich, T.; Faitsch, M.; Herrmann, A.; Scarabosio, A.; the ASDEX Upgrade Team
2016-05-01
Power exhaust is one of the major challenges for the development of a fusion power plant. Predictions based upon a multimachine database give a scrape-off layer power fall-off length {λq}≤slant 1 mm for large fusion devices such as ITER. The power deposition profile on the target is broadened in the divertor by heat transport perpendicular to the magnetic field lines. This profile broadening is described by the power spreading S. Hence both {λq} and S need to be understood in order to estimate the expected divertor heat load for future fusion devices. For the investigation of S and {λq} L-Mode discharges with stable divertor conditions in hydrogen and deuterium were conducted in ASDEX Upgrade. A strong dependence of S on the divertor electron temperature and density is found which is the result of the competition between parallel electron heat conductivity and perpendicular diffusion in the divertor region. For high divertor temperatures it is found that the ion gyro radius at the divertor target needs to be considered. The dependence of the in/out asymmetry of the divertor power load on the electron density is investigated. The influence of the main ion species on the asymmetric behaviour is shown for hydrogen, deuterium and helium. A possible explanation for the observed asymmetry behaviour based on vertical drifts is proposed.
Particle and power deposition on divertor targets in EAST H-mode plasmas
DEFF Research Database (Denmark)
Wang, L.; Xu, G.S.; Guo, H.Y.
2012-01-01
The effects of edge-localized modes (ELMs) on divertor particle and heat fluxes were investigated for the first time in the Experimental Advanced Superconducting Tokamak (EAST). The experiments were carried out with both double null and lower single null divertor configurations, and comparisons w...
Geometry and expected performance of the solid tungsten outer divertor row in JET
Rapp, J.; Pintsuk, G.; Mertens, P.; Altmann, H.; Lomas, P. J.; Riccardo, V.
2010-01-01
At JET new plasma-facing components for the main chamber wall and the divertor are being designed and built to mimic the expected ITER plasma wall conditions in the deuterium-tritium operation phase. The main wall elements at JET will be made of beryllium and the divertor plasma-facing surface will
Yilmaz, Ferkan
2012-06-01
Ergodic capacity is an important performance measure associated with reliable communication at the highest rate at which information can be sent over the channel with a negligible probability of error. In the shadow of this definition, diversity receivers (such as selection combining, equal-gain combining and maximal-ratio combining) and transmission techniques (such as cascaded fading channels, amplify-and-forward multihop transmission) are deployed in mitigating various performance impairing effects such as fading and shadowing in digital radio communication links. However, the exact analysis of ergodic capacity is in general not always possible for all of these forms of diversity receivers and transmission techniques over generalized composite fading environments due to it\\'s mathematical intractability. In the literature, published papers concerning the exact analysis of ergodic capacity have been therefore scarce (i.e., only [1] and [2]) when compared to those concerning the exact analysis of average symbol error probability. In addition, they are essentially targeting to the ergodic capacity of the maximal ratio combining diversity receivers and are not readily applicable to the capacity analysis of the other diversity combiners / transmission techniques. In this paper, we propose a novel moment generating function-based approach for the exact ergodic capacity analysis of both diversity receivers and transmission techniques over generalized composite fading environments. As such, we demonstrate how to simultaneously treat the ergodic capacity analysis of all forms of both diversity receivers and multihop transmission techniques. © 2012 IEEE.
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Generators f for σ -algebras can be used to view the dynamics of an invertible measurable transformation T in terms of the range values of f ∘ T . Such generators are the norm rather than the exception. Related measurable and quantitative methods of estimating a function from the behavior of ergodic averages are also discussed.
Novel relations between the ergodic capacity and the average bit error rate
Yilmaz, Ferkan
2011-11-01
Ergodic capacity and average bit error rate have been widely used to compare the performance of different wireless communication systems. As such recent scientific research and studies revealed strong impact of designing and implementing wireless technologies based on these two performance indicators. However and to the best of our knowledge, the direct links between these two performance indicators have not been explicitly proposed in the literature so far. In this paper, we propose novel relations between the ergodic capacity and the average bit error rate of an overall communication system using binary modulation schemes for signaling with a limited bandwidth and operating over generalized fading channels. More specifically, we show that these two performance measures can be represented in terms of each other, without the need to know the exact end-to-end statistical characterization of the communication channel. We validate the correctness and accuracy of our newly proposed relations and illustrated their usefulness by considering some classical examples. © 2011 IEEE.
Ergodicity of one-dimensional systems coupled to the logistic thermostat
Tapias, Diego; Sanders, David P
2016-01-01
We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum with respect to initial conditions; the absence of visual "holes" in two-dimensional Poincar\\'e sections; the agreement between the histograms in each variable and the theoretical marginal distributions; and the convergence of the global joint distribution to the theoretical one, as measured by the Hellinger distance. Taking a large number of random initial conditions, for certain parameter values of the thermostat we find no indication of regular trajectories and show that the time distribution converges to the ensemble one for an arbitrarily long trajectory for all the systems considered. Our results thus provide a robust numerical indication that the logistic thermostat can serve as a single one-parameter thermostat for stiff one-dimensional systems.
Institute of Scientific and Technical Information of China (English)
2008-01-01
We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection.The existence criterion of the process is firstly considered.We prove that if the sum of the resurrection rates is finite,then there does not exist any process.An existence criterion is then established when the sum of the resurrection rates is infinite.Some equivalent criteria,possessing the advantage of being easily checked,are obtained for the latter case.The uniqueness criterion for such process is also investigated.We prove that although there exist infinitely many of them,there always exists a unique honest process for a given q-matrix.This unique honest process is then constructed.The ergodicity property of this honest process is analysed in detail.We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.
Institute of Scientific and Technical Information of China (English)
LI JunPing; CHEN AnYue
2008-01-01
We consider a modified Markov branching process incorporating with both stateindependent immigration and instantaneous resurrection. The existence criterion of the process is firstly considered. We prove that if the sum of the resurrection rates is finite, then there does not exist any process. An existence criterion is then established when the sum of the resurrection rates is infinite.Some equivalent criteria, possessing the advantage of being easily checked, are obtained for the latter case. The uniqueness criterion for such process is also investigated. We prove that although there exist infinitely many of them, there always exists a unique honest process for a given q-matrix. This unique honest process is then constructed. The ergodicity property of this honest process is analysed in detail.We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.
On Ergodic Secrecy Capacity of Multiple Input Wiretap Channel with Statistical CSIT
Lin, Shih-Chun
2012-01-01
We consider the secure transmission in ergodic fast-Rayleigh fading multiple-input single-output single-antennaeavesdropper (MISOSE) wiretap channels. We assume that the statistics of both the legitimate and eavesdropper channels is the only available channel state information at the transmitter (CSIT). By introducing a new secrecy capacity upper bound, we prove that the secrecy capacity is achieved by Gaussian input without prefixing. To attain this, we form another MISOSE channel for upper-bounding, and tighten the bound by finding the worst correlations between the legitimate and eavesdropper channel coefficients. The resulting upper bound is tighter than the others in the literature which are based on modifying the correlation between the noises at the legitimate receiver and eavesdropper. Next, we fully characterize the ergodic secrecy capacity by showing that the optimal channel input covariance matrix is a scaled identity matrix, with the transmit power allocated uniformly among the antennas. The key t...
Novel Relations between the Ergodic Capacity and the Average Bit Error Rate
Yilmaz, Ferkan
2012-01-01
Ergodic capacity and average bit error rate have been widely used to compare the performance of different wireless communication systems. As such recent scientific research and studies revealed strong impact of designing and implementing wireless technologies based on these two performance indicators. However and to the best of our knowledge, the direct links between these two performance indicators have not been explicitly proposed in the literature so far. In this paper, we propose novel relations between the ergodic capacity and the average bit error rate of an overall communication system using binary modulation schemes for signaling with a limited bandwidth and operating over generalized fading channels. More specifically, we show that these two performance measures can be represented in terms of each other, without the need to know the exact end-to-end statistical characterization of the communication channel. We validate the correctness and accuracy of our newly proposed relations and illustrated their...
Existence of the optimal measurable coupling and ergodicity for Markov processes
Institute of Scientific and Technical Information of China (English)
张绍义
1999-01-01
The existence theorem of the optimal measurable coupling of two probability kernels on a complete separable metric measurable space is proved. Then by this theorem, a general ergodicity theorem for Markov processes is obtained. And as an immediate application to particle systems the uniqueness theorem of the stationary distribution is supplemented, i.e. the uniqueness theorem also implies the existence of the stationary distribution.
New ergodic convergence theorems for non-expansive mappings and m-accretive mappings
Directory of Open Access Journals (Sweden)
Li Wei
2016-01-01
Full Text Available Abstract Two new ergodic convergence theorems for approximating the common element of the set of zero points of an m-accretive mapping and the set of fixed points of an infinite family of non-expansive mappings in a real smooth and uniformly convex Banach space are obtained, which improves some of the previous work. The computational experiments to demonstrate the effectiveness of the proposed iterative algorithms in this paper are conducted.
Ergodic Actions of Convergent Fuchsian groups on quotients of the noncommutative Hardy algebras
Arias, Alvaro
2010-01-01
We establish that particular quotients of the non-commutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group $\\operatorname*{SU}(n,1)$ of automorphisms of the unit ball in $\\mathbb{C}% ^{n}$. To do so, we provide a mean to compute the spectra of quotients of noncommutative Hardy algebra and characterize their automorphisms in term of biholomorphic maps of the unit ball in $\\mathbb{C}^{n}$.
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
von Neumann, John
2010-01-01
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
Kolb, Martin; Wubker, Achim
2011-01-01
We analyze the large time behavior of a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. It is shown, that under weak conditions this degenerate diffusion process is strong mixing, confirming a conjecture of Grothaus and Klar. Moreover, under some additional assumptions even geometric ergodicity is established using probabilistic tools -- described in the book of Meyn and Tweedie -- in combination with methods from stochastic analysis.
A new fuzzy Monte Carlo method for solving SLAE with ergodic fuzzy Markov chains
Directory of Open Access Journals (Sweden)
Maryam Gharehdaghi
2015-05-01
Full Text Available In this paper we introduce a new fuzzy Monte Carlo method for solving system of linear algebraic equations (SLAE over the possibility theory and max-min algebra. To solve the SLAE, we first define a fuzzy estimator and prove that this is an unbiased estimator of the solution. To prove unbiasedness, we apply the ergodic fuzzy Markov chains. This new approach works even for cases with coefficients matrix with a norm greater than one.
DEFF Research Database (Denmark)
Truelsen, Jimi Lee
W. Luo and P. Sarnak have proved quantum unique ergodicity for Eisenstein series on $PSL(2,Z) \\backslash H$. We extend their result to Eisenstein series on $PSL(2,O) \\backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, using...... the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms....
Statistical Inference for Ergodic Point Processes and Application to Limit Order Book
Clinet, Simon; Yoshida, Nakahiro
2015-01-01
We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model belongs to a family of processes indexed by a finite dimensional parameter. When a particular family of laws of large numbers applies to those processes, we establish the consistency, the asymptotic normality and the convergence of moments of both the Quasi Maxim...
Ergodic averages for monotone functions using upper and lower dominating processes
DEFF Research Database (Denmark)
Møller, Jesper; Mengersen, Kerrie
2007-01-01
We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary ...... methods are studied in detail for three models using Markov chain Monte Carlo methods and we also discuss various types of other models for which our methods apply.......We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary...... Markov chain and we eliminate the problem of whether an appropriate burn-in is determined or not. Moreover, when a central limit theorem applies, we show how confidence intervals for the mean can be estimated by bounding the asymptotic variance of the ergodic average based on the equilibrium chain. Our...
Ergodic averages for monotone functions using upper and lower dominating processes
DEFF Research Database (Denmark)
Møller, Jesper; Mengersen, Kerrie
We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary ...... methods are studied in detail for three models using Markov chain Monte Carlo methods and we also discuss various types of other models for which our methods apply.......We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary...... Markov chain and we eliminate the problem of whether an appropriate burn-in is determined or not. Moreover, when a central limit theorem applies, we show how confidence intervals for the mean can be estimated by bounding the asymptotic variance of the ergodic average based on the equilibrium chain. Our...
Ergodic and Outage Performance of Fading Broadcast Channels with 1-Bit Feedback
Niu, Bo; Somekh, Oren; Haimovich, Alexander M
2010-01-01
In this paper, the ergodic sum-rate and outage probability of a downlink single-antenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1-bit feedback per fading block per user is available at the base station. We first study the ergodic sum-rate of the 1-bit feedback scheme, and consider the impact of feedback delay on the system. A closed-form expression for the achievable ergodic sum-rate is presented as a function of the fading temporal correlation coefficient. It is proved that the sum-rate scales as loglogK, which is the same scaling law achieved by the optimal non-delayed full CSI feedback scheme. The sum-rate degradation due to outdated CSI is also evaluated in the asymptotic regimes of either large K or low SNR. The outage performance of the 1-bit feedback scheme for both instantaneous and outdated feedback is then investigated. Expressions for the outage probabilities are derived, along w...
Directory of Open Access Journals (Sweden)
Bahrami Hamid Reza
2007-01-01
Full Text Available The ergodic capacity of MIMO frequency-flat and -selective channels depends greatly on the eigenvalue distribution of spatial correlation matrices. Knowing the eigenstructure of correlation matrices at the transmitter is very important to enhance the capacity of the system. This fact becomes of great importance in MIMO wireless systems where because of the fast changing nature of the underlying channel, full channel knowledge is difficult to obtain at the transmitter. In this paper, we first investigate the effect of eigenvalues distribution of spatial correlation matrices on the capacity of frequency-flat and -selective channels. Next, we introduce a practical scheme known as linear precoding that can enhance the ergodic capacity of the channel by changing the eigenstructure of the channel by applying a linear transformation. We derive the structures of precoders using eigenvalue decomposition and linear algebra techniques in both cases and show their similarities from an algebraic point of view. Simulations show the ability of this technique to change the eigenstructure of the channel, and hence enhance the ergodic capacity considerably.
Two Notes on Measure-Theoretic Entropy of Random Dynamical Systems
Institute of Scientific and Technical Information of China (English)
YuJun ZHU
2009-01-01
In this paper, Brin-Katok local entropy formula and Katok's definition of the measure theoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
SOLPS modeling of the effect on plasma detachment of closing the lower divertor in DIII-D
Sang, C. F.; Stangeby, P. C.; Guo, H. Y.; Leonard, A. W.; Covele, B.; Lao, L. L.; Moser, A. L.; Thomas, D. M.
2017-02-01
Scrape-off layer plasma simulation modeling has been carried out to assess the effect of tightly closing the lower divertor in DIII-D, which at present is almost fully open, on the achievement of cold dissipative/detached divertor conditions. To isolate the impact of other factors on the divertor plasma solution and to make direct comparisons, most of the parameters including the meshes were kept as similar as possible. Only the neutral baffling was modified to compare a fully open divertor with a tightly closed one. The modeling shows that the tightly closed divertor greatly improves trapping of recycling neutrals, thereby increasing radiative and charge exchange losses in the divertor and reducing the electron temperature T et and deposited power density q dep at the target plate. Furthermore, the closed structure enables the divertor plasma to enter into highly dissipative and detached divertor conditions at a significantly lower upstream density. The effects of divertor closure on the neutral density and pressure, and their correlation with the divertor plasma conditions are also demonstrated. The effect of molecular D2-ion D+ elastic collisions and neutral-neutral collisions on the divertor plasma solution are assessed.
Allen, S. L.; Boedo, J. A.; Bozek, A. S.; Brooks, N. H.; Carlstrom, T. N.; Casper, T. A.; Colchin, R. J.; Evans, T. E.; Fenstermacher, M. E.; Friend, M. E.; Isler, R. C.; Jayakumar, R.; Lasnier, C. J.; Leonard, A. W.; Mahdavi, M. A.; Maingi, R.; McKee, G. R.; Moyer, R. A.; Murakami, M.; Osborne, T. H.; O'Neill, R. C.; Petrie, T. W.; Porter, G. D.; Ramsey, A. T.; Schaffer, M. J.; Stangeby, P. C.; Stambaugh, R. D.; Wade, M. R.; Watking, J. G.; West, W. P.; Whyte, D. G.; Wolf, N. S.
2001-03-01
We present the results from DIII-D experiments and modeling focused on the divertor issues of an `Advanced Tokamak' (AT). Operation at high plasma pressure β with good energy confinement H requires core and divertor plasma shaping and current profile J( r) control with ECH current drive. Transport modeling indicates that the available DIII-D ECH power determines a density and temperature regime for sustained DIII-D AT experiments. We demonstrate that a high-δ, unbalanced double null divertor with cryopumping (D-2000) is a flexible AT divertor. Impurity levels in AT experiments have been reduced by careful alignment of the divertor tiles; this, in turn has changed the time evolution of the core J( r) profiles. New physics has been observed near the X-point and private flux regions, including flow reversal and recombination, that is important in understanding and controlling the flows and thereby the radiation in the divertor region, which reduces the divertor heat flux.
Surface heat loads on the ITER divertor vertical targets
Gunn, J. P.; Carpentier-Chouchana, S.; Escourbiac, F.; Hirai, T.; Panayotis, S.; Pitts, R. A.; Corre, Y.; Dejarnac, R.; Firdaouss, M.; Kočan, M.; Komm, M.; Kukushkin, A.; Languille, P.; Missirlian, M.; Zhao, W.; Zhong, G.
2017-04-01
The heating of tungsten monoblocks at the ITER divertor vertical targets is calculated using the heat flux predicted by three-dimensional ion orbit modelling. The monoblocks are beveled to a depth of 0.5 mm in the toroidal direction to provide magnetic shadowing of the poloidal leading edges within the range of specified assembly tolerances, but this increases the magnetic field incidence angle resulting in a reduction of toroidal wetted fraction and concentration of the local heat flux to the unshadowed surfaces. This shaping solution successfully protects the leading edges from inter-ELM heat loads, but at the expense of (1) temperatures on the main loaded surface that could exceed the tungsten recrystallization temperature in the nominal partially detached regime, and (2) melting and loss of margin against critical heat flux during transient loss of detachment control. During ELMs, the risk of monoblock edge melting is found to be greater than the risk of full surface melting on the plasma-wetted zone. Full surface and edge melting will be triggered by uncontrolled ELMs in the burning plasma phase of ITER operation if current models of the likely ELM ion impact energies at the divertor targets are correct. During uncontrolled ELMs in pre-nuclear deuterium or helium plasmas at half the nominal plasma current and magnetic field, full surface melting should be avoided, but edge melting is predicted.
On the W7-X divertor performance under detached conditions
Feng, Y.; Beidler, C. D.; Geiger, J.; Helander, P.; Hölbe, H.; Maassberg, H.; Turkin, Y.; Reiter, D.; W7-X Team
2016-12-01
We present a theoretical/numerical predictive analysis of the performance of the W7-X island divertor under conditions of detachment characterized by intensive radiation. The analysis is based on EMC3-Eirene simulations and the earlier W7-AS experimental and numerical experience. Carbon is employed as a representative radiator. The associated drawbacks, i.e. core contamination and recycling degradation (reduced recycling flux), are evaluated by determining the carbon density at the last closed flux surface (LCFS) and the neutral pressure in the divertor chamber. Optimum conditions are explored in both configuration and plasma parameter space. This study aims to identify the key geometric/magnetic and plasma parameters that affect the performance of detached plasmas in W7-X. Emphasis is placed on what occurs when the islands are enlarged far beyond the maximum size available in W7-AS and whether an island size limit for optimal detachment operation exists, and why. Further issues addressed are the power removal ability of the W7-X edge islands, potentially limiting factors, compatibility between particle and power exhaust, and particle refueling capability of the recycling neutrals.
Spectroscopic characterization of the DIII-D divertor
Isler, R. C.; Wood, R. W.; Klepper, C. C.; Brooks, N. H.; Fenstermacher, M. E.; Leonard, A. W.
1997-02-01
Radiative losses along a fixed view into the divertor chamber of the DIII-D tokamak [Plasma Physics Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol I, p. 159] have been characterized for attached and partially detached discharges by analyzing line-integrated vacuum ultraviolet (VUV) signals. Essentially all the emission can be ascribed to carbon and deuterium. Because the majority of the most intense lines, which lie at wavelengths above 1100 Å, are not accessible to the present instrumentation, extensive use has been made of collisional-radiative (CR) calculations for level populations of the important ions in order to relate the total radiated power to shorter wavelength transitions. In beam-heated plasmas, the fraction of radiation detected from carbon along the VUV spectrometer view is usually between 50% and 80% of the total. Carbon densities are estimated from a simplified approach to modelling the emission using a one-dimensional transport code. For partially detached plasmas the concentrations range from 2%-6% of the electron density; but in attached plasmas it appears that carbon may supply most of the electrons in the divertor region just below the X point. Ion temperatures are measured from Doppler broadening of spectral lines by fitting measured profiles to theoretical lineshapes, which account precisely for atomic sublevel splitting caused by the Zeeman/Paschen-Back effect in the tokamak magnetic field.
An exploration of advanced X-divertor scenarios on ITER
Covele, B.; Valanju, P.; Kotschenreuther, M.; Mahajan, S.
2014-07-01
It is found that the X-divertor (XD) configuration (Kotschenreuther et al 2004 Proc. 20th Int. Conf. on Fusion Energy (Vilamoura, Portugal, 2004) (Vienna: IAEA) CD-ROM file [IC/P6-43] www-naweb.iaea.org/napc/physics/fec/fec2004/datasets/index.html, Kotschenreuther et al 2006 Proc. 21st Int. Conf. on Fusion Energy 2006 (Chengdu, China, 2006) (Vienna: IAEA), CD-ROM file [IC/P7-12] www-naweb.iaea.org/napc/physics/FEC/FEC2006/html/index.htm, Kotschenreuther et al 2007 Phys. Plasmas 14 072502) can be made with the conventional poloidal field (PF) coil set on ITER (Tomabechi et al and Team 1991 Nucl. Fusion 31 1135), where all PF coils are outside the TF coils. Starting from the standard divertor, a sequence of desirable XD configurations are possible where the PF currents are below the present maximum design limits on ITER, and where the baseline divertor cassette is used. This opens the possibility that the XD could be tested and used to assist in high-power operation on ITER, but some further issues need examination. Note that the increased major radius of the super-X-divertor (Kotschenreuther et al 2007 Bull. Am. Phys. Soc. 53 11, Valanju et al 2009 Phys. Plasmas 16 5, Kotschenreuther et al 2010 Nucl. Fusion 50 035003, Valanju et al 2010 Fusion Eng. Des. 85 46) is not a feature of the XD geometry. In addition, we present an XD configuration for K-DEMO (Kim et al 2013 Fusion Eng. Des. 88 123) to demonstrate that it is also possible to attain the XD configuration in advanced tokamak reactors with all PF coils outside the TF coils. The results given here for the XD are far more encouraging than recent calculations by Lackner and Zohm (2012 Fusion Sci. Technol. 63 43) for the Snowflake (Ryutov 2007 Phys. Plasmas 14 064502, Ryutov et al 2008 Phys. Plasmas 15 092501), where the required high PF currents represent a major technological challenge. The magnetic field structure in the outboard divertor SOL (Kotschenreuther 2013 Phys. Plasmas 20 102507) in the recently created
Improvement of the divertor bolometer diagnostic in the ASDEX Upgrade tokamak
Energy Technology Data Exchange (ETDEWEB)
Sehmer, Till; Meister, Hans; Bernert, Matthias; Koll, Juergen; Reimold, Felix; Wischmeier, Marco; Fantz, Ursel [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstr. 2, 85748 Garching (Germany); Collaboration: ASDEX Upgrade Team
2015-05-01
For future fusion devices such as ITER, the radiation balance in the divertor region will have a significant impact on the power exhaust balance. Therefore, scenarios with strongly localized radiation, like radiation in the high field side high density (HFSHD) region, X-Point radiation or radiation in the divertor legs during detachment, will be investigated in the next ASDEX Upgrade (AUG) operation campaign 2015. To obtain accurately the absolute divertor radiation out of these measurements, the AUG foil bolometer diagnostic system in the divertor region has been enhanced; two new cameras have been designed and manufactured. One will be mounted below the roof baffle and contains 28 lines of sight (LOS), which will observe the mentioned regions of particular physical interest. The second camera consists of 4 LOS and will be mounted at the high field side above the inner divertor nose. It will observe radiation arising from the X-Point region and from the outer divertor. The data will be analysed with a tomographic reconstruction algorithm to localize and quantify the divertor radiation.
Motivation and goals of the new heated outer divertor for Alcator C-Mod
Lipschultz, B.; Doody, J.; Ellis, R.; Granetz, R.; Harrison, S.; Labombard, B.; Vieira, R.; Zhang, H.; Zhou, L.
2012-10-01
A precision-aligned, high-temperature outer divertor is being developed for Alcator C-Mod to enhance heatflux handling and to advance our knowledge and experience with high-Z Plasma Facing Components (PFCs) in a reactor-level power density environment. Several departures from the design of the current divertor will be implemented: Instead of 10 toroidal divertor segments that expand toroidally as they heat up, the divertor plate will be toroidally continuous, with no openings or leading edges in the high-heat flux region. It will expand in the radial direction when heated while maintaining good alignment with shallow field line angles (˜ 2 degrees), a requirement for future divertors. Those characteristics will reduce both impurity sources and disruption forces. A second design goal is to be able to control the divertor temperature up to 600^oC by installing heaters in the structure. Given the Arrhenius relation between hydrogen diffusivity and temperature in tungsten (and molybdenum) this will open up a new area of study for tokamaks - exploration of the effect of PFC temperature on fuel retention. Temperature control may also open up a new area of study into the effect of changes in divertor recycling on fueling and core confinement.
Simulation of tokamak SOL and divertor region including heat flux mitigation by gas puffing
Park, Jin-Woo; Na, Yong-Su; Hong, Sang Hee; Ahn, Joon-Wook; Kim, Deok-Kyu; Han, Hyunsun; Shim, Seong Bo; Lee, Hae June
2012-08-01
Two-dimensional (2D), scrape-off layer (SOL)-divertor transport simulations are performed using the integrated plasma-neutral-impurity code KTRAN developed at Seoul National University. Firstly, the code is applied to reproduce a National Spherical Torus eXperiment (NSTX) discharge by using the prescribed transport coefficients and the boundary conditions obtained from the experiment. The plasma density, the heat flux on the divertor plate, and the D α emission rate profiles from the numerical simulation are found to follow experimental trends qualitatively. Secondly, predictive simulations are carried out for the baseline operation mode in Korea Superconducting Tokamak Advanced Research (KSTAR) to predict the heat flux on the divertor target plates. The stationary peak heat flux in the KSTAR baseline operation mode is expected to be 6.5 MW/m2 in the case of an orthogonal divertor. To study the mitigation of the heat flux, we investigated the puffing effects of deuterium and argon gases. The puffing position is assumed to be in front of the strike point at the outer lower divertor plate. In the simulations, mitigation of the peak heat flux at the divertor target plates is found to occur when the gas puffing rate exceeds certain values, ˜1.0 × 1020 /s and ˜5.0 × 1018 /s for deuterium and argon, respectively. Multi-charged impurity transport is also investigated for both NSTX and KSTAR SOL and divertor regions.
The WEST project: Current status of the ITER-like tungsten divertor
Energy Technology Data Exchange (ETDEWEB)
Missirlian, M., E-mail: marc.missirlian@cea.fr; Bucalossi, J.; Corre, Y.; Ferlay, F.; Firdaouss, M.; Garin, P.; Grosman, A.; Guilhem, D.; Gunn, J.; Languille, P.; Lipa, M.; Richou, M.; Tsitrone, E.
2014-10-15
Highlights: • We presented the ITER-like W components occurred for the WEST divertor. • The main features including key elements of the design were detailed. • The main results of studies investigating the integration constraints or issues were reported. • The WEST ITER-like divertor design reached a mature stage to enable the launching of the procurement phase. - Abstract: The WEST (W – for tungsten – Environment in Steady-state Tokamak) project is an upgrade of Tore Supra from a limiter based tokamak with carbon PFCs into an X-point divertor tokamak with full-tungsten armour while keeping its long discharge capability. The WEST project will primarily offer the key capability of testing for the first time the ITER technology in real plasma environment. In particular, the main divertor (i.e. the lower divertor) of the WEST project will be based on actively cooled tungsten monoblock components and will follow as closely as possible the design and the assembling technology, foreseen for the ITER divertor units. The current design of WEST ITER-like tungsten divertor has now reached a mature stage following the 2013 WEST Final Design Review. This paper presents the key elements of the design, reports the technological requirements and reviews the main design and integration issues.
Terry, J. L.; Reinke, M. L.
2017-04-01
Some of the key aspects of divertor detachment that are addressed by bolometry, impurity spectroscopy, hydrogen spectroscopy, and measurements of divertor target heat-flux are reviewed. Measurement requirements for these diagnostic areas are defined, and brief descriptions of the techniques used for these diagnostics are given. Examples from the literature of measurements using these tools applied to detachment are presented. Feedback control of detachment using some of these diagnostics as the ‘sensors’ is reviewed. Challenges and some future directions for these diagnostics in the context of studying divertor detachment are described.
A new approach to scaling of the scrape-off layer and divertor plasma in JET
Energy Technology Data Exchange (ETDEWEB)
Harbour, P.J.; Loarte, A.; Clement, S.; De Kock, L.; Jaeckel, H.J.; Lesourd, M.; O' Brien, D.P.; Summers, D.D.R.; Tagle, J.A. (JET Joint Undertaking, Abingdon (United Kingdom))
1992-12-01
An analytical model of the SOL/divertor magnetic geometry is applied to JET. Exponential decay lengths, [lambda], are related to differences in magnetic fluxes and are expressed in terms of [lambda] at midplane. Consistent values of [lambda] are usually obtained from Langmuir probes in the SOL or in the divertor, and with Lyman-[alpha] and Balmer-[alpha] profiles in the divertor. Scaling of [lambda] is presented: It is only slightly affected by
The global build-up to intrinsic ELM bursts seen in divertor full flux loops in Jet
Chapman, S C; Todd, T N; Watkins, N W; Calderon, F A; Morris, J; Contributors, JET
2015-01-01
A global signature of the build-up to an intrinsic ELM is found in the phase of signals measured in full flux azimuthal loops in the divertor region of JET. Full flux loop signals provide a global measurement proportional to the voltage induced by changes in poloidal magnetic flux; they are electromagnetically induced by the dynamics of spatially integrated current density. We perform direct time-domain analysis of the high time-resolution full flux loop signals VLD2 and VLD3. We analyze plasmas where a steady H-mode is sustained over several seconds, during which all the observed ELMs are intrinsic; there is no deliberate intent to pace the ELMing process by external means. ELM occurrence times are determined from the Be II emission at the divertor. We previously found that the occurrence times of intrinsic ELMs correlate with specific phases of the VLD2 and VLD3 signals. Here, we investigate how the VLD2 and VLD3 phases vary with time in advance of the ELM occurrence time. We identify a build-up to the ELM ...
One-dimensional XY model: Ergodic properties and hydrodynamic limit
Shuhov, A. G.; Suhov, Yu. M.
1986-11-01
We prove theorems on convergence to a stationary state in the course of time for the one-dimensional XY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps the XY dynamics onto a group of Bogoliubov transformations on the CAR C *-algebra over Z 1. The role of stationary states for Bogoliubov transformations is played by quasifree states and for the XY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensional XY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of "normal modes," which is described by a hyperbolic linear differential equation of second order. For the XX model this equation reduces to a first-order transfer equation.
Vapor shielding models and the energy absorbed by divertor targets during transient events
Energy Technology Data Exchange (ETDEWEB)
Skovorodin, D. I., E-mail: dskovorodin@gmail.com; Arakcheev, A. S. [Budker Institute of Nuclear Physics, Novosibirsk 630090 (Russian Federation); Pshenov, A. A.; Eksaeva, E. A.; Marenkov, E. D.; Krasheninnikov, S. I. [National Research Nuclear University MEPhI, Moscow 115409 (Russian Federation)
2016-02-15
The erosion of divertor targets caused by high heat fluxes during transients is a serious threat to ITER operation, as it is going to be the main factor determining the divertor lifetime. Under the influence of extreme heat fluxes, the surface temperature of plasma facing components can reach some certain threshold, leading to an onset of intense material evaporation. The latter results in formation of cold dense vapor and secondary plasma cloud. This layer effectively absorbs the energy of the incident plasma flow, turning it into its own kinetic and internal energy and radiating it. This so called vapor shielding is a phenomenon that may help mitigating the erosion during transient events. In particular, the vapor shielding results in saturation of energy (per unit surface area) accumulated by the target during single pulse of heat load at some level E{sub max}. Matching this value is one of the possible tests to verify complicated numerical codes, developed to calculate the erosion rate during abnormal events in tokamaks. The paper presents three very different models of vapor shielding, demonstrating that E{sub max} depends strongly on the heat pulse duration, thermodynamic properties, and evaporation energy of the irradiated target material. While its dependence on the other shielding details such as radiation capabilities of material and dynamics of the vapor cloud is logarithmically weak. The reason for this is a strong (exponential) dependence of the target material evaporation rate, and therefore the “strength” of vapor shield on the target surface temperature. As a result, the influence of the vapor shielding phenomena details, such as radiation transport in the vapor cloud and evaporated material dynamics, on the E{sub max} is virtually completely masked by the strong dependence of the evaporation rate on the target surface temperature. However, the very same details define the amount of evaporated particles, needed to provide an effective shielding
Stability and heating of a poloidal divertor tokamak
Energy Technology Data Exchange (ETDEWEB)
Biddle, A. P.; Dexter, R. N.; Holly, D. T.; Lipschultz, B.; Osborne, T. H.; Prager, S. C.; Shepard, D.A., Sprott, J.C.; Witherspoon, F. D.
1980-06-01
Five experimental studies - two stability and three heating investigations - have been carried out on Tokapole II, a Tokamak with a four node poloidal divertor. First, discharges have been attained with safety factor q as low as 0.6 over most of the column without degradation of confinement, and correlation of helical instability onset with current profile shape is being studied. Second, the axisymmetric instability has been investigated in detail for various noncircular cross-sectional shapes, and results have been compared with a numerical stability code adapted to the Tokapole machine. Third, application of high power fast wave ion cyclotron resonance heating doubles the ion temperature and permits observation of heating as a function of harmonic number and spatial location of the resonance. Fourth, low power shear Alfven wave propagation is underway to test the applicability of this heating method to tokamaks. Fifth, preionization by electron cyclotron heating has been employed to reduce the startup loop voltage by approx. 60%.
A snowflake divertor: a possible solution to the power exhaust problem for tokamaks
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Cohen, R. H.; Rognlien, T. D.; Umansky, M. V.
2012-11-21
This paper summarizes recent progress in the theory of a snowflake divertor, a possible path to reduce both steady-state and intermittent heat loads on the divertor plates to an acceptable level. The most important feature of a SF divertor is the presence of a large zone of a very weak poloidal magnetic field around the poloidal field (PF) null. Qualitative explanation of a variety of new features characteristic of a SF divertor is provided based on simple scaling relations. The main part of the paper is focused on the concept of spreading of the heat flux by curvature-driven convection near the PF null. References to experimental results from the NSTX and TCV tokamaks are provided.
A snowflake divertor: a possible solution to the power exhaust problem for tokamaks
Ryutov, D. D.; Cohen, R. H.; Rognlien, T. D.; Umansky, M. V.
2012-12-01
This paper summarizes recent progress in the theory of a snowflake divertor, a possible path to reduce both steady-state and intermittent heat loads on the divertor plates to an acceptable level. The most important feature of a SF divertor is the presence of a large zone of a very weak poloidal magnetic field around the poloidal field (PF) null. Qualitative explanation of a variety of new features characteristic of a SF divertor is provided based on simple scaling relations. The main part of the paper is focused on the concept of spreading of the heat flux by curvature-driven convection near the PF null. References to experimental results from the NSTX and TCV tokamaks are provided.
One dimensional simulation on stability of detached plasma in a tokamak divertor
Energy Technology Data Exchange (ETDEWEB)
Nakazawa, Shinji; Nakajima, Noriyoshi; Okamoto, Masao; Ohyabu, Nobuyoshi [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-06-01
The stability of radiation front in the Scrape-Off-Layer (SOL) of a tokamak is studied with a one dimensional fluid code; the time-dependent transport equations are solved in the direction parallel to a magnetic field line. The simulation results show that stable detached solutions exist, where the plasma temperature near the divertor target is {approx}2 eV. It is found that whenever such stable detached states are attained, the strong radiation front is contact with or at a small distance from the divertor target. When the energy externally injected into the SOL is decreased below a critical value, the radiation front starts to move towards the X-point, cooling the SOL plasma. In such cases, no stationary solutions such that the radiation front rests in the divertor channel are observed in our parameter space. This qualitatively corresponds to the results of tokamak divertor experiments which show the movement of radiation front. (author)
Comparison of JET main chamber erosion with dust collected in the divertor
Widdowson, A; Booth, S; Coad, J P; Hakola, A; Heinola, K; Ivanova, S; Koivuranta, S; Likonen, J; Mayer, M; Stamp, M; Contributors, JET-EFDA
2013-01-01
A complete global balance for carbon in JET requires knowledge of the net erosion in the main chamber, net deposition in the divertor and the amount of dust and flakes collecting in the divertor region. This paper describes a number of measurements on aspects of this global picture. Profiler measurements and cross section microscopy on tiles that were removed in the 2009 JET intervention are used to evaluate the net erosion in the main chamber and net deposition in the divertor. In addition the mass of dust and flakes collected from the JET divertor during the same intervention is also reported and included as part of the balance. Spectroscopic measurements of carbon erosion from the main chamber are presented and compared with the erosion measurements for the main chamber.
Development of heat sink concept for near-term fusion power plant divertor
Rimza, Sandeep; Khirwadkar, Samir; Velusamy, Karupanna
2017-04-01
Development of an efficient divertor concept is an important task to meet in the scenario of the future fusion power plant. The divertor, which is a vital part of the reactor has to discharge the considerable fraction of the total fusion thermal power (∼15%). Therefore, it has to survive very high thermal fluxes (∼10 MW/m2). In the present paper, an efficient divertor heat exchanger cooled by helium is proposed for the fusion tokamak. The Plasma facing surface of divertor made-up of several modules to overcome the stresses caused by high heat flux. The thermal hydraulic performance of one such module is numerically investigated in the present work. The result shows that the proposed design is capable of handling target heat flux values of 10 MW/m2. The computational model has been validated against high-heat flux experiments and a satisfactory agreement is noticed between the present simulation and the reported results.
Thermal-hydraulic analysis of the HL-2M divertor using an homogeneous equilibrium model
Lu, Yong; Cai, Lijun; Liu, Yuxiang; Liu, Jian; Yuan, Yinglong; Zheng, Guoyao; Liu, Dequan
2017-09-01
The heat flux of the HL-2M divertor would reach 10 MW m-2 or more at the local area when the device operates at high parameters. Subcooled boiling could occur at high thermal load, which would be simulated based on the homogeneous equilibrium model. The results show that the current design of the HL-2M divertor could withstand the local heat flux 10 MW m-2 at a plasma pulse duration of 5 s, inlet coolant pressure of 1.5 MPa and flow velocity of 4 m s-1. The pulse duration that the HL-2M divertor could withstand is closely related to the coolant velocity. In addition, at the time of 2 min after plasma discharge, the flow velocity decreased from 4 m s-1 to 1 m s-1, and the divertor could also be cooled to the initial temperature before the next plasma discharge commences.
Ion temperature measurement using an ion sensitive probe in the LHD divertor plasma
Energy Technology Data Exchange (ETDEWEB)
Ezumi, N. E-mail: ezumi@ec.nagano-nct.ac.jp; Masuzaki, S.; Ohno, N.; Uesugi, Y.; Takamura, S
2003-03-01
The first reliable measurement of ion temperature in the divertor plasma of the Large Helical Device has been done by using an ion sensitive probe. The satisfactory current-voltage characteristics of the ion collector for evaluating the ion temperature were obtained at the outer part of the divertor leg. Furthermore, simultaneous ion and electron temperature measurements were successfully done in this part. The results show that the ion temperature is higher than the electron temperature in the part. There is a possibility that the profiles of the evaluated ion temperature which shows relatively higher than the electron temperature at the outside of divertor leg are qualitatively explained by particle's orbits around the edge and divertor region.
Miyachi, Hideki
2010-01-01
In this paper, we investigate the structure of the Gardiner-Masur boundary of Teichmuller space. Indeed, we will give a geometric description of boundary comparing to the Duchin-Leininger-Rafi compactification of the space of singular flat structures. We will obtain the coincidence between the Gardiner-Masur boundary and the Thurston boundary at the projective classes of uniquely ergodic measured foliations. We also study the action of the mapping class group on the Gardiner-Masur boundary and characterize the elements by fixed points.
2011-08-01
channel gain of each link in a CAN as a Nakagami -m or a Rice random variable due to the increased likelihood of the presence of a strong specular...UTC from IEEE Xplore. Restrictions apply. 2 . (7) For instance, it is not difficult to show that the MGF of for Nakagami -m fading with i.n.d fading...conjunction with (6), (8) and (9) generalizes the results in [7] to Nakagami -m channels. Similarly, precise estimates of the ergodic capacities with different
Mixing, Ergodic, and Nonergodic Processes with Rapidly Growing Information between Blocks
Dębowski, Łukasz
2011-01-01
We construct mixing processes over an infinite alphabet and ergodic processes over a finite alphabet for which Shannon mutual information between adjacent blocks of length $n$ grows as $n^\\beta$, where $\\beta\\in(0,1)$. The processes are a modification of nonergodic Santa Fe processes, which were introduced in the context of natural language modeling. The rates of mutual information for the latter processes are alike and also established in this paper. As an auxiliary result, it is shown that infinite direct products of mixing or weakly mixing processes are mixing or weakly mixing respectively.
Chaos, ergodicity, and the thermodynamics of lower-dimensional time-independent Hamiltonian systems
Kandrup, Henry E.; Sideris, Ioannis V.; Bohn, Courtlandt L.
2002-01-01
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability may be modeled by a stochastic-oscillator equation [cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)], linearized perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.
Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems
Kandrup, H E; Bohn, C L; Kandrup, Henry E.; Sideris, Ioannis V.
2002-01-01
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability can be modeled by a stochastic-oscillator equation (cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)), linearised perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.
On the asymptotic ergodic capacity of FSO links with generalized pointing error model
Al-Quwaiee, Hessa
2015-09-11
Free-space optical (FSO) communication systems are negatively affected by two physical phenomenon, namely, scintillation due to atmospheric turbulence and pointing errors. To quantize the effect of these two factors on FSO system performance, we need an effective mathematical model for them. Scintillations are typically modeled by the log-normal and Gamma-Gamma distributions for weak and strong turbulence conditions, respectively. In this paper, we propose and study a generalized pointing error model based on the Beckmann distribution. We then derive the asymptotic ergodic capacity of FSO systems under the joint impact of turbulence and generalized pointing error impairments. © 2015 IEEE.
Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps
Yu, Jingyi; Liu, Meng
2017-09-01
In this paper, a three-species stochastic food-chain model with Lévy jumps is proposed and analyzed. Sharp sufficient criteria for the existence and uniqueness of an ergodic stationary distribution are established. The effects of Lévy jumps on the existence of the stationary distribution are revealed: in some cases, the Lévy jumps could make the stationary distribution appear, while in some cases, the Lévy jumps could make the stationary distribution disappear. Some numerical simulations are introduced to illustrate the theoretical results.
Institute of Scientific and Technical Information of China (English)
BAI Zhan-Wu
2008-01-01
@@ We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.
Numerical optimization of tungsten monoblock tile in EAST divertor
Energy Technology Data Exchange (ETDEWEB)
Chen, Xiahua [Harbin Engineering University, Harbin 150001 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Ding, Fang, E-mail: fding@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Mao, Hongmin; Luo, Guangnan; Hu, Zhenhua; Xu, Feng; Niu, Guojian [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2016-10-15
Highlights: • A method based on Kriging model and Uniform Design is developed and applied to the geometry optimization of EAST W tile. • An optimized chamfering geometry is obtained and significantly reduces the maximum temperature on W monoblock. • The incident angle of plasma flux has a strong impact on the optimized chamfering geometry. - Abstract: The ITER-like tungsten divertor with toroidally symmetric 1 mm × 1 mm chamfers on monoblock tiles has been installed in EAST in 2014. Hot spots were experimentally observed mostly along the toridial facing gaps between two columns of W/Cu monoblock units, which are often aggravated by installation misalignment. These hot spots can significantly degrade the power handling capability of W divertor and need to be alleviated. A numerical optimization model for tile chamfering design is built based on the finite element method (FEM), in which the numerical experiments are designed by the uniform table. The calculation results in ANSYS for these experiments are then processed employing the code Design and Analysis of Computer Experiments (DACE) in which the Kriging method is adopted to reconstruct a response surface. The optimum geometry can be derived from the minimum point on the surface. The results show that, under 200 MW/m{sup 2} parallel heat flux with an inclination angle of 3° with respect to tile surface, the maximum temperature on W tile with a 0.5 mm misalignment can be decreased to 2084 °C by adopting an optimized single-sided chamfer, 1.8 times lower than 1 mm × 1 mm symmetrically chamfered tile. The optimum chamfering geometry has a strong dependence on the inclination angle of plasma flux to tile surface. As a result, the monoblock tiles in a flat cassette module need to be chamfered differently to adapt to the varied inclination angles.
Design study of JT-60SA divertor for high heat and particle controllability
Energy Technology Data Exchange (ETDEWEB)
Kawashima, H.; Shimizu, K.; Takizuka, T.; Asakura, N.; Sakurai, S.; Matsukawa, M.; Fujita, T. [Japan Atomic Energy Agency (Japan)
2007-07-01
In steady-state high performance plasma over 41 MW/100 s in the JT-60SA tokamak, the heat and particle flux density on the divertor targets are considerably higher than those of existing devices such as JT-60U. A divertor modeling code, SOLDOR/NEUT2D, has been applied in order to optimiz the JT-60SA divertor design in such conditions. The heat load q{sub heat} on divertor target is estimated for a conceptual divertor design as the first step. Simulation of SOL/divertor plasmas is carried out at lower single null divertor (LSN) configuration with I{sub p}/B{sub t}=3.5 MA/2.5 T. For the present calculation, anticipated SOL power flux of Q{sub total}=35 MW and particle fuelling flux of G{sub ion}=5.10{sup 21}/s (n{sub e-dege}=3.10{sup 19}/m) are applied. The pumping speed (S{sub pump}=50 m{sup 3}/s) is specified by an albedo for neutrals in front of the cryopump set bottom of exhaust chamber. The recycling of deuterium is assumed to be 100% at the first wall. For the first simulation, the carbon contamination in SOL/divertor regions is set to 2% of electron density uniformly. Gas puff flux G{sub puff}=0.5.10{sup 21}/s is introduced from outside midplane. We assume particle diffusion coefficient D=0.3 m{sup 2}/s and thermal diffusivity of electron and ion X{sub e}=X{sub i}=1 m{sup 2}/s. As a result, attached and detached plasma conditions are simulated on outer and inner divertor regions, respectively. The heat load around the outer strike point reaches 31 MW/m{sup 2}, which largely exceeds the allowable range of 15 MW/m{sup 2} for CFC materials. Reduction of heat load must be achieved somehow. An effect of the radiation cooling is simulated to reduce such a large heat load as the second step. To enlarge the radiative cooling, we increased the gas puff flux by a factor of ten and the carbon contamination partly in the outer divertor region from 2% to 4%. It gives a favorable result that the peak heat load is reduced to 12 MW/m{sup 2} with radiation enhancement by a
Beznosov, A. V.; Sherbakov, R. V.; Karatushina, I. V.; Romanov, P. V.
1996-10-01
Experimental investigation of electroinsulating coatings stability on the samples made of stainless stell, vanadium alloy and beryllium has been conducted at 80-350°C. The impact of gas pressure upon the liquid gallium open surface was studied. The stability of electroinsulating film parameters on divertor structure materials was confirmed for the divertor with open liquid metal coolant surface in the vacuum chamber.
Favorable effects of turbulent plasma mixing on the performance of innovative tokamak divertors
Ryutov, D. D.; Cohen, R. H.; Rognlien, T. D.; Umansky, M. V.
2013-10-01
The problem of reducing the heat load on plasma-facing components is one of the most demanding issues for MFE devices. The general approach to the solution of this problem is the use of a specially configured poloidal magnetic field, so called magnetic divertors. In recent years, novel divertors possessing the 2-nd and 3-rd order nulls of the poloidal field (PF) have been proposed. They are called a ``snowflake'' (SF) and a ``cloverleaf'' (CL) divertor, respectively, due to characteristic shape of the magnetic separatrix. Among several beneficial features of such divertors is an effect of strong turbulent plasma mixing that is intrinsic to the zone of weak PF near the null-point. The turbulence spreads the heat flux between multiple divertor exhaust channels and increases the heat flux width within each channel. Among physical processes affecting the onset of convection the curvature-driven mode of axisymmetric rolls is most prominent. The effect is quite significant for the SF and is even stronger for the CL divertor. Projections to future ITER-scale facilities are discussed. Work performed for U.S. DoE by LLNL under Contract DE-AC52-07NA27344.
Critical need for MFE: the Alcator DX advanced divertor test facility
Vieira, R.; Labombard, B.; Marmar, E.; Irby, J.; Wolf, S.; Bonoli, P.; Fiore, C.; Granetz, R.; Greenwald, M.; Hutchinson, I.; Hubbard, A.; Hughes, J.; Lin, Y.; Lipschultz, B.; Parker, R.; Porkolab, M.; Reinke, M.; Rice, J.; Shiraiwa, S.; Terry, J.; Theiler, C.; Wallace, G.; White, A.; Whyte, D.; Wukitch, S.
2013-10-01
Three critical challenges must be met before a steady-state, power-producing fusion reactor can be realized: how to (1) safely handle extreme plasma exhaust power, (2) completely suppress material erosion at divertor targets and (3) do this while maintaining a burning plasma core. Advanced divertors such as ``Super X'' and ``X-point target'' may allow a fully detached, low temperature plasma to be produced in the divertor while maintaining a hot boundary layer around a clean plasma core - a potential game-changer for magnetic fusion. No facility currently exists to test these ideas at the required parallel heat flux densities. Alcator DX will be a national facility, employing the high magnetic field technology of Alcator combined with high-power ICRH and LHCD to test advanced divertor concepts at FNSF/DEMO power exhaust densities and plasma pressures. Its extended vacuum vessel contains divertor cassettes with poloidal field coils for conventional, snowflake, super-X and X-point target geometries. Divertor and core plasma performance will be explored in regimes inaccessible in conventional devices. Reactor relevant ICRF and LH drivers will be developed, utilizing high-field side launch platforms for low PMI. Alcator DX will inform the conceptual development and accelerate the readiness-for-deployment of next-step fusion facilities.
Magnetic field models and their application in optimal magnetic divertor design
Energy Technology Data Exchange (ETDEWEB)
Blommaert, M.; Reiter, D. [Institute of Energy and Climate Research (IEK-4), FZ Juelich GmbH, Juelich (Germany); Baelmans, M. [KU Leuven, Department of Mechanical Engineering, Leuven (Belgium); Heumann, H. [TEAM CASTOR, INRIA Sophia Antipolis (France); Marandet, Y.; Bufferand, H. [Aix-Marseille Universite, CNRS, PIIM, Marseille (France); Gauger, N.R. [TU Kaiserslautern, Chair for Scientific Computing, Kaiserslautern (Germany)
2016-08-15
In recent automated design studies, optimal design methods were introduced to successfully reduce the often excessive heat loads that threaten the divertor target surface. To this end, divertor coils were controlled to improve the magnetic configuration. The divertor performance was then evaluated using a plasma edge transport code and a ''vacuum approach'' for magnetic field perturbations. Recent integration of a free boundary equilibrium (FBE) solver allows to assess the validity of the vacuum approach. It is found that the absence of plasma response currents significantly limits the accuracy of the vacuum approach. Therefore, the optimal magnetic divertor design procedure is extended to incorporate full FBE solutions. The novel procedure is applied to obtain first results for the new WEST (Tungsten Environment in Steady-state Tokamak) divertor currently under construction in the Tore Supra tokamak at CEA (Commissariat a l'Energie Atomique, France). The sensitivities and the related divertor optimization paths are strongly affected by the extension of the magnetic model. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Evaluation of heat and particle controllability on the JT-60SA divertor
Energy Technology Data Exchange (ETDEWEB)
Kawashima, H., E-mail: kawashima.hisato@jaea.go.jp [Japan Atomic Energy Agency, 801-1, Mukoyama, Naka, Ibaraki 311-0193 (Japan); Hoshino, K.; Shimizu, K.; Takizuka, T.; Ide, S.; Sakurai, S.; Asakura, N. [Japan Atomic Energy Agency, 801-1, Mukoyama, Naka, Ibaraki 311-0193 (Japan)
2011-08-01
The JT-60SA divertor design has been established on the basis of engineering requirements and physics analysis. Heat and particle fluxes under the full input power of 41 MW can give severe heat loads on the divertor targets, while the allowable heat load is limited below 15 MW/m{sup 2}. Dependence of the heat flux mitigation on a D{sub 2} gas-puff is evaluated by SONIC simulations for high density (n{sub e{_}ave} {approx} 1 x 10{sup 20} m{sup -3}) high current plasmas. It is found that the peak heat load 10 MW/m{sup 2} with dense (n{sub ed} > 4 x 10{sup 20} m{sup -3}) and cold (T{sub ed}, T{sub id} {<=} 1 eV) divertor plasmas are obtained at a moderate gas-puff of {Gamma}{sub puff} = 15 x 10{sup 21} s{sup -1}. Divertor plasmas are controlled from attached to detached condition using the divertor pump with pumping-speed below 100 m{sup 3}/s. In full non-inductive current drive plasmas with low density (n{sub e{_}ave} {approx} 5 x 10{sup 19} m{sup -3}), the reduction of divertor heat load is achieved with the Ar injection.
Local Dynamics in an Infinite Harmonic Chain
Directory of Open Access Journals (Sweden)
M. Howard Lee
2016-04-01
Full Text Available By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable.
Energy deposition onto HL-2A divertor plates in ELMy H-mode discharges using infrared thermography
Energy Technology Data Exchange (ETDEWEB)
Gao, J.M., E-mail: gaojm@swip.ac.cn; Li, W.; Liu, Y.; Ji, X.Q.; Cheng, J.; Dong, Y.B.; Chen, C.Y.; Feng, B.B.; Lu, J.; Yi, P.; Yang, Q.W.
2015-08-15
Using infrared (IR) thermography, power loads onto the divertor plates have been investigated in ELMy H-mode plasmas on HL-2A. In the ELMy H-mode discharges, ELMs are the largest contributors to the divertor target energy load. Analysis of energy balance shows that up to 45% of the energy losses are deposited onto the divertor targets during ELMs and about 30% are found as plasma radiation. Moreover, divertor heat flux mitigation has been achieved during an ELMy H-mode phase by using Supersonic Molecular Beam Injection (SMBI), characterized by a sharp increase of ELM frequency and a reduction in peak heat flux. The increased plasma radiation energy losses, especially the doubled plasma radiation in the divertor region, should be responsible for the reduction of integrated energy deposition onto divertor targets.
Ergodic Capacity of Cognitive Radio Under Imperfect Channel-State Information
Rezki, Zouheir
2012-09-08
A spectrum-sharing communication system where the secondary user is aware of the instantaneous channel-state information (CSI) of the secondary link but knows only the statistics and an estimated version of the secondary transmitter-primary receiver link is investigated. The optimum power profile and the ergodic capacity of the secondary link are derived for general fading channels [with a continuous probability density function (pdf)] under the average and peak transmit power constraints and with respect to the following two different interference constraints: 1) an interference outage constraint and 2) a signal-to-interference outage constraint. When applied to Rayleigh fading channels, our results show, for example, that the interference constraint is harmful at the high-power regime, because the capacity does not increase with the power, whereas at the low-power regime, it has a marginal impact and no-interference performance, which corresponds to the ergodic capacity under average or peak transmit power constraint in the absence of the primary user, may be achieved. © 2012 IEEE.
A Unified Framework for the Ergodic Capacity of Spectrum Sharing Cognitive Radio Systems
Sboui, Lokman
2012-12-29
We consider a spectrum sharing communication scenario in which a primary and a secondary users are communicating, simultaneously, with their respective destinations using the same frequency carrier. Both optimal power profile and ergodic capacity are derived for fading channels, under an average transmit power and an instantaneous interference outage constraints. Unlike previous studies, we assume that the secondary user has a noisy version of the cross link and the secondary link Channel State Information (CSI). After deriving the capacity in this case, we provide an ergodic capacity generalization, through a unified expression, that encompasses several previously studied spectrum sharing settings. In addition, we provide an asymptotic capacity analysis at high and low signal-to-noise ratio (SNR). Numerical results, applied for independent Rayleigh fading channels, show that at low SNR regime, only the secondary channel estimation matters with no effect of the cross link on the capacity; whereas at high SNR regime, the capacity is rather driven by the cross link CSI. Furthermore, a practical on-off power allocation scheme is proposed and is shown, through numerical results, to achieve the full capacity at high and low SNR regimes and suboptimal rates in the medium SNR regime.
On the ergodic capacity of legacy systems in the presence of next generation interference
Mahmood, Nurul Huda
2011-11-01
Next generation wireless systems facilitating better utilization of the scarce radio spectrum have emerged as a response to inefficient rigid spectrum assignment policies. These are comprised of intelligent radio nodes that opportunistically operate in the radio spectrum of existing legacy systems; yet unwanted interference at the legacy receivers is unavoidable. In order to design efficient next generation systems and to minimize their harmful consequences, it is necessary to realize their impact on the performance of legacy systems. In this work, a generalized framework for the ergodic capacity analysis of such legacy systems in the presence of interference from next generation systems is presented. The analysis is built around a model developed for the statistical representation of the interference at the legacy receivers, which is then used to evaluate the ergodic capacity of the legacy system. Moreover, this analysis is not limited to the context of legacy systems, and is in fact applicaple to any interference limited system. Findings of analytical performance analyses are confirmed through selected computer-based Monte-Carlo simulations. © 2011 IEEE.
Ergodicity of stochastic real Ginzburg-Landau equation driven by $\\alpha$-stable noises
Xu, Lihu
2012-01-01
We study the ergodicity of stochastic real Ginzburg-Landau equation driven by additive $\\alpha$-stable noises, showing that as $\\alpha \\in (3/2,2)$, this stochastic system admits a unique invariant measure. After establishing the existence of invariant measures by the same method as in [9], we prove that the system is strong Feller and accessible to zero. These two properties imply the ergodicity by a simple but useful criterion in [16]. To establish the strong Feller property, we need to truncate the nonlinearity and apply a gradient estimate established in [26] (or see [24]} for a general version for the finite dimension systems). Because the solution has discontinuous trajectories and the nonlinearity is not Lipschitz, we can not solve a control problem to get irreducibility. Alternatively, we use a replacement, i.e., the fact that the system is accessible to zero. In section 3, we establish a maximal inequality for stochastic $\\alpha$-stable convolution, which is crucial for studying the well-posedness, s...
On the ergodic secrecy capacity of the wiretap channel under imperfect main channel estimation
Rezki, Zouheir
2011-11-01
The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels. © 2011 IEEE.
Kinetic studies of divertor heat fluxes in Alcator C-Mod
Pankin, A. Y.; Bateman, G.; Kritz, A. H.; Rafiq, T.; Park, G. Y.; Chang, C. S.; Brunner, D.; Hughes, J. W.; Labombard, B.; Terry, J.
2010-11-01
The kinetic XGC0 code [C.S. Chang et al, Phys. Plasmas 11 (2004) 2649] is used to model the H- mode pedestal and SOL regions in Alcator C-Mod discharges. The self-consistent simulations in this study include kinetic neoclassical physics and anomalous transport models along with the ExB flow shear effects. The heat fluxes on the divertor plates are computed and the fluxes to the outer plate are compared with experimental observations. The dynamics of the radial electric field near the separatrix and in the SOL region are computed with the XGC0 code, and the effect of the anomalous transport on the heat fluxes in the SOL region is investigated. In particular, the particle and thermal diffusivities obtained in the analysis mode are compared with predictions from the theory-based anomalous transport models such as MMM95 [G. Bateman et al, Phys. Plasmas 5 (1998) 1793] and DRIBM [T. Rafiq et al, to appear in Phys. Plasmas (2010)]. It is found that there is a notable pinch effect in the inner separatrix region. Possible physical mechanisms for the particle and thermal pinches are discussed.
Institute of Scientific and Technical Information of China (English)
ZHENG; Zuohuan
2001-01-01
［1］Kristian, J. , Sandage, A. R. , Westphal, J., The extension of the Hubble diagram: Ⅱ. New redshifts and photometry of very distant galaxy clusters, Astrophys. J., 1978, 221: 383.［2］Sandage, A., The redshift-distant relation V. Galaxy co lors as functions of galactic latitude and redshift, Astrophys, J.,1973, 183: 711.［3］Qu, Q. Y., Qin, Z. H., Han, C. S. et al., A relation between magnitudes and redshifts of QSOs with strong interplanetary scientillation, Chinese Astron., 1979, 4: 97.［4］Tinsley, B. M. , The Galaxy counts, color-redshift relation, and related quantities as probes of cosmology and galactic evolu-tion, Astrophys. J., 1977, 211: 621.［5］Spinrad, H., Djorgovski, S., The status of the Hubble diagram in 1986 (eds. Hewitt, A. Burbidge, G. Fang, L. Z. ),Proc. IAU Symp 124 on Observational Cosmology, New York: D. Reidel Publishing Company, 1986, 129.［6］Fang, L. Z., Zhou, Y. Y., Cheng F. Z. et al., Evolution of quasars with resolved components and determination of decel-eration parameter q0, Scientia Sinica, 1979, 22: 1292.［7］Cheng, K. S., Fan, J. H., Li, Y. et al., Do γ-ray burst associated with metal-rich quasars (ed. Cheng, K. S., Singh,H. P.), Proc. of The Pacific Rim Conference on Stellar Astrophysics, August 13-16, 1997, Houg Kong, 1997.［8］Davis, M., Geller, M. J., Huchra, J., The local mean mass density of the universe: new methods for studying galaxy clus-tering, Astrophys. J., 1978, 221: 1.［9］Gott, J. R., Turner, E. L., The mean luminosity and mass densities in the universe, Astrophys. J., 1976, 209: 1.［10］Shapiro, S. L., The density of matter in the form of galaxies, Astron. J., 1971, 76: 291.［11］Fang, L. Z., Hu, F. X., The large-scale inhomogeneities in the universe (eds. Yang, J., Zhu, C. S. ), Proceeding of A-cademia Sinica--Max-Plank Socity Workshop on High Energy Astrophyics Held in Nanjing, China, April 9-17, 1982,New York: Gordon and Breach Science Publishers S.A. 1982, 425［12］Baldwin, J. A., Wampler, E. J., Gaskell, C. M., Emission-line properties of optically and radio-selected complete quasars samples, Astrophys. J., 1989, 338: 630.［13］Yong, P., Sargent, W. L. W. A., High-resolution study of the absorption spectra of three QSOs: evidence for cosmological evolution in the lyman-alpha lines, Astrophys. J., 1982, 252: 10.［14］Lawrence, J., Zucker, J. R., Readhead, A. C. S. et al., Optical spectra of a complete sample of radio sources I. The spectra, Astrophys. J. Suppl., 1996, 107: 541.［15］Junkkarinen, V. T. , Burbidge E. M. , Smith, H. E. , Spectrophyotometry of six broad absoption line QSOs, Astrophys. J. ,1987, 317, 460.［16］Laor, A., Babcall, J. N., Jannuzi, B. T. et al., The ultraviolet emission properties of 13 quasars, Astrophys. J. Suppl.,1995, 99: 1.［17］Baldwin, J. A., Rees, M. J., Longair, M. S. et al., QSOs with narrow emission lines, Astrophys. J., 1988, 327: 103.［18］Shaver, P. A. , Boksenberg A. , Robertson, J. G. , Spectroscopy of the QSO pair Q0028 + 003/Q0029 + 003, Astrophys.J., 1982, 261: L7.［19］Baldwin, J. A., Netzer, H., The emission-line regions of high-redshift QSOs, Astrophys. J., 1978, 226: 1.［20］Wills, B. J., Thompson, K. L., Han, M. et al. , The Hubble space telescope sample of radio-loud quasars: Ultraviolet spectra of the first 31 quasars, Astrophys. J., 1995, 447: 139.［21］Osmer, P. S., Smith, M. G. , Discovery and spectroscopic observations of 27 optical selected quasars with 1.4 ＜ z ＜ 2.5,Astrophys. J., 1977, 213: 607.［22］Storrie-Lombardi, L. J., McMabon, R. G., Irwin, M. J. et al., APM Z ＞ = 4 QSO Survey: Spectra and Intervening Ab-sorption Systems, Astrophys. J., 1996, 468: 121.［23］Young, P. , Sargent, W. L. W. , Boksenberg, A. , Clv absorption in an unbiased sample of 33 QSOs: evidence for the inter-vening galaxy hypothesis, Astrophys. J. Suppl., 1982, 48: 455.［24］Zitelli, V., Mignoli, M., Zarano, B. et al., A spectroscopically complete sample of quasars with Bj ≤ 22.0, MNRAS,1992, 256: 349.［25］Hazard, C. , Morton, D. C., Terlevich, R. et al. , Nine new quasi-stellar objects with borad absorption lines, Astrophys.J. , 1984, 282: 33.［26］Osmer, P. S. , Q0353-383: The best case yet for abundance anomalies in quasars, Astrophys. J. , 1980, 237, 666.［27］Hamann, F. , Zuo, L., Tytler, D. , Broad Ne VIII λ774 emission from quasars in the HST-Fos snapshot survey (ABSNAP),Astrophys. J., 1995, 444: L69.［28］Laor, A. , Bahcall, J. N., Jannuzi, B. T. , The ultraviolet emission properties of five low-redshift active galactic unclei at high signal-to-noise ratio and spectral resolution, Astrophys. J., 1994, 420: 110.［29］Barthel, P. D., Tytler, D. R., Thomson, B., Optical spectra of distant radio loud quasars, A&AS, 1990, 82: 339.［30］Schmidt, M., Schneider, D. P., Gunn, J. E., Pc0910 + 5625: An optically selected quasar with a redshift of 4.04, Astro-phys. J., 1987, 321: L7.［31］Adams, M. T., Coleman, G. D., Stockman, H. S. et al., The spectrum of Markarian 132, Astrophys. J., 1978, 228:758.［32］Hammann, F. , Shields, J. C. , Ferland, G. J. et al. , Broad NE VIII lambda 744 emission from the Quasar PG 148 + 549,Astrophys. J., 1995, 454: 688.［33］Baldwin, J. A., McMahon, R., Hazard, C. et al., QSOs with narrow emission lines, Astrophys. J., 1988, 327: 103.［34］Baldwin, J. A. , Burbidge, E. M. , Hazard, C. et al. , A spectroscopic surrvey of 92 QSO candidates, Astrophys. J. ,1973, 185: 739.［35］Baldwin, J. A. , Ferland, G. J. , Korista, K. T., Very high density clumps and out flowing winds in QSO broad-line re-gions, Astrophys. J., 1996, 461: 664.［36］Ferland, G. J., Baldwin, J. A., Korista, K. T., High metal enrichments in luminous quasars, Astrophys. J., 461: 683.［37］Bceker, R. H., Helfand, D. J., White, R. L., The discovery of an X-ray selected radio-loud quasar at z = 3.9 AJ, 1992,104: 531.［38］Schneider, D. P., Lawrence, C. R., Schmide, M. et al., Deep optical and radio observations of the gravitational lens sys-tem 2016 + 112, Astrophys. J. , 1985, 294: 66.［39］Aldcroft, T. L. , Bechtold, J. , Elvis, M. , MglI absorption in a sample of 56 steep-spectrum quasars, Astrophys. J. Sup-pl., 1994, 93: 1.［40］Verib-Getty, M. P., Veron, P., A catalogue of quasars and active nuclei, ESO Scientific Report, 1996, 17: 1.［41］Hewitt, A., Burbidge, G., A revised and updated catalog of quas-stellar objects, Astrophys, J. Suppl., 1993, 87: 451.［42］Rudy, R. J., Cohan, R. D., Ake, T. B., Ultraviolet and optical spectrophyotometry of the seyfert 1.8 galaxy Markarian 609, Astrophys. J., 1988, 332: 172.［43］Bregrmamn, T. S. , Pastoriza, M. G. , On the metal abundance of low-activity galactic nuclei, Astrophys. J. , 1989, 347:195.［44］Malkan, M. A., Oke, J. B., IUE observations of Markarian 3 and 6: reddening and nonstellar continuum, Astrophys. J. ,1983, 265: 92.［45］Oke, J. B., Goodrich, R. W., IUE and VISUAl spectrophotometry of Markarian 9, Markarian 10, and 3C 390.3, Astro-phys. J., 1981, 243: 445.［46］Crenshaw, D. M. , Peterson, B. M. , Korista, K. , Ultraviolet and optical spectra of high-ionization Seyfert galaxies with nar-row lines, AJ, 1991, 101: 1202.［47］Voit, G. M. , Shull, J. M. , Begelman, M. C. , Broad, variable absorption lines in the Seyfert Galaxy NGC 3516-probing the structure of the emission-line regions, Astrophys. J., 1987, 316: 573.［48］Reichert, G. A., Rodriguez-Pascual, P. M. , Alloin, D. et al., Steps toward determination of the size and structure of the broad-line region in active galactic, Astrophys. J., 1994, 425: 582.［49］Setti, G., Woltjer, L., Hubble Diagram for Quasars, Astrophys. J., 1973, 181: L61.［50］Baldwin, J. A. , Burke, W. L. , Gaskell, M. G. et al. , Relative quasar luminosities determined from emission line strengths, Nature, 1978, 273: 431.［51］Bressan, A., Chiosi, C., Fagotto, F., Spectrophotometric evolution of elliptical galaxies, Astrophys. J. Suppl., 1994, 94:63.［52］Scappa, R. , Urry, C. M. , The Hubble space telescope survey fo BL Lacertea objects, Astrophys. J. , 2000, 532: 740.
Developing and validating advanced divertor solutions on DIII-D for next-step fusion devices
Guo, H. Y.; Hill, D. N.; Leonard, A. W.; Allen, S. L.; Stangeby, P. C.; Thomas, D.; Unterberg, E. A.; Abrams, T.; Boedo, J.; Briesemeister, A. R.; Buchenauer, D.; Bykov, I.; Canik, J. M.; Chrobak, C.; Covele, B.; Ding, R.; Doerner, R.; Donovan, D.; Du, H.; Elder, D.; Eldon, D.; Lasa, A.; Groth, M.; Guterl, J.; Jarvinen, A.; Hinson, E.; Kolemen, E.; Lasnier, C. J.; Lore, J.; Makowski, M. A.; McLean, A.; Meyer, B.; Moser, A. L.; Nygren, R.; Owen, L.; Petrie, T. W.; Porter, G. D.; Rognlien, T. D.; Rudakov, D.; Sang, C. F.; Samuell, C.; Si, H.; Schmitz, O.; Sontag, A.; Soukhanovskii, V.; Wampler, W.; Wang, H.; Watkins, J. G.
2016-12-01
A major challenge facing the design and operation of next-step high-power steady-state fusion devices is to develop a viable divertor solution with order-of-magnitude increases in power handling capability relative to present experience, while having acceptable divertor target plate erosion and being compatible with maintaining good core plasma confinement. A new initiative has been launched on DIII-D to develop the scientific basis for design, installation, and operation of an advanced divertor to evaluate boundary plasma solutions applicable to next step fusion experiments beyond ITER. Developing the scientific basis for fusion reactor divertor solutions must necessarily follow three lines of research, which we plan to pursue in DIII-D: (1) Advance scientific understanding and predictive capability through development and comparison between state-of-the art computational models and enhanced measurements using targeted parametric scans; (2) Develop and validate key divertor design concepts and codes through innovative variations in physical structure and magnetic geometry; (3) Assess candidate materials, determining the implications for core plasma operation and control, and develop mitigation techniques for any deleterious effects, incorporating development of plasma-material interaction models. These efforts will lead to design, installation, and evaluation of an advanced divertor for DIII-D to enable highly dissipative divertor operation at core density (n e/n GW), neutral fueling and impurity influx most compatible with high performance plasma scenarios and reactor relevant plasma facing components (PFCs). This paper highlights the current progress and near-term strategies of boundary/PMI research on DIII-D.
Ergodic Theorems for Noncommutative Lorentz Spaces%非交换Lorentz空间的遍历定理
Institute of Scientific and Technical Information of China (English)
阿尔胜·托合达森; 吐尔德别克
2015-01-01
设(M,τ)是有限von Neumann代数。我们证明了非交换Lorentz空间Lp,q(M)的个体遍历定理。%Let (M,τ) be a finite von Neumann algebra. We proved individual ergodic theorem in the noncommutative Lorentz spaces Lp,q(M).
Pulse plasma sintering of a tungsten/steel divertor module
Energy Technology Data Exchange (ETDEWEB)
Kruszewski, Mirosław J., E-mail: m.kruszewski@inmat.pw.edu.pl; Ciupiński, Łukasz; Rosiński, Marcin; Michalski, Andrzej; Kurzydłowski, Krzysztof J.
2013-10-15
Highlights: • W/WL10 and WL10/steel joints were fabricated via pulse plasma sintering. • Fe interlayer successfully compensated thermal stresses at the WL10/steel joint. • Maximum temperature of a single stage sintering of the module was established. • Better accuracy in machining of W and WL10 elements is needed. -- Abstract: The paper presents the preliminary evaluation of the potential of a pulse plasma sintering (PPS) technique for the fabrication of a He-cooled modular divertor with a multiple-jet cooling module. In this work the W and WL10 elements were directly bonded by PPS. Examination of the microstructure revealed some minor defects at the interface, but the overall quality of the joint was good with no cracks or delamination being detected. To reduce the thermal stress gradient a thin transition layer of iron was used at the WL10/steel interface. In addition an attempt was made to fabricate the complete module by a single sintering process. The microstructures of the fabricated modules were examined and the findings were reported.
Response of NSTX liquid lithium divertor to high heat loads
Energy Technology Data Exchange (ETDEWEB)
Abrams, T., E-mail: tabrams@pppl.gov [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Jaworski, M.A. [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Kallman, J. [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Kaita, R. [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Foley, E.L. [Nova Photonics, Inc., Princeton, NJ 08543 (United States); Gray, T.K. [Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Kugel, H. [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Levinton, F. [Nova Photonics, Inc., Princeton, NJ 08543 (United States); McLean, A.G. [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States); Skinner, C.H. [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States)
2013-07-15
Samples of the NSTX Liquid Lithium Divertor (LLD) with and without an evaporative Li coating were directly exposed to a neutral beam ex-situ at a power of ∼1.5 MW/m{sup 2} for 1–3 s. Measurements of front face and bulk sample temperature were obtained. Predictions of temperature evolution were derived from a 1D heat flux model. No macroscopic damage occurred when the “bare” sample was exposed to the beam but microscopic changes to the surface were observed. The Li-coated sample developed a lithium hydroxide (LiOH) coating, which did not change even when the front face temperature exceeded the pure Li melting point. These results are consistent with the lack of damage to the LLD surface and imply that heating alone may not expose pure liquid Li if the melting point of surface impurities is not exceeded. This suggests that flow and heat are needed for future PFCs requiring a liquid Li surface.
Divertor power spreading in DEMO reactor by impurity seeding
Energy Technology Data Exchange (ETDEWEB)
Zagórski, Roman, E-mail: Roman.Zagorski@ipplm.pl; Gałązka, Krzysztof; Ivanova-Stanik, Irena
2016-11-01
Highlights: • The COREDIV code has been used to simulate DEMO inductive discharges with different impurity seeding (Ne, Ar, Kr) and different sputtering models (with and w/o prompt re-deposition process). • It has been shown that only for Ar and Kr seeding it is possible to achieve H-mode plasma operation with acceptable level of the power to the tungsten target plates. • For neon seeding, such regime of operation seems not to be possible. • Prompt re-deposition model extends the DEMO operation window. - Abstract: Numerical simulation with COREDIV code of DEMO H-mode discharges (tungsten divertor and wall) are performed considering the influence of seeding impurities with different atomic numbers: Ne, Ar and Kr on the DEMO scenarios. The approach is based on integrated numerical modeling using the COREDIV code, which self-consistently solves radial transport equations in the core region and 2D multi-fluid transport in the SOL. In this paper we focus on investigations how the operational domain of DEMO can be influenced by seeding gasses. Simulations with the updated prompt re-deposition model implemented in the code show that only for Ar and Kr, for high enough radial diffusion in the SOL, it is possible to achieve H-mode plasma operation (power to the SOL> L-H transition threshold power) with acceptable level of the power to the target plates. For neon seeding such regime of operation seems not to be possible.
Effects of ELMs on ITER divertor armour materials
Energy Technology Data Exchange (ETDEWEB)
Zhitlukhin, A. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation)]. E-mail: zhitlukh@triniti.ru; Klimov, N. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation); Landman, I. [Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany); Linke, J. [Forschungszentrum Juelich, EURATOM-Association, Juelich (Germany)]. E-mail: j.linke@fz-juelich.de; Loarte, A. [EFDA, Boltzmannstr. 2, 85748 Garching (Germany); Merola, M. [EFDA, Boltzmannstr. 2, 85748 Garching (Germany); Podkovyrov, V. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation); Federici, G. [ITER JWS Garching, Boltzmannstr. 2, 85748 Garching (Germany); Bazylev, B. [Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany); Pestchanyi, S. [Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe (Germany); Safronov, V. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation); Hirai, T. [Forschungszentrum Juelich, EURATOM-Association, Juelich (Germany); Maynashev, V. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation); Levashov, V. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation); Muzichenko, A. [SRC RF TRINITI, Troitsk, 142190, Moscow Region (Russian Federation)
2007-06-15
This paper is concerned with investigation of an erosion of the ITER-like divertor plasma facing components under plasma heat loads expected during the Type I ELMs in ITER. These experiments were carried out on plasma accelerator QSPA at the SRC RF TRINITI under EU/RF collaboration. Targets were exposed by series repeated plasma pulses with heat loads in a range of 0.5-1.5 MJ/m{sup 2} and pulse duration 0.5 ms. Erosion of CFC macrobrushes was determined mainly by sublimation of PAN-fibres that was less than 2.5 {mu}m per pulse. The CFC erosion was negligible at the energy density less than 0.5 MJ/m{sup 2} and was increased to the average value 0.3 {mu}m per pulse at 1.5 MJ/m{sup 2}. The pure tungsten macrobrushes erosion was small in the energy range of 0.5-1.3 MJ/m{sup 2}. The sharp growth of tungsten erosion and the intense droplet ejection were observed at the energy density of 1.5 MJ/m{sup 2}.
Current understanding of divertor detachment: experiments and modelling
Energy Technology Data Exchange (ETDEWEB)
Wischmeier, W; Groth, M; Kallenbach, A; Chankin, A; Coster, D; Dux, R; Herrmann, A; Muller, H; Pugno, R; Reiter, D; Scarabosio, A; Watkins, J; Team, T D; Team, A U
2008-05-23
A qualitative as well as quantitative evaluation of experimentally observed plasma parameters in the detached regime proves to be difficult for several tokamaks. A series of ohmic discharges have been performed in ASDEX Upgrade and DIII-D at similar as possible plasma parameters and at different line averaged densities, {bar n}{sub e}. The experimental data represent a set of well diagnosed discharges against which numerical simulations are compared. For the numerical modeling the fluid-code B2.5 coupled to the Monte Carlo neutrals transport code EIRENE is used. Only the combined enhancement of effects, such as geometry, drift terms, neutral conductance, increased radial transport and divertor target composition, explains a significant fraction of the experimentally observed asymmetries of the ion fluxes as a function of {bar n}{sub e} to the inner and outer target plates in ASDEX Upgrade. The relative importance of the mechanisms leading to detachment are different in DIII-D and ASDEX Upgrade.
Plasma flow interaction with ITER divertor related surfaces
Dojčinović, Ivan P.
2010-11-01
It has been found that the plasma flow generated by quasistationary plasma accelerators can be used for simulation of high energy plasma interaction with different materials of interest for fusion experiments. It is especially important for the studies of the processes such as ELMs (edge localized modes), plasma disruptions and VDEs (vertical displacement events), during which a significant part of the confined hot plasma is lost from the core to the SOL (scrape off layer) enveloping the core region. Experiments using plasma guns have been used to assess erosion from disruptions and ELMs. Namely, in this experiment modification of different targets, like tungsten, molybdenum, CFC and silicon single crystal surface by the action of hydrogen and nitrogen quasistationary compression plasma flow (CPF) generated by magnetoplasma compressor (MPC) has been studied. MPC plasma flow with standard parameters (1 MJ/m2 in 0.1 ms) can be used for simulation of transient peak thermal loads during Type I ELMs and disruptions. Analysis of the targets erosion, brittle destruction, melting processes, and dust formation has been performed. These surface phenomena are results of specific conditions during CPF interaction with target surface. The investigations are related to the fundamental aspects of high energy plasma flow interaction with different material of interest for fusion. One of the purposes is a study of competition between melting and cleavage of treated solid surface. The other is investigation of plasma interaction with first wall and divertor component materials related to the ITER experiment.
Effects of ELMs on ITER divertor armour materials
Zhitlukhin, A.; Klimov, N.; Landman, I.; Linke, J.; Loarte, A.; Merola, M.; Podkovyrov, V.; Federici, G.; Bazylev, B.; Pestchanyi, S.; Safronov, V.; Hirai, T.; Maynashev, V.; Levashov, V.; Muzichenko, A.
2007-06-01
This paper is concerned with investigation of an erosion of the ITER-like divertor plasma facing components under plasma heat loads expected during the Type I ELMs in ITER. These experiments were carried out on plasma accelerator QSPA at the SRC RF TRINITI under EU/RF collaboration. Targets were exposed by series repeated plasma pulses with heat loads in a range of 0.5-1.5 MJ/m2 and pulse duration 0.5 ms. Erosion of CFC macrobrushes was determined mainly by sublimation of PAN-fibres that was less than 2.5 μm per pulse. The CFC erosion was negligible at the energy density less than 0.5 MJ/m2 and was increased to the average value 0.3 μm per pulse at 1.5 MJ/m2. The pure tungsten macrobrushes erosion was small in the energy range of 0.5-1.3 MJ/m2. The sharp growth of tungsten erosion and the intense droplet ejection were observed at the energy density of 1.5 MJ/m2.
Copper matrix composites as heat sink materials for water-cooled divertor target
Directory of Open Access Journals (Sweden)
Jeong-Ha You
2015-12-01
Full Text Available According to the recent high heat flux (HHF qualification tests of ITER divertor target mock-ups and the preliminary design studies of DEMO divertor target, the performance of CuCrZr alloy, the baseline heat sink material for DEMO divertor, seems to only marginally cover the envisaged operation regime. The structural integrity of the CuCrZr heat sink was shown to be affected by plastic fatigue at 20 MW/m². The relatively high neutron irradiation dose expected for the DEMO divertor target is another serious concern, as it would cause significant embrittlement below 250 °C or irradiation creep above 350 °C. Hence, an advanced design concept of the divertor target needs to be devised for DEMO in order to enhance the HHF performance so that the structural design criteria are fulfilled for full operation scenarios including slow transients. The biggest potential lies in copper-matrix composite materials for the heat sink. In this article, three promising Cu-matrix composite materials are reviewed in terms of thermal, mechanical and HHF performance as structural heat sink materials. The considered candidates are W particle-reinforced, W wire-reinforced and SiC fiber-reinforced Cu matrix composites. The comprehensive results of recent studies on fabrication technology, design concepts, materials properties and the HHF performance of mock-ups are presented. Limitations and challenges are discussed.
Design of the Wendelstein 7-X inertially cooled Test Divertor Unit Scraper Element
Energy Technology Data Exchange (ETDEWEB)
Lumsdaine, Arnold, E-mail: lumsdainea@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Boscary, Jean [Max Planck Institute for Plasma Physics, Garching (Germany); Fellinger, Joris [Max Planck Institute for Plasma Physics, Greifswald (Germany); Harris, Jeff [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Hölbe, Hauke; König, Ralf [Max Planck Institute for Plasma Physics, Greifswald (Germany); Lore, Jeremy; McGinnis, Dean [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Neilson, Hutch; Titus, Peter [Princeton Plasma Physics Lab, Princeton, NJ (United States); Tretter, Jörg [Max Planck Institute for Plasma Physics, Garching (Germany)
2015-10-15
Highlights: • The justification for the installation of the Test Divertor Unit Scraper Element is given. • Specially designed operational scenarios for the component are presented. • Plans for the design of the component are detailed. - Abstract: The Wendelstein 7-X stellarator is scheduled to begin operation in 2015, and to achieve full power steady-state operation in 2019. Computational simulations have indicated that for certain plasma configurations in the steady-state operation, the ends of the divertor targets may receive heat fluxes beyond their qualified technological limit. To address this issue, a high heat-flux “scraper element” (HHF-SE) has been designed that can protect the sensitive divertor target region. The surface profile of the HHF-SE has been carefully designed to meet challenging engineering requirements and severe spatial limitations through an iterative process involving physics simulations, engineering analysis, and computer aided design rendering. The desire to examine how the scraper element interacts with the plasma, both in terms of how it protects the divertor, and how it affects the neutral pumping efficiency, has led to the consideration of installing an inertially cooled version during the short pulse operation phase. This Test Divertor Unit Scraper Element (TDU-SE) would replicate the surface profile of the HHF-SE. The design and instrumentation of this component must be completed carefully in order to satisfy the requirements of the machine operation, as well as to support the possible installation of the HHF-SE for steady-state operation.
Characterizing the DIII-D divertor conditions during the tungsten ring experiment
Barton, J. L.; Watkins, J. G.; Wang, H. Q.; Nygren, R. E.; McLean, A.; Makowski, M.; Unterberg, E.; Thomas, D. M.; Guo, H. Y.; Guterl, J.; Buchenauer, B.
2016-10-01
Tungsten (W) is the leading divertor material in tokamaks, but the core W impurity fraction must be kept below 5 ×10-5 in a reactor. The DIII-D tokamak, having all graphite PFCs, has done a series of experiments with two W-coated molybdenum rings in the lower divertor to track W migration after plasma exposure. We characterize the divertor plasma conditions at the DIII-D target plate in L- and ELMing H-mode, and ELM suppressed plasmas. We will present data from an array of Langmuir probes in the divertor and divertor Thomson-scattering. We also compare the heat flux from fast thermocouples (7.5 mm below the surface of the metal tile inserts) and IRTV heat flux profiles from graphite tiles. The plasma conditions will be used to benchmark ERO modeling to aid in understanding the migration of sputtered W onto other plasma facing surfaces and will be compared to post exposure W distribution measured on the graphite tiles. Supported by US DOE under DE-AC04-94AL85000, DE-FC02-04ER54698, DE-AC05-000R22725, and DE-AC52-07NA27344.
Energy Technology Data Exchange (ETDEWEB)
R.J. Maqueda, D.P. Stotler and the NSTX Team.
2010-05-19
While intermittent filamentary structures, also known as blobs, are routinely seen in the low-field-side scrape-off layer of the National Spherical Torus Experiment (NSTX) (Ono et al 2000 Nucl. Fusion 40 557), fine structured filaments are also seen on the lower divertor target plates of NSTX. These filaments, not associated with edge localized modes, correspond to the interaction of the turbulent blobs seen near the midplane with the divertor plasma facing components. The fluctuation level of the neutral lithium light observed at the divertor, and the skewness and kurtosis of its probability distribution function, is similar to that of midplane blobs seen in Dα; e.g. increasing with increasing radii outside the outer strike point (OSP) (separatrix). In addition, their toroidal and radial movement agrees with the typical movement of midplane blobs. Furthermore, with the appropriate magnetic topology, i.e. mapping between the portion of the target plates being observed into the field of view of the midplane gas puff imaging diagnostic, very good correlation is observed between the blobs and the divertor filaments. The correlation between divertor plate filaments and midplane blobs is lost close to the OSP. This latter observation is consistent with the existence of ‘magnetic shear disconnection’ due to the lower X-point, as proposed by Cohen and Ryutov (1997 Nucl. Fusion 37 621).
Investigation of power spreading in a tokamak divertor using numerical tools
Energy Technology Data Exchange (ETDEWEB)
Hoppe, Felix; Scarabosio, Andrea; Wischmeier, Marco [Max-Planck Institut fuer Plasmaphysik, Boltzmannstr. 2, 85748 Garching (Germany); Collaboration: ASDEX Upgrade Team
2013-07-01
Divertors are widely used in today's fusion devices in order to reduce plasma core impurities and improve energy confinement. As the divertor targets are exposed to the largest part of the particle and heat loads reaching the wall, these loads must be reduced to prevent material damage. An enhancement of the plasma-wetted area on the targets is one approach. In low density plasmas, the plasma-wetted area is mainly given by the width of the scrap-off-layer (SOL) plasma at the divertor entrance, modified by heat diffusion into the private flux region (PFR) in the divertor. The heat diffusion broadens the heat flux profile at the targets. This can be approximated by a convolution of the upstream profile with a Gaussian of width S. The SOLPS5.0 code package is used to study the influence of divertor geometry and neutral pressure on S. The code is then validated by comparing the numerical results to the experimental findings in the ASDEX Upgrade tokamak.
ADX: A high Power Density, Advanced RF-Driven Divertor Test Tokamak for PMI studies
Whyte, Dennis; ADX Team
2015-11-01
The MIT PSFC and collaborators are proposing an advanced divertor experiment, ADX; a divertor test tokamak dedicated to address critical gaps in plasma-material interactions (PMI) science, and the world fusion research program, on the pathway to FNSF/DEMO. Basic ADX design features are motivated and discussed. In order to assess the widest range of advanced divertor concepts, a large fraction (>50%) of the toroidal field volume is purpose-built with innovative magnetic topology control and flexibility for assessing different surfaces, including liquids. ADX features high B-field (>6 Tesla) and high global power density (P/S ~ 1.5 MW/m2) in order to access the full range of parallel heat flux and divertor plasma pressures foreseen for reactors, while simultaneously assessing the effect of highly dissipative divertors on core plasma/pedestal. Various options for efficiently achieving high field are being assessed including the use of Alcator technology (cryogenic cooled copper) and high-temperature superconductors. The experimental platform would also explore advanced lower hybrid current drive and ion-cyclotron range of frequency actuators located at the high-field side; a location which is predicted to greatly reduce the PMI effects on the launcher while minimally perturbing the core plasma. The synergistic effects of high-field launchers with high total B on current and flow drive can thus be studied in reactor-relevant boundary plasmas.
Divertor ExB and Parallel Flows on the DIII-D Tokamak
Boedo, J.; Rudakov, D.
2016-10-01
E ×B convection is an important particle transport mechanism responsible for up to 50 % of the total particle flux into the divertor, changing direction with B, and playing a role in divertor asymmetries. The gradient of the plasma potential, Vp =Vf + 2.5Te , reaches 5 kV/m across the SOL-private boundary, causing a poloidal particle flux, calculated as, Γθ = 2 πRne (Vp 1 -Vp 2) /BT , (along flux surfaces) of about 1022 s-1 , comparable to the target flow of 2 ×1022 s-1 , and consistent with previous work. Floating potential Vf, temperature Te, density Ne, and D+ flow were measured in the DIII-D divertor. The data will be compared to simulations by SOLPS and UEDGE. The D+ parallel flow velocity, V ∥ , calculated by multiplying the Mach number by the local sound speed cs =(γ ZkTe /mi) 1 / 2 show increasing velocity towards the plate in attached conditions and bulk sonic flows over the whole detached region in detached conditions. We compare measurements in the divertor to similar measurements made at the midplane to show how divertor conditions reflect upstream. Supported under USDOE Grant DE-FC02-04ER54698.
Numerical analyses of JT-60SA tokamak with tungsten divertor by COREDIV code
Gałązka, K.; Ivanova-Stanik, I.; Stępniewski, W.; Zagórski, R.; Neu, R.; Romanelli, M.; Nakano, T.
2017-04-01
An analysis of radiative power exhaust for the JT-60SA tokamak with a tungsten divertor is performed with the help of the self-consistent, core-edge integrated COREDIV code. Two scenarios of operation (low and high density) were investigated in the scope of different parameters (electron density at the separatrix and the perpendicular transport in the scrape-off layer) with impurity seeding (Ne and Kr). The calculations show that in the case of the tungsten divertor the power load to the divertor plate is mitigated and the central plasma dilution is smaller compared to the carbon divertor. In the most cases the energy flux through the separatrix is above the L–H transition threshold. For the high density case with neon seeding operation in full detachment mode is observed. Changing the diffusion coefficient in the SOL has a strong influence on the result of the calculations as increased radial transport causes stronger screening effect. Also by changing the electron density on the separatrix the influx of heavy impurities (W, Kr) into the core region can be reduced. The results demonstrate that it is easier to achieve sustainable conditions in the divertor region for the high density scenario, whereas for the low density one reducing the auxiliary heating power seems unavoidable to prevent damaging of the target plate, even for strong seeding gas influx.
Ergodic Capacity Analysis of Free-Space Optical Links with Nonzero Boresight Pointing Errors
Ansari, Imran Shafique
2015-04-01
A unified capacity analysis of a free-space optical (FSO) link that accounts for nonzero boresight pointing errors and both types of detection techniques (i.e. intensity modulation/ direct detection as well as heterodyne detection) is addressed in this work. More specifically, an exact closed-form expression for the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system is presented in terms of well-known elementary functions. Capitalizing on these new moments expressions, we present approximate and simple closedform results for the ergodic capacity at high and low SNR regimes. All the presented results are verified via computer-based Monte-Carlo simulations.
A uniform Berry--Esseen theorem on $M$-estimators for geometrically ergodic Markov chains
Hervé, Loïc; Patilea, Valentin; 10.3150/10-BEJ347
2012-01-01
Let $\\{X_n\\}_{n\\ge0}$ be a $V$-geometrically ergodic Markov chain. Given some real-valued functional $F$, define $M_n(\\alpha):=n^{-1}\\sum_{k=1}^nF(\\alpha,X_{k-1},X_k)$, $\\alpha\\in\\mathcal{A}\\subset \\mathbb {R}$. Consider an $M$ estimator $\\hat{\\alpha}_n$, that is, a measurable function of the observations satisfying $M_n(\\hat{\\alpha}_n)\\leq \\min_{\\alpha\\in\\mathcal{A}}M_n(\\alpha)+c_n$ with $\\{c_n\\}_{n\\geq1}$ some sequence of real numbers going to zero. Under some standard regularity and moment assumptions, close to those of the i.i.d. case, the estimator $\\hat{\\alpha}_n$ satisfies a Berry--Esseen theorem uniformly with respect to the underlying probability distribution of the Markov chain.
A Banach space-valued ergodic theorem for amenable groups and applications
Pogorzelski, Felix
2012-01-01
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of quasi tilings for these groups. In light of that, constructions of Ornstein and Weiss are extended by quantitative estimates for the covering properties of the corresponding decompositions. Afterwards, we apply the developed methods to obtain an abstract ergodic theorem for a class of functions mapping subsets of the group into some Banach space. Moreover, applications of this convergence result are studied: the uniform existence of the integrated density of states (IDS) for operators on amenable Cayley graphs; the uniform existence of the IDS for operators on discrete structures being quasi-isometric to some amenable group; the approximation of L2-Betti numbers on cellular CW-complexes; the existence of certain densities of clusters in a percolated Cayley graph.
Escape patterns due to ergodic magnetic limiters in tokamaks with reversed magnetic shear
Energy Technology Data Exchange (ETDEWEB)
Roberto, M. [Instituto Tecnologico de Aeronautica, Centro Tecnico Aeroespacial, Dept. de Fisica, Sao Jose dos Campos, Sao Paulo (Brazil); Da Silva, E.C.; Caldas, I.L. [Sao Paulo Univ., Instituto de Fisica, Sao Paulo (Brazil); Viana, R.L. [Parana Univ., Dept. de Fisica, Curitiba (Brazil)
2004-07-01
In this work we study the ergodic magnetic limiters (EML) action on field lines from the point of view of a chaotic scattering process, considering the so-called exit basins, or sets of points in the chaotic region which originate field lines hitting the wall in some specified region. We divide the tokamak wall into three areas of equal poloidal angular length, corresponding to different exits for a chaotic field line. In order to obtain the exit basins we used a grid chosen inside a small rectangle which comprises a representative part of the chaotic region near the wall. Thus, exit basins were obtained for a tokamak wall with reversed magnetic shear. The no-twist mapping describes the perturbed magnetic field lines with two chains of magnetic islands and chaotic field lines in their vicinity. For a perturbing resonant magnetic field with a fixed helicity, the observed escape pattern changes with the perturbation intensity. (authors)
A Partially Non-Ergodic Ground-Motion Prediction Equation for Europe
Kuehn, Nicolas M
2016-01-01
A partially non-ergodic ground-motion prediction equation is estimated for Europe. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion intensity parameters is assumed to be similar, but not identical in different regions. This is achieved by assuming a hierarchical model, where some coefficients are treated as random variables which are sampled from an underlying global distribution. The coefficients are estimated by Bayesian inference. This allows one to estimate the epistemic uncertainty in the coefficients, and consequently in model predictions, in a principled way. The model is estimated based on peak ground acceleration data from nine different European regions. There are large differences in the amount of earthquakes and records in the different regions. However, due to the hierarchical nature of the model, regions with only few data points borrow strength from other regions with more data. This makes it possible to estimate...
Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force
Dilão, Rui
2014-04-01
We have proposed a mechanism of interaction between two non-linear dissipative oscillators, leading to exact and robust anti-phase and in-phase synchronization. The system we have analyzed is a model for the Huygens's two pendulum clocks system, as well as a model for synchronization mediated by an elastic media. Here, we extend these results to arrays, finite or infinite, of conservative pendula coupled by linear elastic forces. We show that, for two interacting pendula, this mechanism leads always to synchronized anti-phase small amplitude oscillations, and it is robust upon variation of the parameters. For three or more interacting pendula, this mechanism leads always to ergodic non-synchronized oscillations. In the continuum limit, the pattern of synchronization is described by a quasi-periodic longitudinal wave.
Power Allocation for Discrete-Input Non-Ergodic Block-Fading Channels
Nguyen, Khoa D; Rasmussen, Lars K
2007-01-01
We consider power allocation algorithms for fixed-rate transmission over Nakagami-m non-ergodic block-fading channels with perfect transmitter and receiver channel state information and discrete input signal constellations under both short- and long-term power constraints. Optimal power allocation schemes are shown to be direct applications of previous results in the literature. We show that the SNR exponent of the optimal short-term scheme is given by the Singleton bound. We also illustrate the significant gains available by employing long-term power constraints. Due to the nature of the expressions involved, the complexity of optimal schemes may be prohibitive for system implementation. We propose simple sub-optimal power allocation schemes whose outage probability performance is very close to the minimum outage probability obtained by optimal schemes.
Guillaud, Maxime
2010-01-01
We consider interference alignment (IA) over K-user Gaussian MIMO interference channel (MIMO-IC) when the SNR is not asymptotically high. We introduce a generalization of IA which enables receive diversity inside the interference-free subspace. We generalize the existence criterion of an IA solution proposed by Yetis et al. to this case, thereby establishing a multi-user diversity-multiplexing trade-off (DMT) for the interference channel. Furthermore, we derive a closed-form tight lower-bound for the ergodic mutual information achievable using IA over a Gaussian MIMO-IC with Gaussian i.i.d. channel coefficients at arbitrary SNR, when the transmitted signals are white inside the subspace defined by IA. Finally, as an application of the previous results, we compare the performance achievable by IA at various operating points allowed by the DMT, to a recently introduced distributed method based on game theory.
Isolated Word Recognition Using Ergodic Hidden Markov Models and Genetic Algorithm
Directory of Open Access Journals (Sweden)
Warih Maharani
2012-03-01
Full Text Available Speech to Text was one of speech recognition applications which speech signal was processed, recognized and converted into a textual representation. Hidden Markov Model (HMM was the widely used method in speech recognition. However, the level of accuracy using HMM was strongly influenced by the optimalization of extraction process and modellling methods. Hence in this research, the use of genetic algorithm (GA method to optimize the Ergodic HMM was tested. In Hybrid HMM-GA, GA was used to optimize the Baum-welch method in the training process. It was useful to improve the accuracy of the recognition result which is produced by the HMM parameters that generate the low accuracy when the HMM are tested. Based on the research, the percentage increases the level of accuracy of 20% to 41%. Proved that the combination of GA in HMM method can gives more optimal results when compared with the HMM system that not combine with any method.
Ergodic theory and Diophantine approximation for translation surfaces and linear forms
Athreya, Jayadev; Parrish, Andrew; Tseng, Jimmy
2016-08-01
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619-31, 1964 Trans. Am. Math. Soc. 110 493-518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.
Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
Manzo, Carlo; Massignan, Pietro; Lapeyre, Gerald J; Lewenstein, Maciej; Parajo, Maria F Garcia
2014-01-01
The recent discovery of transient immobilization as a cause of nonergodicity in the motion of some biological molecules has triggered great interest for its implications in statistical mechanics and cell biology. Is nonergodic subdiffusion a strategy shared by other biological systems? Can other physical mechanisms lead to similar behaviours? Is it beneficial? Answering to these questions is crucial to unravel the evolutionary strategy behind ergodicity breaking and its relevance for cellular function. Here we show that the motion of DC-SIGN, a transmembrane receptor with unique pathogen recognition capabilities, reveals nonergodic subdiffusion that cannot be explained by transient immobilization. Instead, its behaviour is compatible with inhomogeneity induced by spatiotemporal changes of diffusivity. The experiments are interpreted through a theoretical framework describing anomalous transport in complex media. By studying different DC-SIGN mutants, we establish a link between receptor structure and diffusiv...
Zhao, Yu; Yuan, Sanling; Zhang, Tonghua
2016-08-01
The effect of toxin-producing phytoplankton and environmental stochasticity are interesting problems in marine plankton ecology. In this paper, we develop and analyze a stochastic phytoplankton allelopathy model, which takes both white and colored noises into account. We first prove the existence of the global positive solution of the model. And then by using the stochastic Lyapunov functions, we investigate the positive recurrence and ergodic property of the model, which implies the existence of a stationary distribution of the solution. Moreover, we obtain the mean and variance of the stationary distribution. Our results show that both the two kinds of environmental noises and toxic substances have great impacts on the evolution of the phytoplankton populations. Finally, numerical simulations are carried out to illustrate our theoretical results.
Estimates of linearization discs in $p$-adic dynamics with application to ergodicity
Lindahl, Karl-Olof
2009-01-01
We give lower bounds for the size of linearization discs for power series over $\\mathbb{C}_p$. For quadratic maps, and certain power series containing a `sufficiently large' quadratic term, we find the exact linearization disc. For finite extensions of $\\mathbb{Q}_p$, we give a sufficient condition on the multiplier under which the corresponding linearization disc is maximal (i.e. its radius coincides with that of the maximal disc in $\\mathbb{C}_p$ on which $f$ is one-to-one). In particular, in unramified extensions of $\\mathbb{Q}_p$, the linearization disc is maximal if the multiplier map has a maximal cycle on the unit sphere. Estimates of linearization discs in the remaining types of non-Archimedean fields of dimension one were obtained in \\cite{Lindahl:2004,Lindahl:2009,Lindahl:2009eq}. Moreover, it is shown that, for any complete non-Archimedean field, transitivity is preserved under analytic conjugation. Using results by Oxtoby \\cite{Oxtoby:1952}, we prove that transitivity, and hence minimality, is equ...
Directory of Open Access Journals (Sweden)
I.V. Stasyuk
2012-10-01
Full Text Available The Bose-Einstein condensation in the hard-core boson limit (HCB of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated. For the purpose of considering the non-ergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions. The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point.
Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion
Majda, Andrew J.; Tong, Xin T.
2016-10-01
Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.
Elmore, S; Kirk, A; Thornton, A J; Harrison, J R; Tamain, P; Kocan, M; Bradley, J W
2013-01-01
Knowledge of the ion temperature (Ti) is of key importance for determining heat fluxes to the divertor and plasma facing components, however data regarding this is limited compared to electron temperature (Te) data. Ti measurements at the divertor target, between edge-localised modes (inter-ELM) H-mode, have been made using a novel retarding field energy analyser (RFEA).
Studies of Plasma Detachment Using a One Dimensional Model for Divertor Operation
Vesey, R A; Bateman, G
1995-01-01
To characterize the conditions required to reach advanced divertor regimes, a one-dimensional computational model has been developed based on a coordinate transformation to incorporate two-dimensional effects. This model includes transport of ions, two species each of atoms and molecules, momentum, and ion and electron energy both within and across the flux surfaces. Impurity radiation is calculated using a coronal equilibrium model which includes the effects of charge-exchange recombination. Numerical results indicate that impurity radiation acts to facilitate plasma detachment and enhances the power lost from the divertor channel in escaping neutral atoms by cooling the electrons and suppressing ionization. As divertor particle densities increase, cold and thermal molecules become increasingly important in cooling the plasma, with molecular densities dominating electron and atomic densities under some conditions.
Investigation of SOL parameters and divertor particle flux from electric probe measurements in KSTAR
Energy Technology Data Exchange (ETDEWEB)
Bak, J.G., E-mail: jgbak@nfri.re.kr [National Fusion Research Institute, Daejeon (Korea, Republic of); Kim, H.S. [National Fusion Research Institute, Daejeon (Korea, Republic of); Bae, M.K. [Hanyang University, Seoul (Korea, Republic of); Juhn, J.W.; Seo, D.C.; Bang, E.N. [National Fusion Research Institute, Daejeon (Korea, Republic of); Shim, S.B. [Pusan National University, Pusan (Korea, Republic of); Chung, K.S. [Hanyang University, Seoul (Korea, Republic of); Lee, H.J. [Pusan National University, Pusan (Korea, Republic of); Hong, S.H. [National Fusion Research Institute, Daejeon (Korea, Republic of)
2015-08-15
The upstream scrape-off layer (SOL) profiles and downstream particle fluxes are measured with a fast reciprocating Langmuir probe assembly (FRLPA) at the outboard mid-plane and a fixed edge Langmuir probe array (ELPA) at divertor region, respectively in the KSTAR. It is found that the SOL has a two-layer structure in the outboard wall-limited (OWL) ohmic and L-mode: a near SOL (∼5 mm zone) with a narrow feature and a far SOL with a broader profile. The near SOL width evaluated from the SOL profiles in the OWL plasmas is comparable to the scaling for the L-mode divertor plasmas in the JET and AUG. In the SOL profiles and the divertor particle flux profile during the ELMy H-modes, the characteristic e-folding lengths of electron temperature, plasma density and particle flux during an ELM phase are about two times larger than ones at the inter ELM.
Towards the development of workable acceptance criteria for the divertor CFC monoblock armour
Energy Technology Data Exchange (ETDEWEB)
D' Agata, E. [ITER International Team, ITER Joint Work Site, Boltzmannstr. 2, D-85748 Garching (Germany)]. E-mail: dagatae@itereu.de; Tivey, R. [ITER International Team, ITER Joint Work Site, Boltzmannstr. 2, D-85748 Garching (Germany)
2005-11-15
The plasma-facing components (PFCs) of the ITER divertor will be subjected to high heat flux (HHF). Carbon-fibre composite (CFC) is selected as the armour for the region of highest heat flux where the scrape-off layer of the plasma intercepts the vertical targets (VT). Failure of the armour to heat sink joints will compromise the performance of the divertor and could ultimately result in its failure and the shut down of the ITER machine. There are tens of thousands of CFCs to CuCrZr joints. The aim of the PFC design is to ensure that the divertor can continue to function even with the failure of a few joints. In preparation for writing the procurement specification for the ITER vertical target PFCs, a programme of work is underway with the objective of defining workable acceptance criteria for the PFC armour joints.
Energy Technology Data Exchange (ETDEWEB)
Escourbiac, F; Richou, M; Guigon, R; Durocher, A; Schlosser, J; Grosman, A [CEA/IRFM, F-13108, Saint-Paul-lez-Durance (France); Constans, S [AREVA-NP, Le Creusot (France); Merola, M [ITER Organization, Cadarache (France); Riccardi, B [Fusion For Energy, Barcelona (Spain)], E-mail: frederic.escourbiac@cea.fr
2009-12-15
Experience has shown that a critical part of the high-heat flux (HHF) plasma-facing component (PFC) is the armour to heat sink bond. An experimental study was performed in order to define acceptance criteria with regards to thermal hydraulics and fatigue performance of the International Thermonuclear Experimental Reactor (ITER) divertor PFCs. This study, which includes the manufacturing of samples with calibrated artificial defects relevant to the divertor design, is reported in this paper. In particular, it was concluded that defects detectable with non-destructive examination (NDE) techniques appeared to be acceptable during HHF experiments relevant to heat fluxes expected in the ITER divertor. On the basis of these results, a set of acceptance criteria was proposed and applied to the European vertical target medium-size qualification prototype: 98% of the inspected carbon fibre composite (CFC) monoblocks and 100% of tungsten (W) monoblock and flat tiles elements (i.e. 80% of the full units) were declared acceptable.
Divertor with a third-order null of the poloidal field
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Umansky, M. V. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
2013-09-15
A concept and preliminary feasibility analysis of a divertor with the third-order poloidal field null is presented. The third-order null is the point where not only the field itself but also its first and second spatial derivatives are zero. In this case, the separatrix near the null-point has eight branches, and the number of strike-points increases from 2 (as in the standard divertor) to six. It is shown that this magnetic configuration can be created by a proper adjustment of the currents in a set of three divertor coils. If the currents are somewhat different from the required values, the configuration becomes that of three closely spaced first-order nulls. Analytic approach, suitable for a quick orientation in the problem, is used. Potential advantages and disadvantages of this configuration are briefly discussed.
Analysis of FAST snowflake divertor by EDGE2D/EIRENE
Energy Technology Data Exchange (ETDEWEB)
Viola, B., E-mail: bruno.viola@enea.it [ENEA Unità Tecnica Fusione, C.R. Frascati, Via E. Fermi 45, 00044 Frascati, Rome (Italy); Pericoli Ridolfini, V. [Consorzio CREATE, Università di Napoli Federico II, Via Claudio 21, 80125 Napoli (Italy); Visona, N. [Consorzio RFX, C.so Stati Uniti 4, Padova 35127 (Italy); Corrigan, G.; Harting, D. [Culham Centre of Fusion Energy, OX14 3DB Abingdon (United Kingdom); Maddaluno, G. [ENEA Unità Tecnica Fusione, C.R. Frascati, Via E. Fermi 45, 00044 Frascati, Rome (Italy); Zagórski, R. [Institute of Plasma Physics and Laser Microfusion, 01-497 Warsaw (Poland)
2015-08-15
The snowflake [1,2] divertor is a proposal for solving the heat and particle exhaust problem in fusion grade plasmas. Turning the X-point into a second order null gives the possibility of radially expanding the poloidal flux in the divertor region much more than in a SD, increasing the connection length, redistributing the power load on a larger area and enhancing radiative losses. Since the efforts associated to the design of reactor-relevant configurations, like the snowflake, are large, ENEA is studying this configuration using efficient and flexible numerical tools to design and optimise tokamak equilibrium configurations. Such studies are applied to the Divertor Test Tokamak FAST, a satellite tokamak proposed for the European roadmap towards fusion.
Design and optimization of W/Cu divertor mock-ups
Institute of Scientific and Technical Information of China (English)
Qiong Li; Weiping Shen
2007-01-01
Tungsten is a promising candidate for plasma-facing materials to cover the surface of the divertor plate in the design of an international thermonuclear experimental reactor (ITER). Copper as a heat sink material serves to transfer heat excellently. Divertor mock-ups with W/Cu graded interlayers were designed to reduce thermal stresses. Thermally induced stresses and temperature in a W/Cu divertor mock-up were analyzed using the finite element method. The graded structures with different exponents p and thicknesses were designed and discussed. The conclusions drawn from these analyses are that thermal stresses reach the minimum and the temperature is suitable when exponent p is 1.5 and the thickness of five graded interlayers is 5 mm.
Fast Identification of Recycling Properties of Wall-Released Hydrogenic Neutrals in Divertor Plasma
Institute of Scientific and Technical Information of China (English)
LI Chengyue; DENG Baiquan; YAN Jiancheng; G. A. EMMERT
2007-01-01
A new bipartition neutral transport model was developed for quick identification of the recycling properties of the wall-released hydrogenic neutral particles in the vicinity of the divertor target plate. Based on this model, the numerical calculation results are fairly consistent with the results obtained with the 'multi-generation method'. This model can not only be utilized to provide a source term from neutral transport calculations for the B2 edge plasma transport code, which has been used to simulate edge plasma transport of an HL-2A divertor configuration, but can also be specifically applied for fast classification of the divertor plasma as high recycling or low recycling. Our results also show that the transmissivity is lower in the high-recycling regime.
New bipartition model of neutral particle transport in the HL-2A divertor region
Institute of Scientific and Technical Information of China (English)
DENG Bai-quan; YAN Jian-cheng; PENG Li-lin
2005-01-01
A new bipartition neutral transport model has been developed for simulation of the hydrogenic neutral particle transport in the vicinity of HL-2A divertor target plate. The numerical calculation results on the basis of this model are fairly consistent with the results obtained with the "multi-generation method". One possible application of this model is to provide a source term originating from neutral transport calculation for any other edge plasma transport code, for instance, B-2 code, which has been used to simulate edge plasma transport of the HL-2A divertor configuration. Especially it can be utilized to quickly classify the plasma in divertor region as high or low recycling regime.
Calculation of Divertor Thermal Response as a Function of Material Composition for NSTX
Chaffin, Michael; Maingi, Rajesh
2007-11-01
Present tokamak designs use a magnetic divertor to deposit heat from the edge plasma onto Plasma Facing Components (PFCs) designed to remove the heat. Studying how this heat is distributed under various discharge conditions gives insight into how heat deposition can be optimized, and how different materials respond to plasma heating. In the National Spherical Torus eXperiment (NSTX), infrared cameras are used to measure divertor surface temperature, from which heat flux is computed using a 1D semi-infinite slab model with constant thermal conductivity. Here, a 1D simulation of the PFCs incorporating temperature-dependent thermal properties is used to compute heat flux profiles resolved across time and tile thickness. The PFC response to a given heat flux is also computed, and comparisons of resulting temperature profiles are made for a variety of materials including ATJ graphite (presently in the NSTX divertor), pyrolytic graphite, molybdenum, and tungsten.
Energy Technology Data Exchange (ETDEWEB)
Di Gironimo, Giuseppe, E-mail: giuseppe.digironimo@unina.it [CREATE, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli (Italy); Cacace, Maurizio [CREATE, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli (Italy); Crescenzi, Fabio [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati, Roma (Italy); Labate, Carmelenzo [CREATE, University of Naples Parthenope, Via Acton 38, 80133 Napoli (Italy); Lanzotti, Antonio [CREATE, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli (Italy); Lucca, Flavio [LT Calcoli srl, Piazza Prinetti 26/B, 23807 Merate, LC (Italy); Marzullo, Domenico; Mozzillo, Rocco [CREATE, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli (Italy); Pagani, Irene [LT Calcoli srl, Piazza Prinetti 26/B, 23807 Merate, LC (Italy); Ramogida, Giuseppe; Roccella, Selanna [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati, Roma (Italy); Viganò, Fabio [LT Calcoli srl, Piazza Prinetti 26/B, 23807 Merate, LC (Italy)
2015-10-15
Highlights: • The conceptual design of FAST divertor has been carried out through a continuous process of requirements refinement and design optimization (V-model approach), in order to achieve a design suited to the needs, RH compatible and ITER-like. • Thermal, structural and electromagnetic analyses have been performed, resulting in requirements refinement. • FAST divertor is now characterized by more realistic, reliable and functional features, satisfying thermo-mechanical capabilities and the remote handling (RH) compatibility. - Abstract: Divertor is a crucial component in Tokamaks, aiming to exhaust the heat power and particles fluxes coming from the plasma during discharges. This paper focuses on the optimization process of FAST divertor, aimed at achieving required thermo-mechanical capabilities and the remote handling (RH) compatibility. Divertor RH system final layout has been chosen between different concept solutions proposed and analyzed within the principles of Theory of Inventive Problem Solving (TRIZ). The design was aided by kinematic simulations performed using Digital Mock-Up capabilities of Catia software. Considerable electromagnetic (EM) analysis efforts and top-down CAD approach enabled the design of a final and consistent concept, starting from a very first dimensioning for EM loads. In the final version here presented, the divertor cassette supports a set of tungsten (W) actively cooled tiles which compose the inner and outer vertical targets, facing the plasma and exhausting the main part of heat flux. W-tiles are assembled together considering a minimum gap tolerance (0.1–0.5 mm) to be mandatorily respected. Cooling channels have been re-dimensioned to optimize the geometry and the layout of coolant volume inside the cassette has been modified as well to enhance the general efficiency.
Design of a diagnostic residual gas analyzer for the ITER divertor
Energy Technology Data Exchange (ETDEWEB)
Klepper, C.C., E-mail: kleppercc@ornl.gov [Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169 (United States); Biewer, T.M.; Graves, V.B. [Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169 (United States); Andrew, P. [ITER Organisation, Route de Vinon-sur-Verdon, 13067 St. Paul-lez-Durance (France); Lukens, P.C. [US ITER Project Office, 1055 Commerce Park Dr #1, Oak Ridge, TN 37830 (United States); Marcus, C. [Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169 (United States); Shimada, M., E-mail: shimada.michiya@jaea.go.jp [ITER Organisation, Route de Vinon-sur-Verdon, 13067 St. Paul-lez-Durance (France); Hughes, S.; Boussier, B. [ITER Organisation, Route de Vinon-sur-Verdon, 13067 St. Paul-lez-Durance (France); Johnson, D.W. [US ITER Diagnostics Office, Princeton Plasma Physics Laboratory, Princeton, NJ 08540 (United States); Gardner, W.L. [US ITER Project Office, 1055 Commerce Park Dr #1, Oak Ridge, TN 37830 (United States); Hillis, D.L. [Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169 (United States); Vayakis, G.; Walsh, M. [ITER Organisation, Route de Vinon-sur-Verdon, 13067 St. Paul-lez-Durance (France)
2015-10-15
Highlights: • The divertor DRGA for ITER will measure neutral gas composition in the pumping ducts during plasma. • System must respond in timescales relevant to compositional changes in the divertor plasma. • It is shown that times can vary from 1 to 6 s for fuel (H2, D2, T2) up to 50 s for He (fusion reaction ash). • It is shown that present design delivers ∼ 1 s response even via an 8m long sampling pipe sampling. • Response time validated with VacTran{sup ®} over anticipated the 0.1–10 Pa pressure range in the ducts. - Abstract: One of the ITER diagnostics having reached an advanced design stage is a diagnostic RGA for the divertor, i.e. residual gas analysis system for the ITER divertor, which is intended to sample the divertor pumping duct region during the plasma pulse and to have a response time compatible with plasma particle and impurity lifetimes in the divertor region. Main emphasis is placed on helium (He) concentration in the ducts, as well as the relative concentration between the hydrogen isotopes (mainly in the form of diatomic molecules of H, D, and T). Measurement of the concentration of radiative gases, such as neon (Ne) and nitrogen (N{sub 2}), is also intended. Numerical modeling of the gas flow from the sampled region to the cluster of analysis sensors, through a long (∼8 m long, ∼110 mm diameter) sampling pipe originating from a pressure reducing orifice, confirm that the desired response time (∼1 s for He or D{sub 2}) is achieved with the present design.
A multichannel visible spectroscopy system for the ITER-like W divertor on EAST
Mao, Hongmin; Ding, Fang; Luo, Guang-Nan; Hu, Zhenhua; Chen, Xiahua; Xu, Feng; Yang, Zhongshi; Chen, Jingbo; Wang, Liang; Ding, Rui; Zhang, Ling; Gao, Wei; Xu, Jichan; Wu, Chengrui
2017-04-01
To facilitate long-pulse high power operation, an ITER-like actively cooled tungsten (W) divertor was installed in Experimental Advanced Superconducting Tokamak (EAST) to replace the original upper graphite divertor in 2014. A dedicated multichannel visible spectroscopic diagnostic system has been accordingly developed for the characterization of the plasma and impurities in the W divertor. An array of 22 lines-of-sight (LOSs) provides a profile measurement of the light emitted from the plasma along upper outer divertor, and the other 17 vertical LOSs view the upper inner divertor, achieving a 13 mm poloidal resolution in both regions. The light emitted from the plasma is collected by a specially designed optical lens assembly and then transferred to a Czerny-Turner spectrometer via 40 m quartz fibers. At the end, the spectra dispersed by the spectrometer are recorded with an Electron-Multiplying Charge Coupled Device (EMCCD). The optical throughput and quantum efficiency of the system are optimized in the wavelength range 350-700 nm. The spectral resolution/coverage can be adjusted from 0.01 nm/3 nm to 0.41 nm/140 nm by switching the grating with suitable groove density. The frame rate depends on the setting of LOS number in EMCCD and can reach nearly 2 kHz for single LOS detection. The light collected by the front optical lens can also be divided and partly transferred to a photomultiplier tube array with specified bandpass filter, which can provide faster sampling rates by up to 200 kHz. The spectroscopic diagnostic is routinely operated in EAST discharges with absolute optical calibrations applied before and after each campaign, monitoring photon fluxes from impurities and H recycling in the upper divertor. This paper presents the technical details of the diagnostic and typical measurements during EAST discharges.
Conceptual design studies for the European DEMO divertor: Rationale and first results
Energy Technology Data Exchange (ETDEWEB)
You, J.H., E-mail: you@ipp.mpg.de [Max Planck Institute for Plasma Physics, Boltzmann Str. 2, 85748 Garching (Germany); Mazzone, G.; Visca, E. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Italy); Bachmann, Ch. [EUROfusion PMU, c/o IPP, Boltzmann Str. 2, 85748 Garching (Germany); Autissier, E. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Barrett, T. [CCFE, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Cocilovo, V.; Crescenzi, F. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Italy); Domalapally, P.K. [Research Cnter Rez, Hlavní 130, 250 68 Husinec–Řež (Czech Republic); Dongiovanni, D. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Italy); Entler, S. [Institute of Plasma Physics CAS, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Federici, G. [EUROfusion PMU, c/o IPP, Boltzmann Str. 2, 85748 Garching (Germany); Frosi, P. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Italy); Fursdon, M. [CCFE, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Greuner, H. [Max Planck Institute for Plasma Physics, Boltzmann Str. 2, 85748 Garching (Germany); Hancock, D. [CCFE, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Marzullo, D. [CREATE, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli (Italy); McIntosh, S. [CCFE, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Müller, A.V. [Max Planck Institute for Plasma Physics, Boltzmann Str. 2, 85748 Garching (Germany); Porfiri, M.T. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Italy); and others
2016-11-01
Highlights: • A brief overview is given on the overall R&D activities of the work package Divertor which is a project of the EUROfusion Consortium. • The rationale of the hydraulic, thermal and structural design scheme is described. • The first results obtained for the preliminary DEMO divertor cassette model are presented. - Abstract: In the European fusion roadmap, reliable power handling has been defined as one of the most critical challenges for realizing a commercially viable fusion power. In this context, the divertor is the key in-vessel component, as it is responsible for power exhaust and impurity removal for which divertor target is subjected to very high heat flux loads. To this end, an integrated R&D project was launched in the EUROfusion Consortium in order to deliver a holistic conceptual design solution together with the core technologies for the entire divertor system of a DEMO reactor. The work package ‘Divertor’ consists of two project areas: ‘Cassette design and integration’ and ‘Target development’. The essential mission of the project is to develop and verify advanced design concepts and the required technologies for a divertor system being capable of meeting the physical and system requirements defined for the next-generation European DEMO reactor. In this contribution, a brief overview is presented of the works from the first project year (2014). Focus is put on the loads specification, design boundary conditions, materials requirements, design approaches, and R&D strategy. Initial ideas and first estimates are presented.
Changes in divertor conditions in response to changing core density with RMPs
Briesemeister, A. R.; Ahn, J.-W.; Canik, J. M.; Fenstermacher, M. E.; Frerichs, H.; Lasnier, C. J.; Lore, J. D.; Leonard, A. W.; Makowski, M. A.; McLean, A. G.; Meyer, W. H.; Schmitz, O.; Shafer, M. W.; Unterberg, E. A.; Wang, H. Q.; Watkins, J. G.
2017-07-01
The effects of changes in core density on divertor electron temperature, density and heat flux when resonant magnetic perturbations (RMPs) are applied are presented, notably a reduction in RMP induced secondary radial peaks in the electron temperature profile at the target plate is observed when the core density is increased, which is consistent with modeling. RMPs is used here to indicate non-axisymmetric magnetic field perturbations, created using in-vessel control coils, which have at least one but typically many resonances with the rotational transform of the plasma (Evans et al 2006 Phys. Plasmas 13 056121). RMPs are found to alter inter-ELM heat flux to the divertor by modifying the core plasma density. It is shown that applying RMPs reduces the core density and increases the inter-ELM heat flux to both the inner and outer targets. Using gas puffing to return the core density to the pre-RMP levels more than eliminates the increase in inter-ELM heat flux, but a broadening of the heat flux to the outer target remains. These measurements were made at a single toroidal location, but the peak in the heat flux profile was found near the outer strike point where simulations indicate little toroidal variation should exist and tangentially viewing diagnostics showed no evidence of strong asymmetries. In experiments where divertor Thomson scattering measurements were available it is shown that local secondary peaks in the divertor electron temperature profile near the target plate are reduced as the core density is increased, while peaks in the divertor electron density profile near the target are increased. These trends observed in the divertor electron temperature and density are qualitatively reproduced by scanning the upstream density in EMC3-Eirene modeling. Measurements are presented showing that higher densities are needed to induce detachment of the outer strike point in a case where an increase in electron temperature, likely due to a change in MHD activity
Status of design and experimental activity on module of lithium divertor for KTM tokamak
Energy Technology Data Exchange (ETDEWEB)
Lyublinski, Igor E., E-mail: lyublinski@yandex.ru [JSC “Red Star”, Moscow (Russian Federation); Vertkov, Alexey V.; Zharkov, Mikhail Yu.; Semenov, Vladimir V. [JSC “Red Star”, Moscow (Russian Federation); Mirnov, Sergey V.; Lazarev, Vladimir B. [GSC RF TRINITI, Troitsk, Moscow Region (Russian Federation); Tazhibayeva, Irina L.; Shapovalov, Gennadiy V.; Kulsartov, Timur V.; D’yachenko, Alexandr V. [IAE of National Nuclear Center, Kurchatov (Kazakhstan); Mazzitelli, Giuseppe [Associazione EURATOM-ENEA sulla Fusione, C.R. ENEA Frascati, Rome (Italy); Agostini, Pietro [ENEA Brasimone, Camugnano, BO (Italy)
2013-10-15
Highlights: • Lithium divertor module based on capillary-porous system is created for KTM tokamak. • The hydraulic tests of lithium divertor module were conducted. • The results were compared with the calculation data. • The analysis of results’ discrepancies was conducted. • The lithium divertor module is ready for tests on KTM tokamak. -- Abstract: The projects of ITER and DEMO reactors showed that there are serious difficulties with solving the issues of plasma facing elements (PFE) based on the solid materials. Problems of PFE can be overcome by the use of liquid lithium. Application of lithium will allow to create a self-renewal and MHD stable liquid metal surface of the in-vessel devices possessing practically unlimited service life. Realization of these advantages is based on use of so-called lithium capillary-porous system (CPS) – new material, in which liquid lithium fills a solid matrix from porous material. The progress in development of lithium technology and also lithium experiments in the tokamaks TFTR, T-11M, T-10, FTU, NSTX, LTX, HT-7 and stellarator TJ II is a good basis for development of the project of steady-state operating lithium divertor module for Kazakhstan tokamak. At present the lithium divertor module for KTM tokamak is development and manufacturing. The paper describes main design features of the module of lithium divertor (MLD). The first step of the hydraulic tests of MLD with fully assembled external thermo-stabilization system, which was connected to in-vessel lithium unit, were performed using ethanol as a model heat transfer media. Test results of MLD have shown that operating parameters of designed and manufactured system for thermo-stabilization are sufficient for proper operation; basic hydraulic characteristics of the system are close to expected values.
Design study of ITER-like divertor target for DEMO
Energy Technology Data Exchange (ETDEWEB)
Crescenzi, Fabio, E-mail: fabio.crescenzi@enea.it [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Roma) (Italy); Bachmann, C. [EFDA, Power Plant Physics and Technology, Boltzmannstraße 2, 85748 Garching (Germany); Richou, M. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Roccella, S.; Visca, E. [ENEA, Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, 00044 Frascati (Roma) (Italy); You, J.-H. [Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, 85748 Garching (Germany)
2015-10-15
Highlights: • ‘DEMO’ is a near-term Power Plant Conceptual Study (PPCS). • The ITER-like design concept represents a promising solution also for DEMO plasma facing units. • The optimization of PFUs aims to enhance the thermo-mechanical behaviour of the component. • The optimized geometry was evaluated by ITER SDC-IC criteria and in terms of low cycle fatigue (LCF). - Abstract: A near-term water-cooled target solution has to be evaluated together with the required technologies and its power exhaust limit under ‘DEMO’ conditions. The ITER-like design concept based on the mono-block technology using W as armour material and the CuCrZr-IG as structural material with an interlayer of pure copper represents a promising solution also for DEMO. This work reports the design study of an “optimized” ITER-like Water Cooled Divertor able to withstand a heat flux of 10 MW m{sup −2}, as requested for DEMO operating conditions. The optimization of plasma facing unit (PFU) aims to enhance the thermo-mechanical behaviour of the component by varying some geometrical parameters (monoblock size, interlayer thickness and, tube diameter and thickness). The optimization was performed by means of the multi-variable optimization algorithms using the FEM code ANSYS. The coolant hydraulic conditions (inlet pressure, temperature and velocity) were fixed for simplicity. This study is based on elastic analysis and 3 dimensional modelling. The resulting optimized geometry was evaluated on the basis of the ITER SDC-IC criteria and in terms of low cycle fatigue (LCF). The margin to the critical heat flux (CHF) was also estimated. Further design study (taking into account the effect of neutron radiation on the material properties) together with mock-up fabrication and high-heat-flux (HHF) tests are foreseen in next work programmes.
Optimization of tungsten castellated structures for the ITER divertor
Litnovsky, A.; Hellwig, M.; Matveev, D.; Komm, M.; van den Berg, M.; De Temmerman, G.; Rudakov, D.; Ding, F.; Luo, G.-N.; Krieger, K.; Sugiyama, K.; Pitts, R. A.; Petersson, P.
2015-08-01
In ITER, the plasma-facing components (PFCs) of the first wall and the divertor armor will be castellated to improve their thermo-mechanical stability and to limit forces due to induced currents. The fuel accumulation in the gaps may significantly contribute to the in-vessel fuel inventory. Castellation shaping may be the most straightforward way to minimize the fuel inventory and to alleviate the thermal loads onto castellations. A new castellation shape was proposed and comparative modeling of conventional (rectangular) and shaped castellation was performed for ITER conditions. Shaped castellation was predicted to be capable to operate under stationary heat load of 20 MW/m2. An 11-fold decrease of beryllium (Be) content in the gaps of the shaped cells alone with a 7-fold decrease of carbon content was predicted. In order to validate the predictive capabilities of modeling tools used for ITER conditions, the dedicated modeling with the same codes was made for existing tokamaks and benchmarked with the results of multi-machine experiments. For the castellations exposed in TEXTOR and DIII-D, the carbon amount in the gaps of shaped cells was 1.9-2.3 times smaller than that of rectangular ones. Modeling for TEXTOR conditions yielded to 1.5-fold decrease of carbon content in the gaps of shaped castellation outlining fair agreement with the experiment. At the same time, a number of processes, like enhanced erosion of molten layer yet need to be implemented in the codes in order to increase the accuracy of predictions for ITER.
Baelmans, M.; Blommaert, M.; Dekeyser, W.; Van Oevelen, T.
2017-03-01
Plasma edge transport codes play a key role in the design of future divertor concepts. Their long simulation times in combination with a large number of control parameters turn the design into a challenging task. In aerodynamics and structural mechanics, adjoint-based optimization techniques have proven successful to tackle similar design challenges. This paper provides an overview of achievements and remaining challenges with these techniques for complex divertor design. It is shown how these developments pave the way for fast sensitivity analysis and improved design from different perspectives.
Transport studies in boundary and divertor plasmas of JT-60U
Energy Technology Data Exchange (ETDEWEB)
Kumagai, Akira [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
1999-03-01
This thesis describes an investigation on transport of plasma, neutral particle and impurity in the boundary and divertor of the JT-60U tokamak to provide a better understanding of plasma-surface interactions and divertor physics. The asymmetry between the inboard and outboard divertor on plasma parameters (in-out asymmetry) are usually observed in tokamaks with the divertor. In this study, the in-out asymmetry was investigated under various plasma conditions and discharge parameters. The observed results were discussed with several mechanisms that can produce the in-out asymmetry. It was confirmed experimentally that the importance of each mechanism depends on the plasma parameters and discharge conditions. The current flowing in the scrape-off layer (SOL) due to the in-out asymmetry was observed. The SOL currents in the high density plasma with the occurrence of the plasma detachment were investigated for the first time in this study. The ion temperature in the divertor region is one of the most important factors for both generation and transport of impurity. However, the background ion temperature in the divertor region has not been measured in any tokamak so far. The ion temperature in the divertor region has been measured for the first time with the Doppler broading of the C{sup 3+} ion emission line. The measured temperature was analyzed by an impurity particle transport code. The code calculation showed that the measured temperature reflects the low temperature at the outside of the separatrix in the inboard region. The spectral profile of Balmer-{alpha} (D{sub {alpha}}) line emitted from the deuterium atoms reflects the velocity distribution of neutral particles by the Doppler effect and is effective for investigating the detailed neutral behavior and recycling process. The spatial variation of the D{sub {alpha}} line spectral profile in the divertor region has been measured for the first time in this study. The observed results were compared with the
Spectroscopic measurements of impurity temperatures and parallel ion flows in the DIII-D divertor
Energy Technology Data Exchange (ETDEWEB)
Isler, R.C. [Oak Ridge National Lab., TN (United States); Brooks, N.H.; West, W.P.; Leonard, A.W. [General Atomics, San Diego, CA (United States); McKee, G.R. [Univ. of Wisconsin, Madison, WI (United States); Porter, G.D. [Lawrence Livermore National Lab., CA (United States)
1998-06-01
Impurity ion temperatures and parallel flow velocities in the DIII-D divertor have been measured from the shapes and shifts of visible spectral lines of C II, C III, and B II. Spectral multiplet patterns are analyzed by fitting them to theoretical profiles that incorporate exact calculations for the Zeeman/Paschen-Back effect. Ion temperatures range from 4--20 eV. Both normal flows toward the target plate and reversed flows away from the target plate are observed in the outer divertor leg; only flows toward the plate are detected in the inner leg.
Spectroscopic measurements of impurity temperatures and parallel ion flows in the DIII-D divertor
Isler, R. C.; Brooks, N. H.; West, W. P.; Leonard, A. W.; McKee, G. R.; Porter, G. D.
Impurity ion temperatures and parallel flow velocities in the DIII-D divertor have been measured from the shapes and shifts of visible spectral lines of C II, C III, and B II. Spectral multiplet patterns are analyzed by fitting them to theoretical profiles that incorporate exact calculations for the Zeeman/Paschen-Back effect. Both normal flows toward the target plate and reversed flows away from the target plate are observed in the outer divertor leg; only flows toward the plate are detected in the inner leg.
Development of divertor tungsten coatings for the JET ITER-like wall
Matthews, G. F.; Coad, P.; Greuner, H.; Hill, M.; Hirai, T.; Likonen, J.; Maier, H.; Mayer, M.; Neu, R.; Philipps, V.; Pitts, R.; Riccardo, V.; JET EFDA Contributors
2009-06-01
The main objectives of the JET ITER-like Wall Project are to provide a beryllium main wall and tungsten divertor with at least a 4 year lifetime to allow full evaluation of the materials and related plasma scenarios for ITER. Tungsten coatings will be used over most of the divertor area and this paper describes the latest developments in the coating technology and an analysis of the implications for the coating lifetime and machine operation. Both steady state and transient heat loads are assessed.
Functional evolutions for homogeneous stationary death-immigration spatial dynamics
Finkelshtein, Dmitri
2011-01-01
We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynamics of states and their generating functionals are studied. Ergodic properties for the evolutions are considered.
非交换Orlicz空间的个体遍历定理%Individual Ergodic Theorems for Noncommutative Orlicz Space
Institute of Scientific and Technical Information of China (English)
萨吉代姆·吐尔洪; 吐尔德别克
2014-01-01
设(M,τ)是半有限von Neumann代数,Φ是N函数。证明了非交换Orlicz空间LΦ(M)的个体遍历定理。%Let (M,τ) be a semifinite von Neumann algebra andΦbe an N-function. We proved individual ergodic theorem in the noncommutative Orlicz space LΦ(M).
Directory of Open Access Journals (Sweden)
Mokaedi V. Lekgari
2014-01-01
Full Text Available We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs. We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.
Monte Carlo simulations of tungsten redeposition at the divertor target
Chankin, A. V.; Coster, D. P.; Dux, R.
2014-02-01
Recent modeling of controlled edge-localized modes (ELMs) in ITER with tungsten (W) divertor target plates by the SOLPS code package predicted high electron temperatures (>100 eV) and densities (>1 × 1021 m-3) at the outer target. Under certain scenarios W sputtered during ELMs can penetrate into the core in quantities large enough to cause deterioration of the discharge performance, as was shown by coupled SOLPS5.0/STRAHL/ASTRA runs. The net sputtering yield, however, was expected to be dramatically reduced by the ‘prompt redeposition’ during the first Larmor gyration of W1+ (Fussman et al 1995 Proc. 15th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research (Vienna: IAEA) vol 2, p 143). Under high ne/Te conditions at the target during ITER ELMs, prompt redeposition would reduce W sputtering by factor p-2 ˜ 104 (with p ≡ τionωgyro ˜ 0.01). However, this relation does not include the effects of multiple ionizations of sputtered W atoms and the electric field in the magnetic pre-sheath (MPS, or ‘Chodura sheath’) and Debye sheath (DS). Monte Carlo simulations of W redeposition with the inclusion of these effects are described in the paper. It is shown that for p ≪ 1, the inclusion of multiple W ionizations and the electric field in the MPS and DS changes the physics of W redeposition from geometrical effects of circular gyro-orbits hitting the target surface, to mainly energy considerations; the key effect is the electric potential barrier for ions trying to escape into the main plasma. The overwhelming majority of ions are drawn back to the target by a strong attracting electric field. It is also shown that the possibility of a W self-sputtering avalanche by ions circulating in the MPS can be ruled out due to the smallness of the sputtered W neutral energies, which means that they do not penetrate very far into the MPS before ionizing; thus the W ions do not gain a large kinetic energy as they are accelerated back to the surface by the
Evaluation of copper alloys for fusion reactor divertor and first wall components
DEFF Research Database (Denmark)
Fabritsiev, S.A.; Zinkle, S.J.; Singh, B.N.
1996-01-01
This paper presents a critical analysis of the main factors of radiation damage limiting the possibility to use copper alloys in the ITER divertor and first wall structure. In copper alloys the most significant types of radiation damage in the proposed temperature-dose operation range are swellin...
Optical design study for divertor observation at the stellarator W7-X
König, R.; Hildebrandt, D.; Hübner, T.; Klinkhamer, J.F.F.; Moddemeijer, K.; Vliegenthart, W.A.
2006-01-01
The stellarator W7-X will be capable of running in a quasicontinuous operating mode with 10 MW of electron cyclotron heating (ECRH) heating for 30 min, the duration only being limited by the capacity of the available cooling reservoir. The integrated ten discrete water cooled divertor modules need t
Enhanced -->E*-->B drift effects in the TCV snowflake divertor
G.P. Canal,; Lunt, T.; Reimerdes, H.; Duval, B. P.; Labit, B.; Vijvers, W. A. J.; TCV team,
2015-01-01
Measurements of various plasma parameters at the divertor targets of snowflake (SF) and conventional single-null configurations indicate an enhanced effect of the -->E*-->B drift in the scrape-off layer of plasmas in the SF configuration. Plasma boundary transport simulations using the EMC3-Ei
Optical design study for divertor observation at the stellarator W7-X
König, R.; Hildebrandt, D.; Hübner, T.; Klinkhamer, J.F.F.; Moddemeijer, K.; Vliegenthart, W.A.
2006-01-01
The stellarator W7-X will be capable of running in a quasicontinuous operating mode with 10 MW of electron cyclotron heating (ECRH) heating for 30 min, the duration only being limited by the capacity of the available cooling reservoir. The integrated ten discrete water cooled divertor modules need
Melt damage to the JET ITER-like Wall and divertor
Matthews, G. F.; Bazylev, B.; Baron-Wiechec, A.; Coenen, J.; Heinola, K.; Kiptily, V.; Maier, H.; Reux, C.; Riccardo, V.; Rimini, F.; Sergienko, G.; Thompson, V.; Widdowson, A.; Contributors, JET
2016-02-01
In October 2014, JET completed a scoping study involving high power scenario development in preparation for DT along with other experiments critical for ITER. These experiments have involved intentional and unintentional melt damage both to bulk beryllium main chamber tiles and to divertor tiles. This paper provides an overview of the findings of concern for machine protection in JET and ITER, illustrating each case with high resolution images taken by remote handling or after removal from the machine. The bulk beryllium upper dump plate tiles and some other protection tiles have been repeatedly flash melted by what we believe to be mainly fast unmitigated disruptions. The flash melting produced in this way is seen at all toroidal locations and the melt layer is driven by j × B forces radially outward and upwards against gravity. In contrast, the melt pools caused while attempting to use MGI to mitigate deliberately generated runaway electron beams are localized to several limiters and the ejected material appears less influenced by j × B forces and shows signs of boiling. In the divertor, transient melting of bulk tungsten by ELMs was studied in support of the ITER divertor material decision using a specially prepared divertor module containing an exposed edge. Removal of the module from the machine in 2015 has provided improved imaging of the melt and this confirms that the melt layers are driven by ELMs. No other melt damage to the other 9215 bulk tungsten lamellas has yet been observed.
The Influence of Filaments in the Private Flux Region on Divertor Particle and Power Deposition
Harrison, J R; Thornton, A J; Walkden, N R
2015-01-01
The transport of particles via intermittent filamentary structures in the private flux region of plasmas in the MAST tokamak has been investigated using a fast framing camera recording visible light emission from the volume of the lower divertor, as well as Langmuir probes and IR thermography monitoring particle and power fluxes to plasma-facing surfaces in the divertor. The visible camera data suggests that, in the divertor volume, fluctuations in light emission above the X-point are strongest in the scrape-off layer (SOL). Conversely, in the region below the X-point, it is found that these fluctuations are strongest in the private flux region (PFR) of the inner divertor leg. Detailed analysis of the appearance of these filaments in the camera data suggests that they are approximately circular, around 1-2cm in diameter. The most probable toroidal mode number is between 2 and 3. These filaments eject plasma deeper into the private flux region, sometimes by the production of secondary filaments, moving at a sp...
SPIRAL field mapping on NSTX for comparison to divertor RF heat deposition
Hosea, J. C.; Perkins, R.; Jaworski, M. A.; Kramer, G. J.; Ahn, J.-W.; Bertelli, N.; Gerhardt, S.; Gray, T. K.; LeBlanc, B. P.; Maingi, R.; Phillips, C. K.; Roquemore, L.; Ryan, P. M.; Sabbagh, S.; Taylor, G.; Tritz, K.; Wilson, J. R.; NSTX Team
2014-02-01
Field-aligned losses of HHFW power in the SOL of NSTX have been studied with IR cameras and probes, but the interpretation of the data depends somewhat on the magnetic equilibrium reconstruction. Both EFIT02 and LRDFIT04 magnetic equilibria have been used with the SPIRAL code to provide field mappings in the scrape off layer (SOL) on NSTX from the midplane SOL in front of the HHFW antenna to the divertor regions, where the heat deposition spirals are measured. The field-line mapping spiral produced at the divertor plate with LRDFIT04 matches the HHFW-produced heat deposition best, in general. An independent method for comparing the field-line strike patterns on the outer divertor for the two equilibria is provided by measuring Langmuir probe characteristics in the vicinity of the outer vessel strike radius (OVSR) and observing the effect on floating potential, saturation current, and zero-probe-voltage current (IV=0) with the crossing of the OVSR over the probe. Interestingly, these comparisons also reveal that LRDFIT04 gives the more accurate location of the predicted OVSR, and confirm that the RF power flow in the SOL is essentially along the magnetic field lines. Also, the probe characteristics and IV=0 data indicate that current flows under the OVSR in the divertor tiles in most cases studied.
Lesson from Tungsten Leading Edge Heat Load Analysis in KSTAR Divertor
Hong, Suk-Ho; Pitts, Richard Anthony; Lee, Hyeong-Ho; Bang, Eunnam; Kang, Chan-Soo; Kim, Kyung-Min; Kim, Hong-Tack; ITER Organization Collaboration; Kstar Team Team
2016-10-01
An important design issue for the ITER tungsten (W) divertor and in fact for all such components using metallic plasma-facing elements and which are exposed to high parallel power fluxes, is the question of surface shaping to avoid melting of leading edges. We have fabricated a series of tungsten blocks with a variety of leading edge heights (0.3, 0.6, 1.0, and 2.0 mm), from the ITER worst case to heights even beyond the extreme value tested on JET. They are mounted into adjacent, inertially cooled graphite tile installed in the central divertor region of KSTAR, within the field of view of an infra-red (IR) thermography system with a spatial resolution to 0.4 mm/pixel. Adjustment of the outer divertor strike point position is used to deposit power on the different blocks in different discharges. The measured power flux density on flat regions of the surrounding graphite tiles is used to obtain the parallel power flux, q|| impinging on the various W blocks. Experiments have been performed in Type I ELMing H-mode with Ip = 600 kA, BT = 2 T, PNBI = 3.5 MW, leading to a hot attached divertor with typical pulse lengths of 10 s. Three dimensional ANSYS simulations using q|| and assuming geometric projection of the heat flux are found to be consistent with the observed edge loading. This research was partially supported by Ministry of Science, ICT, and Future Planning under KSTAR project.
Transient thermal hydraulic modeling and analysis of ITER divertor plate system
Energy Technology Data Exchange (ETDEWEB)
El-Morshedy, Salah El-Din [Argonne National Laboratory, Argonne, IL (United States); Atomic Energy Authority, Cairo (Egypt)], E-mail: selmorshedy@etrr2-aea.org.eg; Hassanein, Ahmed [Purdue University, West Lafayette, IN (United States)], E-mail: hassanein@purdue.edu
2009-12-15
A mathematical model has been developed/updated to simulate the steady state and transient thermal-hydraulics of the International Thermonuclear Experimental Reactor (ITER) divertor module. The model predicts the thermal response of the armour coating, divertor plate structural materials and coolant channels. The selected heat transfer correlations cover all operating conditions of ITER under both normal and off-normal situations. The model also accounts for the melting, vaporization, and solidification of the armour material. The developed model is to provide a quick benchmark of the HEIGHTS multidimensional comprehensive simulation package. The present model divides the coolant channels into a specified axial regions and the divertor plate into a specified radial zones, then a two-dimensional heat conduction calculation is created to predict the temperature distribution for both steady and transient states. The model is benchmarked against experimental data performed at Sandia National Laboratory for both bare and swirl tape coolant channel mockups. The results show very good agreements with the data for steady and transient states. The model is then used to predict the thermal behavior of the ITER plasma facing and structural materials due to plasma instability event where 60 MJ/m{sup 2} plasma energy is deposited over 500 ms. The results for ITER divertor response is analyzed and compared with HEIGHTS results.
Impact of nitrogen seeding on carbon erosion in the JET divertor
Brezinsek, S.; Jachmich, S.; Rapp, J.; Meigs, A. G.; Nicholas, C.; O' Mullane, M.; Pospieszczyk, A.; van Rooij, G. J.
2011-01-01
Nitrogen has been introduced in H-mode plasmas in JET in order to study its radiation cooling capability and impact on the erosion of divertor plasma-facing components made of carbon-fiber composites (CFC). Experiments in the ionizing plasma regime with low nitrogen injection show a reduction of the
Design and concept validation of the new solid tungsten divertor for ASDEX Upgrade
Energy Technology Data Exchange (ETDEWEB)
Herrmann, A., E-mail: albrecht.herrmann@ipp.mpg.de; Greuner, H.; Jaksic, N.; Böswirth, B.; Reimold, F.; Scarabosio, A.; Vorbrugg, S.; Wischmeier, M.
2013-10-15
Div-III, a divertor with solid tungsten target tiles for ASDEX Upgrade is designed and tested and will be installed in 2013. It is a further step in exploring tungsten as material for plasma facing components. It avoids the restrictions of tungsten coatings on graphite and realizes an operation range up to 50 MJ energy removing capability in the outer divertor. In addition, it allows physics investigation such as erosion and deuterium retention as well as effects of castellation and target tilting. The design of the target itself and the attachment was optimized with FE-analysis and was intensively high heat tested up to a double overload. Cyclic tests reveal that the target and the attachment can be operated with the design load of 50 MJ without any damage. Even a twofold overload results in local recrystallization and minor cracks but the targets did not fail during operation. The redesign of the divertor structure was used to increase the conductance between the cryo-pump and the divertor region. The impact of the changed pumping efficiency was investigated with SOLPS/Eirene modeling. The modeling results are an indication for an easier access to lower SOL densities as expected for a higher pumping efficiency in the main chamber.
Divertor heat load in ASDEX Upgrade L-mode in presence of external magnetic perturbation
Faitsch, M.; Sieglin, B.; Eich, T.; Herrmann, A.; Suttrop, W.; the ASDEX Upgrade Team
2017-09-01
Power exhaust is one of the major challenges for a future fusion device. Applying a non-axisymmetric external magnetic perturbation is one technique that is studied in order to mitigate or suppress large edge localized modes which accompany the high confinement regime in tokamaks. The external magnetic perturbation induces breaking in the axisymmetry of a tokamak and leads to a 2D heat flux pattern on the divertor target. The 2D heat flux pattern at the outer divertor target is studied on ASDEX Upgrade in stationary L-mode discharges. The amplitude of the 2D characteristic of the heat flux depends on the alignment between the field lines at the edge and the vacuum response of the applied magnetic perturbation spectrum. The 2D characteristic reduces with increasing density. The increasing divertor broadening, S, with increasing density is proposed as the main actuator. This is supported by a generic model using field line tracing and the vacuum field approach that is in quantitative agreement with the measured heat flux. The perturbed heat flux, averaged over a full toroidal rotation of the magnetic perturbation, is identical to the non-perturbed heat flux without magnetic perturbation. The transport qualifiers, power fall-off length {λ }q and divertor broadening, S, are the same within the uncertainty compared to the unperturbed reference. No additional cross field transport is observed.
The impact of divertor detachment on carbon sources in JET L-mode discharges
Brezinsek, S.; Meigs, A. G.; Jachmich, S.; Stamp, M. F.; Rapp, J.; Felton, R.; Pitts, R.A.; Philipps, V.; Huber, A.; Pugno, R.; Sergienko, G.; Pospieszczyk, A.
2009-01-01
Hydrocarbon injection experiments have been performed to investigate the chemical sputtering yield of carbon-fibre composites at elevated temperatures (T-surface similar or equal to 500 K) and detached plasma conditions in the JET outer divertor. A plasma scenario in L-mode with the outer strike-poi
Flow Field and Thermal Analysis of the Divertor Target Plate for HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In the initial phase of the physics experiment, the double-null divertor plates used consist of graphite armor tiles, Mo-alloy intermediate layers and Cu-alloy coolant tubes. In the later operating phase, tungsten will be used as armor tiles.A multi-physical field numerical analysis method is used in this paper. Its analysis model reflects more realistically the real divertor structure than other models. Two-dimensional (2D)and three-dimensional (3D) fluid flow field, temperature distribution and thermal stress analyses of the divertor plates are carried out by the ANSYS code. During the physics experimental phase with a heat flux of 1 MW/m2, a coolant velocity of 5.48 m/s, and a thermal stress of 750 kg/cm2,the graphite armor tiles successfully meet the requirements of temperature, thermal stress and sputtering erosion. The tungsten armor will be considered as a second candidate. The result of simulation can be used for upgrading the design parameters of the HL-2A poloidal divertor.
Evaluation of copper alloys for fusion reactor divertor and first wall components
DEFF Research Database (Denmark)
Fabritsiev, S.A.; Zinkle, S.J.; Singh, B.N.
1996-01-01
This paper presents a critical analysis of the main factors of radiation damage limiting the possibility to use copper alloys in the ITER divertor and first wall structure. In copper alloys the most significant types of radiation damage in the proposed temperature-dose operation range are swellin...
Evaluating gambles using dynamics
Peters, O.; Gell-Mann, M.
2016-02-01
Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in systems with ergodic properties, whereas decision-makers have no access to ensembles, and the variables representing wealth in the usual growth models do not have the relevant ergodic properties. Simultaneously addressing the shortcomings of utility and those of expectations, we propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic "utility functions" appear as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively. We highlight inconsistencies throughout the development of decision theory, whose correction clarifies that our perspective is legitimate. These invalidate a commonly cited argument for bounded utility functions.
In-pile thermocycling testing and post-test analysis of beryllium divertor mockups
Energy Technology Data Exchange (ETDEWEB)
Giniatulin, R.; Mazul, I. [Efremov Inst., St. Petersburg (Russian Federation); Melder, R.; Pokrovsky, A.; Sandakov, V.; Shiuchkin, A.
1998-01-01
The main damaging factors which impact the ITER divertor components are neutron irradiation, cyclic surface heat loads and hydrogen environment. One of the important questions in divertor mockups development is the reliability of beryllium/copper joints and the beryllium resistance under neutron irradiation and thermal cycling. This work presents the experiment, where neutron irradiation and thermocyclic heat loads were applied simultaneously for two beryllium/copper divertor mockups in a nuclear reactor channel to simulate divertor operational conditions. Two mockups with different beryllium grades were mounted facing each other with the tantalum heater placed between them. This device was installed in the active zone of the nuclear reactor SM-2 (Dimitrovgrad, Russia) and the tantalum block was heated by neutron irradiation up to a high temperature. The main part of the heat flux from the tantalum surface was transported to the beryllium surface through hydrogen, as a result the heat flux loaded two mockups simultaneously. The mockups were cooled by reactor water. The device was lowered to the active zone so as to obtain the heating regime and to provide cooling lifted. This experiment was performed under the following conditions: tantalum heater temperature - 1950degC; hydrogen environment -1000 Pa; surface heat flux density -3.2 MW/m{sup 2}; number of thermal cycles (lowering and lifting) -101; load time in each cycle - 200-5000 s; dwell time (no heat flux, no neutrons) - 300-2000 s; cooling water parameters: v - 1 m/s, Tin - 50degC, Pin - 5 MPa; neutron fluence -2.5 x 10{sup 20} cm{sup -2} ({approx}8 years of ITER divertor operation from the start up). The metallographic analysis was performed after experiment to investigate the beryllium and beryllium/copper joint structures, the results are presented in the paper. (author)
Preparation of 3D Printed Divertor Mock-up Design and Fabrication
Energy Technology Data Exchange (ETDEWEB)
Lee, Dong Won; Park, Sung Dae; Kim, Dong Jun; Kim, Suk Kwon; Lee, Eo Hwak [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
The divertor for fusion reactor is known to be able to remove the extreme heat flux up to 10 MW/m2 and the various type of divertors have been developed for enhancing the heat transfer such as hypervapotron, twisted tape insertion, screwed tube, and so on. In order to overcome this limitation, 3D printing method is considered to be used in the fusion reactor divertor design in present study. With the advantages of the 3D printing, the various shapes of the inner divertor cooling tube are investigated to enhance the turbulence of coolant and to reduce the pressure drop. The metallic powder of the fusion reactor candidate material is produced as the preliminary step for using in 3D printer. The material is a reduced activation ferritic-matensitic steel named as ARAA (Advanced Reduced Activation Alloy) which have been independently developed in Korea. Gas atomization method was used to make the spherical particles with average diameter of 100 μm. Several candidates were presented to achieve the excellent heat removal capacity and the low pressure drop. Thermal-hydraulic analysis was performed to confirm the effects of the inner cooling tube geometry with a conventional CFD code, ANSYS-CFX v14.5. The modified screw type called as a rail type twisted tube was presented through the optimization process. This complicated tube could be made by 3D printing technology. (metallic powder). Thermal-hydraulic analysis was conducted to compare the 3 type geometric divertor. A rail type twisted tube has good heat transfer performance in comparison with a conventional twisted tube. The pressure drop of a rail type twisted tube was reduced about 36% compared with a conventional twisted tube.
On the ergodic secret message capacity of the wiretap channel with finite-rate feedback
Rezki, Zouheir
2012-07-01
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers. We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free feedback channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q = 1. We also show that the lower and the upper bounds coincide asymptotically as q → ∞. Finally, asymptotic analysis at high Signal-to-Noise Ratio (SNR) are presented where it is found that the capacity is bounded at high-SNR and present a simple suboptimal scalar quantizer that is capacity achieving, without the need of any numerical optimization, as q → ∞. When applied to Rayleigh fading channels, we show that, at high-SNR, a 4-bit feedback achieves 90% of the secrecy capacity when perfect main CSI is available at the transmitter. © 2012 IEEE.
Kang, Xin; Nallanathan, Arumugam; Garg, Hari Krishna; Zhang, Rui
2008-01-01
A cognitive radio network (CRN) is formed by either allowing the secondary users (SUs) in a secondary communication network (SCN) to opportunistically operate in the frequency bands originally allocated to a primary communication network (PCN) or by allowing SCN to coexist with the primary users (PUs) in PCN as long as the interference caused by SCN to each PU is properly regulated. In this paper, we consider the latter case, known as spectrum sharing, and study the optimal power allocation strategies to achieve the ergodic capacity and the outage capacity of the SU fading channel under different types of power constraints and fading channel models. In particular, besides the interference power constraint at PU, the transmit power constraint of SU is also considered. Since the transmit power and the interference power can be limited either by a peak or an average constraint, various combinations of power constraints are studied. It is shown that there is a capacity gain for SU under the average over the peak ...
Quantifying non-ergodicity of anomalous diffusion with higher order moments.
Schwarzl, Maria; Godec, Aljaž; Metzler, Ralf
2017-06-20
Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q(θ)with birth rate λ＜ death rate μ, the following results are proved, (1) there is an unique q-process in random environment, -P(θ*(0);t) = (-p(θ*(0);t,i,j),i,j ≥ 0), which is ergodic, that is, limt→∞ -p(θ*(0);t,i,j) = -π(θ*(0);j) ≥ 0 does not depend on i ≥ 0 and Σj≥0 -π(θ*(0);j) = 1, (2) there is a bi-immigration birth and death process in random environment (X* = {Xt, t ≥ 0}, ξ* = {ξt, t ∈ (-∞, ∞)}) with random transition matrix -P(θ* (0); t) such that X* is a strictly stationary process.
Institute of Scientific and Technical Information of China (English)
Liu Chuan ZENG
2006-01-01
Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banach space E with a Frechet differentiable norm, and T = {Tt : t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F(T) of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u(.) of T, ∩s∈G co{u(t): t ≥ s} ∩ F(T) consists of at most one point. Furthermore,∩s∈G co{Ttx: t ≥ s}∩ F(T) is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F(T) such that PTs = TsP = P for all s ∈ G and Px ∈ co{Tsx: s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u(t): t ∈ G}to a common fixed point of T.
Geometric ergodicity of a hybrid sampler for Bayesian inference of phylogenetic branch lengths.
Spade, David A; Herbei, Radu; Kubatko, Laura S
2015-10-01
One of the fundamental goals in phylogenetics is to make inferences about the evolutionary pattern among a group of individuals, such as genes or species, using present-day genetic material. This pattern is represented by a phylogenetic tree, and as computational methods have caught up to the statistical theory, Bayesian methods of making inferences about phylogenetic trees have become increasingly popular. Bayesian inference of phylogenetic trees requires sampling from intractable probability distributions. Common methods of sampling from these distributions include Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods, and one way that both of these methods can proceed is by first simulating a tree topology and then taking a sample from the posterior distribution of the branch lengths given the tree topology and the data set. In many MCMC methods, it is difficult to verify that the underlying Markov chain is geometrically ergodic, and thus, it is necessary to rely on output-based convergence diagnostics in order to assess convergence on an ad hoc basis. These diagnostics suffer from several important limitations, so in an effort to circumvent these limitations, this work establishes geometric convergence for a particular Markov chain that is used to sample branch lengths under a fairly general class of nucleotide substitution models and provides a numerical method for estimating the time this Markov chain takes to converge.
Energy Technology Data Exchange (ETDEWEB)
Bucalossi, J., E-mail: jerome.bucalossi@cea.fr; Missirlian, M.; Moreau, P.; Samaille, F.; Tsitrone, E.; Houtte, D. van; Batal, T.; Bourdelle, C.; Chantant, M.; Corre, Y.; Courtois, X.; Delpech, L.; Doceul, L.; Douai, D.; Dougnac, H.; Faïsse, F.; Fenzi, C.; Ferlay, F.; Firdaouss, M.; Gargiulo, L.; and others
2014-10-15
The WEST project recently launched at Cadarache consists in transforming Tore Supra in an X-point divertor configuration while extending its long pulse capability, in order to test the ITER divertor technology. The implementation of a full tungsten actively cooled divertor with plasma facing unit representative of ITER divertor targets will allow addressing risks both in terms of industrial-scale manufacturing and operation of such components. Relevant plasma scenarios are foreseen for extensive testing under high heat load in the 10–20 MW/m{sup 2} range and ITER-like fluences (1000 s pulses). Plasma facing unit monitoring and development of protection strategies will be key elements of the WEST program. WEST is scheduled to enter into operation in 2016, and will provide a key facility to prepare and be prepared for ITER.
The first results of divertor discharge and supersonic molecular beam injection on the HL-2A tokamak
Institute of Scientific and Technical Information of China (English)
Yao Liang-Hua; Yuan Bau-Shan; Feng Bei-Bin; Chen Cheng-Yuan; Hong Wen-Yu; Li Ying-Liang
2007-01-01
HL-2A tokamak is the first tokamak with divertors in China. The plasma boundary and the position of the striking point on the target plates of the HL-2A closed divertor were simulated by the current filament code and they were in agreement with the diagnostic results in the divertor. Supersonic molecular beam injection (SMBI) system was first installed and tested on the HL-2A tokamak in 2004. In the present experiment low pressure SMBI fuelling on the HL-2A and during the period of SMB pulse injection into the HL-2A plasma the power density convected at the target plate surfaces was 0.4 times of that before or after the beam injection. It is a useful fuelling method for decreasing the heat load on the neutralizer plates of the divertor.
DTT: a divertor tokamak test facility for the study of the power exhaust issues in view of DEMO
Albanese, R.; WPDTT2 Team; DTT Project Proposal Contributors, the
2017-01-01
In parallel with the programme to optimize the operation with a conventional divertor based on detached conditions to be tested on the ITER device, a project has been launched to investigate alternative power exhaust solutions for DEMO, aimed at the definition and the design of a divertor tokamak test facility (DTT). The DTT project proposal refers to a set of parameters selected so as to have edge conditions as close as possible to DEMO, while remaining compatible with DEMO bulk plasma performance in terms of dimensionless parameters and given constraints. The paper illustrates the DTT project proposal, referring to a 6 MA plasma with a major radius of 2.15 m, an aspect ratio of about 3, an elongation of 1.6-1.8, and a toroidal field of 6 T. This selection will guarantee sufficient flexibility to test a wide set of divertor concepts and techniques to cope with large heat loads, including conventional tungsten divertors; liquid metal divertors; both conventional and advanced magnetic configurations (including single null, snow flake, quasi snow flake, X divertor, double null); internal coils for strike point sweeping and control of the width of the scrape-off layer in the divertor region; and radiation control. The Poloidal Field system is planned to provide a total flux swing of more than 35 Vs, compatible with a pulse length of more than 100 s. This is compatible with the mission of studying the power exhaust problem and is obtained using superconducting coils. Particular attention is dedicated to diagnostics and control issues, especially those relevant for plasma control in the divertor region, designed to be as compatible as possible with a DEMO-like environment. The construction is expected to last about seven years, and the selection of an Italian site would be compatible with a budget of 500 M€.
Xu, J. C.; Wang, L.; Xu, G. S.; Luo, G. N.; Yao, D. M.; Li, Q.; Cao, L.; Chen, L.; Zhang, W.; Liu, S. C.; Wang, H. Q.; Jia, M. N.; Feng, W.; Deng, G. Z.; Hu, L. Q.; Wan, B. N.; Li, J.; Sun, Y. W.; Guo, H. Y.
2016-08-01
In order to withstand rapid increase in particle and power impact onto the divertor and demonstrate the feasibility of the ITER design under long pulse operation, the upper divertor of the EAST tokamak has been upgraded to actively water-cooled, ITER-like tungsten mono-block structure since the 2014 campaign, which is the first attempt for ITER on the tokamak devices. Therefore, a new divertor Langmuir probe diagnostic system (DivLP) was designed and successfully upgraded on the tungsten divertor to obtain the plasma parameters in the divertor region such as electron temperature, electron density, particle and heat fluxes. More specifically, two identical triple probe arrays have been installed at two ports of different toroidal positions (112.5-deg separated toroidally), which can provide fundamental data to study the toroidal asymmetry of divertor power deposition and related 3-dimension (3D) physics, as induced by resonant magnetic perturbations, lower hybrid wave, and so on. The shape of graphite tip and fixed structure of the probe are designed according to the structure of the upper tungsten divertor. The ceramic support, small graphite tip, and proper connector installed make it possible to be successfully installed in the very narrow interval between the cassette body and tungsten mono-block, i.e., 13.5 mm. It was demonstrated during the 2014 and 2015 commissioning campaigns that the newly upgraded divertor Langmuir probe diagnostic system is successful. Representative experimental data are given and discussed for the DivLP measurements, then proving its availability and reliability.
Energy Technology Data Exchange (ETDEWEB)
Du, Hailong; Sang, Chaofeng [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, Liang [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Bonnin, Xavier [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Sun, Jizhong [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, Dezhen, E-mail: wangdez@dlut.edu.cn [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2016-11-01
Highlights: • The in-out divertor asymmetry is studied using SOLPS. • The discharge operation and the magnetic filed have a great influence on the divertor asymmetry. • The asymmetry is not obvious in low recycling regime as that in high recycling regime. - Abstract: This paper aims to investigate the reason why the divertor in-out asymmetry was not obvious as experimentally observed in EAST only considering the classical drifts from previous simulations (Guo et al., J. Nucl. Mater. 438 (2013) 280; Du et al., J. Nucl. Mater. 463 (2015) 485). With consideration of the classical drifts, a series of different typical discharge scenarios in EAST in different magnetic field geometries were simulated by using the SOLPS5.2 code package. The simulated results reveal that the classical drifts make a major contribution to the in-out divertor asymmetry in the high recycling regime (HRR) and partial detachment (one divertor target begins to detach, while the other divertor remains attached) regime. In comparison, in low recycling regime the classical drifts play a much smaller role in the contributions to the in-out divertor asymmetry, which can explain reasonably the reason for it in Guo et al. (J. Nucl. Mater. 438 (2013) 280). In addition, the magnetic field geometry also has a great impact on the classical drifts inducing the asymmetry; it is found that for lower single-null, upper single-null and connected double-null topologies, in HRR the classical drifts play an dominant role in the contribution to the in-out divertor asymmetry, while for a disconnected double null magnetic field configuration, they play a minor role, which is the reason why the in-out asymmetry was unobvious by considering the drifts in Du et al. (J. Nucl. Mater. 463 (2015) 485).
Glassy protein dynamics and gigantic solvent reorganization energy of plastocyanin
LeBard, David N
2007-01-01
We report the results of Molecular Dynamics simulations of electron transfer activation parameters of plastocyanin metalloprotein involved as electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding that observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for low activation barriers in natural electron transfer proteins characterized by low reaction free energy.
Ergodic secret message capacity of the wiretap channel with finite-rate feedback
Rezki, Zouheir
2014-06-01
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1. © 2002-2012 IEEE.
Upgrade of the infrared camera diagnostics for the JET ITER-like wall divertor.
Balboa, I; Arnoux, G; Eich, T; Sieglin, B; Devaux, S; Zeidner, W; Morlock, C; Kruezi, U; Sergienko, G; Kinna, D; Thomas, P D; Rack, M
2012-10-01
For the new ITER-like wall at JET, two new infrared diagnostics (KL9B, KL3B) have been installed. These diagnostics can operate between 3.5 and 5 μm and up to sampling frequencies of ∼20 kHz. KL9B and KL3B image the horizontal and vertical tiles of the divertor. The divertor tiles are tungsten coated carbon fiber composite except the central tile which is bulk tungsten and consists of lamella segments. The thermal emission between lamellae affects the surface temperature measurement and therefore KL9A has been upgraded to achieve a higher spatial resolution (by a factor of 2). A technical description of KL9A, KL9B, and KL3B and cross correlation with a near infrared camera and a two-color pyrometer is presented.
The development of in-situ calibration method for divertor IR thermography in ITER
Energy Technology Data Exchange (ETDEWEB)
Takeuchi, M.; Sugie, T.; Ogawa, H.; Takeyama, S.; Itami, K. [Japan Atomic Energy Agency (Japan)
2014-08-21
For the development of the calibration method of the emissivity in IR light on the divertor plate in ITER divertor IR thermography system, the laboratory experiments have been performed by using IR instruments. The calibration of the IR camera was performed by the plane black body in the temperature of 100–600 degC. The radiances of the tungsten heated by 280 degC were measured by the IR camera without filter (2.5–5.1 μm) and with filter (2.95 μm, 4.67 μm). The preliminary data of the scattered light of the laser of 3.34 μm that injected into the tungsten were acquired.
Energy Technology Data Exchange (ETDEWEB)
You, J.-H. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Boltzmannstr. 2, D-85748 Garching (Germany)]. E-mail: j.h.you@ipp.mpg.de
2005-01-01
Fibrous metal matrix composites possess advanced mechanical properties compared to conventional alloys. It is expected that the application of these composites to a divertor component will enhance the structural reliability. A possible design concept would be a system consisting of tungsten armour, copper composite interlayer and copper heat sink where the composite interlayer is locally inserted into the highly stressed domain near the bond interface. For assessment of the design feasibility of the composite divertor concept, a non-linear multi-scale finite element analysis was performed. To this end, a micro-mechanics algorithm was implemented into a finite element code. A reactor-relevant heat flux load was assumed. Focus was placed on the evolution of stress state, plastic deformation and ductile damage on both macro- and microscopic scales. The structural response of the component and the micro-scale stress evolution of the composite laminate were investigated.
End loss analyzer system for measurements of plasma flux at the C-2U divertor electrode
Griswold, M. E.; Korepanov, S.; Thompson, M. C.
2016-11-01
An end loss analyzer system consisting of electrostatic, gridded retarding-potential analyzers and pyroelectric crystal bolometers was developed to characterize the plasma loss along open field lines to the divertors of C-2U. The system measures the current and energy distribution of escaping ions as well as the total power flux to enable calculation of the energy lost per escaping electron/ion pair. Special care was taken in the construction of the analyzer elements so that they can be directly mounted to the divertor electrode. An attenuation plate at the entrance to the gridded retarding-potential analyzer reduces plasma density by a factor of 60 to prevent space charge limitations inside the device, without sacrificing its angular acceptance of ions. In addition, all of the electronics for the measurement are isolated from ground so that they can float to the bias potential of the electrode, 2 kV below ground.
In-out divertor flow asymmetries during ELMs in ASDEX Upgrade H-mode plasmas
Energy Technology Data Exchange (ETDEWEB)
Tsalas, M. [NCSR ' Demokritos' , Institute of Nuclear Technology - Radiation Protection, 153 10 Aghia Paraskevi, Attica (Greece) and EDFA-JET CSU, Abingdon OX14 3DB, Oxon (United Kingdom)]. E-mail: maximos@ipta.demokritos.gr; Coster, D. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Fuchs, C. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Herrmann, A. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Kallenbach, A. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Mueller, H.W. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Neuhauser, J. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Rohde, V. [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Garching (Germany); Tsois, N. [NCSR ' Demokritos' , Institute of Nuclear Technology - Radiation Protection, 153 10 Aghia Paraskevi, Attica (Greece)
2007-06-15
In ASDEX Upgrade, a fast reciprocating probe positioned in the lower divertor, capable of accessing the low-field side (LFS) and high-field side (HFS) scrape-off layer (SOL) just below the x-point, as well as the private flux region, was equipped with a Mach head and used to investigate fast flow fluctuations and in-out divertor flow asymmetries during ELMs. We compare the flow behaviour during ELMs in the three separate regions. Flow enhancement is observed in the HFS SOL, with Mach number values reaching or exceeding M = 2, flow reversal in the LFS SOL, and complex fluctuating behaviour in the private flux region (which includes flow reversal). We discuss the possible mechanisms that could drive these observations.
Melt damage simulation of W-macrobrush and divertor gaps after multiple transient events in ITER
Energy Technology Data Exchange (ETDEWEB)
Bazylev, B.N. [Forschungszentrum Karlsruhe, IHM, P.O. Box 3640, 76021 Karlsruhe (Germany)]. E-mail: bazylev@ihm.fzk.de; Janeschitz, G. [Forschungszentrum Karlsruhe, Fusion, P.O. Box 3640, 76021 Karlsruhe (Germany); Landman, I.S. [Forschungszentrum Karlsruhe, IHM, P.O. Box 3640, 76021 Karlsruhe (Germany); Loarte, A. [EFDA-CSU, Max-Planck-Institut fuer Plasmaphysik, D-85748 Garching (Germany); Pestchanyi, S.E. [Forschungszentrum Karlsruhe, IHM, P.O. Box 3640, 76021 Karlsruhe (Germany)
2007-06-15
Tungsten in the form of macrobrush structure is foreseen as one of two candidate materials for the ITER divertor and dome. In ITER, even for moderate and weak ELMs when a thin shielding layer does not protect the armour surface from the dumped plasma, the main mechanisms of metallic target damage remain surface melting and melt motion erosion, which determines the lifetime of the plasma facing components. The melt erosion of W-macrobrush targets with different geometry of brush surface under the heat loads caused by weak ELMs is numerically investigated using the modified code MEMOS. The optimal angle of brush surface inclination that provides a minimum of surface roughness is estimated for given inclination angles of impacting plasma stream and given parameters of the macrobrush target. For multiple disruptions the damage of the dome gaps and the gaps between divertor cassettes caused by the radiation impact is estimated.
Melt damage simulation of W-macrobrush and divertor gaps after multiple transient events in ITER
Bazylev, B. N.; Janeschitz, G.; Landman, I. S.; Loarte, A.; Pestchanyi, S. E.
2007-06-01
Tungsten in the form of macrobrush structure is foreseen as one of two candidate materials for the ITER divertor and dome. In ITER, even for moderate and weak ELMs when a thin shielding layer does not protect the armour surface from the dumped plasma, the main mechanisms of metallic target damage remain surface melting and melt motion erosion, which determines the lifetime of the plasma facing components. The melt erosion of W-macrobrush targets with different geometry of brush surface under the heat loads caused by weak ELMs is numerically investigated using the modified code MEMOS. The optimal angle of brush surface inclination that provides a minimum of surface roughness is estimated for given inclination angles of impacting plasma stream and given parameters of the macrobrush target. For multiple disruptions the damage of the dome gaps and the gaps between divertor cassettes caused by the radiation impact is estimated.
Free-boundary ideal MHD stability of W7-X divertor equilibria
Nührenberg, C.
2016-07-01
Plasma configurations describing the stellarator experiment Wendelstein 7-X (W7-X) are computationally established taking into account the geometry of the test-divertor unit and the high-heat-flux divertor which will be installed in the vacuum chamber of the device (Gasparotto et al 2014 Fusion Eng. Des. 89 2121). These plasma equilibria are computationally studied for their global ideal magnetohydrodynamic (MHD) stability properties. Results from the ideal MHD stability code cas3d (Nührenberg 1996 Phys. Plasmas 3 2401), stability limits, spatial structures and growth rates are presented for free-boundary perturbations. The work focusses on the exploration of MHD unstable regions of the W7-X configuration space, thereby providing information for future experiments in W7-X aiming at an assessment of the role of ideal MHD in stellarator confinement.
Edge and divertor plasma measurements with ion sensitive and Mach probes in LHD
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Y., E-mail: shihaya_uki884@yahoo.co.jp [Nagano National College of Technology, 716 Tokuma, Nagano 381-8550 (Japan); Ezumi, N. [Nagano National College of Technology, 716 Tokuma, Nagano 381-8550 (Japan); Masuzaki, S.; Tanaka, H.; Kobayashi, M. [National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292 (Japan); Sawada, K. [Shinshu University, Wakasato, Nagano 380-8553 (Japan); Ohno, N. [Nagoya University, Furo-cho Chikusa-ku, Nagoya 464-8603 (Japan)
2013-07-15
Spatial profiles of plasma flow and Mach number in the stochastic magnetic boundary layer as well as ion temperature (T{sub i}) and electron temperature (T{sub e}) in the divertor region in Large Helical Device (LHD) have been studied by a movable multiple functions probe, which consists of Mach probes and an ion sensitive probe. The results of ion saturation current measurements indicated plasma flow direction is alternated in the stochastic magnetic boundary. Mach number profiles for different plasma densities have been evaluated experimentally which compared with 3-D transport code. T{sub i} and T{sub e} in the divertor region measured by the ion sensitive probe decreased with increasing line-averaged density. Although T{sub i} was higher than T{sub e} in the low density plasma, both temperatures became almost the same at higher density.
Divertor target profiles and recycling studies in TCV single null lower standard discharges
Energy Technology Data Exchange (ETDEWEB)
Pitts, R.A.; Nieswand, C.; Weisen, H.; Anton, M.; Behn, R.; Chavan, R.F.; Dutch, M.J.; Duval, B.P.; Franke, S.; Hofmann, F.; Joye, B.; Lister, J.B.; Llobet, X.; Martin, Y.; Moret, J.-M.; Petrzilka, J.; Pietrzyk, Z.A.; Piffl, V.; Reinke, P.; Rensink, M.E.; Smith, G.R.; Van Toledo, W. [Ecole Polytech. Federale, Lausanne (Switzerland). Centre de Recherches en Physique des Plasmas]|[Institute of Plasma Physics, Czech Academy of Sciences, Prague (Czech Republic)]|[Universitaet Basel, Institut fuer Physik, Klingelbergstr. 82, CH-4056 Basel (Switzerland)]|[Lawrence Livermore National Laboratory, University of California, Berkeley, CA 94551 (United States)
1997-02-01
A `standard`, single null lower diverted discharge has been developed to enable continuous monitoring of the first wall conditions and to characterise the effectiveness and influence of wall conditioning in the TCV tokamak. Measurements over a period encompassing nearly 2000 ohmic discharges of varying configuration and input power show the global confinement time and main plasma impurity concentrations to be good general indicators of the first wall condition, whilst divertor target profiles demonstrate strikingly the short term beneficial effects of He glow. Good agreement, consistent with a reduction in recycling at the plates is found between the predictions of the fluid code UEDGE and the observed outer divertor profiles of T{sub e} and n{sub e} before and after He glow. (orig.).
Conditional exponents, entropies and a measure of dynamical self-organization
Mendes, R V
1998-01-01
In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants.
Wu, Fuke; Yin, George; Mei, Hongwei
2017-02-01
This work is devoted to stochastic functional differential equations (SFDEs) with infinite delay. First, existence and uniqueness of the solutions of such equations are examined. Because the solutions of the delay equations are not Markov, a viable alternative for studying further asymptotic properties is to use solution maps or segment processes. By examining solution maps, this work investigates the Markov properties as well as the strong Markov properties. Also obtained are adaptivity and continuity, mean-square boundedness, and convergence of solution maps from different initial data. This paper then examines the ergodicity of underlying processes and establishes existence of the invariant measure for SFDEs with infinite delay under suitable conditions.
Impurity profiles at the JET divertor targets compared with the DIVIMP code
Energy Technology Data Exchange (ETDEWEB)
Matthews, G.F.; Gottardi, N.A.C.; Harbour, P.J.; Horton, L.D.; Jackel, H.J.; De Kock, L.; Loarte, A.; Maggi, C.F.; O' Brien, D.P.J.; Simonini, R.; Spence, J.; Stamp, M.F.; Stott, P.E.; Summers, H.P.; Tagle, J.; Von Hellerman, M. (JET Joint Undertaking, Abingdon (United Kingdom)); Stangeby, P.C.; Elder, J.D. (Univ. Toronto, Inst. for Aerospace Studies, Downsview, Ontario (Canada))
1992-12-01
In this paper we describe the simulation of edge diagnostics in JET using the DIVIMP (divertor impurity) Monte Carlo code. We concentrate on two ohmic pulses and show how the results are influenced by a variety of modeling assumptions. Our results show that a wall source must be included to explain the diagnostic signals. The wall source is shown to be a significant source of impurity in the discharges studied and more generally. (orig.).
Initial operation of the divertor Thompson scattering diagnostic on DIII-D
Energy Technology Data Exchange (ETDEWEB)
Carlstrom, T.N.; Hsieh, C.L.; Stockdale, R.E. [and others
1996-05-01
The first Thomson scattering measurements of n{sub e} and T{sub e} in the divertor region of a tokamak are reported. These data are used as input to boundary physics codes such as UEDGE and DEGAS and to benchmark the predictive capabilities of these codes. These measurements have also contributed to the characterization of tokamak disruptions. A Nd:YAG laser (20 Hz, 1 J, 15 ns, 1064 nm) is directed vertically through the lower divertor region of the DIII-D tokamak. A custom, aspherical collection lens (f /6.8) images the laser beam from 1-21 cm above the target plates into eight spatial channels with 1.5 cm vertical and 0.3 cm radial resolution. 2D mapping of the divertor region is achieved by sweeping the divertor X-point location radially through the fixed laser beam location. Fiber optics carry the light to polychromators whose interference filters have been optimized for low T{sub e} measurements. Silicon avalanche photo diodes measure both the scattered and plasma background light. Temperatures and densities are typically in the range of 5-200 eV and 1 - 10 x 10{sup 19} m{sup -3} respectively. Low temperatures, T{sub e} < 1 eV, and high densities, n{sub e} > 8x10{sup 20} m{sup -3} have been observed in detached plasmas. Background light levels have not been a significant problem. Reduction of the laser stray light permits Rayleigh calibration. Because of access difficulties, no in-vessel vacuum alignment target could be used. Instead, an in situ laser alignment monitor provides alignment information for each laser pulse. Results are compared with Langmuir probe measurements where good agreement is found except for regions of high n{sub e} and low T{sub e} as measured by Thomson scattering.
HRP facility for fabrication of ITER vertical target divertor full scale plasma facing units
Energy Technology Data Exchange (ETDEWEB)
Visca, Eliseo, E-mail: eliseo.visca@enea.it [Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, IT-00044 Frascati (Roma) (Italy); Roccella, S. [Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, IT-00044 Frascati (Roma) (Italy); Candura, D.; Palermo, M. [Ansaldo Nucleare S.p.A., Corso Perrone 25, IT-16152 Genova (Italy); Rossi, P.; Pizzuto, A. [Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, IT-00044 Frascati (Roma) (Italy); Sanguinetti, G.P. [Ansaldo Nucleare S.p.A., Corso Perrone 25, IT-16152 Genova (Italy); Mancini, A.; Verdini, L.; Cacciotti, E.; Cerri, V.; Mugnaini, G.; Reale, A.; Giacomi, G. [Unità Tecnica Fusione, ENEA C. R. Frascati, via E. Fermi 45, IT-00044 Frascati (Roma) (Italy)
2015-10-15
Highlights: • R&D activities for the manufacturing of ITER divertor high heat flux plasma-facing components (HHFC). • ENEA and Ansaldo have jointly manufactured several actively cooled monoblock mock-ups and prototypical components. • ENEA and ANSALDO NUCLEARE jointly participate to the European program for the qualification of the manufacturing technology for the ITER divertor IVT. • Successful manufacturing by HRP (Hot Radial Pressing) of first full-scale full-W armored IVT qualification prototype. - Abstract: ENEA and Ansaldo Nucleare S.p.A. (ANN) have being deeply involved in the European development activities for the manufacturing of the ITER Divertor Inner Vertical Target (IVT) plasma-facing components. During normal operation the heat flux deposited on the bottom segment of divertor is 5–10 MW/m{sup 2} but the capability to remove up to 20 MW/m{sup 2} during transient events of 10 s must also be demonstrated. In order to fulfill ITER requirements, ENEA has set up and widely tested a manufacturing process, named Hot Radial Pressing (HRP). The last challenge is now to fabricate full-scale prototypes of the IVT, aimed to be qualified for the next step, i.e. the series production. On the basis of the experience of manufacturing hundreds of small mock-ups, ENEA designed and installed a new suitable HRP facility. The objective of getting a final shaped plasma facing unit (PFU) that satisfies these requirements is an ambitious target because tolerances set by ITER/F4E are very tight. The setting-up of the equipment started with the fabrication of full scale and representative ‘dummies’ in which stainless steel instead of CFC or W was used for monoblocks. The results confirmed that dimensions were compliant with the required tolerances. The paper reports a brief description of the innovative HRP equipment and the dimensional check results after HRP of the first full-scale full-W PFU.
The snowflake divertor, physics of a new concept for power exhaust of fusion plasmas
Energy Technology Data Exchange (ETDEWEB)
Lunt, Tilmann; Feng, Yuehe [Max-Planck-Institut fuer Plasmaphysik, Garching/Greifswald (Germany); Canal, Gustavo; Reimerdes, Holger [Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland)
2014-07-01
Fusion reactors based on the tokamak design will have to deal with very high heat loads on the divertor plates. One of the approaches to solve this heat load problem is the so called 'snowflake divertor', a magnetic configuration with two nearby x-points and two additional divertor legs. In this contribution we report on 'EMC3-Eirene' simulations of the plasma- and neutral particle transport in the scrape-off layer of the swiss tokamak TCV of a series of snowflake equilibria with different values of σ, the distance between the x-points normalized to the minor radius of the plasma. The constant anomalous transport coefficients were chosen such that the power- and particle deposition profiles at the primary inner strike point match the Langmuir probe measurements for the σ=0.1 case. At one of the secondary strike points, however, a significantly larger power flux than that predicted by the simulation was measured by the probes, indicating the presence of an enhanced transport across the primary separatrix. We discuss the possible reason for this enhanced transport as well as its scaling with machine size. Another prediction from the simulation is that the density as well as the radiation maximum are moving from the recycling region in front of the plates upwards to the x-point.
Infrared thermography inspection for monoblock divertor target in JT-60SA
Energy Technology Data Exchange (ETDEWEB)
Nakamura, Shigetoshi, E-mail: nakamura.shigetoshi@jaea.go.jp; Sakurai, Shinji; Ozaki, Hidetsugu; Seki, Yohji; Yokoyama, Kenji; Sakasai, Akira; Tsuru, Daigo
2014-10-15
Highlights: • Infrared thermography inspection is modified to inspect JT-60SA divertor targets. • Infrared thermography inspection is effective to detect joining defects of targets. • Numerical analysis is in good agreement with inspection results of mock-up targets. • Database for setting screening criteria has been constructed by numerical analysis. - Abstract: Carbon fiber composite (CFC) monoblock divertor target is required for power handling in JT-60SA. Quality of the targets depends on a joining technology in manufacturing process. To inspect the quality of more than 900 target pieces, efficient non-destructive inspection is needed. An infrared thermography inspection (IR inspection), has been proposed by ITER and IRFM, where the quality between CFC and a cooling tube is examined by a use of transient thermal response at a rapid switch from hot to cold water flow. In JT-60SA divertor target, a screw tube will be employed to obtain high heat transfer efficiency with simple structure. Since the time response of the screw tube is much faster than that of smooth tube, it is required to confirm the feasibility of this IR inspection. Thus, the effect of joining defects on transient thermal response of the targets has been investigated experimentally by using the mock-up targets containing defects which are artificially made. It was found that the IR inspection can detect the defects. Moreover, screening criteria of IR inspection for acceptable monoblock target is discussed.
Plasma convection near the magnetic null of a snowflake divertor during an ELM event
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D.D.; Cohen, R.H.; Rognlien, T.D.; Umansky, M.V. [Lawrence Livermore National Laboratory, Livermore, CA (United States)
2012-06-15
A snowflake magnetic configuration is created in a tokamak when the poloidal magnetic field and its first spatial derivatives become zero at a certain point. The separatrix then acquires a characteristic hexagonal shape reminiscent of a snowflake. We study new features of the plasma macroscopic equilibrium and stability in the vicinity of the snowflake null. We note that, compared to the standard X-point divertor, the zone of weak poloidal magnetic field is much larger. The weak poloidal field leads to development of intense plasma convection over the expanded area around the null-point during the ejection phase of an edge localized mode (ELM) event when the plasma pressure in the scrape-off layer increases compared to its inter-ELM value. Intense convection may lead to a roughly-equal splitting of the heat flux between the 4 snowflake divertor legs and to a broadening of the plasma wetted area in each leg, thereby mitigating damage to divertor plates (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
A numerical study of plasma detachment conditions in JET divertor plasmas
Energy Technology Data Exchange (ETDEWEB)
Simonini, R.; Corrigan, G.; Radford, G.; Spence, J.; Taroni, A.; Weber, S. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking
1994-07-01
Simulation results obtained with the EDGE2D/U code confirm that for a given particle inventory in the SOL (including the divertor), the main parameter determining whether or not particle, momentum and energy detachment occurs, is the residual power P - P{sub lost}, where P is the total power entering the SOL and P{sub lost} is the power lost by transport to walls and by volume losses in the SOL outside the region where detachment takes place. For particle contents leading to reasonable values of the separatrix mid-plane density, detachment is found if the residual power is low enough. Typically the residual power must be inferior to 3 MW for good detachment, with the exact value depending on the geometry of the divertor, the transport assumptions and the neutral recirculation scheme. The results show that divertor plasma conditions relevant for the study of power exhaust and impurity control problems are possible in JET. 9 refs., 2 figs., 1 tab.
High heat flux Langmuir probe array for the DIII-D divertor platesa)
Watkins, J. G.; Taussig, D.; Boivin, R. L.; Mahdavi, M. A.; Nygren, R. E.
2008-10-01
Two modular arrays of Langmuir probes designed to handle a heat flux of up to 25 MW/m2 for 10 s exposures have been installed in the lower divertor target plates of the DIII-D tokamak. The 20 pyrolytic graphite probe tips have more than three times higher thermal conductivity and 16 times larger mass than the original DIII-D isotropic graphite probes. The probe tips have a fixed 12.5° surface angle to distribute the heat flux more uniformly than the previous 6 mm diameter domed collectors and a symmetric "rooftop" design to allow operation with reversed toroidal magnetic field. A large spring-loaded contact area improves heat conduction from each probe tip through a ceramic insulator into a cooled graphite divertor floor tile. The probe tips, brazed to molybdenum foil to ensure good electrical contact, are mounted in a ceramic tray for electrical isolation and reliable cable connections. The new probes are located 1.5 cm radially apart in a staggered arrangement near the entrance to the lower divertor pumping baffle and are linearly spaced 3 cm apart on the shelf above the in-vessel cryopump. Typical target plate profiles of Jsat, Te, and Vf with 4 mm spatial resolution are shown.
Study of power load pattern on EAST divertor using PFCFlux code
Energy Technology Data Exchange (ETDEWEB)
Zhang, Bin, E-mail: binzhang@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Firdaouss, Mehdi [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Gong, Xianzu [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Ekedahl, Annika [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Peng, Xuebing [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Zhang, Xiaodong, E-mail: xdzhang@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2016-06-15
Highlights: • This paper demonstrates the modeling result of power load pattern on EAST graphite divertor by using the PFCFlux code. • The grazing angle varies both poloidally and toroidally, changing by half a degree over the distance of 50 mm away from the strike point. • The correlation between both grazing angle and flux expansion and the magnetic equilibrium parameters are found by using the linear regression method. • The modeling result indicates that the edges of graphite tiles of EAST divertor are perfectly shadowed. - Abstract: The power load pattern on an EAST divertor component, spanning six tiles in the poloidal direction, has been studied with the PFCFlux code. A total of 49 different EAST plasma equilibria in lower single null configuration are used in the study. It is found that the incidence angle, or grazing angle, varies both toroidally and poloidally on the target, changing by approximately half a degree over a distance of 50 mm from the strike point. Strong correlations between the triangularity of the magnetic equilibrium and both the grazing angle and the flux expansion are found by using linear regression. A smaller value of triangularity gives wider plasma-wetted region on the target in lower-outer configuration, and a narrower plasma-wetted region in lower-inner configuration.
Investigation of momentum loss mechanisms in the divertor region of ASDEX Upgrade with EMC3-Eirene
Energy Technology Data Exchange (ETDEWEB)
Brida, Dominik [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany); Physik-Department E28, Technische Universitaet Muenchen, Garching (Germany); Lunt, Tilmann; Wischmeier, Marco [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany); Collaboration: the ASDEX Upgrade Team
2015-05-01
In future fusion devices, such as ITER and DEMO, it will be necessary to prevent direct contact between the hot confined plasma and the vessel wall. This will be achieved by employing divertors, which offer a number of desirable advantages, such as screening of impurities from the core plasma, improved energy confinement (H-mode) and effective pumping of helium ash and hydrogen. However, due to material limits, the power and particle flux as well as the temperature at the target must be reduced to acceptable levels. This can be attained by operating the divertor in a (partially) detached regime, which requires considerable volumetric energy and momentum losses in the divertor region. Previous studies identified ion-neutral friction as the principal momentum loss factor. For this contribution the fluid code EMC3-Eirene was applied to simulate ASDEX Upgrade discharges with increasing plasma densities and investigate the role of different momentum loss mechanisms by switching on and off respective terms in the simulation. Interestingly, even without the charge-exchange collisions a strong momentum loss is observed in the simulation.
Experience gained with the 3D machining of the W7-X HHF divertor target elements
Energy Technology Data Exchange (ETDEWEB)
Junghanns, P. [Max Planck Institute for Plasma Physics, Greifswald (Germany); Boscary, J., E-mail: jean.boscary@ipp.mpg.de [Max Planck Institute for Plasma Physics, Garching (Germany); Peacock, A. [Max Planck Institute for Plasma Physics, Garching (Germany)
2015-10-15
Highlights: • The Wendelstein 7-X surface of the actively cooled divertor is built up of 890 individually 3D machined target elements. • To date 300 target elements have been 3D machined with an accuracy of ±0.015 mm. • Copper discovered on the surface of few elements is no risk to operation. - Abstract: The high heat flux (HHF) divertor of W7-X consists of 100 target modules assembled from 890 actively water-cooled target elements protected with CFC tiles. The divertor surface will be built up of individually 3D machined target elements with 89 individual element types. To date 300 of the 890 target elements have been 3D machined with a very good accuracy. To achieve this successful result, a prototyping phase has been conducted to qualify the manufacturing route and to define the acceptance criteria with measures taken to minimize the risk of unacceptable damage during the manufacturing. After the 3D-machining, during the incoming inspection, copper infiltration from the interface between the CFC tiles and the CuCrZr heat sink to the plasma facing surface was detected in a small number of elements.
HSX as an example of a resilient non-resonant divertor
Bader, A.; Boozer, A. H.; Hegna, C. C.; Lazerson, S. A.; Schmitt, J. C.
2017-03-01
This paper describes an initial description of the resilient divertor properties of quasi-symmetric (QS) stellarators using the HSX (Helically Symmetric eXperiment) configuration as a test-case. Divertors in high-performance QS stellarators will need to be resilient to changes in plasma configuration that arise due to evolution of plasma pressure profiles and bootstrap currents for divertor design. Resiliency is tested by examining the changes in strike point patterns from the field line following, which arise due to configurational changes. A low strike point variation with high configuration changes corresponds to high resiliency. The HSX edge displays resilient properties with configuration changes arising from the (1) wall position, (2) plasma current, and (3) external coils. The resilient behavior is lost if large edge islands intersect the wall structure. The resilient edge properties are corroborated by heat flux calculations from the fully 3-D plasma simulations using EMC3-EIRENE. Additionally, the strike point patterns are found to correspond to high curvature regions of magnetic flux surfaces.
Engineering challenges and development of the ITER Blanket System and Divertor
Energy Technology Data Exchange (ETDEWEB)
Merola, Mario, E-mail: mario.merola@iter.org; Escourbiac, Frederic; Raffray, Alphonse Rene; Chappuis, Philippe; Hirai, Takeshi; Gicquel, Stefan
2015-10-15
The ITER Blanket System and the Divertor are the main components which directly face the plasma. Being the first physical barrier to the plasma, they have very demanding design requirements, which include accommodating: (1) surface heat flux and neutronic volumetric heating, (2) electromagnetic loads, (3) nuclear shielding function, (4) capability of being assembled and remote-handled, (5) interfaces with other in-vessel components, and (6) high heat flux technologies and complex welded structures in the design. The main functions of the Blanket System have been substantially expanded and it has now also to provide limiting surfaces that define the plasma boundary during startup and shutdown. As regards the Divertor, the ITER Council decided in November 2013 to start the ITER operation with a full-tungsten armour in order to minimize costs and already gain operational experience with tungsten during the non-active phase of the machine. This paper gives an overview of the design and technology qualification of the Blanket System and the Divertor.
Understanding of Neutral Gas Transport in the Alcator C-Mod Tokamak Divertor
Energy Technology Data Exchange (ETDEWEB)
D.P. Stotler; C.S. Pitcher; C.J. Boswell; B. LaBombard; J.L. Terry; J.D. Elder; S. Lisgo
2002-05-07
A series of experiments on the effect of divertor baffling on the Alcator C-Mod tokamak provides stringent tests on models of neutral gas transport in and around the divertor region. One attractive feature of these experiments is that a trial description of the background plasma can be constructed from experimental measurements using a simple model, allowing the neutral gas transport to be studied with a stand-alone code. The neutral-ion and neutral-neutral elastic scattering processes recently added to the DEGAS 2 Monte Carlo neutral transport code permit the neutral gas flow rates between the divertor and main chamber to be simulated more realistically than before. Nonetheless, the simulated neutral pressures are too low and the deuterium Balmer-alpha emission profiles differ qualitatively from those measured, indicating an incomplete understanding of the physical processes involved in the experiment. Some potential explanations are examined and opportunities for future exploration a re highlighted. Improvements to atomic and surface physics data and models will play a role in the latter.
Thermo-mechanical and damage analyses of EAST carbon divertor under type-I ELMy H-mode operation
Energy Technology Data Exchange (ETDEWEB)
Li, W.X. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Song, Y.T. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Ye, M.Y. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Peng, X.B., E-mail: pengxb@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Wu, S.T. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Qian, X.Y.; Zhu, C.C. [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026 (China)
2016-04-15
Highlights: • Type-I ELMy H-mode is one of the most severe operating environment in tokamak. • An actual time-history heat load has been used in thermo-mechanical analysis. • The analysis results are time-dependent during the whole discharge process. • The analysis could be very useful in evaluating the operational capability of the divertor. - Abstract: The lower carbon divertor has been used since 2008 in EAST, and many significant physical results, like the 410 s long pulse discharge and the 32 s H-mode operation, have been achieved. As the carbon divertor will still be used in the next few years while the injected auxiliary heating power would be increased gradually, it’s necessary to evaluate the operational capability of the carbon divertor under the heat loads during future operation. In this paper, an actual time-history heat load during type-I ELMy H-mode from EAST experiment, as one of the most severe operating environment in tokamak, has been used in the calculation and analysis. The finite element (FE) thermal and mechanical calculations have been carried out to analysis the stress and deformation of the carbon divertor during the heat loads. According to the results, the main impact on the overall temperature comes from the relative stable phase before and after the type-I ELMs and local peak load, and the transient thermal load such as type-I ELMy only has a significant effect on the surface temperature of the graphite tiles. The carbon divertor would work with high stress near the screw bolts in the current operational conditions, because of high preload and conservative frictional coefficient between the bolts and heatsink. For the future operation, new plasma facing materials (PFM) and divertor technology should be developed.
Energy Technology Data Exchange (ETDEWEB)
Huang, Yan [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034 (China); Sun, Jizhong, E-mail: jsun@dlut.edu.cn [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Hu, Wanpeng; Sang, Chaofeng [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Wang, Dezhen, E-mail: wangdez@dlut.edu.cn [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China)
2016-01-15
Highlights: • Thermal performance of three edge-shaped divertor tiles was assessed numerically. • All the divertor tiles exposed to type-I ELMs like ITER's will melt. • The rounded edge tile thermally performs the best in all tiles of interest. • The incident energy flux density was evaluated with structural effects considered. - Abstract: Thermal performance of the divertor tile with different edge shapes was assessed numerically along the poloidal direction by a two-dimensional heat conduction model with considering the geometrical effects of castellated divertor tiles on the properties of its adjacent plasma. The energy flux density distribution arriving at the castellated divertor tile surface was evaluated by a two-dimension-in-space and three-dimension-in-velocity particle-in-cell plus Monte Carlo Collisions code and then the obtained energy flux distribution was used as input for the heat conduction model. The simulation results showed that the divertor tiles with any edge shape of interest (rectangular edge, slanted edge, and rounded edge) would melt, especially, in the edge surface region of facing plasma poloidally under typical heat flux density of a transient event of type-I ELMs for ITER, deposition energy of 1 MJ/m{sup 2} in a duration of 600 μs. In comparison with uniform energy deposition, the vaporizing erosion was reduced greatly but the melting erosion was aggravated noticeably in the edge area of plasma facing diveror tile. Of three studied edge shapes, the simulation results indicated that the divertor plate with rounded edge was the most resistant to the thermal erosion.
An operational non destructive examination for ITER divertor plasma facing components
Energy Technology Data Exchange (ETDEWEB)
Durocher, A.; Escourbiac, F.; Farjon, J.L.; Vignal, N.; Cismondi, F. [Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Merola, M. [ITER International Team, Cadarache, 13 - St Paul Lez Durance (France); Riccardi, B. [CEFDA CSU-Garching, Garching bei Munchen (Germany)
2007-07-01
Full text of publication follows: To meet the power exhaust - heat flux of 20 MW/m{sup 2} - requirements of Plasma Facing Components (PFCs) during plasma operation requires control of their thermal and mechanical integrity. As heat exhaust capability and lifetime of PFCs during in-situ operation are linked to the manufacturing quality, it is an absolute requirement to develop reliable nondestructive examination methods, in particular of the CFC-CuCrZr joint, throughout the manufacturing process. Within the framework of Tokamak Tore Supra upgrade, a pioneering activity has been developed to evaluate the capability of the PFC to be efficiently cooled. In 1998 a test bed - so called SATIR - based on the heat transient method was developed by the CEA and is used today as an inspection tool in order to guarantee the PFCs performances. The technical procurement plan of ITER Divertor targets stated that all Cu cast layers on CFC armour should be subjected to 100% thermographic examination. Each ITER Party should demonstrate its technical capability to carry out the PFC with the required cooling efficiently. The ITER Divertor PFCs pose new challenges especially for the mono-block CFC thickness, and the number of full scale units to be tested which is higher than on any existing or under construction fusion machine. The SATIR method as functional inspection has been identified as the basis test to decide upon the final acceptance of the Divertor PFCs. In order to increase the detection sensitivity of SATIR test bed, several possibilities have been assessed i) the increase of the convective heat transfer coefficient, which improved in a significant way the sensitivity of SATIR diagnostic on ITER components. ii) the installation of a digital infrared camera and the improvement of the thermal signal processing, has led to a considerable increase of performances iii) an innovative process based on spatial image autocorrelation will allow to localize the interlayer defect
Design, fabrication, and testing of a helium-cooled module for the ITER divertor
Energy Technology Data Exchange (ETDEWEB)
Baxi, C.B.; Smith, J.P.; Youchison, D.
1994-08-01
The International Thermonuclear Reactor (ITER) will have a single-null divertor with total power flow of 200 MW and a peak heat flux of about 5 MW/m{sup 2}. The reference coolant for the divertor is water. However, helium is a viable alternative and offers advantages from safety considerations, such as excellent radiation stability and chemical inertness. In order to prove the feasibility of helium cooling at ITER relevant heat flux conditions, General Atomics designed, fabricated, and tested a helium-cooled divertor module. The module was made from dispersion strengthened copper, with a heat flux surface 25 mm wide and 80 mm long, designed for twice the ITER divertor heat flux. Different techniques were examined to enhance the heat transfer, which in turn reduced the flow and pumping power required to cool the module. It was concluded that an extended surface was the most practical solution. An optimization study was performed to find the best extended surface parameters. The optimum extended surface geometry consisted of fins: 10 mm high, 0.4 mm thick with a 1 mm pitch. It was estimated to require a pumping power of 150 W to remove 20 kW of power. This is more than an order of magnitude reduction in pumping power requirement, compared to smooth surface. The module was fabricated by electric discharge machining (EDM) process. The testing was carried out at SNLA during August 1993. The testing confirmed the design calculations. The peak heat flux during the test was 10 MW/m{sup 2} applied over a surface area of 20 cm{sup 2}. The pumping power calculated from flow rate and pressure drop measurement was about 160 W, which was less than 1% of the power removed. It is planned to test the module to higher temperature limits and higher heat fluxes during coming months. As a result of this effort we conclude that helium cooling of the ITER divertor is feasible without requiring a very large helium pressure or a large pumping power.
ADX: a high field, high power density, advanced divertor and RF tokamak
LaBombard, B.; Marmar, E.; Irby, J.; Terry, J. L.; Vieira, R.; Wallace, G.; Whyte, D. G.; Wolfe, S.; Wukitch, S.; Baek, S.; Beck, W.; Bonoli, P.; Brunner, D.; Doody, J.; Ellis, R.; Ernst, D.; Fiore, C.; Freidberg, J. P.; Golfinopoulos, T.; Granetz, R.; Greenwald, M.; Hartwig, Z. S.; Hubbard, A.; Hughes, J. W.; Hutchinson, I. H.; Kessel, C.; Kotschenreuther, M.; Leccacorvi, R.; Lin, Y.; Lipschultz, B.; Mahajan, S.; Minervini, J.; Mumgaard, R.; Nygren, R.; Parker, R.; Poli, F.; Porkolab, M.; Reinke, M. L.; Rice, J.; Rognlien, T.; Rowan, W.; Shiraiwa, S.; Terry, D.; Theiler, C.; Titus, P.; Umansky, M.; Valanju, P.; Walk, J.; White, A.; Wilson, J. R.; Wright, G.; Zweben, S. J.
2015-05-01
The MIT Plasma Science and Fusion Center and collaborators are proposing a high-performance Advanced Divertor and RF tokamak eXperiment (ADX)—a tokamak specifically designed to address critical gaps in the world fusion research programme on the pathway to next-step devices: fusion nuclear science facility (FNSF), fusion pilot plant (FPP) and/or demonstration power plant (DEMO). This high-field (⩾6.5 T, 1.5 MA), high power density facility (P/S ˜ 1.5 MW m-2) will test innovative divertor ideas, including an ‘X-point target divertor’ concept, at the required performance parameters—reactor-level boundary plasma pressures, magnetic field strengths and parallel heat flux densities entering into the divertor region—while simultaneously producing high-performance core plasma conditions that are prototypical of a reactor: equilibrated and strongly coupled electrons and ions, regimes with low or no torque, and no fuelling from external heating and current drive systems. Equally important, the experimental platform will test innovative concepts for lower hybrid current drive and ion cyclotron range of frequency actuators with the unprecedented ability to deploy launch structures both on the low-magnetic-field side and the high-magnetic-field side—the latter being a location where energetic plasma-material interactions can be controlled and favourable RF wave physics leads to efficient current drive, current profile control, heating and flow drive. This triple combination—advanced divertors, advanced RF actuators, reactor-prototypical core plasma conditions—will enable ADX to explore enhanced core confinement physics, such as made possible by reversed central shear, using only the types of external drive systems that are considered viable for a fusion power plant. Such an integrated demonstration of high-performance core-divertor operation with steady-state sustainment would pave the way towards an attractive pilot plant, as envisioned in the ARC concept
Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold
Institute of Scientific and Technical Information of China (English)
LIAO Shan-tao
2006-01-01
Let Mn be an n-dimensional compact C∞-differentiable manifold,n≥2,and let S be a C1 -differential system on Mn.The system induces a one-parameter C1 transformation group φt(-∞＜t＜∞) over Mn and,thus,naturally induces a one-parameter transformation group of the tangent bundle of Mn.The aim of this paper,in essence,is to study certain ergodic properties of this latter transformation group.Among various results established in the paper,we mention here only the following,which might describe quite well the nature of our study.(A) Let M be the set of regular points in Mn of the differential system S.With respect to a given C∞ Riemannian metric of Mn,we consider the bundle (ζ)# of all (n-2) spheres Qxn-2,x∈M,where Qxn-2 for each x consists of all unit tangent vectors of Mn orthogonal to the trajectory through x.Then,the differential system S gives rise naturally to a one-parameter transformation group Ψt#(-∞＜t＜∞) of (ζ)#.For an l-frame α=(u1,u2,…,ul) of Mn at a point x in M,1 ≥l≥n-1,each ui being in (ζ)#,we shall denote the volume of the parallelotope in the tangent space of Mn at x with edges u1,u2,…,ut by v(α),and let η*α(t)=v(Ψ#t (u1),Ψ#t(u2),…,Ψ#t (ul)).This is a continuous real function of t.Let I*+(α)=-limT→∞1/T∫T0η*α(t)dt,I*-(α)=-limT→-∞1/T∫T0η*α(t)dt.α is said to be positively linearly independent of the mean if I+*(α)＞0.Similarly,α is said to be negatively linearly independent of the mean if I_ *(a)＞0.A point x of M is said to possess positive generic index κ=κ+*(x) if,at x,there is a κ-frame α= (u1,u2,…,Uκ),ui ∈(ζ)#,of Mn having the property of being positively linearly independent in the mean,but at x,every l-frame β=(v1,v2,…,vl),vi ∈(ζ)#,of Mn with l＞κ does not have the same property.Similarly,we define the negative generic index κ_*(x) of x.For a nonempty closed subset F of Mn consisting of regular points of S,invariant under φt(-∞＜t＜∞),let the (positive and
Soukhanovskii, V. A.; Kaita, R.; Stratton, B.
2016-11-01
A radiative divertor technique is planned for the NSTX-U tokamak to prevent excessive erosion and thermal damage of divertor plasma-facing components in H-mode plasma discharges with auxiliary heating up to 12 MW. In the radiative (partially detached) divertor, extrinsically seeded deuterium or impurity gases are used to increase plasma volumetric power and momentum losses. A real-time feedback control of the gas seeding rate is planned for discharges of up to 5 s duration. The outer divertor leg plasma electron temperature Te estimated spectroscopically in real time will be used as a control parameter. A vacuum ultraviolet spectrometer McPherson Model 251 with a fast charged-coupled device detector is developed for temperature monitoring between 5 and 30 eV, based on the Δn = 0, 1 line intensity ratios of carbon, nitrogen, or neon ion lines in the spectral range 300-1600 Å. A collisional-radiative model-based line intensity ratio will be used for relative calibration. A real-time Te-dependent signal within a characteristic divertor detachment equilibration time of ˜10-15 ms is expected.
Energy Technology Data Exchange (ETDEWEB)
Asakura, N., E-mail: asakura.nobuyuki@jaea.go.jp [Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212 (Japan); Hoshino, K. [Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212 (Japan); Shimizu, K. [Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 (Japan); Shinya, K. [Toshiba Nuclear Engineering Services Co., Isogo, Yokohama 25-8523 (Japan); Utoh, H.; Tokunaga, S.; Tobita, K. [Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212 (Japan); Ohno, N. [Graduate School of Engineering, Nagoya Univ., Nagoya 464-8603 (Japan)
2015-08-15
A short super-X divertor (SXD) is proposed as an option for the Demo divertor, where the field line length from the divertor null to the outer target was largely increased compared to a similar-size conventional divertor. Physics and engineering design studies for a 3 GW-level fusion power Demo reactor (SlimCS) (Tobita et al., 2009) have recently progressed. Minimal number of the divertor coils were installed inside the toroidal field coil, i.e. interlink-winding. Arrangement of the poloidal field coils and their currents were determined, taking into account of the engineering design such as vacuum vessel and the neutron shield structures, and the divertor maintenance scenario. Divertor plasma simulation showed that significant radiation region is produced between the super-X null and the target. Radiation loss in the divertor was increased, producing fully detached plasmas efficiently. Advantages of the short SXD were demonstrated, but the total peak heat load was a marginal level (10 MW m{sup −2}) for the engineering design.
Energy Technology Data Exchange (ETDEWEB)
Briesemeister, A.R., E-mail: briesemeister@fusion.gat.com [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States); Isler, R.C. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States); Allen, S.L. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Ahn, J.-W. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States); McLean, A.G. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States); Unterberg, E.A.; Hillis, D.L. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831 (United States); Fenstermacher, M.E.; Meyer, W.H. [Lawrence Livermore National Laboratory, 700 East Ave, Livermore, CA 94550 (United States)
2015-08-15
Externally applied non-axisymmetric magnetic fields are shown to have little effect on the impurity ion flow velocity and temperature as measured by the multichord divertor spectrometer in the DIII-D divertor for both attached and detached conditions. These experiments were performed in H-mode plasmas with the grad-B drift toward the target plates, with and without n = 3 resonant magnetic perturbations (RMPs). The flow velocity in the divertor is shown to change by as much as 30% when deuterium gas puffing is used to create detachment of the divertor plasma. No measurable changes in the C III flow were observed in response to the RMP fields for the conditions used in this work. Images of the C III emission are used along with divertor Thomson scattering to show that the local electron and C III temperatures are equilibrated for the conditions shown.
DEFF Research Database (Denmark)
Wang, L.; Xu, G.S.; Guo, H.Y.;
2013-01-01
-III ELMy H-modes. The energy loss and divertor power load are systematically characterized for these different ELMy H-modes to provide a physics basis for the next-step high-power long-pulse operations in EAST. Both type-I and compound ELMs exhibit good confinement (H98(y,2) ∼ 1). A significant loss...... is about 10 MW m−2, as determined from the divertor-embedded triple Langmuir probe system with high time resolution. As expected, type-III ELMs lead to much smaller divertor power loads with a peak heat flux of about 2 MW m−2. Peak power loads for compound ELMs are between those for type-I and type...
Thornton, A J; Chapman, I T; Harrison, J R
2013-01-01
Edge localised modes (ELMs) are a concern for future devices as they can limit the operational lifetime of the divertor. The mitigation of ELMs can be performed by the application of resonant magnetic perturbations (RMPs) which act to degrade the pressure gradient in the edge of the plasma. Investigations of the effect of RMPs on MAST have been performed in a range of plasmas using perturbations with toroidal mode numbers of n=3, 4 and 6. It has been seen that the RMPs increase the ELM frequency, which gives rise to a corresponding decrease in the ELM energy. The reduced ELM energy decreases the peak heat flux to the divertor, with a three fold reduction in the ELM energy, generating a 1.5 fold reduction in the peak heat flux. Measurements of the divertor heat flux profile show evidence of strike point splitting consistent with modelling using the vacuum code ERGOS.
Numerical study of the ITER divertor plasma with the B2-EIRENE code package
Energy Technology Data Exchange (ETDEWEB)
Kotov, V.; Reiter, D. [Forschungszentrum Juelich (DE). Inst. fuer Energieforschung (IEF), Plasmaphysik (IEF-4); Kukushkin, A.S. [ITER International Team, Cadarache (France)
2007-11-15
The problem of plasma-wall interaction and impurity control is one of the remaining critical issues for development of an industrial energy source based on nuclear fusion of light isotopes. In this field sophisticated integrated numerical tools are widely used both for the analysis of current experiments and for predictions guiding future device design. The present work is dedicated to the numerical modelling of the edge plasma region in divertor configurations of large-scale tokamak fusion devices. A well established software tool for this kind of modelling is the B2-EIRENE code. It was originally developed for a relatively hot (>> 10 eV) ''high recycling divertor''. It did not take into account a number of physical effects which can be potentially important for ''detached conditions'' (cold, - several eV, - high density, - {approx} 10{sup 21} m{sup -3}, - plasma) typical for large tokamak devices. This is especially critical for the modelling of the divertor plasma of ITER: an international project of an experimental tokamak fusion reactor to be built in Cadarache, France by 2016. This present work is devoted to a major upgrade of the B2-EIRENE package, which is routinely used for ITER modelling, essentially with a significantly revised version of EIRENE: the Monte-Carlo neutral transport code. The main part of the thesis address three major groups of the new physical effects which have been added to the model in frame of this work: the neutral-neutral collisions, the up-to date hydrogen molecular reaction kinetics and the line radiation transport. The impact of the each stage of the upgrade on the self-consistent (between plasma, the neutral gas and the radiation field) solution for the reference ITER case is analysed. The strongest effect is found to be due to the revised molecular collision kinetics, in particular due to hitherto neglected elastic collisions of hydrogen molecules with ions. The newly added non
Error Analysis of Modified Langevin Dynamics
Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia
2016-08-01
We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.
Kinetic modeling of divertor heat load fluxes in the Alcator C-Mod and DIII-D tokamaks
Energy Technology Data Exchange (ETDEWEB)
Pankin, A. Y. [Tech-X Corporation, Boulder, Colorado 80303 (United States); Rafiq, T.; Kritz, A. H. [Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 (United States); Park, G. Y. [National Fusion Research Institute, Daejeon, 305-333 (Korea, Republic of); Chang, C. S.; Ku, S. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Brunner, D.; Hughes, J. W.; LaBombard, B.; Terry, J. L. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Groebner, R. J. [General Atomics, San Diego, California 92121 (United States)
2015-09-15
The guiding-center kinetic neoclassical transport code, XGC0 [Chang et al., Phys. Plasmas 11, 2649 (2004)], is used to compute the heat fluxes and the heat-load width in the outer divertor plates of Alcator C-Mod and DIII-D tokamaks. The dependence of the width of heat-load fluxes on neoclassical effects, neutral collisions, and anomalous transport is investigated using the XGC0 code. The XGC0 code includes realistic X-point geometry, a neutral source model, the effects of collisions, and a diffusion model for anomalous transport. It is observed that the width of the XGC0 neoclassical heat-load is approximately inversely proportional to the total plasma current I{sub p.} The scaling of the width of the divertor heat-load with plasma current is examined for an Alcator C-Mod discharge and four DIII-D discharges. The scaling of the divertor heat-load width with plasma current is found to be weaker in the Alcator C-Mod discharge compared to scaling found in the DIII-D discharges. The effect of neutral collisions on the 1/I{sub p} scaling of heat-load width is shown not to be significant. Although inclusion of poloidally uniform anomalous transport results in a deviation from the 1/I{sub p} scaling, the inclusion of the anomalous transport that is driven by ballooning-type instabilities results in recovering the neoclassical 1/I{sub p} scaling. The Bohm or gyro-Bohm scalings of anomalous transport do not strongly affect the dependence of the heat-load width on plasma current. The inclusion of anomalous transport, in general, results in widening the width of neoclassical divertor heat-load and enhances the neoclassical heat-load fluxes on the divertor plates. Understanding heat transport in the tokamak scrape-off layer plasmas is important for strengthening the basis for predicting divertor conditions in ITER.
Production and fabrication of vanadium alloys for the radiative divertor program of DIII-D
Energy Technology Data Exchange (ETDEWEB)
Johnson, W.R.; Smith, J.P.; Stambaugh, R.D.
1996-04-01
V-4Cr-4-Ti alloy has been recently selected for use in the manufacture of a portion of the DIII-D Radiative Divertor modification, as part of an overall DIII-D vanadium alloy deployment effort developed by General Atomics (GA) in conjunction with the Argonne and Oak Ridge National Laboratories (ANL or ORNL). The goal of this work is to produce a production-scale heat of the alloy and fabricate it into product forms for the manufacture of a portion of the Radiative Divertor (RD) for the DIII-D tokamak, to develop the fabrications technology for manufacture of the vanadium alloy radiative Divertor components, and to determine the effects of typical tokamak environments in the behavior of the vanadium alloy. The production of a {approx}1300-kg heat of V-4Cr-4Ti alloy is currently in progress at Teledyne Wah Chang of Albany, oregon (TWCA) to provide sufficient material for applicable product forms. Two unalloyed vanadium ingots for the alloy have already been produced by electron beam melting of raw processes vanadium. Chemical compositions of one ingot and a portion of the second were acceptable, and Charpy V-Notch (CVN) impact test performed on processed ingot samples indicated ductile behavior. Material from these ingots are currently being blended with chromium and titanium additions, and will be vacuum-arc remelted into a V-4Cr-4Ti alloy ingot and converted into product forms suitable for components of the DIII-D RD structure. Several joining methods selected for specific applications in fabrication of the RD components are being investigated, and preliminary trials have been successful in the joining of V-alloy to itself by both resistance and inertial welding processes and to Inconel 625 by inertial welding.
A convective divertor utilizing a 2nd-order magnetic field null
Rognlien, Thomas
2014-10-01
New results motivate a detailed study of a magnetic divertor concept characterized by strong plasma convection near a poloidal magnetic field (Bp) null region. The configuration is that of a near-2nd-order Bp null (Bp ~ Δ r2) , as in a snowflake divertor. The concept has 2 key features: (A) Convection spreads the heat flux between multiple divertor legs and further broadens the heat-flux profile within each leg, thereby greatly reducing target-plate heat loads. (B) The heat flux is further reduced by line radiation in each leg in detachment-like ionization zones. Theory indicates that convective turbulence arises when the poloidal plasma beta, βp = 2μ0nT/B p 2 >> 1 . Measurements in TCV now more fully quantify earlier NSTX and TCV observations of plasma mixing, and related modeling of TCV indicates that strongly enhanced null-region transport is present. Convective mixing provides a stabilizing mechanism to prevent the ionization fronts (hydrogenic and impurity) from collapsing to a highly radiating core MARFE. Also, the radiating zone maps to a very small region at the midplane owing to the very weak Bp in the convective region, thus minimizing its impact on the core plasma. Detailed calculations are reported that combine features A and B noted above. The plasma mixing mechanisms are described together with the corresponding transport model implemented in the 2D UEDGE edge transport code. UEDGE calculations are presented that quantify the roles of mixing, impurity radiation, and detachment stability for a realistic snowflake configuration. Work in collaboration with D.D. Ryutov, S.I. Krasheninnikov, and M.V. Umansky. Performed for the U.S. DoE by LLNS, LLC, LLNL, under Contract DE-AC52-07NA27344.
Energy Technology Data Exchange (ETDEWEB)
Snowdon, K.J. [Newcastle Univ. (United Kingdom). Dept. of Physics; Tawara, H.
1997-01-01
The mechanisms which may lead to the departure of molecular species from surfaces exposed to low energy (0.1-100 eV) particle or photon and electron irradiation are reviewed. Where possible, the charge and electronic state, angular, translational and internal energy distributions of the departing molecules are described and the physical origin of the nature of those distributions identified. The consequences, for the departing molecules, of certain material choices become apparent from such an analysis. Such information may help guide the choice of appropriate materials for plasma facing components of gas-blanket type divertors such as that recently proposed for the International Thermonuclear Experimental Reactor (ITER). (author). 71 refs.
A new radiation-hard endoscope for divertor spectroscopy on JET
Energy Technology Data Exchange (ETDEWEB)
Huber, A., E-mail: A.Huber@fz-juelich.de [Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Jülich, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich (Germany); Brezinsek, S.; Mertens, Ph.; Schweer, B.; Sergienko, G.; Terra, A. [Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Jülich, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich (Germany); Arnoux, G.; Balshaw, N. [Euratom-CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Clever, M. [Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Jülich, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich (Germany); Edlingdon, T. [Euratom-CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Egner, S. [Kayser-Threde GmbH, D-81379 Munich (Germany); Farthing, J. [Euratom-CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Hartl, M. [Kayser-Threde GmbH, D-81379 Munich (Germany); Horton, L. [EFDA-JET Close Support Unit, Culham Science Centre, Culham OX14 3DB (United Kingdom); Kampf, D. [Kayser-Threde GmbH, D-81379 Munich (Germany); Klammer, J. [KRP-Mechatec Engineering GbR, D-85748 Garching b. Muenchen (Germany); Lambertz, H.T. [Institute of Energy and Climate Research – Plasma Physics, Forschungszentrum Jülich, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich (Germany); Matthews, G.F. [Euratom-CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Morlock, C.; Murari, A. [EFDA-JET Close Support Unit, Culham Science Centre, Culham OX14 3DB (United Kingdom); and others
2013-10-15
Highlights: ► A new radiation-hard endoscope with optimised divertor view has been developed on JET. ► A high optical transmittance (≥30%) in the operating wavelength range from 390 nm to 2500 nm has been achieved. ► The endoscope delivers high spatial resolution ≤2 mm at the object plane and ≤3 mm over the whole depth of field (±0.7 m). ► The new optical design includes options for the in situ calibration of the endoscope transmittance. ► A new type of shutter based on pneumatic techniques has been developed in view of ITER and integrated into the endoscope. -- Abstract: In preparation for ITER, JET has been upgraded with a new ITER-like wall (ILW) whereby the main plasma-facing components, previously made of carbon, have been replaced by Be in the main chamber and W in the divertor. A new endoscope with optimised divertor view has been developed in order to survey and monitor the emission of specific impurities such as tungsten, beryllium and the possibly remaining carbon in the tungsten divertor of the JET-ILW. It operates in the wavelength range from 390 nm to 2500 nm with high optical transmittance (≥30%) as well as high spatial resolution, that is ≤2 mm at the object plane and ≤3 mm over the whole depth of field (±0.7 m). The endoscope is a prototype for testing an ITER relevant design concept based on reflective optics only. The endoscope has an optimised observation in the near ultraviolet and in the blue spectral region to ensure the detection of the W I-emission line at 400.8 nm. In parallel to the new optical design, a new type of ITER-like shutter system based on pneumatic techniques has been developed and integrated in the endoscope head. The new optical design includes options for an in situ calibration of the endoscope transmittance during the experimental campaign.
On the asymmetries of ELM divertor power deposition in JET and ASDEX Upgrade
DEFF Research Database (Denmark)
Eich, T.; Kallenbach, A.; Fundamenski, W.
2009-01-01
. The paper discusses a comparable simple extension of the model by introducing a non-zero characteristic velocity of the Maxwellian distributed particles. This way the experimentally observed temporal evolution as well as the in/out energy imbalance can be described. The extended model named free......An analytical expression was derived for describing the divertor target power during ELMs based on the model discussed in [W. Fundamenski, R.A. Pitts, Plasma Phys. Control. Fus. 48 (2006) 109] where the power load arises from a Maxwellian distribution of particles released into the SOL region...
Testing candidate interlayers for an enhanced water-cooled divertor target
Energy Technology Data Exchange (ETDEWEB)
Hancock, David, E-mail: david.hancock@ccfe.ac.uk [CCFE, Culham Science Centre, Oxfordshire OX14 3DB (United Kingdom); Barrett, Tom; Foster, James; Fursdon, Mike; Keech, Gregory; McIntosh, Simon; Timmis, William [CCFE, Culham Science Centre, Oxfordshire OX14 3DB (United Kingdom); Rieth, Michael; Reiser, Jens [Karlsruhe Institute of Technology, IAM-AWP, P.O. Box 3640, 76021 Karlsruhe (Germany)
2015-10-15
Highlights: • We introduce an optimised divertor target concept: the “Thermal Break”. • We suggest a candidate interlayer material for this concept: FeltMetal. • We describe a bespoke rig for testing the thermal conductivity of this material. • We present preliminary results for a number of samples. - Abstract: The design of a divertor target for DEMO remains one of the most challenging engineering tasks to be overcome on the path to fusion power. Under the European DEMO programme, a promising concept known as Thermal Break has been developed at CCFE. This concept is a variation of the ITER tungsten divertor in which the pure Copper interlayer between Copper Chrome Zirconium coolant pipe and Tungsten monoblock armour is replaced with a low thermal conductivity compliant interlayer, with the aim of reducing the thermal mismatch stress between the armour and structure. One candidate material for this interlayer is FeltMetal™ (Technetics Group, USA). This material consists of an amorphous matrix of fine copper wires which are sintered onto a thin copper foil, creating a sheet of approximately 1 mm thickness. FeltMetal has been successfully used for many years to provide compliant sliding electrical contacts for the MAST TF coils and on ALCATOR C-Mod and extensive material testing has therefore been undertaken to quantify thermal and mechanical properties. These tests, however, have not been performed under vacuum or DEMO-relevant conditions. A bespoke experimental test rig has therefore been designed and constructed with which to measure the interlayer thermal conductance as a function of temperature and pressure under vacuum conditions. The design of this apparatus and the results of experiments on FeltMetal as well as other candidate interlayers are presented here. In parallel, joint mockups using the candidate interlayers have been prepared and Thermal Break divertor target mockups have been manufactured, requiring the development of a dedicated
High heat flux plasma generator for new divertor plasma simulator in Nagoya University
Energy Technology Data Exchange (ETDEWEB)
Narita, S.; Ezumi, N.; Ohno, N.; Uesugi, Y.; Takamura, S. [Nagoya Univ. (Japan)
1997-12-31
A new divertor simulator called NAGDIS-II has been constructed in order to investigate edge plasma physics in fusion devices. Improved TP-D type plasma source, which consists of LaB{sub 6} cathode with a Mo hollow shield and external heating system, water-cooled intermediate electrode and anode was employed to make a high density plasma in the NAGDIS-II. The performance and reliability of the discharge system was confirmed by quantitatively measuring neutral pressure, heating efficiency and plasma parameters. (author)
Energy Technology Data Exchange (ETDEWEB)
Pitcher, C.S.; Boozer, A.H.; Murmann, H.; Schweinzer, J.; Suttrop, W.; Salzmann, H. [Max-Planck-Institut fuer Plasmaphysik, IPP-EURATOM Association, D--85748 Garching (Germany); ASDEX Upgrade Team% NBI Group
1997-07-01
Experimental evidence is presented from the ASDEX Upgrade (Axially Symmetric Divertor Experiment) tokamak [{ital Plasma Physics and Controlled Nuclear Fusion Research 1993} (International Atomic Energy Agency, Vienna, 1994), Vol. I, p. 127] of a robust relation between the edge radial pressure gradient and the global confinement of the plasma. This relation transcends the power flowing across flux surfaces near the edge and thus suggests that the usual model of cross-field heat transport, where local gradients increase with increasing local power flow, is not appropriate. {copyright} {ital 1997 American Institute of Physics.}
The role of ''momentum removal'' in divertor detachment
Energy Technology Data Exchange (ETDEWEB)
Kukushkin, A.S. [Kurchatov Institute, Moscow (Russian Federation); NRNU MEPhI, Moscow (Russian Federation); Pacher, H.D. [INRS-EMT, Varennes, Quebec (Canada)
2016-08-15
The role of ''momentum removal'' (the drag force on the plasma ion flow) in divertor detachment is considered and analysed in detail. This analysis of the 2D modelling results shows that the drag force cannot reduce the power and particle flux to the target directly. However, it is essential for creating the conditions for efficient radiation and volumetric plasma recombination, which in turn do the job. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Simulation of radiative divertor plasmas by Ar seeding with the full W-wall in JT-60SA
Energy Technology Data Exchange (ETDEWEB)
Kawashima, H.; Shimizu, K.; Nakano, T.; Asakura, N. [Japan Atomic Energy Agency, Naka, Ibaraki (Japan); Hoshino, K. [Japan Atomic Energy Agency, Rokkasho, Aomori (Japan)
2016-08-15
Radiative divertor plasmas for JT-60SA with a full tungsten (W) wall, which is one of options in future, have been simulated with a SOL/divertor integrated code, SONIC. A conventional modified-coronal radiation (MCR) model with a finite confinement time is used for both Ar and W for the purpose of wide-range parameter surveys for the divertor plasma to obtain the required conditions (q{sub t} ≤ 10 MW/m{sup 2}, n{sup Sep}{sub e-mid} = 3∝8 x 10{sup 19} m{sup -3}, P{sub rad} < ∝30 MW), saving the calculation time. At low W density ratio (n{sub W}/n{sub i} = 1 x 10{sup -5}), due to low radiative power from W ions, Ar density ratio (n{sub Ar}/n{sub i} ≥ 1.0 x 10{sup -3}) and a strong gas puff (Γ{sub p} ≥ 3.0 x 10{sup 22} s{sup -1}) are inevitable to suppress the divertor heat flux down to 10 MW/m{sup 2}. Increasing n{sub W}/n{sub i} to 1 x 10{sup -3} in the divertor region, the divertor heat load becomes low and the operative regions are expanded. While, the W production shall be suppressed since the W radiation is increased with replacement of Ar radiation and the particle recycling decreased. A Monte-Carlo module (IMPMC) implemented in SONIC for Ar seeding reveals that the spatial distribution of Ar ions is predominantly determined by shell structures of the Ar ions. The consistency between IMPMC and MCR calculations is demonstrated for the averaged n{sub Ar}/n{sub i} ratio, the electron density and temperature profiles on the divertor target and typical parameter such as the divertor heat load. It shows that the detailed analysis with IMPMC model can be speedily obtained, using a steady state solution obtained by MCR model as an initial state. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Obrosova, N. K.; Shananin, A. A.
2015-04-01
A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by an attempt to analyze the problems of functioning of low competitive macroeconomic structures. The model is formalized in the form of a Bellman equation, for which a closed-form solution is found. The stochastic process of product stock variations is proved to be ergodic and its final probability distribution is found. Expressions for the average production load and the average product stock are found by analyzing the stochastic process. A system of model equations relating the model variables to official statistical parameters is derived. The model is identified using data from the Fiat and KAMAZ companies. The influence of the credit interest rate on the firm market value assessment and the production load level are analyzed using comparative statics methods.
Energy Technology Data Exchange (ETDEWEB)
Queiros, S.M. Duarte [Unilever R and D Port Sunlight, Quarry Road East, CH63 3JW (United Kingdom)], E-mail: silvio.queiros@unilever.com
2009-04-13
In this Letter we analyse the behaviour of the probability density function of the sum of N deterministic variables generated from the triangle map of Casati-Prosen. For the case in which the map is both ergodic and mixing the resulting probability density function quickly concurs with the Normal distribution. However, when the map is weakly chaotic, and fuzzily not mixing, the resulting probability density functions are described by power-laws. Moreover, contrarily to what it would be expected, as the number of added variables N increases the distance to Gaussian distribution increases. This behaviour goes against standard central limit theorem. By extrapolation of our finite size results we preview that in the limit of N going to infinity the distribution has the same asymptotic decay as a Lorentzian (or a q=2-Gaussian)
Directory of Open Access Journals (Sweden)
C. Poongodi
2011-01-01
Full Text Available Problem Statement: In MIMO system, capacity mainly depends on the channel and the antenna characteristics. The capacity can be improved by proper design of antenna elements and choosing appropriate array configuration and the directive elements give more capacity than omni directional elements. The dual polarized antennas are better than single polarized antennas as the former can provide two information channels. The mutual coupling also changes the capacity considerably. When the spacing between the elements is less than 0.5λ, the effect of mutual coupling is more. Approach: This study analyzes the capacity of Echelon, H-shaped; V-shaped free standing dipoles and printed dipole arrays of a MIMO system. The channel model for multi-polarized antennas is used in the simulations. The mutual coupling between the dipoles of different orientations is also included to make simulation more realistic. MIMO system with relay network is used to improve the coverage and reliability and to reduce the interference in wireless network. So we have analyzed the characterization of the ergodic capacity of amplify-and-forward (AF MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. Results: This study presents the results for channel capacity for different antenna configuration and the exact Ergodic capacity, closed form expression for the high SNR regime and tight closed form upper and lower bounds for amplify and forward relay system using the probability density function of an unordered eigenvalues. Conclusion/Recommendations: The Echelon, H-shaped; V-shaped free standing dipoles offer better capacity results in conventional MIMO system. The results produced are valid for all SNR values and for arbitrary numbers of antennas at the source, relay and destination. We also demonstrate a relationship between the conventional point-to-point MIMO Channels and dual-hop AF MIMO relay channel.
Thermal analysis of an exposed tungsten edge in the JET divertor
Energy Technology Data Exchange (ETDEWEB)
Arnoux, G., E-mail: gilles.arnoux@ccfe.ac.uk [CCFE Association, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Coenen, J. [Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung – Plasmaphysik, 52425 Jülich (Germany); Bazylev, B. [Forshungzentrum Karlsruhe GmbH, P.O.Box 3640, D-76021 Karlsruhe (Germany); Corre, Y. [CEA/DSM/IRFM, CEA Cadarache, 13108 Saint Paul Lez Durance (France); Matthews, G.F.; Balboa, I. [CCFE Association, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Clever, M. [Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung – Plasmaphysik, 52425 Jülich (Germany); Dejarnac, R. [IPP.CR, Institute of Plasma Physics AS CR, Za Slovankou 3, 182 21 Praha 8 (Czech Republic); Devaux, S.; Eich, T. [Max-Planck-Institut für Plasmaphysik, D-85748 Garching (Germany); Gauthier, E. [CEA/DSM/IRFM, CEA Cadarache, 13108 Saint Paul Lez Durance (France); Frassinetti, L. [Fusion Plasma Physics, EES, KTH, SE-10044 Stockholm (Sweden); Horacek, J. [IPP.CR, Institute of Plasma Physics AS CR, Za Slovankou 3, 182 21 Praha 8 (Czech Republic); Jachmich, S. [Laboratory for Plasma Physics Koninklijke Militaire School – Ecole Royale Militaire, Renaissancelaan, 30 Avenue de la Renaissance, B-1000 Brussels (Belgium); Kinna, D. [CCFE Association, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Marsen, S. [Max-Planck-Institut für Plasmaphysik, Teilinsitut Greifswald, D-17491 Greifswald (Germany); and others
2015-08-15
Highlights: • We provide experimental evidences that melting of the JET tungsten divertor is achieved by transients only. • The measurements show that less than half the parallel heat flux reaches the melted sample. • We propose ideas to investigate to explain the missing heat flux. - Abstract: In the recent melt experiments with the JET tungsten divertor, we observe that the heat flux impacting on a leading edge is 3–10 times lower than a geometrical projection would predict. The surface temperature, tungsten vaporisation rate and melt motion measured during these experiments is consistent with the simulations using the MEMOS code, only if one applies the heat flux reduction. This unexpected observation is the result of our efforts to demonstrate that the tungsten lamella was melted by ELM induced transient heat loads only. This paper describes in details the measurements and data analysis method that led us to this strong conclusion. The reason for the reduced heat flux are yet to be clearly established and we provide some ideas to explore. Explaining the physics of this heat flux reduction would allow to understand whether it can be extrapolated to ITER.