Non-existence of Normal Tokamak Equilibria with Negative Central Current
Energy Technology Data Exchange (ETDEWEB)
G.W. Hammett; S.C. Jardin; B.C. Stratton
2003-02-18
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current-drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.
Tokamak-like Vlasov equilibria
Tasso, H
2014-01-01
Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.
TOKAMAK EQUILIBRIA WITH CENTRAL CURRENT HOLES AND NEGATIVE CURRENT DRIVE
Energy Technology Data Exchange (ETDEWEB)
CHU, M.S.; PARKS, P.B.
2002-06-01
OAK B202 TOKAMAK EQUILIBRIA WITH CENTRAL CURRENT HOLES AND NEGATIVE CURRENT DRIVE. Several tokamak experiments have reported the development of a central region with vanishing currents (the current hole). Straightforward application of results from the work of Greene, Johnson and Weimer [Phys. Fluids, 3, 67 (1971)] on tokamak equilibrium to these plasmas leads to apparent singularities in several physical quantities including the Shafranov shift and casts doubts on the existence of this type of equilibria. In this paper, the above quoted equilibrium theory is re-examined and extended to include equilibria with a current hole. It is shown that singularities can be circumvented and that equilibria with a central current hole do satisfy the magnetohydrodynamic equilibrium condition with regular behavior for all the physical quantities and do not lead to infinitely large Shafranov shifts. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization, i.e. no negative currents can be driven in the central region.
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Tasso, H
2015-01-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Analytical solutions for Tokamak equilibria with reversed toroidal current
Energy Technology Data Exchange (ETDEWEB)
Martins, Caroline G. L.; Roberto, M.; Braga, F. L. [Departamento de Fisica, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, Sao Paulo 12228-900 (Brazil); Caldas, I. L. [Instituto de Fisica, Universidade de Sao Paulo, 05315-970 Sao Paulo, SP (Brazil)
2011-08-15
In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.
Comparison of electron drift waves in numerical and analytical tokamak equilibria
Energy Technology Data Exchange (ETDEWEB)
Rafiq, T; Anderson, J; Persson, M [Department of Electromagnetics and Euratom/VR Association, Chalmers University of Technology, S-41296 Goeteborg (Sweden)
2004-01-01
In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalized s-alpha model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.
Tokamak equilibria with strong toroidal current density reversal
Ludwig, G. O.; Rodrigues, Paulo; Bizarro, João P. S.
2013-05-01
The equilibrium of large magnetic islands in the core of a tokamak under conditions of strong toroidal current density reversal is investigated by a new method. The method uses distinct spectral representations to describe each simply connected region as well as the containing shell geometry. This ideal conducting shell may substitute for the plasma edge region or take a virtual character representing the external equilibrium field effect. The internal equilibrium of the islands is solved within the framework of the variational moment method. Equivalent surface current densities are defined on the boundaries of the islands and on the thin containing shell, giving a straightforward formulation to the interaction between regions. The equilibrium of the island-shell system is determined by matching moments of the Dirichlet boundary conditions. Finally, the macroscopic stability against a class of tilting displacements is examined by means of an energy principle. It is found out that the up-down symmetric islands are stable to this particular perturbation and geometry but the asymmetric system presents a bifurcation in the equilibrium.
Kinetic modeling of 3D equilibria in a tokamak
Albert, C. G.; Heyn, M. F.; Kasilov, S. V.; Kernbichler, W.; Martitsch, A. F.; Runov, A. M.
2016-11-01
External resonant magnetic perturbations (RMPs) can modify the magnetic topology in a tokamak. In this case the magnetic field cannot generally be described by ideal MHD equilibrium equations in the vicinity of resonant magnetic surfaces where parallel and perpendicular relaxation timescales are comparable. Usually, resistive MHD models are used to describe these regions. In the present work, a kinetic model is used for this purpose. Within this model, plasma response, current and charge density are computed with help of a Monte Carlo method, where guiding center orbit equations are solved using a semianalytical geometrical integrator. Besides its higher efficiency in comparison to usual integrators this method is not sensitive to noise in field quantities. The computed charges and currents are used to calculate the electromagnetic field with help of a finite element solver. A preconditioned iterative scheme is applied to search for a self-consistent solution. The discussed method is aimed at the nonlinear kinetic description of RMPs in experiments on Edge Localized Mode (ELM) mitigation by external perturbation coil systems without simplification of the device geometry.
EFFECT OF PROFILES AND SHAPE ON IDEAL STABILITY OF ADVANCED TOKAMAK EQUILIBRIA
Energy Technology Data Exchange (ETDEWEB)
MAKOWSKI,MA; CASPER,TA; FERRON,JR; TAYLOR,TS; TURNBULL,AD
2003-08-01
OAK-B135 The pressure profile and plasma shape, parameterized by elongation ({kappa}), triangularity ({delta}), and squareness ({zeta}), strongly influence stability. In this study, ideal stability of single null and symmetric, double-null, advanced tokamak (AT) configurations is examined. All the various shapes are bounded by a common envelope and can be realized in the DIII-D tokamak. The calculated AT equilibria are characterized by P{sub 0}/
{approx} 2.0-4.5, weak negative central shear, high q{sub min} (> 2.0), high bootstrap fraction, an H-mode pedestal, and varying shape parameters. The pressure profile is modeled by various polynomials together with a hyperbolic tangent pedestal, consistent with experimental observations. Stability is calculated with the DCON code and the resulting stability boundary is corroborated by GATO runs.
Jeon, Y M
2015-01-01
A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is encountered after all in equilibrium calculation with a free-boundary condition. The other is an extension to deal with a new divertor geometry such as snowflake or X divertors. For validations, the uniqueness of a solution is confirmed by the independence on variations of computational domain, the mathematical correctness and accuracy of equilibrium profiles are checked by a direct comparison with an analytic equilibrium known as a generalized Solovev equilibrium, and the governing force balance relation is tested by examining the intrinsic axisymmetric instabilities. As a valuable application, a snowflake equilibrium that requires a second order zero of the poloidal magnetic field is discussed in the circumstance of KSTAR coil system.
CASTOR3D: linear stability studies for 2D and 3D tokamak equilibria
Strumberger, E.; Günter, S.
2017-01-01
The CASTOR3D code, which is currently under development, is able to perform linear stability studies for 2D and 3D, ideal and resistive tokamak equilibria in the presence of ideal and resistive wall structures and coils. For these computations ideal equilibria represented by concentric nested flux surfaces serve as input (e.g. computed with the NEMEC code). Solving an extended eigenvalue problem, the CASTOR3D code takes simultaneously plasma inertia and wall resistivity into account. The code is a hybrid of the CASTOR_3DW stability code and the STARWALL code. The former is an extended version of the CASTOR and CASTOR_FLOW code, respectively. The latter is a linear 3D code computing the growth rates of resistive wall modes in the presence of multiply-connected wall structures. The CASTOR_3DW code, and some parts of the STARWALL code have been reformulated in a general 3D flux coordinate representation that allows to choose between various types of flux coordinates. Furthermore, the implemented many-valued current potentials in the STARWALL part allow a correct treatment of the m = 0, n = 0 perturbation. In this paper, we outline the theoretical concept, and present some numerical results which illustrate the present status of the code and demonstrate its numerous application possibilities.
Stable bootstrap-current driven equilibria for low aspect ratio tokamaks
Energy Technology Data Exchange (ETDEWEB)
Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S. [General Atomics, San Diego, CA (United States); Pearlstein, L.D. [Lawrence Livermore National Lab., CA (United States); Sauter, O.; Villard, L. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
Low aspect ratio tokamaks can potentially provide a high ratio of plasma pressure to magnetic pressure {beta} and high plasma current I at a modest size, ultimately leading to a high power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma. A high value of the Troyon factor {beta}{sub N} and strong shaping are required to allow simultaneous operation at high {beta} and high bootstrap current fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both {beta}{sub N} and {beta} are defined in terms of the vacuum toroidal field. Equilibria with {beta} {sub N}{>=}8 and {beta} {approx_equal}35% to 55% exist which are stable to n = {infinity} ballooning modes, and stable to n = 0,1,2,3 kink modes with a conducting wall. The dependence of {beta} and {beta}{sub N} with respect to aspect ratio is also considered. (author) 9 figs., 14 refs.
Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria
Energy Technology Data Exchange (ETDEWEB)
Bowden, G. W.; Hole, M. J. [Plasma Theory and Modelling, Research School of Physics and Engineering, Australian National University, Acton 2601, Australian Capital Territory (Australia); Könies, A. [Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-17491 Greifswald (Germany)
2015-09-15
In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.
Ferraro, N. M.; Jardin, S. C.; Lao, L. L.; Shephard, M. S.; Zhang, F.
2016-05-01
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Energy Technology Data Exchange (ETDEWEB)
Ferraro, N. M., E-mail: nferraro@pppl.gov; Lao, L. L. [General Atomics, La Jolla, California 92186 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Shephard, M. S.; Zhang, F. [Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2016-05-15
Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.
Optimization study of normal conductor tokamak for commercial neutron source
Fujita, T.; Sakai, R.; Okamoto, A.
2017-05-01
The optimum conceptual design of tokamak with normal conductor coils was studied for minimizing the cost for producing a given neutron flux by using a system code, PEC. It is assumed that the fusion neutrons are used for burning transuranics from the fission reactor spent fuel in the blanket and a fraction of the generated electric power is circulated to opearate the tokamak with moderate plasma fusion gain. The plasma performance was assumed to be moderate ones; {β\\text{N}}~∼ ~3{--}4 in the aspect ratio A~=~2{--}3 and {{H}98y2}~=~1 . The circulating power is an important factor affecting the cost. Though decreasing the aspect ratio is useful to raise the plasma beta and decrease the toroidal field, the maximum field in the coil starts to rise in the very low aspect ratio range and then the circulating power increases with decrease in the plasma aspect ratio A below A~∼ ~2 , while the construction cost increases with A . As a result, the cost per neutron has its minimum around A~∼ ~2.2 , namely, between ST and the conventional tokamak. The average circulating power fraction is expected to be ~51%.
Intrinsic rotation driven by non-Maxwellian equilibria in Tokamak plasmas.
Barnes, M; Parra, F I; Lee, J P; Belli, E A; Nave, M F F; White, A E
2013-08-02
The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of cocurrent toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.
Intrinsic rotation driven by non-Maxwellian equilibria in tokamak plasmas
Barnes, M; Lee, J P; Belli, E A; Nave, M F F; White, A E
2013-01-01
The effect of small deviations from a Maxwellian equilibrium on turbulent momentum transport in tokamak plasmas is considered. These non-Maxwellian features, arising from diamagnetic effects, introduce a strong dependence of the radial flux of co-current toroidal angular momentum on collisionality: As the plasma goes from nearly collisionless to weakly collisional, the flux reverses direction from radially inward to outward. This indicates a collisionality-dependent transition from peaked to hollow rotation profiles, consistent with experimental observations of intrinsic rotation.
Fitzpatrick, Richard
2016-05-01
The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡d ln Ti/d ln ne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.
Energy Technology Data Exchange (ETDEWEB)
Meglicki, Z
1995-09-19
We describe in detail the implementation of a weighted differences code, which is used to simulate a tokamak using the Maschke-Perrin solution as an initial condition. The document covers the mainlines of the program and the most important problem-specific functions used in the initialization, static tests, and dynamic evolution of the system. The mathematics of the Maschke-Perrin solution is discussed in parallel with its realisation within the code. The results of static and dynamic tests are presented in sections discussing their implementation.The code can also be obtained by ftp -anonymous from cisr.anu.edu.au Directory /pub/papers/meglicki/src/tokamak. This code is copyrighted. (author). 13 refs.
Energy Technology Data Exchange (ETDEWEB)
Meglicki, Z
1995-09-19
We describe in detail the implementation of a weighted differences code, which is used to simulate a tokamak using the Maschke-Perrin solution as an initial condition. The document covers the mainlines of the program and the most important problem-specific functions used in the initialization, static tests, and dynamic evolution of the system. The mathematics of the Maschke-Perrin solution is discussed in parallel with its realisation within the code. The results of static and dynamic tests are presented in sections discussing their implementation.The code can also be obtained by ftp -anonymous from cisr.anu.edu.au Directory /pub/papers/meglicki/src/tokamak. This code is copyrighted. (author). 13 refs.
Indian Academy of Sciences (India)
Ramesh Narayanan; A N Sekar Iyengar
2010-10-01
The behaviour of runaway electrons in the SINP tokamak, which can be operated in a normal edge safety factor () (NQ) discharge configuration as well as in a low (LQ) configuration, was experimentally investigated, during the initial plasma generation phase. An energy analysis of the runaway electron dynamics in the rise phase of the SINP tokamak discharges was also made. A comparison of the runaway electron diffusion coefficients in NQ and LQ is carried out in this paper.
Institute of Scientific and Technical Information of China (English)
Song Yuntao; Satoshi NISHIO
2005-01-01
The center post is the most critical component as an inboard part of the toroidal field coil for the low aspect ratio tokamak. During the discharge it endures not only a tremendous ohmic heating owing to its carrying a rather high current but also a large nuclear heating and irradiation owing to the plasma operation. All the severe operating conditions, including the structure stress intensity and the stability of the structure, largely limit the maximum allowable current density. But in order to contain a very high dense plasma, it is hoped that the fusion power plant system can operate with a much high maximum magnetic field BT ≥12 T～15 T in the center post. A new method is presented in this paper to improve the maximum magnetic field up to 17 T and to investigate the possibility of the normal conducting center post to be used in the future fusion tokamak power plant.
Houyin, Wang; Jiansheng, Hu; Yaowei, Yu; Bin, Cao; Jinhua, Wu; Guoqing, Shen; Zhao, Wan; EAST, Contributors
2017-01-01
Although the deuterium and helium have almost the same mass, a Penning Optical Gas Analyzer (POGA) system on the basis of the spectroscopic method and Penning discharging has been designed on EAST, since 2014. The POGA system was developed successfully in 2015, it was the first time that EAST could detect helium partial pressure in deuterium plasma (wall conditioning and plasma operation scenario). With dedicated calibration and proper adjustment of the parameters, the minimum concentration of helium in deuterium gas can be measured as about 0.5% instead of 1% on the other tokamak devices. Moreover, the He and D2 partial pressures are measured simultaneously. At present, the measurable range of deuterium partial pressure is 1 × 10-7 mbar to 1 × 10-5 mbar, meanwhile the range of helium is 1 × 10-8 mbar to 1 × 10-5 mbar. The measurable range can be modified by means of the adjustment of POGA system’s parameters. It is possible to detect the interesting part of the gas with a time resolution of less than 5 ms (the 200 ms because of conductance of transfer pipe at present). The POGA system was routinely employed to wall conditioning and helium enrichment investigation in 2015. Last but not the least, the low temperature plasma of POGA is generated by normal penning gauge Pfeiffer IKR gauge instead of Alcatel CF2P, which has been suspended for a few years and was used for almost all the POGA systems in the world.
Resistive edge mode instability in stellarator and tokamak geometries
Mahmood, M. Ansar; Rafiq, T.; Persson, M.; Weiland, J.
2008-09-01
Geometrical effects on linear stability of electrostatic resistive edge modes are investigated in the three-dimensional Wendelstein 7-X stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] and the International Thermonuclear Experimental Reactor [Progress in the ITER Physics Basis, Nucl. Fusion 7, S1, S285 (2007)]-like equilibria. An advanced fluid model is used for the ions together with the reduced Braghinskii equations for the electrons. Using the ballooning mode representation, the drift wave problem is set as an eigenvalue equation along a field line and is solved numerically using a standard shooting technique. A significantly larger magnetic shear and a less unfavorable normal curvature in the tokamak equilibrium are found to give a stronger finite-Larmor radius stabilization and a more narrow mode spectrum than in the stellarator. The effect of negative global magnetic shear in the tokamak is found to be stabilizing. The growth rate on a tokamak magnetic flux surface is found to be comparable to that on a stellarator surface with the same global magnetic shear but the eigenfunction in the tokamak is broader than in the stellarator due to the presence of large negative local magnetic shear (LMS) on the tokamak surface. A large absolute value of the LMS in a region of unfavorable normal curvature is found to be stabilizing in the stellarator, while in the tokamak case, negative LMS is found to be stabilizing and positive LMS destabilizing.
Equilibria, Fixed Points, and Complexity Classes
Yannakakis, Mihalis
2008-01-01
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or ...
Computation of two-fluid, flowing equilibria
Steinhauer, Loren; Kanki, Takashi; Ishida, Akio
2006-10-01
Equilibria of flowing two-fluid plasmas are computed for realistic compact-toroid and spherical-tokamak parameters. In these examples the two-fluid parameter ɛ (ratio of ion inertial length to overall plasma size) is small, ɛ ˜ 0.03 -- 0.2, but hardly negligible. The algorithm is based on the nearby-fluids model [1] which avoids a singularity that otherwise occurs for small ɛ. These representative equilibria exhibit significant flows, both toroidal and poloidal. Further, the flow patterns display notable flow shear. The importance of two-fluid effects is demonstrated by comparing with analogous equilibria (e.g. fixed toroidal and poloidal current) for a static plasma (Grad-Shafranov solution) and a flowing single-fluid plasma. Differences between the two-fluid, single-fluid, and static equilibria are highlighted: in particular with respect to safety factor profile, flow patterns, and electrical potential. These equilibria are computed using an iterative algorithm: it employs a successive-over-relaxation procedure for updating the magnetic flux function and a Newton-Raphson procedure for updating the density. The algorithm is coded in Visual Basic in an Excel platform on a personal computer. The computational time is essentially instantaneous (seconds). [1] L.C. Steinhauer and A. Ishida, Phys. Plasmas 13, 052513 (2006).
OPTIMUM PLASMA STATES FOR NEXT STEP TOKAMAKS
Energy Technology Data Exchange (ETDEWEB)
LIN-LIU,YR; STAMBAUGH,RD
2002-11-01
OAK A271 OPTIMUM PLASMA STATES FOR NEXT STEP TOKAMAKS. The dependence of the ideal ballooning {beta} limit on aspect ratio, A, and elongation {kappa} is systematically explored for nearly 100% bootstrap current driven tokamak equilibria in a wide range of the shape parameters (A = 1.2-7.0, {kappa} = 1.5-6.0 with triangularity {delta} = 0.5). The critical {beta}{sub N} is shown to be optimal at {kappa} = 3.0-4.0 for all A studied and increases as A decreases with a dependence close to A{sup -0.5}. The results obtained can be used as a theoretical basis for the choice of optimum aspect ratio and elongation of next step burning plasma tokamaks or tokamak reactors.
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Neoclassical transport in high [beta] tokamaks
Energy Technology Data Exchange (ETDEWEB)
Cowley, S.C.
1992-12-01
Neoclassical, transport in high [beta] large aspect ratio tokamaks is calculated. The variational method introduced by Rosenbluth, et al., is used to calculate the full Onsager matrix in the banana regime. These results are part of a continuing study of the high [beta] large aspect ratio equilibria introduced in Cowley, et al. All the neoclassical coefficients are reduced from their nominal low [beta] values by a factor ([var epsilon]/q[sup 2][beta])[sup [1/2
Axisymmetric instability in a noncircular tokamak
Energy Technology Data Exchange (ETDEWEB)
Lipschultz, B.
1979-10-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes - the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria.
Phase Equilibria Diagrams Database
SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase) The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.
Learning efficient correlated equilibria
Borowski, Holly P.
2014-12-15
The majority of distributed learning literature focuses on convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize more efficient collective behavior than even the best Nash equilibrium. However, there are no existing distributed learning algorithms that converge to specific correlated equilibria. In this paper, we provide one such algorithm which guarantees that the agents\\' collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior through distributed learning involves incorporating a common random signal into the learning environment.
Computational Aspects of Equilibria
Yannakakis, Mihalis
Equilibria play a central role in game theory and economics. They characterize the possible outcomes in the interaction of rational, optimizing agents: In a game between rational players that want to optimize their payoffs, the only solutions in which no player has any incentive to switch his strategy are the Nash equilibria. Price equilibria in markets give the prices that allow the market to clear (demand matches supply) while the traders optimize their preferences (utilities). Fundamental theorems of Nash [34] and Arrow-Debreu [2] established the existence of the respective equilibria (under suitable conditions in the market case). The proofs in both cases use a fixed point theorem (relying ultimately on a compactness argument), and are non-constructive, i.e., do not yield an algorithm for constructing an equilibrium. We would clearly like to compute these predicted outcomes. This has led to extensive research since the 60’s in the game theory and mathematical economics literature, with the development of several methods for computation of equilibria, and more generally fixed points. More recently, equilibria problems have been studied intensively in the computer science community, from the point of view of modern computation theory. While we still do not know definitely whether equilibria can be computed in general efficiently or not, these investigations have led to a better understanding of the computational complexity of equilibria, the various issues involved, and the relationship with other open problems in computation. In this talk we will discuss some of these aspects and our current understanding of the relevant problems. We outline below the main points and explain some of the related issues.
Resurrecting Equilibria Through Cycles
DEFF Research Database (Denmark)
Barnett, Richard C.; Bhattacharya, Joydeep; Bunzel, Helle
In an overlapping generations model, momentary equilibria are defined as points that lie on the intergenerational offer curve, i.e., they satisfy agents' optimality conditions and market clearing at any date. However, some dynamic sequences commencing from such points may not be considered valid ...
Equilibria with Coordination Failures
Herings, P.J.J.; van der Laan, G.; Talman, A.J.J.
2004-01-01
This paper extends the recent literature on equilibria with coordination failures to arbitrary convex sets of admissible prices.We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a uni.ed treatment to all cases considered in the literature so far.At a QCE
Energy Technology Data Exchange (ETDEWEB)
Rawls, J.M. (ed.)
1979-10-01
An overall review of the tokamak program is given with particular emphasis upon developments over the past five years in the theoretical and experimental elements of the program. A summary of the key operating parameters for the principal tokamaks throughout the world is given. Also discussed are key issues in plasma confinement, plasma heating, and tokamak design. (MOW)
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
Energy Technology Data Exchange (ETDEWEB)
Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Bhattacharjee, A.; Lazerson, S. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
2015-09-15
We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at the resonant surface.
Energy Technology Data Exchange (ETDEWEB)
Reid, R.L.; Barrett, R.J.; Brown, T.G.; Gorker, G.E.; Hooper, R.J.; Kalsi, S.S.; Metzler, D.H.; Peng, Y.K.M.; Roth, K.E.; Spampinato, P.T.
1985-03-01
The FEDC Tokamak Systems Code calculates tokamak performance, cost, and configuration as a function of plasma engineering parameters. This version of the code models experimental tokamaks. It does not currently consider tokamak configurations that generate electrical power or incorporate breeding blankets. The code has a modular (or subroutine) structure to allow independent modeling for each major tokamak component or system. A primary benefit of modularization is that a component module may be updated without disturbing the remainder of the systems code as long as the imput to or output from the module remains unchanged.
Song, Yuntao; Du, Shijun
2013-01-01
Tokamak Engineering Mechanics offers concise and thorough coverage of engineering mechanics theory and application for tokamaks, and the material is reinforced by numerous examples. Chapter topics include general principles, static mechanics, dynamic mechanics, thermal fluid mechanics and multiphysics structural mechanics of tokamak structure analysis. The theoretical principle of the design and the methods of the analysis for various components and load conditions are presented, while the latest engineering technologies are also introduced. The book will provide readers involved in the study
Economic considerations of commercial tokamak options
Energy Technology Data Exchange (ETDEWEB)
Dabiri, A.E.
1986-05-01
Systems studies have been performed to assess commercial tokamak options. Superconducting, as well as normal, magnet coils in either first or second stability regimes have been considered. A spherical torus (ST), as well as an elongated tokamak (ET), is included in the study. The cost of electricity (COE) is selected as the figure of merit, and beta and first-wall neutron wall loads are selected to represent the physics and technology characteristics of various options. The results indicate that an economical optimum for tokamaks is predicted to require a beta of around 10%, as predicted to be achieved in the second stability regime, and a wall load of about 5 MW/m/sup 2/, which is assumed to be optimum technologically. This tokamak is expected to be competitive with fission plants if efficient, noninductive current drive is developed. However, if this regime cannot be attained, all other tokamaks operating in the first stability regime, including spherical torus and elongated tokamak and assuming a limiting wall load of 5 MW/m/sup 2/, will compete with one another with a COE of about 50 mill/kWh. This 40% higher than the COE for the optimum reactor in the second stability regime with fast-wave current drive. The above conclusions pertain to a 1200-MW(e) net electric power plant. A comparison was also made between ST, ET, and superconducting magnets in the second stability regime with fast-wave current drive at 600 MW(e).
Ball, Justin
2016-01-01
Bulk toroidal rotation has proven capable of stabilising both dangerous MHD modes and turbulence. In this thesis, we explore a method to drive rotation in large tokamaks: up-down asymmetry in the magnetic equilibrium. We seek to maximise this rotation by finding optimal up-down asymmetric flux surface shapes. First, we use the ideal MHD model to show that low order external shaping (e.g. elongation) is best for creating up-down asymmetric flux surfaces throughout the device. Then, we calculate realistic up-down asymmetric equilibria for input into nonlinear gyrokinetic turbulence analysis. Analytic gyrokinetics shows that, in the limit of fast shaping effects, a poloidal tilt of the flux surface shaping has little effect on turbulent transport. Since up-down symmetric surfaces do not transport momentum, this invariance to tilt implies that devices with mirror symmetry about any line in the poloidal plane will drive minimal rotation. Accordingly, further analytic investigation suggests that non-mirror symmetri...
Adsorption analysis equilibria and kinetics
Do, Duong D
1998-01-01
This book covers topics of equilibria and kinetics of adsorption in porous media. Fundamental equilibria and kinetics are dealt with for homogeneous as well as heterogeneous particles. Five chapters of the book deal with equilibria and eight chapters deal with kinetics. Single component as well as multicomponent systems are discussed. In kinetics analysis, we deal with the various mass transport processes and their interactions inside a porous particle. Conventional approaches as well as the new approach using Maxwell-Stefan equations are presented. Various methods to measure diffusivity, such
Quantum equilibria for macroscopic systems
Energy Technology Data Exchange (ETDEWEB)
Grib, A [Department of Theoretical Physics and Astronomy, Russian State Pedagogical University, St. Petersburg (Russian Federation); Khrennikov, A [Centre for Mathematical Modelling in Physics and Cognitive Sciences Vaexjoe University (Sweden); Parfionov, G [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation); Starkov, K [Department of Mathematics, St. Petersburg State University of Economics and Finances (Russian Federation)
2006-06-30
Nash equilibria are found for some quantum games with particles with spin-1/2 for which two spin projections on different directions in space are measured. Examples of macroscopic games with the same equilibria are given. Mixed strategies for participants of these games are calculated using probability amplitudes according to the rules of quantum mechanics in spite of the macroscopic nature of the game and absence of Planck's constant. A possible role of quantum logical lattices for the existence of macroscopic quantum equilibria is discussed. Some examples for spin-1 cases are also considered.
Institutions, Equilibria and Efficiency
DEFF Research Database (Denmark)
Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways. Efficiency and price regulation are studied when markets are incomplete and existence of equilibria...... membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include: determinacy in OLG with cash-in-advance constraints, income distribution and democracy...... in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group...
Protolytic equilibria of bromazepam
Directory of Open Access Journals (Sweden)
DUSAN M. SLADIC
2002-03-01
Full Text Available The protolytic equilibria of bromazepam, an ampholyte sparingly soluble in water, in homogeneous and heterogeneous systems were studied in the pH range 014 at 25 ?C and at ionic strength of 0.1 mol/dm3 (NaCl. On the basis of 13C-NMR spectra, the protonation site was predicted in acidic media the pyridine nitrogen of bormazepam is protonated. The acidity constants of bromazepam were determined spectrophotometrically (pKa1 2.83 and pKa2 11.60 and potentiometrically (pKa1 2.99. In the heterogeneous system the following equilibrium constants were determined: Ks0 = [HA] (pKs0 3.44, Ks1 = [H2A+]/[H3O+] (pKs1 0.61, and Ks2 = [A-][H3O+] (pKs2 15.04.
The CHEASE code for toroidal MHD equilibria
Energy Technology Data Exchange (ETDEWEB)
Luetjens, H. [Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique; Bondeson, A. [Chalmers Univ. of Technology, Goeteborg (Sweden). Inst. for Electromagnetic Field Theory and Plasma Physics; Sauter, O. [ITER-San Diego, La Jolla, CA (United States)
1996-03-01
CHEASE solves the Grad-Shafranov equation for the MHD equilibrium of a Tokamak-like plasma with pressure and current profiles specified by analytic forms or sets of data points. Equilibria marginally stable to ballooning modes or with a prescribed fraction of bootstrap current can be computed. The code provides a mapping to magnetic flux coordinates, suitable for MHD stability calculations or global wave propagation studies. The code computes equilibrium quantities for the stability codes ERATO, MARS, PEST, NOVA-W and XTOR and for the global wave propagation codes LION and PENN. The two-dimensional MHD equilibrium (Grad-Shafranov) equation is solved in variational form. The discretization uses bicubic Hermite finite elements with continuous first order derivates for the poloidal flux function {Psi}. The nonlinearity of the problem is handled by Picard iteration. The mapping to flux coordinates is carried out with a method which conserves the accuracy of the cubic finite elements. The code uses routines from the CRAY libsci.a program library. However, all these routines are included in the CHEASE package itself. If CHEASE computes equilibrium quantities for MARS with fast Fourier transforms, the NAG library is required. CHEASE is written in standard FORTRAN-77, except for the use of the input facility NAMELIST. CHEASE uses variable names with up to 8 characters, and therefore violates the ANSI standard. CHEASE transfers plot quantities through an external disk file to a plot program named PCHEASE using the UNIRAS or the NCAR plot package. (author) figs., tabs., 34 refs.
Jump conditions in transonic equilibria
Energy Technology Data Exchange (ETDEWEB)
Guazzotto, L.; Betti, R. [Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States)
2013-04-15
In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al.[Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that 'standard' (low-{beta}, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high-{beta}, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches are described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large {beta}, while they agree with the results obtained with the old implementation of FLOW in lower-{beta} equilibria.
Effects of the equilibrium model on impurity transport in tokamaks
Skyman, Andreas; Tegnered, Daniel; Nordman, Hans; Anderson, Johan; Strand, Pär
2014-01-01
Gyrokinetic simulations of ion temperature gradient mode and trapped electron mode driven impurity transport in a realistic tokamak geometry are presented and compared with results using simplified geometries. The gyrokinetic results, obtained with the GENE code in both linear and non-linear modes are compared with data and analysis for a dedicated impurity injection discharge at JET. The impact of several factors on heat and particle transport is discussed, lending special focus to tokamak geometry and rotational shear. To this end, results using s-alpha and concentric circular equilibria are compared with results with magnetic geometry from a JET experiment. To further approach experimental conditions, non-linear gyrokinetic simulations are performed with collisions and a carbon background included. The impurity peaking factors, computed by finding local density gradients corresponding to zero particle flux, are discussed. The impurity peaking factors are seen to be reduced by a factor of ~2 in realistic ge...
On Uniqueness of coalitional equilibria
Finus, M.; Mouche, van P.H.M.; Rundshagen, B.
2014-01-01
For the so-called "new approach" of coalitio formation it is important that coalitional equilibria are unique. Uniqueness comes down to existene and to semi-uniqueness, i.e.\\\\that there exists at most one equilibrium. Although conditions for existence are not problematic, conditions for semi-uniquen
Correct Representation of Conformational Equilibria.
Fulop, F.; And Others
1983-01-01
In representing conformational equilibria of compounds having only one chiral center, erroneous formulas showing different antipodes on the two sides of the equilibrium are rare. In contrast, with compounds having two or more chiral centers especially with saturated heterocycles, this erroneous representation occurs frequently in the chemical…
Energy Technology Data Exchange (ETDEWEB)
Wootton, A.J.
1993-04-01
This progress report covers the period from November 1, 1990 to April 30, 1993. During that period, TEXT was operated as a circular tokamak with a material limiter. It was devoted to the study of basic plasma physics, in particular to study of fluctuations, turbulence, and transport. The purpose is to operate and maintain TEXT Upgrade as a complete facility for applied tokamak physics, specifically to conduct a research program under the following main headings: (1) to elucidate the mechanisms of working gas, impurity, and thermal transport in tokamaks, in particular to understand the role of turbulence; (2) to study physics of the edge plasma, in particular the turbulence; (3) to study the physics or resonant magnetic fields (ergodic magnetic divertors, intra island pumping); and (4) to study the physics of electron cyclotron heating (ECRH). Results of studies in each of these areas are reported.
INTEGRATED PLASMA CONTROL FOR ADVANCED TOKAMAKS
Energy Technology Data Exchange (ETDEWEB)
HUMPHREYS,D.A; FERRON,J.R; JOHNSON,R.D; LEUER,J.A; PENAFLOR,B.G; WALKER,M.L; WELANDER,A.S; KHAYRUTDINOV,R.R; DOKOUKA,V; EDGELL,D.H; FRANSSON,C.M
2003-10-01
OAK-B135 Advanced tokamaks (AT) are distinguished from conventional tokamaks by their high degree of shaping, achievement of profiles optimized for high confinement and stability characteristics, and active stabilization of MHD instabilities to attain high values of normalized beta and confinement. These high performance fusion devices thus require accurate regulation of the plasma boundary, internal profiles, pumping, fueling, and heating, as well as simultaneous and well-coordinated MHD control action to stabilize such instabilities as tearing modes and resistive wall modes. Satisfying the simultaneous demands on control accuracy, reliability, and performance for all of these subsystems requires a high degree of integration in both design and operation of the plasma control system in an advanced tokamak. The present work describes the approach, benefits, and progress made in integrated plasma control with application examples drawn from the DIII-D tokamak. The approach includes construction of plasma and system response models, validation of models against operating experiments, design of integrated controllers which operate in concert with one another as well as with supervisory modules, simulation of control action against off-line and actual machine control platforms, and iteration of the design-test loop to optimize performance.
An Algorithm for Computing All Berge Equilibria
Directory of Open Access Journals (Sweden)
H. W. Corley
2015-01-01
Full Text Available An algorithm is presented in this note for determining all Berge equilibria for an n-person game in normal form. This algorithm is based on the notion of disappointment, with the payoff matrix (PM being transformed into a disappointment matrix (DM. The DM has the property that a pure strategy profile of the PM is a BE if and only if (0,…,0 is the corresponding entry of the DM. Furthermore, any (0,…,0 entry of the DM is also a more restrictive Berge-Vaisman equilibrium if and only if each player’s BE payoff is at least as large as the player’s maximin security level.
Adsorption equilibria of dimethylnaphthalene isomers
Energy Technology Data Exchange (ETDEWEB)
Rota, R.; Morbidelli, M. [Politecnico di Milano (Italy). Dipt. di Chimica Fisica Applicata; Rombi, E.; Monaci, R.; Ferino, I.; Solinas, V. [Univ. di Cagliari (Italy). Dipt. di Scienze Chimiche
1996-01-01
Commercial sources of DMNs are the aromatic petroleum fraction of the appropriate boiling range and the coal liquefaction products. Adsorption processes for separating mixtures of dimethylnaphthalene (DMN) isomers are of potential interest for the production of 2,6-DMN. In this work, the adsorption equilibria of liquid mixtures of DMN isomers on zeolites have been investigated experimentally. The separation factors between the various isomers have been found to depend strongly on the composition of the fluid phase. A suitable equilibrium model, based on the adsorbed solution theory, has been developed to describe the multicomponent adsorption equilibria in the entire range of interest. Its performance has been tested using binary and ternary equilibrium data.
Oomens, A. A. M.
1998-01-01
From a discussion of fusion reactor designs based on today's well-established experience gained in the operation of large tokamaks, it is concluded that such reactors are economically not attractive. The physics involved in the various options for concept improvement is described and the main e
Oomens, A. A. M.
1996-01-01
From a discussion of fusion reactor designs based on today's well-established experience gained in the operation of large tokamaks, it is concluded that such reactors are economically not attractive. The physics involved in the various options for concept improvement is described and the main e
Transport in gyrokinetic tokamaks
Energy Technology Data Exchange (ETDEWEB)
Mynick, H.E.; Parker, S.E.
1995-01-01
A comprehensive study of transport in full-volume gyrokinetic (gk) simulations of ion temperature gradient driven turbulence in core tokamak plasmas is presented. Though this ``gyrokinetic tokamak`` is much simpler than experimental tokamaks, such simplicity is an asset, because a dependable nonlinear transport theory for such systems should be more attainable. Toward this end, we pursue two related lines of inquiry. (1) We study the scalings of gk tokamaks with respect to important system parameters. In contrast to real machines, the scalings of larger gk systems (a/{rho}{sub s} {approx_gt} 64) with minor radius, with current, and with a/{rho}{sub s} are roughly consistent with the approximate theoretical expectations for electrostatic turbulent transport which exist as yet. Smaller systems manifest quite different scalings, which aids in interpreting differing mass-scaling results in other work. (2) With the goal of developing a first-principles theory of gk transport, we use the gk data to infer the underlying transport physics. The data indicate that, of the many modes k present in the simulation, only a modest number (N{sub k} {approximately} 10) of k dominate the transport, and for each, only a handful (N{sub p} {approximately} 5) of couplings to other modes p appear to be significant, implying that the essential transport physics may be described by a far simpler system than would have been expected on the basis of earlier nonlinear theory alone. Part of this analysis is the inference of the coupling coefficients M{sub kpq} governing the nonlinear mode interactions, whose measurement from tokamak simulation data is presented here for the first time.
Phase equilibria basic principles, applications, experimental techniques
Reisman, Arnold
2013-01-01
Phase Equilibria: Basic Principles, Applications, Experimental Techniques presents an analytical treatment in the study of the theories and principles of phase equilibria. The book is organized to afford a deep and thorough understanding of such subjects as the method of species model systems; condensed phase-vapor phase equilibria and vapor transport reactions; zone refining techniques; and nonstoichiometry. Physicists, physical chemists, engineers, and materials scientists will find the book a good reference material.
Energy Technology Data Exchange (ETDEWEB)
Chen, J.; Nakajima, N.; Okamoto, M.
1998-12-01
By means of a global mode analysis of ideal MHD modes for Mercier-unstable equilibria in a planar axis L=2/M=10 heliotron/torsatron system with an inherently large Shafranov shift, the conjecture from local mode analysis for Mercier-unstable equilibria given in [N. Nakajima, Phys. Plasmas 3, 4556 (1996)] has been confirmed and the properties of pressure-driven modes, namely, ballooning modes and interchange modes, inherent to such three-dimensional systems have been clarified. The change of the local magnetic shear due to the Shafranov shift, which is related to toroidicity, reduces the field line bending stabilizing effects on ballooning modes. According to the degree of the reduction of the local magnetic shear by the Shafranov shift, the Mercier-unstable equilibria are categorized into toroidicity-dominant (strong reduction) and helicity-dominant (weak reduction) Mercier-unstable equilibria. Since the local magnetic curvature due to helicity has the same period M in the toroidal direction as the toroidal field period of the equilibria, the characteristics of the pressure-driven modes in such Mercier-unstable equilibria dramatically change, both according to the reduction of the local magnetic shear by the Shafranov shift and also according to the relative magnitude of the typical toroidal mode number n of the perturbation compared with the toroidal field period of the equilibria M. In the toroidicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for low toroidal mode numbers n < M, to tokamak-like poloidally localized ballooning modes with a weak toroidal mode coupling for moderate toroidal mode numbers n - M, and finally to both poloidally and toroidally localized ballooning modes purely inherent to three-dimensional systems for fairly high toroidal mode numbers n >> M. In the helicity-dominant Mercier-unstable equilibria, the pressure-driven modes change from interchange modes for n < M or n - M, directly to both
Phase Equilibria of Stored Chemical Energy Reactants.
1984-07-25
The reaction of lithium aluminum alloy with water at high temperature is considered in terms of phase equilibria in the system Li-A1-0-H. A...thermodynamic analysis of the system reveals the potential importance of lithium hydride as a reaction product. Major needs for experimental phase equilibria data
Inefficiency of Nash Equilibria. I
1982-03-12
continuously for U’ near csEA a’ This also shows that for il close to , D6?’)(X) fl (IW’, f ) - * for a a hence we may assume U0 open.all * 6 A A Furthermore...34 Journal of Economic Theory 22 (1980), 363-376. 14] P. Dubey, A. as-Colell and M. Shubik, "Efficiency Properties of Strategic Market Games: An...Axiomatic Approach," Journal of Economic Theory 22 (1980), 339-362. [5] P. Dubey and J. D. Rogsvski, "Inefficiency of Nash Equilibria: II," forthcoming
Motion Control along Relative Equilibria
DEFF Research Database (Denmark)
Nordkvist, Nikolaj
2008-01-01
The subject of this thesis is control of mechanical systems as they evolve along the steady motions called relative equilibria. These trajectories are of interest in theory and applications and have the characterizing property that the system's body-fixed velocity is constant. For example, constant...... on a Lie group is locally controllable along a relative equilibrium. These conditions subsume the well-known local controllability conditions for equilibrium points. Second, for systems that have fewer controls than degrees of freedom, we present a novel algorithm to control simple mechanical control...
Use of reconstructed 3D VMEC equilibria to match effects of toroidally rotating discharges in DIII-D
Wingen, A.; Wilcox, R. S.; Cianciosa, M. R.; Seal, S. K.; Unterberg, E. A.; Hanson, J. M.; Hirshman, S. P.; Lao, L. L.; Logan, N. C.; Paz-Soldan, C.; Shafer, M. W.
2017-01-01
A technique for tokamak equilibrium reconstructions is used for multiple DIII-D discharges, including L-mode and H-mode cases when weakly 3D fields ≤ft(δ B/B˜ {{10}-3}\\right) are applied. The technique couples diagnostics to the non-linear, ideal MHD equilibrium solver VMEC, using the V3FIT code, to find the most likely 3D equilibrium based on a suite of measurements. It is demonstrated that V3FIT can be used to find non-linear 3D equilibria that are consistent with experimental measurements of the plasma response to very weak 3D perturbations, as well as with 2D profile measurements. Observations at DIII-D show that plasma rotation larger than 20 krad s-1 changes the relative phase between the applied 3D fields and the measured plasma response. Discharges with low averaged rotation (10 krad s-1) and peaked rotation profiles (40 krad s-1) are reconstructed. Similarities and differences to forward modeled VMEC equilibria, which do not include rotational effects, are shown. Toroidal phase shifts of up to {{30}\\circ} are found between the measured and forward modeled plasma responses at the highest values of rotation. The plasma response phases of reconstructed equilibra on the other hand match the measured ones. This is the first time V3FIT has been used to reconstruct weakly 3D tokamak equilibria.
Self-consistent equilibria in cylindrical reversed-field pinch
Energy Technology Data Exchange (ETDEWEB)
Lo Surdo, C. [ENEA, Centro Ricerche Frascati, Rome (Italy). Dip. di Energia; Paccagnella, R.; Guo, S. [CNR, Padua (Italy). Istituto Gas Ionizzati
1995-07-01
The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: (a) to the lowest order, and according to a standard ansatz, the turbulent DEF say {epsilon}{sup t}, is expressed as a homogeneous transform of the magnetic field B of degree 1, {epsilon}{sup t}=({alpha}) (B), with {alpha}{identical_to}a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; (b) {epsilon}{sup t} does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both {alpha} and the resistivity tensor {eta} are isotropic and constant, the magnetic field is force-free with abnormality equal to {alpha}{eta}{sub 0}/{eta}, in the limit of vanishing {beta}; that is, the well-known J.B. Taylor`result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall).
Existence of Multiagent Equilibria with Limited Agents
Bowling, M; 10.1613/jair.1332
2011-01-01
Multiagent learning is a necessary yet challenging problem as multiagent systems become more prevalent and environments become more dynamic. Much of the groundbreaking work in this area draws on notable results from game theory, in particular, the concept of Nash equilibria. Learners that directly learn an equilibrium obviously rely on their existence. Learners that instead seek to play optimally with respect to the other players also depend upon equilibria since equilibria are fixed points for learning. From another perspective, agents with limitations are real and common. These may be undesired physical limitations as well as self-imposed rational limitations, such as abstraction and approximation techniques, used to make learning tractable. This article explores the interactions of these two important concepts: equilibria and limitations in learning. We introduce the question of whether equilibria continue to exist when agents have limitations. We look at the general effects limitations can have on agent b...
Time-resolved spectroscopy in the Rijnhuizen Tokamak Project tokamak
Box, F. M. A.; Howard, J.; VandeKolk, E.; Meijer, F. G.
1997-01-01
At the Rijnhuizen Tokamak Project tokamak spectrometers are used to diagnose the velocity distribution and abundances of impurity ions. Quantities can be measured as a function of time, and the temporal resolution depends on the line emissivity and can be as good as 0.2 ms for the strongest lines.
Time-resolved spectroscopy in the Rijnhuizen Tokamak Project tokamak
Box, F. M. A.; Howard, J.; VandeKolk, E.; Meijer, F. G.
1997-01-01
At the Rijnhuizen Tokamak Project tokamak spectrometers are used to diagnose the velocity distribution and abundances of impurity ions. Quantities can be measured as a function of time, and the temporal resolution depends on the line emissivity and can be as good as 0.2 ms for the strongest lines. S
Neoclassical transport in high {beta} tokamaks
Energy Technology Data Exchange (ETDEWEB)
Cowley, S.C.
1992-12-01
Neoclassical, transport in high {beta} large aspect ratio tokamaks is calculated. The variational method introduced by Rosenbluth, et al., is used to calculate the full Onsager matrix in the banana regime. These results are part of a continuing study of the high {beta} large aspect ratio equilibria introduced in Cowley, et al. All the neoclassical coefficients are reduced from their nominal low {beta} values by a factor ({var_epsilon}/q{sup 2}{beta}){sup {1/2}} II. This factor is the ratio of plasma volume in the boundary layer to the volume in the core. The fraction of trapped particles on a given flux surface (f{sub t}) is also reduced by this factor so that
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas
Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; Luce, T. C.; Taylor, N. Z.; Terranova, D.; Turco, F.; Wilcox, R. S.; Wingen, A.; Cappello, S.; Chrystal, C.; Escande, D. F.; Holcomb, C. T.; Marrelli, L.; Paz-Soldan, C.; Piron, L.; Predebon, I.; Zaniol, B.; DIII-D, The; RFX-Mod Teams
2017-07-01
Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8-1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.
Magnetic confinement experiment -- 1: Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Goldston, R.J.
1994-12-31
This report reviews presentations made at the 15th IAEA Conference on Plasma Physics and Controlled Nuclear Fusion on experimental tokamak physics, particularly on advances in core plasma physics, divertor and edge physics, heating and current drive, and tokamak concept optimization.
Nonlinear Simulation Studies of Tokamaks and STs
Energy Technology Data Exchange (ETDEWEB)
W. Park; J. Breslau; J. Chen; G.Y. Fu; S.C. Jardin; S. Klasky; J. Menard; A. Pletzer; B.C. Stratton; D. Stutman; H.R. Strauss; L.E. Sugiyama
2003-07-07
The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.
Ball, Justin; Lee, Jungpyo; Cerfon, Antoine J
2016-01-01
Tokamaks with up-down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad-Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes up-down asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when specific experimental parameters are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of $\\beta'$ (i.e. the radial gradient of $\\beta$) on the magnetic equilibrium was also included....
Axisymmetric instability in a noncircular tokamak: experiment and theory
Energy Technology Data Exchange (ETDEWEB)
Lipschultz, B.; Prager, S.C.; Todd, A.M.M.; Delucia, J.
1979-09-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes -- the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria. Experimentally, the square is vertically stable and both dee's unstable to a vertical nonrigid axisymmetric shift. The central magnetic axis displacement grows exponentially with a growth time approximately 10/sup 3/ poloidal Alfven times plasma time. Proper initial positioning of the plasma on the midplane allows passive feedback to nonlinearly restore vertical motion to a small stable oscillation. Experimental poloidal flux plots are produced directly from internal magnetic probe measurements.
On the topological stability of magnetostatic equilibria
Tsinganos, K. C.; Rosner, R.; Distler, J.
1984-01-01
The topological stability of MHD equilibria is investigated by exploring the formal analogy, in the ideal MHD limit, between the topology of magnetic lines of force in coordinate space and the topology of integral surfaces of one- and two-dimensional Hamiltonian systems in phase space. It is demonstrated that in an astrophysical setting, symmetric magnetostatic equilibria satisfying the ideal MHD equations are exceptional. The principal result of the study is that previous infinitesimal perturbation theory calculations can be generalized to include finite-amplitude and symmetry-breaking effects. The effect of the ergodicity of perturbed symmetric equilibria on heat dispersal in magnetically dominated plasmas is discussed.
Equilibria in Dynamic Selfish Routing
Anshelevich, Elliot; Ukkusuri, Satish
In both transportation and communication networks we are faced with “selfish flows”, where every agent sending flow over the network desires to get it to its destination as soon as possible. Such flows have been well studied in time-invariant networks in the last few years. A key observation that must be taken into account in defining and studying selfish flow, however, is that a flow can take a non-negligible amount of time to travel across the network from the source to destination, and that network states like traffic load and congestion can vary during this period. Such flows are called dynamic flows (a.k.a. flows over time). This variation in network state as the flow progresses through the network results in the fundamentally different and significantly more complex nature of dynamic flow equilibria, as compared to those defined in static network settings.
Inefficient equilibria in transition economy
Directory of Open Access Journals (Sweden)
Sergei Guriev
1999-01-01
Full Text Available The paper studies a general equilibrium in an economy where all market participants face a bid-ask spread. The spread may be caused by indirect business taxes, middlemen rent-seeking, delays in payments or liquidity constraints or price uncertainty. Wherever it comes from the spread causes inefficiency of the market equilibrium. We discuss some institutions that can decrease the inefficiency. One is second currency (barter exchange in the inter-firm transactions. It is shown that the general equilibrium in an economy with second currency is effective though is still different from Arrow–Debreu equilibrium. Another solution can be introduction of mutual trade credit. In the economy with trade credit there are multiple equilibria that are more efficient than original bid-ask spread but still not as efficient as Arrow–Debreu one, too. The implications for firms' integration and applicability to Russian economy are discussed.
Ideal MHD stability of very high beta tokamaks
Energy Technology Data Exchange (ETDEWEB)
Chance, M.S.; Jardin, S.C.; Kessel, C.; Manickam, J.; Monticello, D. (Princeton Univ., NJ (USA). Plasma Physics Lab.); Peng, Y.K.M.; Holmes, J.A.; Strickler, D.J.; Whitson, J.C. (Oak Ridge National Lab., TN (USA)); Glasser, A.H. (Los Alamos National Lab., NM (USA)); Sykes, A. (UKAEA Culham Lab., Abingdon (UK)); Ramos, J.J. (Massachusetts Inst. of Tech., Cambridge, MA (USA). Plasma Fusion Center)
1990-12-01
Achieving very high {beta} and high {beta}{sub p} simultaneously in tokamaks generally implies that the second stability region against ballooning modes must be accessed. We describe several approaches for doing this, which are characterized by the choice of constraints imposed on the equilibrium profiles and the cross-sectional shape of the plasma. The combination of high toroidal beta, restricting the current density to vanish at the edge of the plasma and maintaining a monotonic q profile, proves to be the most stringent. Consideration of equilibria with high {epsilon}{beta}{sub p} but low {beta} facilitates accessibility with peaked pressure profiles and high values of q{sub 0}. Allowing the pressure gradient and, hence, the current density to be finite at the plasma edge allows all surfaces to lie within the second stability regime. For free boundary plasmas with divertors, the divertor stabilized edge region remains in the first stability regime while the plasma core reaches into the second regime. Careful tailoring of the profiles must be used to traverse the unstable barrier commonly seen near the edge of these plasmas. The CAMINO code allows us to compute s-{alpha} curves for general tokamak geometry. These diagrams enable us to construct equilibria whose profiles are only constrained, at worst, to be marginally stable everywhere, but do not necessarily satisfy the constraints on the current or {beta}. There are theoretical indications that under certain conditions the external kinks possess a second region of stability at high q{sub 0} that is analogous to that of the ballooning modes. It is found that extremely accurate numerical means must be developed and applied to confidently establish the validity of these results. 14 refs., 5 figs., 1 tab.
Nedospasov, A. V.
1992-12-01
Edge turbulence is of decisive importance for the distribution of particle and energy fluxes to the walls of tokamaks. Despite the availability of extensive experimental data on the turbulence properties, its nature still remains a subject for discussion. This paper contains a review of the most recent theoretical and experimental studies in the field, including mainly the studies to which Wootton (A.J. Wooton, J. Nucl. Mater. 176 & 177 (1990) 77) referred to most in his review at PSI-9 and those published later. The available theoretical models of edge turbulence with volume dissipation due to collisions fail to fully interpret the entire combination of experimental facts. In the scrape-off layer of a tokamak the dissipation prevails due to the flow of current through potential shifts near the surface of limiters of divertor plates. The different origins of turbulence at the edge and in the core plasma due to such dissipation are discussed in this paper. Recent data on the electron temperature fluctuations enabled one to evaluate the electric probe measurements of turbulent flows of particles and heat critically. The latest data on the suppression of turbulence in the case of L-H transitions are given. In doing so, the possibility of exciting current instabilities in biasing experiments (rather than only to the suppression of existing turbulence) is given some attention. Possible objectives of further studies are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Rudakov, D; Yu, J; Boedo, J; Hollmann, E; Krasheninnikov, S; Moyer, R; Muller, S; Yu, A; Rosenberg, M; Smirnov, R; West, W; Boivin, R; Bray, B; Brooks, N; Hyatt, A; Wong, C; Fenstermacher, M; Groth, M; Lasnier, C; McLean, A; Stangeby, P; Ratynskaia, S; Roquemore, A; Skinner, C; Solomon, W M
2008-04-23
Dust production and accumulation impose safety and operational concerns for ITER. Diagnostics to monitor dust levels in the plasma as well as in-vessel dust inventory are currently being tested in a few tokamaks. Dust accumulation in ITER is likely to occur in hidden areas, e.g. between tiles and under divertor baffles. A novel electrostatic dust detector for monitoring dust in these regions has been developed and tested at PPPL. In DIII-D tokamak dust diagnostics include Mie scattering from Nd:YAG lasers, visible imaging, and spectroscopy. Laser scattering resolves size of particles between 0.16-1.6 {micro}m in diameter; the total dust content in the edge plasmas and trends in the dust production rates within this size range have been established. Individual dust particles are observed by visible imaging using fast-framing cameras, detecting dust particles of a few microns in diameter and larger. Dust velocities and trajectories can be determined in 2D with a single camera or 3D using multiple cameras, but determination of particle size is problematic. In order to calibrate diagnostics and benchmark dust dynamics modeling, pre-characterized carbon dust has been injected into the lower divertor of DIII-D. Injected dust is seen by cameras, and spectroscopic diagnostics observe an increase of carbon atomic, C2 dimer, and thermal continuum emissions from the injected dust. The latter observation can be used in the design of novel dust survey diagnostics.
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.
Simulation of bootstrap current in 2D and 3D ideal magnetic fields in tokamaks
Raghunathan, M.; Graves, J. P.; Cooper, W. A.; Pedro, M.; Sauter, O.
2016-09-01
We aim to simulate the bootstrap current for a MAST-like spherical tokamak using two approaches for magnetic equilibria including externally caused 3D effects such as resonant magnetic perturbations (RMPs), the effect of toroidal ripple, and intrinsic 3D effects such as non-resonant internal kink modes. The first approach relies on known neoclassical coefficients in ideal MHD equilibria, using the Sauter (Sauter et al 1999 Phys. Plasmas 6 2834) expression valid for all collisionalities in axisymmetry, and the second approach being the quasi-analytic Shaing-Callen (Shaing and Callen 1983 Phys. Fluids 26 3315) model in the collisionless regime for 3D. Using the ideal free-boundary magnetohydrodynamic code VMEC, we compute the flux-surface averaged bootstrap current density, with the Sauter and Shaing-Callen expressions for 2D and 3D ideal MHD equilibria including an edge pressure barrier with the application of resonant magnetic perturbations, and equilibria possessing a saturated non-resonant 1/1 internal kink mode with a weak internal pressure barrier. We compare the applicability of the self-consistent iterative model on the 3D applications and discuss the limitations and advantages of each bootstrap current model for each type of equilibrium.
Braided magnetic fields: equilibria, relaxation and heating
Pontin, D I; Russell, A J B; Hornig, G
2015-01-01
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling. The key results obtained from recent modelling efforts are summarised, in the context of testable predictions for the laboratory. We discuss the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity - as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We discuss the properties of this relaxation, and in particular the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor's hypo...
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
Arnab Basu; Samik Basu; Mahan MJ
2014-11-01
Given a multifunction from to the -fold symmetric product Sym$_{k}(X)$, we use the Dold–Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré duality in addition to the Dold–Thom theorem.
Ignition curves for deuterium/helium-3 fuel in spherical tokamak reactor
Indian Academy of Sciences (India)
Motevalli S M; Fadaei F
2016-04-01
In this paper, ignition curve for deuterium/helium-3 fusion reaction is studied. Four fusion reactions are considered. Zero-dimensional model for the power balance equation has been used. The closed ignition curves for $\\rho$ = constant (ratio of particle to energy confinement time) have been derived. The results of our calculations show that ignited equilibria for deuterium/helium-3 fuel in a spherical tokamak is only possible for $\\rho$ = 5.5 and 6. Then, by using the energy confinement scaling and parameters of the spherical tokamak reactor, the plasma stability limits have been obtained in $n_e, T$ plane and, to determine the thermal instability of plasma, the time dependent transport equations have been solved.
Network Connection Games with Disconnected Equilibria
Brandes, Ulrik; Nick, Bobo
2008-01-01
In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost, and the utility is a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the utility for a pair of disconnected players to a finite value. Our analysis concentrates on existence, structure, and cost of disconnected regular and strong Nash equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected (strong) Nash equilibria can evolve. Components of these equilibria must be (strong) Nash equilibria of a smaller NCG. However, in contrast to the NCG, for almost all parameter values no tree is a stable componen...
Federal Laboratory Consortium — Alcator C-Mod at the Massachusetts Institute of Technology is operated as a DOE national user facility. Alcator C-Mod is a unique, compact tokamak facility that uses...
High resolution equilibrium calculations of pedestal and SOL plasma in tokamaks
Medvedev, S. Yu; Martynov, A. A.; Drozdov, V. V.; Ivanov, A. A.; Poshekhonov, Yu Yu
2017-02-01
For integrated modeling of equilibrium, stability and dynamics of the divertor tokamak plasma with scrape-off layer (SOL) high resolution equilibrium calculations are needed. A new version of the CAXE equilibrium code computes the tokamak equilibrium on a numerical grid adaptive to magnetic surfaces both in the plasma region with closed flux surfaces and in the SOL region with open magnetic lines. The plasma profiles can be prescribed independently in each region with nested flux surfaces, and realistic SOL profiles with very short pressure drop off length can be accurately treated. The influence of the finite current density in SOL on the connection length is studied. From the point of view of the MHD equilibrium and stability modeling, self-consistent calculations of diverted tokamak configurations with finite current density at the separatrix require taking into account plasma outside the separatrix. Calculated high resolution equilibria provide an input to new versions of the ideal MHD stability codes treating tokamak plasma with SOL. The study of the influence of the pressure gradient profile in the pedestal plasma inside and outside the separatrix on the pedestal height limit set by external kink-ballooning mode stability is presented. Another possible application of the high resolution pedestal and SOL equilibrium code is a coupling to the SOLPS code with a purpose to increase equilibrium accuracy and support self-consistent plasma flow/equilibrium modeling.
The ETE spherical Tokamak project
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Andrade, Maria Celia Ramos de; Barbosa, Luis Filipe Wiltgen [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] [and others]. E-mail: ludwig@plasma.inpe.br
1999-07-01
This paper describes the general characteristics of spherical tokamaks, with a brief overview of work in the area of spherical torus already performed or in progress at several institutions. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and status of construction in September, 1998 at the Associated plasma Laboratory (LAP) of the National Institute for Space Research (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, G.O.; Del Bosco, E.; Ferreira, J.G.; Berni, L.A.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Ueda, M.; Barroso, J.J.; Castro, P.J. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma; Barbosa, L.F.W. [Universidade do Vale do Paraiba (UNIVAP), Sao Jose dos Campos, SP (Brazil). Faculdade de Engenharia, Arquitetura e Urbanismo; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Div. de Mecanica Espacial e Controle; The high-power microwave sources group
2003-12-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the steps in the development of the ETE (Experimento Tokamak Esferico) project, its research program, technical characteristics and operating conditions as of December, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Spherical tokamak development in Brazil
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)
2003-07-01
The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
The ARIES tokamak reactor study
Energy Technology Data Exchange (ETDEWEB)
1989-10-01
The ARIES study is a community effort to develop several visions of tokamaks as fusion power reactors. The aims are to determine the potential economics, safety, and environmental features of a range of possible tokamak reactors, and to identify physics and technology areas with the highest leverage for achieving the best tokamak reactor. Three ARIES visions are planned, each having a different degree of extrapolation from the present data base in physics and technology. The ARIES-I design assumes a minimum extrapolation from current tokamak physics (e.g., 1st stability) and incorporates technological advances that can be available in the next 20 to 30 years. ARIES-II is a DT-burning tokamak which would operate at a higher beta in the 2nd MHD stability regime. It employs both potential advances in the physics and expected advances in technology and engineering. ARIES-II will examine the potential of the tokamak and the D{sup 3}He fuel cycle. This report is a collection of 14 papers on the results of the ARIES study which were presented at the IEEE 13th Symposium on Fusion Engineering (October 2-6, 1989, Knoxville, TN). This collection describes the ARIES research effort, with emphasis on the ARIES-I design, summarizing the major results, the key technical issues, and the central conclusions.
Information Anatomy of Stochastic Equilibria
Directory of Open Access Journals (Sweden)
Sarah Marzen
2014-08-01
Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.
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.
Fusion potential for spherical and compact tokamaks
Energy Technology Data Exchange (ETDEWEB)
Sandzelius, Mikael
2003-02-01
The tokamak is the most successful fusion experiment today. Despite this, the conventional tokamak has a long way to go before being realized into an economically viable power plant. In this master thesis work, two alternative tokamak configurations to the conventional tokamak has been studied, both of which could be realized to a lower cost. The fusion potential of the spherical and the compact tokamak have been examined with a comparison of the conventional tokamak in mind. The difficulties arising in the two configurations have been treated from a physical point of view concerning the fusion plasma and from a technological standpoint evolving around design, materials and engineering. Both advantages and drawbacks of either configuration have been treated relative to the conventional tokamak. The spherical tokamak shows promising plasma characteristics, notably a high {beta}-value but have troubles with high heat loads and marginal tritium breeding. The compact tokamak operates at a high plasma density and a high magnetic field enabling it to be built considerably smaller than any other tokamak. The most notable down-side being high heat loads and neutron transport problems. With the help of theoretical reactor studies, extrapolating from where we stand today, it is conceivable that the spherical tokamak is closer of being realized of the two. But, as this study shows, the compact tokamak power plant concept offers the most appealing prospect.
Instability of Magnetic Equilibria in Barotropic Stars
Mitchell, J P; Reisenegger, A; Spruit, H; Valdivia, J A; Langer, N
2014-01-01
In stably stratified stars, numerical magneto-hydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal fields that stabilize each other. In this work, we test the hypothesis that stable stratification is a requirement for the existence of such stable equilibria. For this purpose, we follow numerically the evolution of magnetic fields in barotropic (and thus neutrally stable) stars, starting from two different types of initial conditions, namely random disordered magnetic fields, as well as linked poloidal-toroidal configurations resembling the previously found equilibria. With many trials, we always find a decay of the magnetic field over a few Alfv\\'en times, never a stable equilibrium. This strongly suggests that there are no stable equilibria in barotropic stars, thus clearly invalidating the assumption of barotropic equations of state often imposed on the search of magneti...
Multiple Equilibria in Noisy Rational Expectations Economies
DEFF Research Database (Denmark)
Palvolgyi, Domotor; Venter, Gyuri
This paper studies equilibrium uniqueness in standard noisy rational expectations economies with asymmetric or differential information a la Grossman and Stiglitz (1980) and Hellwig (1980). We show that the standard linear equilibrium of Grossman and Stiglitz (1980) is the unique equilibrium......-sloping” demand curves, (iv) higher prices leading to future returns that are higher in expectation (price drift) and (v) more positively skewed. Discontinuous equilibria can be arbitrarily close to being fully-revealing. Finally, discontinuous equilibria with the same construction also exist in Hellwig (1980)....
Binary Solid-Liquid Phase Equilibria
Ellison, Herbert R.
1978-01-01
Indicates some of the information that may be obtained from a binary solid-liquid phase equilibria experiment and a method to write a computer program that will plot an ideal phase diagram to which the experimental results may be compared. (Author/CP)
Instability of magnetic equilibria in barotropic stars
Mitchell, J. P.; Braithwaite, J.; Reisenegger, A.; Spruit, H.; Valdivia, J. A.; Langer, N.
2015-02-01
In stably stratified stars, numerical magnetohydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal fields that stabilize each other. In this work, we test the hypothesis that stable stratification is a requirement for the existence of such stable equilibria. For this purpose, we follow numerically the evolution of magnetic fields in barotropic (and thus neutrally stable) stars, starting from two different types of initial conditions, namely random disordered magnetic fields, as well as linked poloidal-toroidal configurations resembling the previously found equilibria. With many trials, we always find a decay of the magnetic field over a few Alfvén times, never a stable equilibrium. This strongly suggests that there are no stable equilibria in barotropic stars, thus clearly invalidating the assumption of barotropic equations of state often imposed on the search of magnetic equilibria. It also supports the hypothesis that, as dissipative processes erode the stable stratification, they might destabilize previously stable magnetic field configurations, leading to their decay.
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
Intermediates and Generic Convergence to Equilibria
DEFF Research Database (Denmark)
Freitas, Michael Marcondes de; Wiuf, Carsten; Feliu, Elisenda
2016-01-01
Known graphical conditions for the generic or global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions...
Phase equilibria of carbohydrates in polar solvents
DEFF Research Database (Denmark)
Jonsdottir, Svava Osk; Rasmussen, Peter
1999-01-01
A method for calculating interaction energies and interaction parameters with molecular mechanics methods is extended to predict solid-liquid equilibria (SLE) for saccharides in aqueous solution, giving results in excellent agreement with experimental values. Previously, the method has been shown...
MHD activity in the ISX-B tokamak: experimental results and theoretical interpretation
Energy Technology Data Exchange (ETDEWEB)
Carreras, B.A.; Dunlap, J.L.; Bell, J.D.; Charlton, L.A.; Cooper, W.A.; Dory, R.A.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.
1982-01-01
The observed spectrum of MHD fluctuations in the ISX-B tokamak is clearly dominated by the n=1 mode when the q=1 surface is in the plasma. This fact agrees well with theoretical predictions based on 3-D resistive MHD calculations. They show that the (m=1; n=1) mode is then the dominant instability. It drives other n=1 modes through toroidal coupling and n>1 modes through nonlinear couplings. These theoretically predicted mode structures have been compared in detail with the experimentally measured wave forms (using arrays of soft x-ray detectors). The agreement is excellent. More detailed comparisons between theory and experiment have required careful reconstructions of the ISX-B equilibria. The equilibria so constructed have permitted a precise evaluation of the ideal MHD stability properties of ISX-B. The present results indicate that the high ..beta.. ISX-B equilibria are marginally stable to finite eta ideal MHD modes. The resistive MHD calculations also show that at finite ..beta.. there are unstable resistive pressure driven modes.
An enhanced tokamak startup model
Goswami, Rajiv; Artaud, Jean-François
2017-01-01
The startup of tokamaks has been examined in the past in varying degree of detail. This phase typically involves the burnthrough of impurities and the subsequent rampup of plasma current. A zero-dimensional (0D) model is most widely used where the time evolution of volume averaged quantities determines the detailed balance between the input and loss of particle and power. But, being a 0D setup, these studies do not take into consideration the co-evolution of plasma size and shape, and instead assume an unchanging minor and major radius. However, it is known that the plasma position and its minor radius can change appreciably as the plasma evolves in time to fill in the entire available volume. In this paper, an enhanced model for the tokamak startup is introduced, which for the first time takes into account the evolution of plasma geometry during this brief but highly dynamic period by including realistic one-dimensional (1D) effects within the broad 0D framework. In addition the effect of runaway electrons (REs) has also been incorporated. The paper demonstrates that the inclusion of plasma cross section evolution in conjunction with REs plays an important role in the formation and development of tokamak startup. The model is benchmarked against experimental results from ADITYA tokamak.
Fitzpatrick, Richard
2015-01-01
The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes is calculated using an improved, neoclassical, four-field, drift-MHD model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to ...
High-pressure fluid phase equilibria phenomenology and computation
Deiters, Ulrich K
2012-01-01
The book begins with an overview of the phase diagrams of fluid mixtures (fluid = liquid, gas, or supercritical state), which can show an astonishing variety when elevated pressures are taken into account; phenomena like retrograde condensation (single and double) and azeotropy (normal and double) are discussed. It then gives an introduction into the relevant thermodynamic equations for fluid mixtures, including some that are rarely found in modern textbooks, and shows how they can they be used to compute phase diagrams and related properties. This chapter gives a consistent and axiomatic approach to fluid thermodynamics; it avoids using activity coefficients. Further chapters are dedicated to solid-fluid phase equilibria and global phase diagrams (systematic search for phase diagram classes). The appendix contains numerical algorithms needed for the computations. The book thus enables the reader to create or improve computer programs for the calculation of fluid phase diagrams. introduces phase diagram class...
Ball, Justin; Parra, Felix I.; Lee, Jungpyo; Cerfon, Antoine J.
2016-12-01
Tokamaks with up-down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad-Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes up-down asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of {β\\prime} (i.e. the radial gradient of β) on the magnetic equilibrium was also included, which was found to significantly reduce momentum transport. Including these two competing effects broadens the rotation profile, but leaves the on-axis value of the rotation roughly unchanged. Consequently, the shape of the β profile has a significant effect on the rotation profile of an up-down asymmetric tokamak.
Computing Equilibria of Two Player Games
DEFF Research Database (Denmark)
Sørensen, Troels Bjerre
with computing equilibria of game theoretic models where only two agents are involved. The work described ranges from the theoretical development of algorithms for computing refined equilibria, which satisfy additional constraints beyond being an equilibrium, to the practical solving of real life games. Part I...... Theory. The application areas of Game Theory fathoms most academic disciplines, all the way from Political Science and Economics through Biology to Computer Science. It also has played an important role in areas Philosophy and Ethics. It has even been used to politically justify military conflicts...... to the prediction. Predicting behavior of rational agents has many application areas. The phrasing of the last paragraph was vague for sole purpose of not implying any restriction on what agents are and in what context they act. The whole area of reasoning about rational interaction of agents is known as Game...
The pressure tensor in tangential equilibria
Directory of Open Access Journals (Sweden)
F. Mottez
2004-09-01
Full Text Available The tangential equilibria are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. Such equilibria can be spatially periodic (like waves, or they can separate two regions with asymptotic uniform conditions (like MHD tangential discontinuities. It is possible to compute the velocity moments of the particle distribution function. Even in very simple cases, the pressure tensor is not isotropic and not gyrotropic. The differences between a scalar pressure and the pressure tensor derived in the frame of the Maxwell-Vlasov theory are significant when the gradient scales are of the order of the Larmor radius; they concern mainly the ion pressure tensor.
Multiple equilibria in a simple elastocapillary system
Taroni, Michele
2012-09-28
We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
Phase equilibria in stratified thin liquid films stabilized by colloidal particles
Blawzdziewicz, J.; Wajnryb, E.
2005-01-01
Phase equilibria between regions of different thickness in thin liquid films stabilized by colloidal particles are investigated using a quasi-two-dimensional thermodynamic formalism. Appropriate equilibrium conditions for the film tension, normal pressure, and chemical potential of the particles in the film are formulated, and it is shown that the relaxation of these parameters occurs consecutively on three distinct time scales. Film stratification is described quantitatively for a hard-spher...
Equilibria of Generalized Cut and Choose Protocols
DEFF Research Database (Denmark)
Branzei, Simina; Caragiannis, Ioannis; Kurokawa, David
Classic cake cutting protocols — which fairly allocate a divisible good among agents with heterogeneous preferences — are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To answer this question we adopt a novel algo rithmic approach, proposing a concrete computa...... the stronger fairness notion of envy-freeness. Finally, we show that under an obliviousness restriction, which still allows the computation of approximately envy-free allocations, GCC protocols are guaranteed to have exact subgame perfect Nash equilibria...
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.
Relative Equilibria in the Spherical, Finite Density 3-Body Problem
Scheeres, D J
2016-01-01
The relative equilibria for the spherical, finite density 3 body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical 5 relative equilibria for the point-mass 3-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the 3-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
A compact Tokamak transmutation reactor
Institute of Scientific and Technical Information of China (English)
QiuLi－Jian; XiaoBing－Jia
1997-01-01
The low aspect ration tokamak is proposed for the driver of a transmutation reactor.The main parameters of the reactor core,neutronic analysis of the blanket are given>the neutron wall loading can be lowered from the magnitude order of 1 MW/m2 to 0.5MW/m2 which is much easier to reach in the near future,and the transmutation efficiency (fission/absorption ratio)is raised further.The blanket power density is about 200MW/m3 which is not difficult to deal with.The key components such as diverter and center conductor post are also designed and compared with conventional TOkamak,Finally,by comparison with the other drivers such as FBR,PWR and accelerator,it can be anticipated that the low aspect ratio transmutation reactor would be one way of fusion energy applications in the near future.
Bootstrap Current in Spherical Tokamaks
Institute of Scientific and Technical Information of China (English)
王中天; 王龙
2003-01-01
Variational principle for the neoclassical theory has been developed by including amomentum restoring term in the electron-electron collisional operator, which gives an additionalfree parameter maximizing the heat production rate. All transport coefficients are obtained in-cluding the bootstrap current. The essential feature of the study is that the aspect ratio affects thefunction of the electron-electron collision operator through a geometrical factor. When the aspectratio approaches to unity, the fraction of circulating particles goes to zero and the contribution toparticle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is inrough agreement with Hazeltine. When the aspect ratio approaches to infinity, the results are inagreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theoryis particularly important for the calculation of bootstrap current in spherical tokamaks and thepresent tokamaks, in which the square root of the inverse aspect ratio, in general, is not small.
Cryogenic needs for future tokamaks
Katheder, H.
The ITER tokamak is a machine using superconducting magnets. The windings of these magnets will be subjected to high heat loads resulting from a combination of nuclear energy absorption and AC-losses. It is estimated that about 100 kW at 4.5 K are needed. The total cooling mass flow rate will be around 10 - 15 kg/s. In addition to the large cryogenic power required for the superconducting magnets cryogenic power is also needed for refrigerated radiation shield, various cryopumps, fuel processing and test beds. A general description of the overall layout and the envisaged refrigerator cycle, necessary cold pumps and ancillary equipment is given. The basic cryogenic layout for the ITER tokakmak design, as developed during the conceptual design phase and a short overview about existing tokamak designs using superconducting magnets is given.
Options for an ignited tokamak
Energy Technology Data Exchange (ETDEWEB)
Sheffield, J.
1984-02-01
It is expected that the next phase of the fusion program will involve a tokamak with the goals of providing an ignited plasma for pulses of hundreds of seconds. A simple model is described in this memorandum which establishes the physics conditions for such a self-sustaining plasma, for given ion and electron thermal diffusivities, in terms of R/a, b/a, I, B/q, epsilon ..beta../sub p/, anti T/sub i/, and anti T/sub e//anti T/sub i/. The model is used to produce plots showing the wide range of tokamaks that may ignite or have a given ignition margin. The constraints that limit this range are discussed.
Magnetic confinement experiment. I: Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Goldston, R.J.
1995-08-01
Reports were presented at this conference of important advances in all the key areas of experimental tokamak physics: Core Plasma Physics, Divertor and Edge Physics, Heating and Current Drive, and Tokamak Concept Optimization. In the area of Core Plasma Physics, the biggest news was certainly the production of 9.2 MW of fusion power in the Tokamak Fusion Test Reactor, and the observation of unexpectedly favorable performance in DT plasmas. There were also very important advances in the performance of ELM-free H- (and VH-) mode plasmas and in quasi-steady-state ELM`y operation in JT-60U, JET, and DIII-D. In all three devices ELM-free H-modes achieved nT{tau}`s {approximately} 2.5x greater than ELM`ing H-modes, but had not been sustained in quasi-steady-state. Important progress has been made on the understanding of the physical mechanism of the H-mode in DIII-D, and on the operating range in density for the H-mode in Compass and other devices.
Energy Technology Data Exchange (ETDEWEB)
Dabiri, A.E.
1986-07-01
The concept of multiplexing for a fusion power core as an option for producing power is explored. Superconducting, as well as normal magnet, coils in either first or second stability regimes are considered. The results show that multiplex plants with superconducting magnets operating in the second stability regime could be competitive with the single-unit plants in some unit sizes. The key issues that impact the expected benefits of multiplexing must be investigated further. These are factory fabrication, economy of scale, the extent of equipment sharing, inherent safety, maintainability, and utility load management.
The role of limiter in Egyptor Tokamak
Ei-Sisi, A B
2002-01-01
In Egyptor Tokamak, the limiter is used for separation of the plasma from the vessel. In this work an overview of limiter types, and construction of limiter in Egyptor Tokamak is discussed. Also simulation results of the radial electron density distribution in case of limiter are presented. The results of the simulation are in agreement with the experimental and analytical results.
Shape reconstruction of merging spherical tokamak plasma in UTST device
Ushiki, Tomohiko; Itagaki, Masafumi; Inomoto, Michiaki
2016-10-01
Spherical tokamak (ST) merging method is one of the ST start-up methods which heats the plasma through magnetic reconnection. In the present study reconstruction of eddy current profile and plasma shape was performed during spherical tokamak merging only using external sensor signals by the Cauchy condition surface (CCS) method. CCS method have been implemented for JT-60 (QST), QUEST (Kyushu University), KSTAR (NFRI), RELAX (KIT), and LHD (Nifs). In this method, CCS was assumed inside each plasmas, where both flux function and its normal derivative are unknown. Effect of plasma current was replaced by the boundary condition of CCS, assuming vacuum field everywhere. Also, the nodal points for the boundary integrals of eddy current density were set using quadratic elements in order to express the complicated vacuum vessel shape. Reconstructed profiles of the eddy current and the magnetic flux were well coincided with the reference in each phase of merging process. Magnetic sensor installation plan for UTST was determined from these calculation results. This work was supported by the JSPS A3 Foresight Program ``Innovative Tokamak Plasma Startup and Current Drive in Spherical Torus''.
Dudebout, Nicolas
2014-12-15
This paper proves that exogenous empirical-evidence equilibria (xEEEs) in perfect-monitoring repeated games induce correlated equilibria of the associated one-shot game. An empirical-evidence equilibrium (EEE) is a solution concept for stochastic games. At equilibrium, agents\\' strategies are optimal with respect to models of their opponents. These models satisfy a consistency condition with respect to the actual behavior of the opponents. As such, EEEs replace the full-rationality requirement of Nash equilibria by a consistency-based bounded-rationality one. In this paper, the framework of empirical evidence is summarized, with an emphasis on perfect-monitoring repeated games. A less constraining notion of consistency is introduced. The fact that an xEEE in a perfect-monitoring repeated game induces a correlated equilibrium on the underlying one-shot game is proven. This result and the new notion of consistency are illustrated on the hawk-dove game. Finally, a method to build specific correlated equilibria from xEEEs is derived.
Linear optimal control of tokamak fusion devices
Energy Technology Data Exchange (ETDEWEB)
Kessel, C.E.; Firestone, M.A.; Conn, R.W.
1989-05-01
The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
Correlated Equilibria of Classical Strategic Games with Quantum Signals
La Mura, P
2003-01-01
Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.
A unifying approach to existence of Nash equilibria
Balder, E.J.
2001-01-01
An approach initiated in [4] is shown to unify results about the existence of (i) Nash equilibria in games with at most countably many players, (ii) Cournot-Nash equilibrium distributions for large, anonymous games, and (iii) Nash equilibria (both mixed and pure) for continuum games. A new, central
Cycles and Multiple Equilibria in the Market for Durable Lemons
M.C.W. Janssen (Maarten); V.A. Karamychev (Vladimir)
2000-01-01
textabstractWe investigate the nature of market failure in a dynamic version of Akerlof (1970) where identical cohorts of a durable good enter the market over time. In the dynamic model, equilibria with qualitatively different properties emerge. Typically, in equilibria of the dynamic model, sellers
High temperature phase equilibria and phase diagrams
Kuo, Chu-Kun; Yan, Dong-Sheng
2013-01-01
High temperature phase equilibria studies play an increasingly important role in materials science and engineering. It is especially significant in the research into the properties of the material and the ways in which they can be improved. This is achieved by observing equilibrium and by examining the phase relationships at high temperature. The study of high temperature phase diagrams of nonmetallic systems began in the early 1900s when silica and mineral systems containing silica were focussed upon. Since then technical ceramics emerged and more emphasis has been placed on high temperature
Entropy and Equilibria in Competitive Systems
Directory of Open Access Journals (Sweden)
A. Y. Klimenko
2013-12-01
Full Text Available This paper investigates the applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for the characterisation of systems with transitive competition when mutations deviate from Gibbs mutations. Different types of equilibria in competitive systems are considered and analysed. As competition rules become more and more intransitive, thermodynamic analogies are eroded, and the behaviour of the system can become complex. This work analyses the phenomenon of punctuated evolution in the context of the competitive risk/benefit dilemma.
Ball, Justin
2016-01-01
Introducing up-down asymmetry into the tokamak magnetic equilibria appears to be a feasible method to drive fast intrinsic toroidal rotation in future large devices. In this paper we investigate how the intrinsic momentum transport generated by up-down asymmetric shaping scales with the mode number of the shaping effects. Making use the gyrokinetic tilting symmetry (Ball et al (2016) Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopes created by the beating of different high-order shaping effects. This reveals that the presence of an envelope can change the scaling of the momentum flux from exponentially small in the limit of large shaping mode number to just polynomially small. This enhancement of the momentum transport requires the envelope to be both up-down asymmetric and have a spatial scale on the order of the minor radius.
Ball, Justin; Parra, Felix I.
2017-02-01
Introducing up-down asymmetry into the tokamak magnetic equilibria appears to be a feasible method to drive fast intrinsic toroidal rotation in future large devices. In this paper we investigate how the intrinsic momentum transport generated by up-down asymmetric shaping scales with the mode number of the shaping effects. Making use the gyrokinetic tilting symmetry (Ball et al 2016 Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopes created by the beating of different high-order shaping effects. This reveals that the presence of an envelope can change the scaling of the momentum flux from exponentially small in the limit of large shaping mode number to just polynomially small. This enhancement of the momentum transport requires the envelope to be both up-down asymmetric and have a spatial scale on the order of the minor radius.
Energy Technology Data Exchange (ETDEWEB)
Stewart, W.A.
1990-05-01
This thesis describes the development of a design tool for the poloidal field magnet system of a tokamak. Specifically, an existing program for determining the poloidal field coil currents has been modified to: support the general case of asymmetric equilibria and coil sets, determine the coil currents subject to constraints on the maximum values of those currents, and determine the coil currents subject to limits on the forces those coils may carry. The equations representing the current limits and coil force limits are derived and an algorithm based on Newton's method is developed to determine a set of coil currents which satisfies those limits. The resulting program allows the designer to quickly determine whether or not a given coil set is capable of supporting a given equilibrium. 25 refs.
Anomalous particle pinch in Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Miskane, F.; Garbet, X. [Association Euratom-CEA/Cadarache, Dept. de Recherches sur la Fusion Controlee, DRFC, 13 - Saint-Paul-lez-Durance (France); Dezairi, A.; Saifaoui, D. [Faculte des Sciences Ain Chok, Casablanca (Morocco)
2000-06-01
The diffusion coefficient in phase space usually varies with the particle energy. A consequence is the dependence of the fluid particle flux on the temperature gradient. If the diffusion coefficient in phase space decreases with the energy in the bulk of the thermal distribution function, the particle thermodiffusion coefficient which links the particle flux to the temperature gradient is negative. This is a possible explanation for the inward particle pinch that is observed in tokamaks. A quasilinear theory shows that such a thermodiffusion is generic for a tokamak electrostatic turbulence at low frequency. This effect adds to the particle flux associated with the radial gradient of magnetic field. This behavior is illustrated with a perturbed electric potential, for which the trajectories of charged particle guiding centers are calculated. The diffusion coefficient of particles is computed and compared to the quasilinear theory, which predicts a divergence at low velocity. It is shown that at low velocity, the actual diffusion coefficient increases, but remains lower than the quasilinear value. Nevertheless, this differential diffusion between cold and fast particles leads to an inward flux of particles. (author)
3D low-beta magnetized plasma equilibria from external shaping
Hassam, A.; Tenbarge, J.; Landreman, M.; Dorland, W.; Sengupta, W.
2016-10-01
A 3D nonlinear dissipative MHD code is in development to allow relaxation to low-beta MHD equilibrium inside a shaped 3D conducting boundary with prescribed conserved axial magnetic flux and no external current. Formation of magnetic islands is expected. Heat sources would be eventually introduced to allow the possibility of non-stationary convection depending on the stability properties of the accessible MHD equilibria. The initial development will be done using the code UMHD. The initial emphasis will be on recovering expected physics in simpler 3D geometries. A primary objective is to minimize numerical boundary noise. In particular, codes which specify the normal magnetic field B.n on bounding surfaces are prone to noise generation. We plan to shape the boundary to conform to the desired field shape so that B.n is zero on the boundary. Non-orthogonal coordinates will be chosen to effect this. We will test noise reduction within the tangential field approach. Results obtained to date support this conjecture. Initial results from simple 2D code equilibria have been verified against analytic solution of equilibria in weak shaping. Initial results also recover the expected features of the Hahm- Kulsrud island formation solution. Work supported by US DOE.
Prediction of vapour-liquid equilibria for the kinetic study of processes based on synthesis gas
Energy Technology Data Exchange (ETDEWEB)
Di Serio, M.; Tesser, R.; Cozzolino, M.; Santacesaria, E. [Naples Univ., Napoli (Italy). Dept. of Chemistry
2006-07-01
Syngas is normally used in the production of a broad range of chemicals and fuels. In many of these processes multiphase reactors, gas-liquid or gas-liquid-solid are used. Kinetic studies in multiphase systems are often complicated by the non-ideal behaviour of reagents and/or products that are consistently partitioned between the liquid and the vapour phase. Moreover, as often kinetic data are collected in batch conditions for the liquid phase, activity coefficients of the partitioned components can consistently change during the time as a consequence of changing the composition of the reaction mixture. Therefore, it is necessary, in these cases, to known the vapor-liquid equilibria (VLE) in order to collect and to interpret correctly the kinetic data. The description of phase equilibria, at high pressures, is usually performed by means of an EOS (Equation of State) allowing the calculation of fugacity coefficients, for each component, in both phases and determining the partition coefficients but the EOS approach involves the experimental determination of the interaction parameters for all the possible binary system of the mixture. For multicomponent mixtures a complete experimental determination of vapourliquid equilibria is very hard, also considering the high pressure and temperatures used. Some predictive group contribution methods have been recently developed. In this paper, we will describe in detail the application of these methods to the methanol homologation, as an example, with the scope of determining more reliable kinetic parameters for this reaction. (orig.)
Tokamak Plasmas : Mirnov coil data analysis for tokamak ADITYA
Indian Academy of Sciences (India)
D Raju; R Jha; P K Kaw; S K Mattoo; Y C Saxena; Aditya Team
2000-11-01
The spatial and temporal structures of magnetic signal in the tokamak ADITYA is analysed using recently developed singular value decomposition (SVD) technique. The analysis technique is ﬁrst tested with simulated data and then applied to the ADITYA Mirnov coil data to determine the structure of current peturbation as the discharge progresses. It is observed that during the current rise phase, current perturbation undergoes transition from = 5 poloidal structure to = 4 and then to = 3. At the time of current termination, = 2 perturbation is observed. It is observed that the mode frequency remains nearly constant (≈10 kHz) when poloidal mode structure changes from = 4 to = 2. This may be either an indication of mode coupling or a consequences of changes in the plasma electron temperature and density scale length.
Helical core reconstruction of a DIII-D hybrid scenario tokamak discharge
Cianciosa, M.; Wingen, A.; Hirshman, S. P.; Seal, S. K.; Unterberg, E. A.; Wilcox, R. S.; Piovesan, P.; Lao, L.; Turco, F.
2017-07-01
This paper presents the first fully 3-dimensional (3D) equilibrium reconstruction of a helical core in a tokamak device. Using a new parallel implementation of the Variational Moments Equilibrium Code (PARVMEC) coupled to V3FIT, 3D reconstructions can be performed at resolutions necessary to produce helical states in nominally axisymmetric tokamak equilibria. In a flux pumping experiment performed on DIII-D, an external n = 1 field was applied while a 3/2 neoclassical tearing mode was suppressed using ECCD. The externally applied field was rotated past a set of fixed diagnostics at a 20 Hz frequency. The modulation, observed to be strongest in the core SXR and MSE channels, indicates a localized rotating 3D structure locked in phase with the applied field. Signals from multiple time slices are converted to a virtual rotation of modeled diagnostics adding 3D signal information. Starting from an axisymmetric equilibrium reconstruction solution, the reconstructed broader current profile flattens the q-profile, resulting in an m = 1, n = 1 perturbation of the magnetic axis that is ∼ 50× larger than the applied n = 1 deformation of the edge. Error propagation confirms that the displacement of the axis is much larger than the uncertainty in the axis position validating the helical equilibrium. ).
Close pairs of relative equilibria for identical point vortices
DEFF Research Database (Denmark)
Dirksen, Tobias; Aref, Hassan
2011-01-01
Numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane reveals configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. New numerical solutions of this kind are found...... also has this property, and new relative equilibria close to the nested, symmetrically arranged, regular heptagons have been found. The centered regular nonagon is also marginally stable. Again, a new family of close relative equilibria has been found. The closest relative equilibrium pairs occur...
CONSTRUCTING EXAMPLES WITH 5 EQUILIBRIA FOR SYMMETRIC 3 × 2 CES / LES PURE EXCHANGE ECONOMIES
Institute of Scientific and Technical Information of China (English)
Huang Hui; Shi Xiaojun; Zhang Shunming
2012-01-01
This paper explores the existence of multiple equilibria for symmetric 3 individual,2 good CES / LES pure exchange economies.Analytically,we show that there are no more than 5 equilibria in such economies.The number of equilibria varies from 5 to 3 then to 1.We generalize our analytical results of existence of 1,3,5 equilibria for a wide range of parametrizations.We also provide concrete examples of 1,3,5 equilibria with parameter zones specified.
Simulation of dust statistical characteristics in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Smirnov, R.D.; Pigarov, A.Yu.; Krasheninnikov, S.I.; Rosenberg, M.; Mendis, D.A. [University of California, San Diego, La Jolla, California, 92093 (United States)
2008-03-15
In this work we analyze the size (radius) distribution function of dust particles in tokamak plasmas during a steady state discharge. A relation between the radius distribution function of dust in the plasma and the radius distribution of dust injected from tokamak walls is obtained using a Green's function formalism. Numerical simulations of the dust radius distribution function in a tokamak plasma with the Dust Transport (DUSTT) code are used to obtain the analytical form of the Green's function semi-empirically. It is demonstrated that the Green's function obtained can be used to predict qualitatively the dust size distributions in the tokamak plasmas. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
New Thermodynamic Paradigm of Chemical Equilibria
Zilbergleyt, B
2011-01-01
The paper presents new thermodynamic paradigm of chemical equilibrium, setting forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTd). Along with previous results by the author during the last decade, this work contains also some new developments of DTd. Based on the Onsager's constitutive equations, reformulated by the author thermodynamic affinity and reaction extent, and Le Chatelier's principle, DTd brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces (TdF), acting against a chemical system. Basic expression of DTd is the chemical system logistic map of thermodynamic states that ties together energetic characteristics of chemical reaction, occurring in the system, the system shift from "true" thermodynamic equilibrium (TdE), and causing that shift external thermodynamic forces. Solutions to the basic map are pitchfork bifurcation diagrams in coordinates "shift from TdE - growth factor (or TdF)"; points, corresponding to the ...
Magnetic equilibria for X-Diverted plasmas
Pekker, M.; Valanju, P.; Kotschenreuther, M.; Wiley, J.; Mahajan, S.
2006-10-01
The X-divertor has been proposed to solve heat exhaust problems for reactors beyond ITER. By generating an extra X-point downstream from the main X-point, the X-divertor greatly expands magnetic flux at the divertor plates. As a result, the heat is distributed over a larger area and the line length is greatly increased. We have developed coil sets for X-diverted magnetic equilibria for many devices (NSTX, PEGASUS, EAST, HL-2A, CREST, and a CTF). These demonstrate that the XD configuration can be created for highly shaped plasmas using moderate coil currents. For reactors, all coils can be placed behind 1 m of shielding. We have also shown that XD configurations are robust to modest plasma perturbations and VDEs; this is in contrast to the sensitivity of highly tilted divertor plates.
One-dimensional Vlasov-Maxwell equilibria
Greene, John M.
1993-06-01
The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm's law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
The ETE spherical Tokamak project. IAEA report
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Gerson Otto; Del Bosco, E.; Berni, L.A.; Ferreira, J.G.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Barroso, J.J.; Castro, P.J.; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: ludwig@plasma.inpe.br
2002-07-01
This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and operating conditions as of October, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)
Plasma diagnostics using synchrotron radiation in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Fidone, I.; Giruzzi, G.; Granata, G.
1995-09-01
This report deal with the use of synchrotron radiation in tokamaks. The main advantage of this new method is that it enables to overcome several deficiencies, caused by cut-off, refraction, and harmonic overlap. It also makes it possible to enhance the informative contents of the familiar low harmonic scheme. The basic theory of the method is presented and illustrated by numerical applications, for plasma parameters of relevance in present and next step tokamaks. (TEC). 10 refs., 13 figs.
Energy Technology Data Exchange (ETDEWEB)
Evans, K.E. Jr.; Baker, C.C.; Brooks, J.N.; Ehst, D.A.; Finn, P.A.; Jung, J.; Mattas, R.F.; Misra, B.; Smith, D.L.; Stevens, H.C.
1980-11-01
A tokamak D-D reactor design, utilizing the advantages of a deuterium-fueled reactor but with parameters not unnecessarily extended from existing D-T designs, is presented. Studies leading to the choice of a design and initial studies of the design are described. The studies are in the areas of plasma engineering, first-wall/blanket/shield design, magnet design, and tritium/fuel/vacuum requirements. Conclusions concerning D-D tokamak reactors are stated.
Stability of the toroidicity-induced Alfven eigenmode in axisymmetric toroidal equilibria
Energy Technology Data Exchange (ETDEWEB)
Fu, G.Y.; Cheng, C.Z.; Wong, K.L.
1993-09-01
The stability of toroidicity-induced Alfven eigenmodes (TAE) is investigated in general tokamak equilibria with finite aspect ratio and finite plasma beta. The finite orbit width of the hot particles and the collisional damping of the trapped electrons are included. For the trapped hot particles, the finite orbit width is found to be stabilizing. For the circulating hot particles, the finite orbit width effect is stabilizing for larger values of v{sub h}/v{sub A} (> 1) and destabilizing for smaller values of v{sub h}/v{sub A} (< 1), where v{sub h} is the hot particle speed and v{sub A} is the Alfven speed. The collisional damping of the trapped electrons is found to have a much weaker dependence on the collision frequency than the previous analytic results. The contribution of the curvature term to the trapped electron collisional damping is negligible compared to that of the parallel electric field term for typical parameters. The calculated critical hot particle beta values for the TAE instability are consistent with the experimental measurements.
Seal, S. K.; Cianciosa, M. R.; Hirshman, S. P.; Wingen, A.; Wilcox, R. S.; Unterberg, E. A.
2016-10-01
High-fidelity reconstruction of plasma equilibria in confinement devices like stellarators and tokamaks with external three dimensional (3D) fields is computationally very expensive and routinely requires days, even weeks, to complete using serial approaches. Here, we present the performance results of coupling the 3D plasma reconstruction code, V3FIT, with PARVMEC, the recently developed parallel version of VMEC. We present the parallel design of this coupled software along with a scalability analysis to identify its performance bottlenecks. Dependence of its scalability limits on model parameters is derived. These analyses are supported by scaling studies on over 6,000 processor cores of a Cray XC30 supercomputer. PARVMEC, which dominates the total runtime of the reconstruction procedure, is shown to deliver speedup improvements of over one to two orders of magnitude, depending on whether the equilibrium computations are carried out in a free or fixed boundary mode. The overall speedup of the coupled reconstruction code is shown to deliver over 40X improvement enabling fusion scientists to carry out high-fidelity 3D plasma reconstruction analyses in only a few hours instead of in days/weeks for the first time. This work was supported by the U.S. D.O.E. contract DE-AC05-00OR22725.
Fusion burn equilibria sensitive to the ratio between energy and helium transport
Jakobs, Merlijn; Lopes Cardozo, Niek; Jaspers, Roger
2014-12-01
An analysis of the burn equilibria of fusion reactors of the tokamak family is presented. The global (zero-dimensional) analysis is self-consistent in that it takes into account the dependence of the energy confinement on the variables of the burning plasma, such as temperature and density. Universal burn contours are presented for a selection of commonly used scaling laws for energy confinement. It is shown that the output power of a fusion reactor is to good approximation inversely proportional to the particle confinement time, due to the choking effect of the accumulation of helium, the ash of the fusion reaction. It is further shown that, whereas a fusion reactor requires a minimum energy confinement time to ignite, the output power reaches a maximum for an energy confinement that lies about 30% above this minimum. Further improvement of confinement will lower the output, although in some cases the β limit will be the limiting factor. Given that for maximum performance density the confinement and fuel mix are best chosen to be optimal, the particle confinement is proposed as an attractive parameter for burn control.
Liquid Metal Walls, Lithium, And Low Recycling Boundary Conditions In Tokamaks
Energy Technology Data Exchange (ETDEWEB)
R. Majeski
2010-01-15
At present, the only solid material believed to be a viable option for plasma-facing components (PFCs) in a fusion reactor is tungsten. Operated at the lower temperatures typical of present-day fusion experiments, tungsten is known to suffer from surface degradation during long-term exposure to helium-containing plasmas, leading to reduced thermal conduction to the bulk, and enhanced erosion. Existing alloys are also quite brittle at temperatures under 700oC. However, at a sufficiently high operating temperature (700 - 1000 oC), tungsten is selfannealing and it is expected that surface damage will be reduced to the point where tungsten PFCs will have an acceptable lifetime in a reactor environment. The existence of only one potentially viable option for solid PFCs, though, constitutes one of the most significant restrictions on design space for DEMO and follow-on fusion reactors. In contrast, there are several candidates for liquid metal-based PFCs, including gallium, tin, lithium, and tin-lithium eutectics. We will discuss options for liquid metal walls in tokamaks, looking at both high and low recycling materials. We will then focus in particular on one of the candidate liquids, lithium. Lithium is known to have a high chemical affinity for hydrogen, and has been shown in test stands1 and fusion experiments2,3 to produce a low recycling surface, especially when liquid. Because it is also low-Z and is usable in a tokamak over a reasonable temperature range (200 - 400 oC), it has been now been used as a PFC in several confinement experiments (TFTR, T11- M, CDX-U, NSTX, FTU, and TJ-II), with favorable results. The consequences of substituting low recycling walls for the traditional high recycling variety on tokamak equilibria are very extensive. We will discuss some of the expected modifications, briefly reviewing experimental results, and comparing the results to expectations.
The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG
Ali, Halima; Punjabi, Alkesh
2013-05-01
Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33-45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565-1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83
The freedom to choose neutron star magnetic field equilibria
Glampedakis, Kostas
2016-01-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetised neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
Learning Equilibria with Partial Information in Decentralized Wireless Networks
Rose, Luca; Lasaulce, Samson; Debbah, Mérouane
2011-01-01
In this article, a survey of several important equilibrium concepts for decentralized networks is presented. The term decentralized is used here to refer to scenarios where decisions (e.g., choosing a power allocation policy) are taken autonomously by devices interacting with each other (e.g., through mutual interference). The iterative long-term interaction is characterized by stable points of the wireless network called equilibria. The interest in these equilibria stems from the relevance of network stability and the fact that they can be achieved by letting radio devices to repeatedly interact over time. To achieve these equilibria, several learning techniques, namely, the best response dynamics, fictitious play, smoothed fictitious play, reinforcement learning algorithms, and regret matching, are discussed in terms of information requirements and convergence properties. Most of the notions introduced here, for both equilibria and learning schemes, are illustrated by a simple case study, namely, an interfe...
Stable equilibria of elliptic roly-poly toys
Hong, Seok-In
2016-11-01
As an instructive (gravitational potential) energy approach, we show that the elliptic roly-poly has a richer and more useful profile (including the tilted configuration) of stable equilibria than conventional spherical or cylindrical roly-polys.
Existence of General Competitive Equilibria: A Variational Approach
Directory of Open Access Journals (Sweden)
G. Anello
2016-01-01
Full Text Available We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities.
Characteristics of Plasma Turbulence in the Mega Amp Spherical Tokamak
Ghim, Young-chul
2013-01-01
Turbulence is a major factor limiting the achievement of better tokamak performance as it enhances the transport of particles, momentum and heat which hinders the foremost objective of tokamaks. Hence, understanding and possibly being able to control turbulence in tokamaks is of paramount importance, not to mention our intellectual curiosity of it.
Electron thermal transport in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Konings, J.A.
1994-11-30
The process of fusion of small nuclei thereby releasing energy, as it occurs continuously in the sun, is essential for the existence of mankind. The same process applied in a controlled way on earth would provide a clean and an abundant energy source, and be the long term solution of the energy problem. Nuclear fusion requires an extremely hot (10{sup 8} K) ionized gas, a plasma, that can only be maintained if it is kept insulated from any material wall. In the so called `tokamak` this is achieved by using magnetic fields. The termal insulation, which is essential if one wants to keep the plasma at the high `fusion` temperature, can be predicted using basic plasma therory. A comparison with experiments in tokamaks, however, showed that the electron enery losses are ten to hundred times larger than this theory predicts. This `anomalous transport` of thermal energy implies that, to reach the condition for nuclear fusion, a fusion reactor must have very large dimensions. This may put the economic feasibility of fusion power in jeopardy. Therefore, in a worldwide collaboration, physicists study tokamak plasmas in an attempt to understand and control the energy losses. From a scientific point of view, the mechanisms driving anomalous transport are one of the challenges in fudamental plasma physics. In Nieuwegein, a tokamak experiment (the Rijnhuizen Tokamak Project, RTP) is dedicated to the study of anomalous transport, in an international collaboration with other laboratories. (orig./WL).
Unifying dynamical and structural stability of equilibria
Arnoldi, Jean-François; Haegeman, Bart
2016-09-01
We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
PARALLEL ASSAY OF OXYGEN EQUILIBRIA OF HEMOGLOBIN
Lilly, Laura E.; Blinebry, Sara K.; Viscardi, Chelsea M.; Perez, Luis; Bonaventura, Joe; McMahon, Tim J.
2013-01-01
Methods to systematically analyze in parallel the function of multiple protein or cell samples in vivo or ex vivo (i.e. functional proteomics) in a controlled gaseous environment have thus far been limited. Here we describe an apparatus and procedure that enables, for the first time, parallel assay of oxygen equilibria in multiple samples. Using this apparatus, numerous simultaneous oxygen equilibrium curves (OECs) can be obtained under truly identical conditions from blood cell samples or purified hemoglobins (Hbs). We suggest that the ability to obtain these parallel datasets under identical conditions can be of immense value, both to biomedical researchers and clinicians who wish to monitor blood health, and to physiologists studying non-human organisms and the effects of climate change on these organisms. Parallel monitoring techniques are essential in order to better understand the functions of critical cellular proteins. The procedure can be applied to human studies, wherein an OEC can be analyzed in light of an individual’s entire genome. Here, we analyzed intraerythrocytic Hb, a protein that operates at the organism’s environmental interface and then comes into close contact with virtually all of the organism’s cells. The apparatus is theoretically scalable, and establishes a functional proteomic screen that can be correlated with genomic information on the same individuals. This new method is expected to accelerate our general understanding of protein function, an increasingly challenging objective as advances in proteomic and genomic throughput outpace the ability to study proteins’ functional properties. PMID:23827235
Bilinear Relative Equilibria of Identical Point Vortices
DEFF Research Database (Denmark)
Aref, H.; Beelen, Peter; Brøns, Morten
2012-01-01
-axis and n on the x-axis. We define generating polynomials q(z) and p(z), respectively, for each set of vortices. A second-order, linear ODE for p(z) given q(z) is derived. Several results relating the general solution of the ODE to relative equilibrium configurations are established. Our strongest result......A new class of bilinear relative equilibria of identical point vortices in which the vortices are constrained to be on two perpendicular lines, conveniently taken to be the x- and y-axes of a Cartesian coordinate system, is introduced and studied. In the general problem we have m vortices on the y......, obtained using Sturm’s comparison theorem, is that if p(z) satisfies the ODE for a given q(z) with its imaginary zeros symmetric relative to the x-axis, then it must have at least n−m+2 simple, real zeros. For m=2 this provides a complete characterization of all zeros, and we study this case in some detail...
Microtearing modes in tokamak discharges
Energy Technology Data Exchange (ETDEWEB)
Rafiq, T.; Kritz, A. H. [Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 (United States); Weiland, J. [Department of Applied Physics, Chalmers University, S41296 Gothenburg (Sweden); Luo, L. [IBM Research, Oak Ridge, Tennessee 37831 (United States); Pankin, A. Y. [Tech-X Corporation, Boulder, Colorado 80308 (United States)
2016-06-15
Microtearing modes (MTMs) have been identified as a source of significant electron thermal transport in tokamak discharges. In order to describe the evolution of these discharges, it is necessary to improve the prediction of electron thermal transport. This can be accomplished by utilizing a model for transport driven by MTMs in whole device predictive modeling codes. The objective of this paper is to develop the dispersion relation that governs the MTM driven transport. A unified fluid/kinetic approach is used in the development of a nonlinear dispersion relation for MTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, arbitrary electron-ion collisionality, electron temperature and density gradients, magnetic curvature, and the effects associated with the parallel propagation vector. An iterative nonlinear approach is used to calculate the distribution function employed in obtaining the nonlinear parallel current and the nonlinear dispersion relation. The third order nonlinear effects in magnetic fluctuations are included, and the influence of third order effects on a multi-wave system is considered. An envelope equation for the nonlinear microtearing modes in the collision dominant limit is introduced in order to obtain the saturation level. In the limit that the mode amplitude does not vary along the field line, slab geometry, and strong collisionality, the fluid dispersion relation for nonlinear microtearing modes is found to agree with the kinetic dispersion relation.
Microtearing modes in tokamak discharges
Rafiq, T.; Weiland, J.; Kritz, A. H.; Luo, L.; Pankin, A. Y.
2016-06-01
Microtearing modes (MTMs) have been identified as a source of significant electron thermal transport in tokamak discharges. In order to describe the evolution of these discharges, it is necessary to improve the prediction of electron thermal transport. This can be accomplished by utilizing a model for transport driven by MTMs in whole device predictive modeling codes. The objective of this paper is to develop the dispersion relation that governs the MTM driven transport. A unified fluid/kinetic approach is used in the development of a nonlinear dispersion relation for MTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, arbitrary electron-ion collisionality, electron temperature and density gradients, magnetic curvature, and the effects associated with the parallel propagation vector. An iterative nonlinear approach is used to calculate the distribution function employed in obtaining the nonlinear parallel current and the nonlinear dispersion relation. The third order nonlinear effects in magnetic fluctuations are included, and the influence of third order effects on a multi-wave system is considered. An envelope equation for the nonlinear microtearing modes in the collision dominant limit is introduced in order to obtain the saturation level. In the limit that the mode amplitude does not vary along the field line, slab geometry, and strong collisionality, the fluid dispersion relation for nonlinear microtearing modes is found to agree with the kinetic dispersion relation.
Mie potentials for phase equilibria calculations: application to alkanes and perfluoroalkanes.
Potoff, Jeffrey J; Bernard-Brunel, Damien A
2009-11-05
Transferable united-atom force fields, based on n - 6 Lennard-Jones potentials, are presented for normal alkanes and perfluorocarbons. It is shown that by varying the repulsive exponent the range of the potential can be altered, leading to improved predictions of vapor pressures while also reproducing saturated liquid densities to high accuracy. Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine the vapor liquid coexistence curves, vapor pressures, heats of vaporization, and critical points for normal alkanes methane through tetradecane, and perfluorocarbons perfluoromethane through perfluorooctane. For all molecules studied, saturated liquid densities are reproduced to within 1% of experiment. Vapor pressures for normal alkanes and perfluorocarbons were predicted to within 3% and 6% of experiment, respectively. Calculations performed for binary mixture vapor-liquid equilibria for propane + pentane show excellent agreement with experiment, while slight deviations are observed for the ethane + perfluoroethane mixture.
Global gyrokinetic simulation of tokamak transport
Energy Technology Data Exchange (ETDEWEB)
Furnish, G.; Horton, W.; Kishimoto, Y.; LeBrun, M.J.; Tajima, T. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies]|[Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan)
1998-10-01
A kinetic simulation code based on the gyrokinetic ion dynamics in global general metric (including a tokamak with circular or noncircular cross-section) has been developed. This gyrokinetic simulation is capable of examining the global and semi-global driftwave structures and their associated transport in a tokamak plasma. The authors investigate the property of the ion temperature gradient (ITG) or {eta}{sub i}({eta}{sub i} {equivalent_to} {partial_derivative}{ell}nT{sub i}/{partial_derivative}{ell}n n{sub i}) driven drift waves in a tokamak plasma. The emergent semi-global drift wave modes give rise to thermal transport characterized by the Bohm scaling.
Physics of Tokamak Plasma Start-up
Mueller, Dennis
2012-10-01
This tutorial describes and reviews the state-of-art in tokamak plasma start-up and its importance to next step devices such as ITER, a Fusion Nuclear Science Facility and a Tokamak/ST demo. Tokamak plasma start-up includes breakdown of the initial gas, ramp-up of the plasma current to its final value and the control of plasma parameters during those phases. Tokamaks rely on an inductive component, typically a central solenoid, which has enabled attainment of high performance levels that has enabled the construction of the ITER device. Optimizing the inductive start-up phase continues to be an area of active research, especially in regards to achieving ITER scenarios. A new generation of superconducting tokamaks, EAST and KSTAR, experiments on DIII-D and operation with JET's ITER-like wall are contributing towards this effort. Inductive start-up relies on transformer action to generate a toroidal loop voltage and successful start-up is determined by gas breakdown, avalanche physics and plasma-wall interaction. The goal of achieving steady-sate tokamak operation has motivated interest in other methods for start-up that do not rely on the central solenoid. These include Coaxial Helicity Injection, outer poloidal field coil start-up, and point source helicity injection, which have achieved 200, 150 and 100 kA respectively of toroidal current on closed flux surfaces. Other methods including merging reconnection startup and Electron Bernstein Wave (EBW) plasma start-up are being studied on various devices. EBW start-up generates a directed electron channel due to wave particle interaction physics while the other methods mentioned rely on magnetic helicity injection and magnetic reconnection which are being modeled and understood using NIMROD code simulations.
The Spherical Tokamak MEDUSA for Mexico
Ribeiro, C.; Salvador, M.; Gonzalez, J.; Munoz, O.; Tapia, A.; Arredondo, V.; Chavez, R.; Nieto, A.; Gonzalez, J.; Garza, A.; Estrada, I.; Jasso, E.; Acosta, C.; Briones, C.; Cavazos, G.; Martinez, J.; Morones, J.; Almaguer, J.; Fonck, R.
2011-10-01
The former spherical tokamak MEDUSA (Madison EDUcation Small Aspect.ratio tokamak, R Mexican Fusion Network. Strong liaison within national and international plasma physics communities is expected. New activities on plasma & engineering modeling are expected to be developed in parallel by using the existing facilities such as a multi-platform computer (Silicon Graphics Altix XE250, 128G RAM, 3.7TB HD, 2.7GHz, quad-core processor), ancillary graph system (NVIDIA Quadro FE 2000/1GB GDDR-5 PCI X16 128, 3.2GHz), and COMSOL Multiphysics-Solid Works programs.
Tokamak Engineering Technology Facility scoping study
Energy Technology Data Exchange (ETDEWEB)
Stacey, W.M. Jr.; Abdou, M.A.; Bolta, C.C.
1976-03-01
A scoping study for a Tokamak Engineering Technology Facility (TETF) is presented. The TETF is a tokamak with R = 3 m and I/sub p/ = 1.4 MA based on the counterstreaming-ion torus mode of operation. The primary purpose of TETF is to demonstrate fusion technologies for the Experimental Power Reactor (EPR), but it will also serve as an engineering and radiation test facility. TETF has several technological systems (e.g., superconducting toroidal-field coil, tritium fuel cycle, impurity control, first wall) that are prototypical of EPR.
Overview of spherical tokamak research in Japan
Takase, Y.; Ejiri, A.; Fujita, T.; Fukumoto, N.; Fukuyama, A.; Hanada, K.; Idei, H.; Nagata, M.; Ono, Y.; Tanaka, H.; Uchida, M.; Horiuchi, R.; Kamada, Y.; Kasahara, H.; Masuzaki, S.; Nagayama, Y.; Oishi, T.; Saito, K.; Takeiri, Y.; Tsuji-Iio, S.
2017-10-01
Nationally coordinated research on spherical tokamak is being conducted in Japan. Recent achievements include: (i) plasma current start-up and ramp-up without the use of the central solenoid by RF waves (in electron cyclotron and lower hybrid frequency ranges), (ii) plasma current start-up by AC Ohmic operation and by coaxial helicity injection, (iii) development of an advanced fuelling technique by compact toroid injection, (iv) ultra-long-pulse operation and particle control using a high temperature metal wall, (v) access to the ultra-high-β regime by high-power reconnection heating, and (vi) improvement of spherical tokamak plasma stability by externally applied helical field.
Tokamak Spectroscopy for X-Ray Astronomy
Fournier, Kevin B.; Finkenthal, M.; Pacella, D.; May, M. J.; Soukhanovskii, V.; Mattioli, M.; Leigheb, M.; Rice, J. E.
2000-01-01
This paper presents the measured x-ray and Extreme Ultraviolet (XUV) spectra of three astrophysically abundant elements (Fe, Ca and Ne) from three different tokamak plasmas. In every case, each spectrum touches on an issue of atomic physics that is important for simulation codes to be used in the analysis of high spectral resolution data from current and future x-ray telescopes. The utility of the tokamak as a laboratory test bed for astrophysical data is demonstrated. Simple models generated with the HULLAC suite of codes demonstrate how the atomic physics issues studied can affect the interpretation of astrophysical data.
Electron cyclotron emission diagnostics on KSTAR tokamak.
Jeong, S H; Lee, K D; Kogi, Y; Kawahata, K; Nagayama, Y; Mase, A; Kwon, M
2010-10-01
A new electron cyclotron emission (ECE) diagnostics system was installed for the Second Korea Superconducting Tokamak Advanced Research (KSTAR) campaign. The new ECE system consists of an ECE collecting optics system, an overmode circular corrugated waveguide system, and 48 channel heterodyne radiometer with the frequency range of 110-162 GHz. During the 2 T operation of the KSTAR tokamak, the electron temperatures as well as its radial profiles at the high field side were measured and sawtooth phenomena were also observed. We also discuss the effect of a window on in situ calibration.
Electron cyclotron emission diagnostics on KSTAR tokamak
Energy Technology Data Exchange (ETDEWEB)
Jeong, S. H. [Korea Atomic Energy Research Institute, 1045 Daedeokdaero, Daejeon 305-353 (Korea, Republic of); Lee, K. D.; Kwon, M. [National Fusion Research Institute, 113 Gwahangno, Daejeon 305-333 (Korea, Republic of); Kogi, Y. [Fukuoka Institute of Technology, Higashiku, Fukuoka 811-0295 (Japan); Kawahata, K.; Nagayama, Y. [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Mase, A. [KASTEC, Kyushu University, Kasuga, Fukuoka 816-8580 (Japan)
2010-10-15
A new electron cyclotron emission (ECE) diagnostics system was installed for the Second Korea Superconducting Tokamak Advanced Research (KSTAR) campaign. The new ECE system consists of an ECE collecting optics system, an overmode circular corrugated waveguide system, and 48 channel heterodyne radiometer with the frequency range of 110-162 GHz. During the 2 T operation of the KSTAR tokamak, the electron temperatures as well as its radial profiles at the high field side were measured and sawtooth phenomena were also observed. We also discuss the effect of a window on in situ calibration.
Tokamak power systems studies, FY 1985
Energy Technology Data Exchange (ETDEWEB)
Baker, C.C.; Brooks, J.N.; Ehst, D.A.; Smith, D.L.; Sze, D.K.
1985-12-01
The Tokamak Power System Studies (TPSS) at ANL in FY-1985 were devoted to exploring innovative design concepts which have the potential for making substantial improvements in the tokamak as a commercial power reactor. Major objectives of this work included improved reactor economics, improved environmental and safety features, and the exploration of a wide range of reactor plant outputs with emphasis on reduced plant sizes compared to STARFIRE. The activities concentrated on three areas: plasma engineering, impurity control, and blanket/first wall/shield technology. 205 refs., 125 figs., 107 tabs.
Mathematical Model for Multicomponent Adsorption Equilibria Using Only Pure Component Data
DEFF Research Database (Denmark)
Marcussen, Lis
2000-01-01
A mathematical model for nonideal adsorption equilibria in multicomponent mixtures is developed. It is applied with good results for pure substances and for prediction of strongly nonideal multicomponent equilibria using only pure component data. The model accounts for adsorbent...
Energy Technology Data Exchange (ETDEWEB)
Sheffield, J.
1985-01-01
During recent years improvements have been made to tokamak startup procedures, which are important to the optimization of ignited tokamaks. The use of rf-assisted startup and noninductive current drive has led to substantial reduction and even complete elimination of the volt-seconds used during startup, relaxing constraints on poloidal coil, vacuum vessel, and structure design. This paper reviews these and other improvements and discusses the various bulk heating techniques that may be used to ignite a D-T plasma.
The mechanics of rocking stones: equilibria on separated scales
Domokos, Gábor; Szabó, Tímea
2011-01-01
Rocking stones, balanced in counter-intuitive positions have always intrigued geologists. In our paper we explain this phenomenon based on high-precision scans of pebbles which exhibit similar behavior. We construct their convex hull and the heteroclinic graph carrying their equilibrium points. By systematic simplification of the arising Morse-Smale complex in a one-parameter process we show that equilibria occur typically in highly localized groups (flocks), the number of the latter can be reliably observed and determined by hand experiments. Both local and global (micro and macro) equilibria can be either stable or unstable. Most commonly, rocks and pebbles are balanced on stable local equilibria belonging to stable flocks. However, it is possible to balance a convex body on a stable local equilibrium belonging to an unstable flock and this is the intriguing mechanical scenario corresponding to rocking stones. Since outside observers can only reliably perceive flocks, the last described situation will appea...
Nematic Equilibria on a Two-Dimensional Annulus
Lewis, A. H.
2017-01-16
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Recent progress in the relative equilibria of point vortices — In memoriam Hassan Aref
DEFF Research Database (Denmark)
Beelen, Peter; Brøns, Morten; Krishnamurthy, Vikas S.;
2013-01-01
Hassan Aref, who sadly passed away in 2011, was one of the world's leading researchers in the dynamics and equilibria of point vortices. We review two problems on the subject of point vortex relative equilibria in which he was engaged at the time of his death: bilinear relative equilibria and the...
It takes two to tango: Equilibria in a model of sales
M.R. Baye (Michael); D. Kovenock (Dan); C.G. de Vries (Casper)
1992-01-01
textabstractWe show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria im
On the existence and convergence of price equilibria for random economies
Nummelin, Esa
2000-01-01
We study an exchange economy comprising $n$ agents,where the excess demands by the agents are random variables. We show that under certain conditions the set of price equilibria is nonempty. We also prove a theorem concerning the convergence of the random price equilibria toward the price equilibria of an associated “expectation economy.”
Long-range correlations and coherent structures in magnetohydrodynamic equilibria.
Weichman, Peter B
2012-12-01
The equilibrium theory of the 2D magnetohydrodynamic equations is derived, accounting for the full infinite hierarchies of conserved integrals. An exact description in terms of two coupled elastic membranes emerges, producing long-ranged correlations between the magnetic and velocity fields. This is quite different from the results of previous variational treatments, which relied on a local product ansatz for the thermodynamic Gibbs distribution. The equilibria display the same type of coherent structures, such as compact eddies and zonal jets, previously found in pure fluid equilibria. Possible consequences of this for recent simulations of the solar tachocline are discussed.
A method of computational magnetohydrodynamics defining stable Scyllac equilibria.
Betancourt, O; Garabedian, P
1977-02-01
A computer code has been developed for the numerical calculation of sharp boundary equilibria of a toroidal plasma with diffuse pressure profile. This generalizes earlier work that was done separately on the sharp boundary and diffuse models, and it allows for large amplitude distortions of the plasma in three-dimensional space. By running the code, equilibria that are stable to the so-called m = 1, k = 0 mode have been found for Scyllac, which is a high beta toroidal confinement device of very large aspect ratio.
Compact tokamak reactors. Part 1 (analytic results)
Energy Technology Data Exchange (ETDEWEB)
Wootton, A.J.; Wiley, J.C.; Edmonds, P.H.; Ross, D.W.
1996-09-13
We discuss the possible use of tokamaks for thermonuclear power plants, in particular tokamaks with low aspect ratio and copper toroidal field coils. Three approaches are presented. First we review and summarize the existing literature. Second, using simple analytic estimates, the size of the smallest tokamak to produce an ignited plasma is derived. This steady state energy balance analysis is then extended to determine the smallest tokamak power plant, by including the power required to drive the toroidal field, and considering two extremes of plasma current drive efficiency. The analytic results will be augmented by a numerical calculation which permits arbitrary plasma current drive efficiency; the results of which will be presented in Part II. Third, a scaling from any given reference reactor design to a copper toroidal field coil device is discussed. Throughout the paper the importance of various restrictions is emphasized, in particular plasma current drive efficiency, plasma confinement, plasma safety factor, plasma elongation, plasma beta, neutron wall loading, blanket availability and recirculating electric power. We conclude that the latest published reactor studies, which show little advantage in using low aspect ratio unless remarkably high efficiency plasma current drive and low safety factor are combined, can be reproduced with the analytic model.
Tokamak startup with electron cyclotron heating
Energy Technology Data Exchange (ETDEWEB)
Holly, D J; Prager, S C; Shepard, D A; Sprott, J C
1980-04-01
Experiments are described in which the startup voltage in a tokamak is reduced by approx. 60% by the use of a modest amount of electron cyclotron resonance heating power for preionization. A 50% reduction in volt-second requirement and impurity reflux are also observed.
Advanced tokamak concepts and reactor designs
Oomens, A. A. M.
2000-01-01
From a discussion of fusion reactor designs based on today's well-established experience gained in the operation of large tokamaks, it is concluded that such reactors are economically not attractive. The physics involved in the various options for concept improvement is described, some examples
Tokamak Transport Studies Using Perturbation Analysis
Cardozo, N. J. L.; Dehaas, J. C. M.; Hogeweij, G. M. D.; Orourke, J.; Sips, A.C.C.; Tubbing, B. J. D.
1990-01-01
Studies of the transport properties of tokamak plasmas using perturbation analysis are discussed. The focus is on experiments with not too large perturbations, such as sawtooth induced heat and density pulse propagation, power modulation and oscillatory gas-puff experiments. The approximations made
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).
UCLA Tokamak Program Close Out Report.
Energy Technology Data Exchange (ETDEWEB)
Taylor, Robert John [UCLA/retired
2014-02-04
The results of UCLA experimental fusion program are summarized. Starting with smaller devices like Microtor, Macrotor, CCT and ending the research on the large (5 m) Electric Tokamak. CCT was the most diagnosed device for H-mode like physics and the effects of rotation induced radial fields. ICRF heating was also studied but plasma heating of University Type Tokamaks did not produce useful results due to plasma edge disturbances of the antennae. The Electric Tokamak produced better confinement in the seconds range. However, it presented very good particle confinement due to an "electric particle pinch". This effect prevented us from reaching a quasi steady state. This particle accumulation effect was numerically explained by Shaing's enhanced neoclassical theory. The PI believes that ITER will have a good energy confinement time but deleteriously large particle confinement time and it will disrupt on particle pinching at nominal average densities. The US fusion research program did not study particle transport effects due to its undue focus on the physics of energy confinement time. Energy confinement time is not an issue for energy producing tokamaks. Controlling the ash flow will be very expensive.
Tokamak Transport Studies Using Perturbation Analysis
Cardozo, N. J. L.; Dehaas, J. C. M.; Hogeweij, G. M. D.; Orourke, J.; Sips, A.C.C.; Tubbing, B. J. D.
1990-01-01
Studies of the transport properties of tokamak plasmas using perturbation analysis are discussed. The focus is on experiments with not too large perturbations, such as sawtooth induced heat and density pulse propagation, power modulation and oscillatory gas-puff experiments. The approximations made
Sokkalingam, Nandhini; Kamath, Ganesh; Coscione, Maria; Potoff, Jeffrey J
2009-07-30
The transferable potentials for phase equilibria force field is extended to dimethylmethylphosphonate (DMMP), sarin, and soman by introducing a new interaction site representing the phosphorus atom. Parameters for the phosphorus atom are optimized to reproduce the liquid densities at 303 and 373 K and the normal boiling point of DMMP. Calculations for sarin and soman are performed in predictive mode, without further parameter optimization. Vapor-liquid coexistence curves, critical properties, vapor pressures and heats of vaporization are predicted over a wide range of temperatures with histogram reweighting Monte Carlo simulations in the grand canonical ensemble. Excellent agreement with experiment is achieved for all compounds, with unsigned errors of less than 1% for vapor pressures and normal boiling points and under 5% for heats of vaporization and liquid densities at ambient conditions.
Nanoscale effects on thermodynamics and phase equilibria in oxide systems.
Navrotsky, Alexandra
2011-08-22
Because different solid materials (phases) have different surface energies, equilibria among them will be significantly affected by particle size. This Minireview summarizes experimental (calorimetric) data for the surface energies of oxides and discusses shifts in the stability of polymorphs, the thermodynamics of hydration, and oxidation-reduction reactions in nanoscale oxide systems.
Should Elliptical Galaxies Be Idealised as Collisionless Equilibria?
Kandrup, Henry E.
2000-01-01
This talk summarises several different lines of argument suggesting that one should not expect cuspy nonaxisymmetric galaxies to exist as robust, long-lived collisionless equilibria, i.e., that such objects should not be idealised as time-independent solutions to the collisionless Boltzmann equation.
Shallow-water vortex equilibria and their stability
Płotka, H.; Dritschel, D. G.
2011-12-01
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale LD called the "Rossby deformation length" relating the strength of stratification to that of the background rotation rate. Specifically, LD = c/f where is a characteristic gravity-wave speed, g is gravity (or "reduced" gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call "quasi-equilibria". These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
On Pure and (approximate) Strong Equilibria of Facility Location Games
Hansen, Thomas Dueholm
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every agent pays individually a (weighted) connection cost to the chosen location. We study the Price of Stability (PoS) of pure Nash equilibria and the Price of Anarchy of strong equilibria (SPoA), that generalize pure equilibria by being resilient to coalitional deviations. A special case of recently studied network design games, Facility Location merits separate study as a classic model with numerous applications and individual characteristics: our analysis for unweighted agents on metric networks reveals constant upper and lower bounds for the PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. Strong equilibria do not always exist, even for the unweighted metric case. For this cas...
Deep water periodic waves as Hamiltonian relative equilibria
van Groesen, Embrecht W.C.; Lie She Liam, L.S.L.; Lakhturov, I.; Andonowati, A.; Biggs, N.
2007-01-01
We use a recently derived KdV-type of equation for waves on deep water to study Stokes waves as relative equilibria. Special attention is given to investigate the cornered Stokes-120 degree wave as a singular solution in the class of smooth steady wave profiles.
Computation of Stackelberg Equilibria of Finite Sequential Games
DEFF Research Database (Denmark)
Bosanski, Branislav; Branzei, Simina; Hansen, Kristoffer Arnsfelt
2015-01-01
The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player~1 (the leader) first commits to a strategy that is publicly announced, then Player~2 (the follower) plays a best response to the leader's choice. We study Stackelberg equilibria in finite...
QUASI-EQUILIBRIA IN MARKETS WITH NON-CONVEX PREFERENCES.
An upper bound is placed on social divergence from general equilibrium , due to non-convexity of the traders’ preference relations. Existence and significance of certain quasi-equilibria are investigated. If there is a sufficiently large number of traders in the market, the existence of a configuration arbitrarily close to equilibrium is demonstrated. (Author)
Asset pricing puzzles explained by incomplete Brownian equilibria
DEFF Research Database (Denmark)
Christensen, Peter Ove; Larsen, Kasper
We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income. The investors can trade continuously on a finit...... markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Shallow-water vortex equilibria and their stability
Energy Technology Data Exchange (ETDEWEB)
Plotka, H; Dritschel, D G, E-mail: hanna@mcs.st-andrews.ac.uk, E-mail: dgd@mcs.st-andrews.ac.uk [School of Mathematics and Statistics, University of St Andrews, North Haugh, St. Andrews KY16 9SS (United Kingdom)
2011-12-22
We first describe the equilibrium form and stability of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L{sub D} called the 'Rossby deformation length' relating the strength of stratification to that of the background rotation rate. Specifically, L{sub D} = c/f where c={radical}gH is a characteristic gravity-wave speed, g is gravity (or 'reduced' gravity in a two-layer context where one layer is infinitely deep), H is the mean active layer depth, and f is the Coriolis frequency (here constant). We next introduce ageostrophic effects by using the full shallow-water model to generate what we call 'quasi-equilibria'. These equilibria are not strictly steady, but radiate such weak gravity waves that they are steady for all practical purposes. Through an artificial ramping procedure, we ramp up the potential vorticity anomaly of the fluid particles in our quasi-geostrophic equilibria to obtain shallow-water quasi-equilibria at finite Rossby number. We show a few examples of these states in this paper.
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...
High-pressure fluid-phase equilibria: Experimental methods and systems investigated (2005-2008)
DEFF Research Database (Denmark)
Fonseca, José; Dohrn, Ralf; Peper, Stephanie
2011-01-01
A review of systems is given, for which experimental high-pressure phase-equilibrium data were published in the period between 2005 and 2008, continuing a series of reviews. To find candidates for articles that are of interest for this survey a three-stage search strategy was used including...... a systematic search of the contents of the 17 most important journals of the field. Experimental methods for the investigation of high-pressure phase equilibria were classified, described and illustrated using examples from articles of the period between 2005 and 2008. For the systems investigated......, the reference, the temperature and pressure range of the data, and the experimental method used for the measurements is given in 54 tables. Vapor–liquid equilibria, liquid–liquid equilibria, vapor–liquid–liquid equilibria, solid–liquid equilibria, solid–vapor equilibria, solid–vapor–liquid equilibria, critical...
Structural Stability of Tokamak Equilibrium: Transport Barriers
Energy Technology Data Exchange (ETDEWEB)
Solano, E. R.
2001-07-01
A generalised theory of structural stability of differential equations is introduced and applied to the Grad-Shafranov equation. It is discussed how the formation and loss of transport barrier could be associated with the appearance/disappearance of equilibria. The equilibrium conjecture is presented: transport barriers are associated with locally diamagnetic regions in the plasma, and affected by the paramagnetism of the bootstrap current. (Author) 18 refs.
Modelling of electron transport and of sawtooth activity in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Angioni, C
2001-10-01
Transport phenomena in tokamak plasmas strongly limit the particle and energy confinement and represent a crucial obstacle to controlled thermonuclear fusion. Within the vast framework of transport studies, three topics have been tackled in the present thesis: first, the computation of neoclassical transport coefficients for general axisymmetric equilibria and arbitrary collisionality regime; second, the analysis of the electron temperature behaviour and transport modelling of plasma discharges in the Tokamak a configuration Variable (TCV); third, the modelling and simulation of the sawtooth activity with different plasma heating conditions. The work dedicated to neoclassical theory has been undertaken in order to first analytically identify a set of equations suited for implementation in existing Fokker-Planck codes. Modifications of these codes enabled us to compute the neoclassical transport coefficients considering different realistic magnetic equilibrium configurations and covering a large range of variation of three key parameters: aspect ratio, collisionality, and effective charge number. A comparison of the numerical results with an analytical limit has permitted the identification of two expressions for the trapped particle fraction, capable of encapsulating the geometrical effects and thus enabling each transport coefficient to be fitted with a single analytical function. This has allowed us to provide simple analytical formulae for all the neoclassical transport coefficients valid for arbitrary aspect ratio and collisionality in general realistic geometry. This work is particularly useful for a correct evaluation of the neoclassical contribution in tokamak scenarios with large bootstrap cur- rent fraction, or improved confinement regimes with low anomalous transport and for the determination of the plasma current density profile, since the plasma conductivity is usually assumed neoclassical. These results have been included in the plasma transport code
Energy Technology Data Exchange (ETDEWEB)
Lopez C, R.; Melendez L, L.; Valencia A, R.; Chavez A, E.; Colunga S, S.; Gaytan G, E
1992-02-15
In this work the obtained results of the investigation about the experimental characterization of those low energy pulsed discharges of the Tokamak Novillo are reported. With this it is possible to fix the one operation point but appropriate of the Tokamak to condition the chamber in the smallest possible time for the cleaning discharges regime before beginning the main discharge. The characterization of the cleaning discharges in those Tokamaks is an unique process and characteristic of each device, since the good points of operation are consequence of those particularities of the design of the machine. In the case of the Tokamak Novillo, besides characterizing it a contribution is made to the cleaning discharges regime which consists on the one product of the current peak to peak of plasma by the duration of the discharge Ip{sub t} like reference parameter for the optimization of the operation of the device in the cleaning discharge regime. The maximum value of the parameter I{sub (p)}t, under different work conditions, allowed to find the good operation point to condition the discharges chamber of the Tokamak Novillo in short time and to arrive to a regime in which is not necessary the preionization for the obtaining of the cleaning discharges. (Author)
Banana orbits in elliptic tokamaks with hole currents
Martin, P.; Castro, E.; Puerta, J.
2015-03-01
Ware Pinch is a consequence of breaking of up-down symmetry due to the inductive electric field. This symmetry breaking happens, though up-down symmetry for magnetic surface is assumed. In previous work Ware Pinch and banana orbits were studied for tokamak magnetic surface with ellipticity and triangularity, but up-down symmetry. Hole currents appear in large tokamaks and their influence in Ware Pinch and banana orbits are now considered here for tokamaks magnetic surfaces with ellipticity and triangularity.
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.
DEFF Research Database (Denmark)
Krøll, Annette Elisabeth; Marcussen, Lis
1997-01-01
An equilibrium equation for pure component adsorption is compared to experiments and to the vacancy solution theory. The investigated equilibrium equation is a special case of a model for prediction of multicomponent adsorption equilibria.The vacancy solution theory for multicomponent systems req...
Magnetic sensor for steady state tokamak
Energy Technology Data Exchange (ETDEWEB)
Neyatani, Yuzuru; Mori, Katsuharu; Oguri, Shigeru; Kikuchi, Mitsuru [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
1996-06-01
A new type of magnetic sensor has been developed for the measurement of steady state magnetic fields without DC-drift such as integration circuit. The electromagnetic force induced to the current which leads to the sensor was used for the measurement. For the high frequency component which exceeds higher than the vibration frequency of sensor, pick-up coil was used through the high pass filter. From the results using tokamak discharges, this sensor can measure the magnetic field in the tokamak discharge. During {approx}2 hours measurement, no DC drift was observed. The sensor can respond {approx}10ms of fast change of magnetic field during disruptions. We confirm the extension of measured range to control the current which leads to the sensor. (author).
Boundary Plasma Turbulence Simulations for Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Xu, X; Umansky, M; Dudson, B; Snyder, P
2008-05-15
The boundary plasma turbulence code BOUT models tokamak boundary-plasma turbulence in a realistic divertor geometry using modified Braginskii equations for plasma vorticity, density (ni), electron and ion temperature (T{sub e}; T{sub i}) and parallel momenta. The BOUT code solves for the plasma fluid equations in a three dimensional (3D) toroidal segment (or a toroidal wedge), including the region somewhat inside the separatrix and extending into the scrape-off layer; the private flux region is also included. In this paper, a description is given of the sophisticated physical models, innovative numerical algorithms, and modern software design used to simulate edge-plasmas in magnetic fusion energy devices. The BOUT code's unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics.
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.
Module description of TOKAMAK equilibrium code MEUDAS
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2002-01-01
The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)
Self-Organized Stationary States of Tokamaks.
Jardin, S C; Ferraro, N; Krebs, I
2015-11-20
We demonstrate that in a 3D resistive magnetohydrodynamic simulation, for some parameters it is possible to form a stationary state in a tokamak where a saturated interchange mode in the center of the discharge drives a near helical flow pattern that acts to nonlinearly sustain the configuration by adjusting the central loop voltage through a dynamo action. This could explain the physical mechanism for maintaining stationary nonsawtoothing "hybrid" discharges, often referred to as "flux pumping."
Resistive interchange instability in reversed shear tokamaks
Energy Technology Data Exchange (ETDEWEB)
Furukawa, Masaru; Nakamura, Yuji; Wakatani, Masahiro [Graduate School of Energy Science, Kyoto University, Uji, Kyoto (Japan)
1999-04-01
Resistive interchange modes become unstable due to the magnetic shear reversal in tokamaks. In the present paper, the parameter dependences, such as q (safety factor) profile and the magnetic surface shape are clarified for improving the stability, using the local stability criterion. It is shown that a significant reduction of the beta limit is obtained for the JT-60U reversed shear configuration with internal transport barrier, since the local pressure gradient increases. (author)
Internal Kink Instability in Shaped Tokamaks
Institute of Scientific and Technical Information of China (English)
王中天; 王龙
2002-01-01
A criterion of an ideal internal kink mode is derived for a shaped tokamak configuration in which q-profile is very flat in the core region. A combining criterion is obtained including the necessary criterion of Mercier and the sufficient criterion of Lortz. The new criterion makes progress compared with the necessary criterion of Mercier. In the elongated plasma, a poloidal beta can cause instability, while the triangularity has a stabilizing effect. The result is applicable for DIII-D and SUNIST.
EU Integrated Tokamak Modelling (ITM) Task Force
Institute of Scientific and Technical Information of China (English)
A Becoulet
2007-01-01
@@ At the end of 2003, the European Fusion Development Agreement (EFDA) structure set-up a long-term European task force (TF) in charge of "co-ordinating the development of a coherent set of validated simulation tools for the purpose of benchmarking on existing tokamak experiments, with the ultimate aim of providing a comprehensive simulation package for ITER plasmas" [http://www.efda-taskforce-itm.org/].
Tokamaks: from A D Sakharov to the present (the 60-year history of tokamaks)
Azizov, E. A.
2012-02-01
The paper is prepared on the basis of the report presented at the session of the Physical Sciences Division of the Russian Academy of Sciences (RAS) at the Lebedev Physical Institute, RAS on 25 May 2011, devoted to the 90-year jubilee of Academician Andrei D Sakharov - the initiator of controlled nuclear fusion research in the USSR. The 60-year history of plasma research work in toroidal devices with a longitudinal magnetic field suggested by Andrei D Sakharov and Igor E Tamm in 1950 for the confinement of fusion plasma and known at present as tokamaks is described in brief. The recent (2006) agreement among Russia, the EU, the USA, Japan, China, the Republic of Korea, and India on the joint construction of the international thermonuclear experimental reactor (ITER) in France based on the tokamak concept is discussed. Prospects for using the tokamak as a thermonuclear (14 MeV) neutron source are examined.
Bulk ion heating with ICRF waves in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Mantsinen, M. J., E-mail: mervi.mantsinen@bsc.es [Catalan Institution for Research and Advanced Studies, Barcelona (Spain); Barcelona Supercomputing Center, Barcelona (Spain); Bilato, R.; Bobkov, V. V.; Kappatou, A.; McDermott, R. M.; Odstrčil, T.; Tardini, G.; Bernert, M.; Dux, R.; Maraschek, M.; Noterdaeme, J.-M.; Ryter, F.; Stober, J. [Max-Planck-Institut für Plasmaphysik, Garching (Germany); Nocente, M. [Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, Milano (Italy); Istituto di Fisica del Plasma “P. Caldirola”, CNR, Milano (Italy); Hellsten, T. [Dept. of Fusion Plasma Physics, EES, KTH, Stockholm (Sweden); Mantica, P.; Tardocchi, M. [Istituto di Fisica del Plasma “P. Caldirola”, CNR, Milano (Italy); Nielsen, S. K.; Rasmussen, J.; Stejner, M. [Technical University of Denmark, Department of Physics, Lyngby (Denmark); and others
2015-12-10
Heating with ICRF waves is a well-established method on present-day tokamaks and one of the heating systems foreseen for ITER. However, further work is still needed to test and optimize its performance in fusion devices with metallic high-Z plasma facing components (PFCs) in preparation of ITER and DEMO operation. This is of particular importance for the bulk ion heating capabilities of ICRF waves. Efficient bulk ion heating with the standard ITER ICRF scheme, i.e. the second harmonic heating of tritium with or without {sup 3}He minority, was demonstrated in experiments carried out in deuterium-tritium plasmas on JET and TFTR and is confirmed by ICRF modelling. This paper focuses on recent experiments with {sup 3}He minority heating for bulk ion heating on the ASDEX Upgrade (AUG) tokamak with ITER-relevant all-tungsten PFCs. An increase of 80% in the central ion temperature T{sub i} from 3 to 5.5 keV was achieved when 3 MW of ICRF power tuned to the central {sup 3}He ion cyclotron resonance was added to 4.5 MW of deuterium NBI. The radial gradient of the T{sub i} profile reached locally values up to about 50 keV/m and the normalized logarithmic ion temperature gradients R/LT{sub i} of about 20, which are unusually large for AUG plasmas. The large changes in the T{sub i} profiles were accompanied by significant changes in measured plasma toroidal rotation, plasma impurity profiles and MHD activity, which indicate concomitant changes in plasma properties with the application of ICRF waves. When the {sup 3}He concentration was increased above the optimum range for bulk ion heating, a weaker peaking of the ion temperature profile was observed, in line with theoretical expectations.
Initial DEMO tokamak design configuration studies
Energy Technology Data Exchange (ETDEWEB)
Bachmann, Christian, E-mail: christian.bachmann@efda.org [EFDA, Boltzmannstraße 2, 85748 Garching (Germany); Aiello, G. [CEA-Saclay, DEN, DM2S, SEMT, F-91191 Gif-Sur-Yvette (France); Albanese, R.; Ambrosino, R. [ENEA/CREATE, Universita di Napoli Federico II, Naples (Italy); Arbeiter, F. [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Aubert, J. [CEA-Saclay, DEN, DM2S, SEMT, F-91191 Gif-Sur-Yvette (France); Boccaccini, L.; Carloni, D. [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Federici, G. [EFDA, Boltzmannstraße 2, 85748 Garching (Germany); Fischer, U. [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Kovari, M. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Li Puma, A. [CEA-Saclay, DEN, DM2S, SEMT, F-91191 Gif-Sur-Yvette (France); Loving, A. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Maione, I. [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Mattei, M. [ENEA/CREATE, Universita di Napoli Federico II, Naples (Italy); Mazzone, G. [ENEA C.R. Frascati, via E. Fermi 45, 00044 Frascati, Roma (Italy); Meszaros, B. [EFDA, Boltzmannstraße 2, 85748 Garching (Germany); Palermo, I. [Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid (Spain); Pereslavtsev, P. [Karlsruhe Institute of Technology (KIT), Karlsruhe (Germany); Riccardo, V. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); and others
2015-10-15
Highlights: • A definition of main DEMO requirements. • A description of the DEMO tokamak design configuration. • A description of issues yet to be solved. - Abstract: To prepare the DEMO conceptual design phase a number of physics and engineering assessments were carried out in recent years in the frame of EFDA concluding in an initial design configuration of a DEMO tokamak. This paper gives an insight into the identified engineering requirements and constraints and describes their impact on the selection of the technologies and design principles of the main tokamak components. The EU DEMO program aims at making best use of the technologies developed for ITER (e.g., magnets, vessel, cryostat, and to some degree also the divertor). However, other systems in particular the breeding blanket require design solutions and advanced technologies that will only partially be tested in ITER. The main differences from ITER include the requirement to breed, to extract, to process and to recycle the tritium needed for plasma operation, the two orders of magnitude larger lifetime neutron fluence, the consequent radiation dose levels, which limit remote maintenance options, and the requirement to use low-activation steel for in-vessel components that also must operate at high temperature for efficient energy conversion.
Relativistic runaway electrons in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Jaspers, R.E.
1995-02-03
Runaway electrons are inherently present in a tokamak, in which an electric field is applied to drive a toroidal current. The experimental work is performed in the tokamak TEXTOR. Here runaway electrons can acquire energies of up to 30 MeV. The runaway electrons are studied by measuring their synchrotron radiation, which is emitted in the infrared wavelength range. The studies presented are unique in the sense that they are the first ones in tokamak research to employ this radiation. Hitherto, studies of runaway electrons revealed information about their loss in the edge of the discharge. The behaviour of confined runaways was still a terra incognita. The measurement of the synchrotron radiation allows a direct observation of the behaviour of runaway electrons in the hot core of the plasma. Information on the energy, the number and the momentum distribution of the runaway electrons is obtained. The production rate of the runaway electrons, their transport and the runaway interaction with plasma waves are studied. (orig./HP).
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.
SOL Width Scaling in the MAST Tokamak
Ahn, Joon-Wook; Counsell, Glenn; Connor, Jack; Kirk, Andrew
2002-11-01
Target heat loads are determined in large part by the upstream SOL heat flux width, Δ_h. Considerable effort has been made in the past to develop analytical and empirical scalings for Δh to allow reliable estimates to be made for the next-step device. The development of scalings for a large spherical tokamak (ST) such as MAST is particularly important both for development of the ST concept and for improving the robustness of scalings derived for conventional tokamaks. A first such scaling has been developed in MAST DND plasmas. The scaling was developed by flux-mapping data from the target Langmuir probe arrays to the mid-plane and fitting to key upstream parameters such as P_SOL, bar ne and q_95. In order to minimise the effects of co-linearity, dedicated campaigns were undertaken to explore the widest possible range of each parameter while keeping the remainder as fixed as possible. Initial results indicate a weak inverse dependence on P_SOL and approximately linear dependence on bar n_e. Scalings derived from consideration of theoretical edge transport models and integration with data from conventional devices is under way. The established scaling laws could be used for the extrapolations to the future machine such as Spherical Tokamak Power Plant (STPP). This work is jointly funded by Euratom and UK Department of Trade and Industry. J-W. Ahn would like to recognise the support of a grant from the British Foreign & Commonwealth Office.
Nondiffusive plasma transport at tokamak edge
Krasheninnikov, S. I.
2000-10-01
Recent findings show that cross field edge plasma transport at tokamak edge does not necessarily obey a simple diffusive law [1], the only type of a transport model applied so far in the macroscopic modeling of edge plasma transport. Cross field edge transport is more likely due to plasma filamentation with a ballistic motion of the filaments towards the first wall. Moreover, it so fast that plasma recycles on the main chamber first wall rather than to flow into divertor as conventional picture of edge plasma fluxes suggests. Crudely speaking particle recycling wise diverted tokamak operates in a limiter regime due to fast anomalous non-diffusive cross field plasma transport. Obviously that this newly found feature of edge plasma anomalous transport can significantly alter a design of any future reactor relevant tokamaks. Here we present a simple model describing the motion of the filaments in the scrape off layer and discuss it implications for experimental observations. [1] M. Umansky, S. I. Krasheninnikov, B. LaBombard, B. Lipschultz, and J. L. Terry, Phys. Plasmas 6 (1999) 2791; M. Umansky, S. I. Krasheninnikov, B. LaBombard and J. L. Terry, Phys. Plasmas 5 (1998) 3373.
Local and Global Bifurcations With Nonhyperbolic Equilibria
Institute of Scientific and Technical Information of China (English)
孙建华; 罗定军
1994-01-01
The normal forms of coupling functions governing local and global bifurcations are studied for a generic (d+1) -parameter family of three-dimensional systems with a heteroclinic orbit connecting a hyperbolic saddle and a nonhyperbolic equilibrium occurring in the saddle-node,transcritical and pitchfork bifurcations,respectively.Singularity theory and a version of Melnikov function are used in this paper.
Saturation of Alfvén modes in tokamak plasmas investigated by Hamiltonian mapping techniques
Briguglio, S.; Schneller, M.; Wang, X.; Di Troia, C.; Hayward-Schneider, T.; Fusco, V.; Vlad, G.; Fogaccia, G.
2017-07-01
Nonlinear dynamics of single toroidal number Alfvén eigenmodes destabilised by the the resonant interaction with fast ions is investigated, in tokamak equilibria, by means of Hamiltonian mapping techniques. The results obtained by two different simulation codes, XHMGC and HAGIS, are presented for n = 2 Beta induced Alfvén eigenmodes and, respectively n = 6 toroidal Alfvén eigenmodes. Simulations of the bump-on-tail instability performed by a 1-dimensional code, PIC1DP, are also analysed for comparison. As a general feature, modes saturate as the resonant-particle distribution function is flattened over the whole region where mode-particle power transfer can take place in the linear phase. Such region is limited by the narrowest of resonance width and mode width. In the former case, mode amplitude at saturation exhibits a quadratic scaling with the linear growth rate; in the latter case, the scaling is linear. These results are explained in terms of the approximate analytic solution of a nonlinear pendulum model. They are also used to prove that the radial width of the single poloidal harmonic sets an upper limit to the radial displacement of circulating fast ions produced by a single-toroidal-number gap mode in the large n limit, irrespectively of the possible existence of a large global mode structure formed by many harmonics.
An alternative method of constructing axisymmetric toroidal equilibria with nonparallel flow
Kuiroukidis, Ap; Throumoulopoulos, G. N.
2016-11-01
An alternative method based on an inverse aspect ratio (ɛ) expansion which reduces the axisymmetric equilibrium problem to a set of ODEs containing terms of arbitrary order in ɛ is employed to solve a generalized Grad-Shafranov equation with incompressible sheared flow nonparallel to the magnetic field. The method is applied to construct equilibria with either circular magnetic surfaces and reversed magnetic shear or D-shaped magnetic surfaces and normal magnetic shear. From the former equilibrium, it turns out that the electric field results in an increase of the reversed magnetic shear, thus indicating potential synergetic effects of the sheared flow and the magnetic shear in the formation of an internal transport barrier in consistent with experimental evidence.
Experimental methods for phase equilibria at high pressures.
Dohrn, Ralf; Fonseca, José M S; Peper, Stephanie
2012-01-01
Knowledge of high-pressure phase equilibria is crucial in many fields, e.g., for the design and optimization of high-pressure chemical and separation processes, carbon capture and storage, hydrate formation, applications of ionic liquids, and geological processes. This review presents the variety of methods to measure phase equilibria at high pressures and, following a classification, discusses the measurement principles, advantages, challenges, and error sources. Examples of application areas are given. A detailed knowledge and understanding of the different methods is fundamental not only for choosing the most suitable method for a certain task but also for the evaluation of experimental data. The discrepancy between the (sometimes low) true accuracy of published experimental data and the (high) accuracy claimed by authors is addressed. Some essential requirements for the generation of valuable experimental results are summarized.
Phase diagrams and heterogeneous equilibria a practical introduction
Predel, Bruno; Pool, Monte
2004-01-01
This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.
Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation
Raimondi, A.; Tebaldi, C.
2008-04-01
A general n-node network is considered for which, in absence of interactions, each node is governed by a logistic equation. Interactions among the nodes take place in the form of competition, which also includes adaptive abilities through a (short term) memory effect. As a consequence the dynamics of the network is governed by a system of n2 nonlinear ordinary differential equations. As a first step, equilibria and their stability are investigated analytically for the general network in dependence of the relevant parameters, namely the strength of competition, the adaptation rate and the network size. The existence of classes of invariant subspaces, related to symmetries, allows the introduction of a reduced model, four dimensional, where n appears as a parameter, which give full account of existence and stability for the equilibria in the network.
A simulation study of a controlled tokamak plasma
Fujii, N.; Niwa, Y.
1980-03-01
A tokamak circuit theory, including results of numerical simulation studies, is applied to a control system synthesized for a Joule heated tokamak plasma. The treatment is similar to that of Ogata and Ninomiya (1979) except that in this case a quadrupole field coil current is considered coexisting with image induced on a vacuum chamber.
Soft-X-Ray Tomography Diagnostic at the Rtp Tokamak
Da Cruz, D. F.; Donne, A. J. H.
1994-01-01
An 80-channel soft x-ray tomography system has been constructed for diagnosing the RTP (Rijnhuizen Tokamak Project) tokamak plasma. Five pinhole cameras, each with arrays of 16 detectors are distributed more or less homogeneously around a poloidal plasma cross section. The cameras are positioned clo
Magnetohydrodynamic Waves and Instabilities in Rotating Tokamak Plasmas
Haverkort, J.W.
2013-01-01
One of the most promising ways to achieve controlled nuclear fusion for the commercial production of energy is the tokamak design. In such a device, a hot plasma is confined in a toroidal geometry using magnetic fields. The present generation of tokamaks shows significant plasma rotation, primarily
Magnetohydrodynamic Waves and Instabilities in Rotating Tokamak Plasmas
J.W. Haverkort (Willem)
2013-01-01
htmlabstractOne of the most promising ways to achieve controlled nuclear fusion for the commercial production of energy is the tokamak design. In such a device, a hot plasma is confined in a toroidal geometry using magnetic fields. The present generation of tokamaks shows significant plasma rotation
Generalized statistical model for multicomponent adsorption equilibria on zeolites
Energy Technology Data Exchange (ETDEWEB)
Rota, R.; Gamba, G.; Paludetto, R.; Carra, S.; Morbidelli, M. (Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (IT))
1988-05-01
The statistical thermodynamic approach to multicomponent adsorption equilibria on zeolites has been extended to nonideal systems, through the correction of cross coefficients characterizing the interaction between unlike molecules. Estimation of the model parameters requires experimental binary equilibrium data. Comparisons with the classical model based on adsorbed solution theory are reported for three nonideal ternary systems. The two approaches provide comparable results in the simulation of binary and ternary adsorption equilibrium data at constant temperature and pressure.
Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
Solon, Alexandre P.; Stenhammar, Joakim; Cates, Michael E.; Kafri, Yariv; Tailleur, Julien
2016-01-01
Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high density. Starting from a continuum description of diffusive scalar active matter, we give a general prescription for phase equilibria that amounts, at a hydrodynamics scale, to extremalizing a generalized free energy. We illustrate our approach on two well known models: self-propelled particles interacting either through a density-dependent pro...
Approximation of stochastic equilibria for dynamic systems with colored noise
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Ural Federal University, Lenina 51, Ekaterinburg, 620083 (Russian Federation)
2015-03-10
We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.
Correlated Equilibria in Continuous Games: Characterization and Computation
2008-12-22
Annals of Mathematics Studies, pages 75 – 86. Princeton University Press, Princeton, NJ, 1953. [9] M. Dresher, S. Karlin, and L. S. Shapley. Polynomial...games. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games I, number 24 in Annals of Mathematics Studies, pages 161 – 180...J. Lipton and E. Markakis. Nash equilibria via polynomial equations. In Proceedings of LATIN, 2004. [18] J. F. Nash. Non-cooperative games. Annals of Mathematics , 54
Liquid equilibria in the Fe-Ni-Mn system
Energy Technology Data Exchange (ETDEWEB)
Schuermann, E. [Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Inst. fuer Eisenhuettenkunde und Giessereiwesen; Djurdjevic, M.; Nedeljkovic, L. [Belgrade Univ. (Yugoslavia). Faculty of Technology and Metallurgy
1997-12-01
New literature results on the liquid equilibria in the three edge binary systems make necessary a reconsideration and correction of liquidus surfaces of the {gamma} and {delta} solid solutions hitherto outlined in the literature. Therefore, with respect to the critically reinterpreted edge binary systems, the shape of the stable liquidus surface of the {gamma} and {delta} solid solutions has been newly outlined. (orig.) 7 refs.
Relative Equilibria in the Spherical, Finite Density Three-Body Problem
Scheeres, D. J.
2016-10-01
The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum.
Nash equilibria in multi-agent motor interactions.
Directory of Open Access Journals (Sweden)
Daniel A Braun
2009-08-01
Full Text Available Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.
Solution influence on biomolecular equilibria - Nucleic acid base associations
Pohorille, A.; Pratt, L. R.; Burt, S. K.; Macelroy, R. D.
1984-01-01
Various attempts to construct an understanding of the influence of solution environment on biomolecular equilibria at the molecular level using computer simulation are discussed. First, the application of the formal statistical thermodynamic program for investigating biomolecular equilibria in solution is presented, addressing modeling and conceptual simplications such as perturbative methods, long-range interaction approximations, surface thermodynamics, and hydration shell. Then, Monte Carlo calculations on the associations of nucleic acid bases in both polar and nonpolar solvents such as water and carbon tetrachloride are carried out. The solvent contribution to the enthalpy of base association is positive (destabilizing) in both polar and nonpolar solvents while negative enthalpies for stacked complexes are obtained only when the solute-solute in vacuo energy is added to the total energy. The release upon association of solvent molecules from the first hydration layer around a solute to the bulk is accompanied by an increase in solute-solvent energy and decrease in solvent-solvent energy. The techniques presented are expectd to displace less molecular and more heuristic modeling of biomolecular equilibria in solution.
On the complexity of Nash dynamics and Sink Equilibria
Mirrokni, Vahab
2009-01-01
Studying Nash dynamics is an important approach for analyzing the outcome of games with repeated selfish behavior of self-interested agents. Sink equilibria has been introduced by Goemans, Mirrokni, and Vetta for studying social cost on Nash dynamics over pure strategies in games. However, they do not address the complexity of sink equilibria in these games. Recently, Fabrikant and Papadimitriou initiated the study of the complexity of Nash dynamics in two classes of games. In order to completely understand the complexity of Nash dynamics in a variety of games, we study the following three questions for various games: (i) given a state in game, can we verify if this state is in a sink equilibrium or not? (ii) given an instance of a game, can we verify if there exists any sink equilibrium other than pure Nash equilibria? and (iii) given an instance of a game, can we verify if there exists a pure Nash equilibrium (i.e, a sink equilibrium with one state)? In this paper, we almost answer all of the above question...
Fast island phase identification for tearing mode feedback control on J-TEXT tokamak
Rao, B.; Li, D.; Hu, F. R.; Ding, Y. H.; Hu, Q. M.; Jin, H.
2016-11-01
A new method to control the tearing mode (TM) in tokamaks has been proposed [Q. Hu and Q. Yu, Nucl. Fusion 56, 034001 (5pp.) (2016)], according to which, the external resonant magnetic perturbation needs to be applied in certain magnetic island phase regions. Therefore, it is very important to identify the helical phase of magnetic islands in real time. The TM in tokamak plasmas is normally rotating and carries magnetic oscillations, which are known as Mirnov oscillations and can be detected by Mirnov probes. When the O-point or X-point of the magnetic island passes through the probe, the signal will experience a zero-crossing. A poloidal Mirnov probe array and a corresponding island phase identification method are presented. A field-programmable gate array is used to provide the magnetic island helical phase in real time by using multichannel zero crossing detection. This system has been developed on the J-TEXT tokamak and works well. This paper introduces the establishment of the fast magnetic island phase identifying system.
Global particle in cell simulation of radio frequency waves in tokamak ∖fs20
Kuley, Animesh; Lin, Z.; Bao, J.; Lau, C.; Sun, G. Y.
2016-10-01
We are looking into a new nonlinear kinetic simulation model to study the radio frequency heating and current drive of fusion plasmas using toroidal code GTC. In this model ions are considered as fully kinetic (FK) particles using Vlasov equation and the electrons are treated as drift kinetic (DK) particles using drift kinetic equation. We have benchmarked this numerical model to verify the linear physics of normal modes, conversion of slow and fast waves and its propagation in the core region of the tokamak using the Boozer coordinates. In the nonlinear simulation of ion Bernstein wave (IBW) in a tokamak, parametric decay instability (PDI) is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasi-mode (ICQM). The ICQM induces an ion perpendicular heating, with a heating rate proportional to the pump wave intensity. Finally, in the electromagnetic LH simulation, nonlinear wave trapping of electrons is verified and plasma current is nonlinearly driven. Presently we are working on the development of new PIC simulation model using cylindrical coordinates to address the RF wave propagation from the edge of the tokamak to the core region and the parametric instabilities associated with this RF waves. We have verified the cyclotron integrator using Boris push method.
Role of edge turbulence and shear flows in density limit on HL-2A tokamak
Hong, Rongjie; Tynan, George; Xu, Min; Nie, Lin; Guo, Dong; Ke, Rui; Long, Ting; Wu, Yifang; Yuan, Boda
2016-10-01
The tokamak density limit has long been suspected as a consequence of the enhanced turbulent transport in edge plasmas. In this study, evolutions of the turbulence and shear flows were investigated at different normalized density ne /nG in the plasma boundary region of HL-2A tokamak using Langmuir probes. As the density limit was approached, the equilibrium profile of density was flattened in the Scrape-Off Layer (SOL) and steepened inside the separatrix, while the edge cooling was observed from the electron temperature profile. The turbulent cross-field transport also increased substantially with the ne /nG and the collisionality. In addition, the amplitude of the poloidal phase velocity decreased at higher densities. This destruction of the shear layer was associated with the collapse of the Reynolds stress and thus the reduction in the nonlinear energy transfer from high-frequency fluctuations to low-frequency shear flows. These observations indicate an important role of the edge turbulence and the turbulence-driven shear flow in the underlying physics of tokamak density limit. Thank the HL-2A team for machine operation. Partly supported by DOE Grant No. DE-SC0008378.
Progress toward steady-state tokamak operation exploiting the high bootstrap current fraction regime
Ren, Q. L.; Garofalo, A. M.; Gong, X. Z.; Holcomb, C. T.; Lao, L. L.; McKee, G. R.; Meneghini, O.; Staebler, G. M.; Grierson, B. A.; Qian, J. P.; Solomon, W. M.; Turnbull, A. D.; Holland, C.; Guo, W. F.; Ding, S. Y.; Pan, C. K.; Xu, G. S.; Wan, B. N.
2016-06-01
Recent DIII-D experiments have increased the normalized fusion performance of the high bootstrap current fraction tokamak regime toward reactor-relevant steady state operation. The experiments, conducted by a joint team of researchers from the DIII-D and EAST tokamaks, developed a fully noninductive scenario that could be extended on EAST to a demonstration of long pulse steady-state tokamak operation. Improved understanding of scenario stability has led to the achievement of very high values of βp and βN , despite strong internal transport barriers. Good confinement has been achieved with reduced toroidal rotation. These high βp plasmas challenge the energy transport understanding, especially in the electron energy channel. A new turbulent transport model, named TGLF-SAT1, has been developed which improves the transport prediction. Experiments extending results to long pulse on EAST, based on the physics basis developed at DIII-D, have been conducted. More investigations will be carried out on EAST with more additional auxiliary power to come online in the near term.
Tokamak Plasmas : Measurement of temperature ﬂuctuations and anomalous transport in the SINP tokamak
Indian Academy of Sciences (India)
R Kumar; S K Saha
2000-11-01
Temperature ﬂuctuations have been measured in the edge region of the SINP tokamak. We ﬁnd that these ﬂuctuations have a comparatively high level (30–40%) and a broad spectrum. The temperature ﬂuctuations show a quite high coherence with density and potential ﬂuctuations and contribute considerably to the anomalous particle ﬂux.
System assessment of helical reactors in comparison with tokamaks
Energy Technology Data Exchange (ETDEWEB)
Yamazaki, K.; Imagawa, S.; Muroga, T.; Sagara, A.; Okamura, S.
2002-10-01
A comparative assessment of tokamak and helical reactors has been performed using equivalent physics/engineering model and common costing model. Higher-temperature plasma operation is required in tokamak reactors to increase bootstrap current fraction and to reduce current-drive (CD) power. In helical systems, lower-temperature operation is feasible and desirable to reduce helical ripple transport. The capital cost of helical reactor is rather high, however, the cost of electricity (COE) is almost same as that of tokamak reactor because of smaller re-circulation power (no CD power) and less-frequent blanket replacement (lower neutron wall loading). The standard LHD-type helical reactor with 5% beta value is economically equivalent to the standard tokamak with 3% beta. The COE of lower-aspect ratio helical reactor is on the same level of high-{beta}{sub N} tokamak reactors. (author)
2011-01-01
Modeling the Thermodynamic and Transport Properties of Decahydronaphthalene/Propane Mixtures: Phase Equilibria , Density, and Viscosity Nathaniel...Decahydronaphthalene/Propane Mixtures: Phase Equilibria , Density, And Viscosity 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Keywords: phase equilibria ; modified Sanchez-Lacombe equation of state
CASTOR: Normal-mode analysis of resistive MHD plasmas
Kerner, W.; Goedbloed, J. P.; Huysmans, G. T. A.; Poedts, S.; Schwarz, E.
1998-01-01
The CASTOR (complex Alfven spectrum of toroidal plasmas) code computes the entire spectrum of normal-modes in resistive MHD for general tokamak configurations. The applied Galerkin method, in conjunction with a Fourier finite-element discretisation, leads to a large scale eigenvalue problem A (x)
Stability and attractive basins of multiple equilibria in delayed two-neuron networks
Institute of Scientific and Technical Information of China (English)
Huang Yu-Jiao; Zhang Hua-Guang; Wang Zhan-Shan
2012-01-01
Multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation functions of 2r (r ≥ 1) corner points is studied.Sufficient conditions are established for checking the existence of (2r + 1)2 equilibria in delayed recurrent neural networks.Under these conditions,(r + 1)2 equilibria are locally exponentially stable,and (2r + 1)2 - (r + 1)2 - r2 equilibria are unstable.Attractive basins of stable equilibria are estimated,which are larger than invariant sets derived by decomposing state space.One example is provided to illustrate the effectiveness of our results.
Liu, Yangqing; Tan, Yi; Ke, Rui; Yang, Hao; Wang, Wenhao; Gao, Zhe
2015-07-01
Potential isolation and long cable drive are very important in acquiring certain signals from tokamak diagnostics. Compact, battery powered, wireless digitizers for in situ data acquisition have been developed and routinely used in the sino-united spherical tokamak to solve the problems of isolation and long cables. The wireless digitizers utilize the integrated analog to digital converters and the static random access memory of microcontrollers but transfer data wirelessly. They consist of simple and concise circuits but have considerable performances of 12-16 bit in resolution and 500-1000 kS/s in sample rate. Wireless triggering and energy saving are two major challenges of the wireless digitizers. Wireless transceivers in the data link layer are used as trigger and can reduce the trigger jitters to be smaller than 1 μs. In order to reduce the energy consumption, the wireless digitizers are waken only when the tokamak is about to discharge. After discharges, they turn to a periodic checking mode with current consumption smaller than 200 μA. Because of low duty cycle, the wireless digitizers have a battery life of up to four weeks. In general, the wireless digitizers have better performance than normal isolation amplifiers and can greatly simplify the cable connections. They are very suitable for the data acquisition of dangerous and/or susceptible analog signals in tokamaks.
Energy Technology Data Exchange (ETDEWEB)
Barbosa, Luis Felipe de F.P.W.; Del Bosco, Edson
1997-12-31
This reports presents a summary on the thermonuclear fusion and application for energy supply purposes. The tokamak device operation and the magnetic field production systems are described. The ETE tokamak is a small aspect ratio device designed for plasma physics and thermonuclear fusion studies, which presently is under construction at the Laboratorio Associado de Plasma (LAP), Instituto Nacional de Pesquisas Espaciais (INPE) - S.J. dos Campos - S. Paulo. (author) 55 refs., 40 figs.
Energetic particles in spherical tokamak plasmas
McClements, K. G.; Fredrickson, E. D.
2017-05-01
Spherical tokamaks (STs) typically have lower magnetic fields than conventional tokamaks, but similar mass densities. Suprathermal ions with relatively modest energies, in particular beam-injected ions, consequently have speeds close to or exceeding the Alfvén velocity, and can therefore excite a range of Alfvénic instabilities which could be driven by (and affect the behaviour of) fusion α-particles in a burning plasma. STs heated with neutral beams, including the small tight aspect ratio tokamak (START), the mega amp spherical tokamak (MAST), the national spherical torus experiment (NSTX) and Globus-M, have thus provided an opportunity to study toroidal Alfvén eigenmodes (TAEs), together with higher frequency global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (CAEs), which could affect beam current drive and channel fast ion energy into bulk ions in future devices. In NSTX GAEs were correlated with a degradation of core electron energy confinement. In MAST pulses with reduced magnetic field, CAEs were excited across a wide range of frequencies, extending to the ion cyclotron range, but were suppressed when hydrogen was introduced to the deuterium plasma, apparently due to mode conversion at ion-ion hybrid resonances. At lower frequencies fishbone instabilities caused fast particle redistribution in some MAST and NSTX pulses, but this could be avoided by moving the neutral beam line away from the magnetic axis or by operating the plasma at either high density or elevated safety factor. Fast ion redistribution has been observed during GAE avalanches on NSTX, while in both NSTX and MAST fast ions were transported by saturated kink modes, sawtooth crashes, resonant magnetic perturbations and TAEs. The energy dependence of fast ion redistribution due to both sawteeth and TAEs has been studied in Globus-M. High energy charged fusion products are unconfined in present-day STs, but have been shown in MAST to provide a useful diagnostic of beam ion
Application of MDSplus on EAST Tokamak
Institute of Scientific and Technical Information of China (English)
QU Lianzheng; LUO Jiarong; LI lingling; ZHANG Mingxing; WANG Yong
2007-01-01
EAST is a fully superconducting Tokamak in China used for controlled fusion research. MDSplus, a special software package for fusion research, has been used successfully as a central repository for analysed data and PCS (Plasma Control System) data since the debugging experiment in the spring of 2006 . In this paper, the reasons for choosing MDSplus as the analysis database and the way to use it are presented in detail, along with the solution to the problem that part of the MDSplus library does not work in the multithread mode. The experiment showed that the data system based on MDSplus operated stably and it could provide a better performance especially for remote users.
Differential and Integral Models of TOKAMAK
Directory of Open Access Journals (Sweden)
Ivo Dolezel
2004-01-01
Full Text Available Modeling of 3D electromagnetic phenomena in TOKAMAK with typically distributed main and additional coils is not an easy business. Evaluated must be not only distribution of the magnetic field, but also forces acting in particular coils. Use of differential methods (such as FDM or FEM for this purpose may be complicated because of geometrical incommensurability of particular subregions in the investigated area or problems with the boundary conditions. That is why integral formulation of the problem may sometimes be an advantages. The theoretical analysis is illustrated on an example processed by both methods, whose results are compared and discussed.
Neutron skyshine calculations for the PDX tokamak
Energy Technology Data Exchange (ETDEWEB)
Wheeler, F.J.; Nigg, D.W.
1979-01-01
The Poloidal Divertor Experiment (PDX) at Princeton will be the first operating tokamak to require a substantial radiation shield. The PDX shielding includes a water-filled roof shield over the machine to reduce air scattering skyshine dose in the PDX control room and at the site boundary. During the design of this roof shield a unique method was developed to compute the neutron source emerging from the top of the roof shield for use in Monte Carlo skyshine calculations. The method is based on simple, one-dimensional calculations rather than multidimensional calculations, resulting in considerable savings in computer time and input preparation effort. This method is described.
3D MHD Simulations of Tokamak Disruptions
Woodruff, Simon; Stuber, James
2014-10-01
Two disruption scenarios are modeled numerically by use of the CORSICA 2D equilibrium and NIMROD 3D MHD codes. The work follows the simulations of pressure-driven modes in DIII-D and VDEs in ITER. The aim of the work is to provide starting points for simulation of tokamak disruption mitigation techniques currently in the CDR phase for ITER. Pressure-driven instability growth rates previously observed in simulations of DIIID are verified; Halo and Hiro currents produced during vertical displacements are observed in simulations of ITER with implementation of resistive walls in NIMROD. We discuss plans to exercise new code capabilities and validation.
On circulating power of steady state tokamaks
Energy Technology Data Exchange (ETDEWEB)
Itoh, Kimitaka [National Inst. for Fusion Science, Nagoya (Japan); Itoh, Sanae; Fukuyama, Atsushi; Yagi, Masatoshi
1996-03-01
Circulating power for the sustenance and profile control of the steady state tokamak plasmas is discussed. The simultaneous fulfillment of the MHD stability at high beta value, the improved confinement and the stationary equilibrium requires the rotation drive as well as the current drive. In addition to the current drive efficiency, the efficiency for the rotation drive is investigated. The direct rotation drive by the external torque, such as the case of beam injection, is not efficient enough. The mechanism and the magnitude of the spontaneous plasma rotation are studied. (author)
Development of atomic beam probe for tokamaks
Energy Technology Data Exchange (ETDEWEB)
Berta, M., E-mail: bertam@sze.hu [Széchenyi István University, EURATOM Association, Győr (Hungary); Institute of Plasma Physics AS CR, v.v.i., Prague (Czech Republic); Anda, G.; Aradi, M.; Bencze, A.; Buday, Cs.; Kiss, I.G.; Tulipán, Sz.; Veres, G.; Zoletnik, S. [Wigner – RCP, HAS, EURATOM Association, Budapest (Hungary); Havlícek, J.; Háček, P. [Institute of Plasma Physics AS CR, v.v.i., Prague (Czech Republic); Charles University in Prague, Faculty of Mathematics and Physics (Czech Republic)
2013-11-15
Highlights: • ABP is newly developed diagnostic. • Unique measurement method for the determination of plasma edge current variations caused by different transient events such as ELMs. • The design process has been fruitfully supported by the physically motivated computer simulations. • Li-BES system has been modified accordingly to the needs of the ABP. -- Abstract: The concept and development of a new detection method for light alkali ions stemming from diagnostic beams installed on medium size tokamak is described. The method allows us the simultaneous measurement of plasma density fluctuations and fast variations in poloidal magnetic field, therefore one can infer the fast changes in edge plasma current. The concept has been worked out and the whole design process has been done at Wigner RCP. The test detector with appropriate mechanics and electronics is already installed on COMPASS tokamak. General ion trajectory calculation code (ABPIons) has also been developed. Detailed calculations show the possibility of reconstruction of edge plasma current density profile changes with high temporal resolution, and the possibility of density profile reconstruction with better spatial resolution compared to standard Li-BES measurement, this is important for pedestal studies.
Simulating W Impurity Transport in Tokamaks
Younkin, Timothy R.; Green, David L.; Lasa, Ane; Canik, John M.; Wirth, Brian D.
2016-10-01
The extreme heat and charged particle flux to plasma facing materials in magnetically confined fusion devices has motivated Tungsten experiments such as the ``W-Ring'' experiment on the DIII-D tokamak to investigate W divertor viability. In this domain, the transport of W impurities from their tile locations to other first-wall tiles is highly relevant to material lifetimes and tokamak operation. Here we present initial results from a simulation of this W transport. Given that sputtered impurities may experience prompt redeposition near the divertor strikepoint, or migrate far from its origin to the midplane, there is a need to track the global, 3-D, impurity redistribution. This is done by directly integrating the 6-D Lorentz equation of motion (plus thermal gradient terms and relevant Monte-Carlo operators) for the impurity ions and neutrals under background plasma parameters determined by the SOLPS edge plasma code. The geometric details of the plasma facing components are represented to a fidelity sufficient to examine the global impurity migration trends with initial work also presented on advanced surface meshing capabilities targeting high fidelity simulation. This work is supported by U.S. DOE Office of Science SciDAC project on plasma-surface interactions under US DOE contract DE-AC05-00OR22725.
Electromagnetic simulations of tokamaks and stellarators
Energy Technology Data Exchange (ETDEWEB)
Cole, Michael; Mishchenko, Alexey [Max-Planck-Institut fuer Plasmaphysik, EURATOM-Assoziation, Wendelsteinstrasse 1, 17491 Greifswald (Germany)
2014-07-01
A practical fusion reactor will require a plasma β of around 5%. In this range Alfvenic effects become important. Since a practical reactor will also produce energetic alpha particles, the interaction between Alfvenic instabilities and fast ions is of particular interest. We have developed a fluid electron, kinetic ion hybrid model that can be used to study this problem. Compared to fully gyrokinetic electromagnetic codes, hybrid codes offer faster running times and greater flexibility, at the cost of reduced completeness. The model has been successfully verified against the worldwide ITPA Toroidal Alfven Eigenmode (TAE) benchmark, and the ideal MHD code CKA for the internal kink mode in a tokamak. Use of the model can now be turned toward cases of practical relevance. Current work focuses on simulating fishbones in a tokamak geometry, which may be of relevance to ITER, and producing the first non-perturbative self-consistent simulations of TAE in a stellarator, which may be of relevance both to Wendelstein 7-X and any future stellarator reactor. Preliminary results of these studies are presented.
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...
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
A systems assessment of the five Starlite tokamak power plants
Energy Technology Data Exchange (ETDEWEB)
Bathke, C.G.
1996-07-01
The ARIES team has assessed the power-plant attractiveness of the following five tokamak physics regimes: (1) steady state, first stability regime; (2) pulsed, first stability regime; (3) steady state, second stability regime; (4) steady state, reversed shear; and (5) steady state, low aspect ratio. Cost-based systems analysis of these five tokamak physics regimes suggests that an electric power plant based upon a reversed-shear tokamak is significantly more economical than one based on any of the other four physics regimes. Details of this comparative systems analysis are described herein.
Systems assessment of the five Starlite tokamak power plants
Energy Technology Data Exchange (ETDEWEB)
Bathke, C.G. [Los Alamos National Lab., NM (United States)
1996-12-31
The ARIES team has assessed the power-plant attractiveness of the following five tokamak physics regimes: (1) steady state, first stability regime; (2) pulsed, first stability regime; (3) steady state, second stability regime; (4) steady state, reversed shear; and (5) steady state, low aspect ratio. Cost-based systems analysis of these five tokamak physics regimes suggests that an electric power plant based upon a reversed-shear tokamak is significantly more economical than one based on any of the other four physics regimes. Details of this comparative systems analysis are described herein. 11 refs., 3 figs., 1 tab.
A systems assessment of the five Starlite tokamak power plants
Energy Technology Data Exchange (ETDEWEB)
Bathke, C.G.
1996-07-01
The ARIES team has assessed the power-plant attractiveness of the following five tokamak physics regimes: (1) steady state, first stability regime; (2) pulsed, first stability regime; (3) steady state, second stability regime; (4) steady state, reversed shear; and (5) steady state, low aspect ratio. Cost-based systems analysis of these five tokamak physics regimes suggests that an electric power plant based upon a reversed-shear tokamak is significantly more economical than one based on any of the other four physics regimes. Details of this comparative systems analysis are described herein.
Nonlinear stabilization of tokamak microturbulence by fast ions
Citrin, J; Garcia, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Johnson, T; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.
Ions Measurement at the Edge of HT-7 Tokamak
Institute of Scientific and Technical Information of China (English)
Ling Bili; Wang Enyao; Gao wei; Wan Baonian; Li Jiangang
2005-01-01
A reliable method of measuring ions and ion temperature in tokamak plasma is necessary, for which an omegatron-like instrument has been developed on the HT-7 tokamak. The basic layout of the omegatron-like instrument is shown in this article. The measurement of working gas ion has been performed in the last experimental campaign on HT-7 tokamak. The relations among ion current, the electron repeller voltage and trap voltage have been investigated. This omegatron-like instrument has also provided the edge-plasma ion temperature.
Power Deposition on Tokamak Plasma-Facing Components
Arter, Wayne; Fishpool, Geoff
2014-01-01
The SMARDDA software library is used to model plasma interaction with complex engineered surfaces. A simple flux-tube model of power deposition necessitates the following of magnetic fieldlines until they meet geometry taken from a CAD (Computer Aided Design) database. Application is made to 1) models of ITER tokamak limiter geometry and 2) MASTU tokamak divertor designs, illustrating the accuracy and effectiveness of SMARDDA, even in the presence of significant nonaxisymmetric ripple field. SMARDDA's ability to exchange data with CAD databases and its speed of execution also give it the potential for use directly in the design of tokamak plasma facing components.
Thermodynamic assessment of hydrothermal alkali feldspar-mica-aluminosilicate equilibria
Sverjensky, Dimitri A.; Hemley, J. J.; D'angelo, W. M.
1991-04-01
The thermodynamic properties of minerals retrieved from consideration of solid-solid and dehydration equilibria with calorimetric reference values, and those of aqueous species derived from studies of electrolytes, are not consistent with experimentally measured high-temperature solubilities in the systems K 2O- and Na 2O-Al 2O 3-SiO 2-H 2O-HCl (e.g., K-fs - Ms - Qtz - K + - H +). This introduces major inaccuracies into the computation of ionic activity ratios and the acidities of diagenetic, metamorphic, and magmatic hydrothermal fluids buffered by alkali silicate-bearing assemblages. We report a thermodynamic analysis of revised solubility equilibria in these systems that integrates the thermodynamic properties of minerals obtained from phase equilibria studies ( BERMAN, 1988) with the properties of aqueous species calculated from a calibrated equation of state ( SHOCK and HELGESON, 1988). This was achieved in two separate steps. First, new values of the free energies and enthalpies of formation at 25°C and 1 bar for the alkali silicates muscovite and albite were retrieved from the experimental solubility equilibria at 300°C and P sat. Because the latter have stoichiometric reaction coefficients different from those for solid-solid and dehydration equilibria, our procedure preserves exactly the relative thermodynamic properties of the alkali-bearing silicates ( BERMAN, 1988). Only simple arithmetic adjustments of -1,600 and -1,626 ( ±500) cal/mol to all the K- and Na-bearing silicates, respectively, in BERMAN (1988) are required. In all cases, the revised values are within ±0.2% of calorimetric values. Similar adjustments were derived for the properties of minerals from HELGESON et al. (1978). Second, new values of the dissociation constant of HCl were retrieved from the solubility equilibria at temperatures and pressures from 300-600°C and 0.5-2.0 kbars using a simple model for aqueous speciation. The results agree well with the conductance
Phase equilibria in the In–Sb–Bi system at 300 ºC
Directory of Open Access Journals (Sweden)
DUSKO MINIC
2006-07-01
Full Text Available Binary thermodynamic data, successfully used for phase diagram calculations of the binary systems In–Sb, Bi–Sb and In–Bi, were used fort the prediction of phase equilibria in the ternary system In–Sb–Bi at 300 ºC. The predicted equilibria were compared with the results of SEM–EDX analysis.
Looking for multiple equilibria when geography matters : German city growth and the WWII shock
Bosker, Maarten; Brakman, Steven; Garretsen, Harry; Schramm, Marc
2007-01-01
Based on the methodology of Davis and Weinstein, we look for multiple equilibria in German city growth. Bytaking the bombing of Germany during WWII as an example of a large, temporary shock, we analyze whether German city growth is characterized by multiple equilibria. In doing so, we allow for spat
Tokamak Plasmas : Internal magnetic ﬁeld measurement in tokamak plasmas using a Zeeman polarimeter
Indian Academy of Sciences (India)
M Jagadeeshwari; J Govindarajan
2000-11-01
In a tokamak plasma, the poloidal magnetic ﬁeld proﬁle closely depends on the current density proﬁle. We can deduce the internal magnetic ﬁeld from the analysis of circular polarization of the spectral lines emitted by the plasma. The theory of the measurement and a detailed design of the Zeeman polarimeter constructed to measure the poloidal ﬁeld proﬁle in the ADITYA tokamak are presented. The Fabry-Perot which we have employed in our design, with photodiode arrays followed by lock-in detection of the polarization signal, allows the measurement of the fractional circular polarization. In this system He-II line with wavelength 4686 Å is adopted as the monitoring spectral line. The line emission used in the present measurement is not well localized in the plasma, necessiating the use of a spatial inversion procedure to obtain the local values of the ﬁeld.
On multicomponent adsorption equilibria of xylene mixtures on zeolites
Energy Technology Data Exchange (ETDEWEB)
Paludetto, R.; Storti, G.; Gamba, G.; Carra, S.; Morbidelli, M.
1987-11-01
Adsorption equilibria of two ternary systems involving m-xylene, p-xylene, and either toluene or isopropylbenzene on zeolite K-Y have been studied. Due to nonideal behavior of the adsorbed phase, m- and p-xylene selectivity is strongly dependent upon composition. In particular, it is found that the addition of a third component can either enhance or depress such selectivity values. Ternary experimental data are well predicted by the developed equilibrium model, whose parameters can be estimated based only on experimental data relative to pure and binary mixtures. Finally, the role of these nonidealities in the equilibrium behavior on the dynamics of adsorption separation columns is discussed.
Liquid-liquid equilibria for ternary polymer mixtures
Oh, Suk Yung; Bae, Young Chan
2011-01-01
A molecular thermodynamic model for multicomponent systems based on a closed-packed lattice model is presented based on two contributions; entropy and energy contribution. The calculated liquid-liquid equilibria of ternary chainlike mixtures agreed with Monte Carlo simulation results. The proposed model can satisfactorily predict Types 0, 1, 2 and 3 phase separations of the Treybal classification. The model parameters obtained from the binary systems were used to directly predict real ternary systems and the calculated results correlated well with experimental data using few adjustable parameters. Specific interactions in associated binary systems were considered using a secondary lattice.
On Pure and (approximate) Strong Equilibria of Facility Location Games
DEFF Research Database (Denmark)
Hansen, Thomas Dueholm; Telelis, Orestis A.
2008-01-01
We study social cost losses in Facility Location games, where n selfish agents install facilities over a network and connect to them, so as to forward their local demand (expressed by a non-negative weight per agent). Agents using the same facility share fairly its installation cost, but every...... networks we prove upper and lower bounds on PoS, while an O(ln n) upper bound implied by previous work is tight for non-metric networks. We also prove a constant upper bound for the SPoA of metric networks when strong equilibria exist. For the weighted game on general networks we prove existence of e...
Anomeric and tautomeric equilibria in D-2-glucosamine Schiff bases
Kołodziej, B.; Grech, E.; Schilf, W.; Kamieński, B.; Makowski, M.; Rozwadowski, Z.; Dziembowska, T.
2007-11-01
The structure of some glucosamine Schiff bases has been studied by means of ab initio RHF and DFT calculation and CP/MAS 13C and 15N NMR measurements. The anomeric and tautomeric equilibria in a DMSO solution have been studied by 1H, 13C and 15N NMR spectroscopy. The anomeric composition of D-2-glucosamine Schiff bases in the solid state and in DMSO solution has been shown to depends on the tautomeric form of Schiff bases and electronic properties of substituents on the aromatic ring.
Application of conformal solution theory to gas-gas equilibria
Energy Technology Data Exchange (ETDEWEB)
Tan, P.Y.; Luks, K.D.; Kozak, J.J.
1971-08-01
The conformal solution theory (CST) is applied to the problem of gas-gas immiscibility. It is found that the occurrence of this phenomena can be predicted in the system He-Xe; in particular, the calculated critical locus is in satisfactory agreement with the experimental data of de Swaan Arons and Diepen, provided a suitable reference is chosen. Furthermore, using CST as a guide, it was found that criteria could be developed, related to Temkin's criteria, which permit the prediction and classification of the 3 types of gas-gas equilibria known to occur in mixtures of nonpolar molecules. (10 refs.)
Cryptographically Blinded Games: Leveraging Players' Limitations for Equilibria and Profit
DEFF Research Database (Denmark)
Hubacek, Pavel; Park, Sunoo
2014-01-01
In this work we apply methods from cryptography to enable mutually distrusting players to implement broad classes of mediated equilibria of strategic games without trusted mediation. Our implementation uses a pre-play 'cheap talk' phase, consisting of non- binding communication between players pr...... prior to play in the original game. In the cheap talk phase, the players run a secure multi-party computation protocol to sample from an equilibrium of a "cryptographically blinded" version of the game, in which actions are encrypted...
Solitonlike solutions of magnetostatic equilibria: Plane-symmetric case
Yoshino, Hirotaka
2008-01-01
We present the plane-symmetric solitonlike solutions of magnetostatic equilibria by solving the nonlinear Grad-Shafranov (GS) equation numerically. The solutions have solitonlike and periodic structures in the $x$ and $y$ directions, respectively, and $z$ is the direction of plane symmetry. Although such solutions are unstable against the numerical iteration, we give the procedure to realize the sufficient convergence. Our result provides the definite answer for the existence of the solitonlike solutions that was questioned in recent years. The method developed in this paper will make it possible to study the axisymmetric solitonlike solutions of the nonlinear GS equation, which could model astrophysical jets with knotty structures.
Nas-Walras equilibria of a large economy.
Minelli, E; Polemarchakis, H M
2000-05-09
Individuals exchange contracts for the delivery of commodities in competitive markets and, simultaneously, act strategically; actions affect utilities across individuals directly or through the payoffs of contracts. This encompasses economies with asymmetric information. Nash-Walras equilibria exist for large economies, even if utility functions are not quasi-concave and choice sets are not convex, which is the case in standard settings; the separation of the purchase from the sale of contracts and the pooling of the deliveries on contracts guarantee that the markets for commodities clear.
A new trial of tokamak in-vessel inspection manipulator
Energy Technology Data Exchange (ETDEWEB)
Du, Liang; Yuan, Jianjun, E-mail: yuanjj@sjtu.edu.cn; Zhang, Weijun; Li, Fashe
2015-10-15
In this paper, we discuss the design and partial implementation of an in-vessel inspection manipulator in detail, which is considered to serve for China's Experimental Advanced Superconducting Tokamak (EAST). Besides the ordinary kinematic/dynamic constraints and specifications for a multiple degrees of freedom (DOF) manipulator suitable for EAST in-vessel inspection, there is extra necessity in design for the extreme in-vessel environment, e.g., high temperature and high vacuum. Based on our recent developed active cooling system, a specific proposal is explored, which employs ordinary commercial mechanical/electrical components only, as if the manipulator works in normal temperature environment. This paper also emphasizes some challenging technical issues toward an implementation, such as an optimization of thermal gradient/cooling path in the manipulator, a trade-off between large reachable space and large rotation angle of each joint, a special designed revolute joint structure for cooling tube arrangement and so on. We use an EtherCAT based real time control platform connecting drivers and sensors, which achieves a robust closed-loop system and a clean cable aspect simultaneously. In the later part of the paper, basic mechanical tests and inspection process are described. Evaluation on recent progress and future work toward a whole-scale test is stated and expected.
Initial Plasma Startup Test on SUNIST Spherical Tokamak
Institute of Scientific and Technical Information of China (English)
Wang Ying(王莹); Zeng Li(曾立); He Yexi(何也熙); SUMST Team
2003-01-01
The goal of the Sino-United Spherical Tokamak (SUNIST) at Tsinghua University is to extend the understanding of toroidal plasma physics at a low aspect ratio (R/a ≈ 1.3) and to demonstrate a maintainable target plasma by non-inductive startup. The SUNIST device is designed to operate with up to 13 kA of ohmic heating field current, and to 0.15 T of toroidal field at 10 kA of discharge current. All of the poloidal fields can provide 30 mVs of Volt-seconds transformer. Experimental results of plasma startup show that SUNIST has remarkable characteristics of high ramp rate (dIp/dt ≈ 50 MA/s ), high normalized current IN of about 2.8 (IN = Ip/aBT),and high-efficiency (Ip/IROD ≈ 0.4) production of plasma current while operating at a low toroidal field. Major disruption phenomena have not been observed from magnetic diagnostics of all testing shots. Initial discharges with 52 kA of plasma current (exceeding the designed value of 50 kA),2 ms of pulse length and 50 MA/s of ramp rate have been achieved easily with pre-ionized filament.
Tokamak Plasmas : Observation of ﬂoating potential asymmetry in the edge plasma of the SINP tokamak
Indian Academy of Sciences (India)
Krishnendu Bhattacharyya; N R Ray
2000-11-01
Edge plasma properties in a tokamak is an interesting subject of study from the view point of conﬁnement and stability of tokamak plasma. The edge plasma of SINP-tokamak has been investigated using specially designed Langmuir probes. We have observed a poloidal asymmetry of ﬂoating potentials, particularly the top-bottom ﬂoating potential differences are quite noticeable, which in turn produces a vertical electric ﬁeld (v). This v remains throughout the discharge but changes its direction at certain point of time which seems to depend on applied vertical magnetic ﬁeld v).
Quasi-Leontief utility functions on partially ordered sets II: Nash equilibria
Briec, Walter; Horvath, Charles
2011-01-01
We prove that, under appropriate conditions, an abstract game with quasi-Leontief payoff functions $u_i : \\prod_{j=1}^nX_j\\to\\mathbb{R}$ has a Nash equilibria. When all the payoff functions are globally quasi-Leontief, the existence and the characterization of efficient Nash equilibria mainly follows from the analysis carried out in part I. When the payoff functions are individually quasi-Leontief functions the matter is somewhat more complicated. We assume that all the strategy spaces are compact topological semilattices, and under appropriate continuity conditions on the payoff functions, we show that there exists an efficient Nash equilibria using the Eilenberg-Montgomery Fixed Point Theorem for acyclic valued upper semicontinuous maps defined on an absolute retract and some non trivial properties of topological semilattices. The map in question is defined on the set of Nash equilibria and its fixed points are exactly the efficient Nash equilibria.
Equilibrium reconstruction in the TCA/Br tokamak; Reconstrucao do equilibrio no tokamak TCA/BR
Energy Technology Data Exchange (ETDEWEB)
Sa, Wanderley Pires de
1996-12-31
The accurate and rapid determination of the Magnetohydrodynamic (MHD) equilibrium configuration in tokamaks is a subject for the magnetic confinement of the plasma. With the knowledge of characteristic plasma MHD equilibrium parameters it is possible to control the plasma position during its formation using feed-back techniques. It is also necessary an on-line analysis between successive discharges to program external parameters for the subsequent discharges. In this work it is investigated the MHD equilibrium configuration reconstruction of the TCA/BR tokamak from external magnetic measurements, using a method that is able to fast determine the main parameters of discharge. The thesis has two parts. Firstly it is presented the development of an equilibrium code that solves de Grad-Shafranov equation for the TCA/BR tokamak geometry. Secondly it is presented the MHD equilibrium reconstruction process from external magnetic field and flux measurements using the Function Parametrization FP method. this method. This method is based on the statistical analysis of a database of simulated equilibrium configurations, with the goal of obtaining a simple relationship between the parameters that characterize the equilibrium and the measurements. The results from FP are compared with conventional methods. (author) 68 refs., 31 figs., 16 tabs.
Impact of physics and technology innovations on compact tokamak fusion pilot plants
Menard, Jonathan
2016-10-01
For magnetic fusion to be economically attractive and have near-term impact on the world energy scene it is important to focus on key physics and technology innovations that could enable net electricity production at reduced size and cost. The tokamak is presently closest to achieving the fusion conditions necessary for net electricity at acceptable device size, although sustaining high-performance scenarios free of disruptions remains a significant challenge for the tokamak approach. Previous pilot plant studies have shown that electricity gain is proportional to the product of the fusion gain, blanket thermal conversion efficiency, and auxiliary heating wall-plug efficiency. In this work, the impact of several innovations is assessed with respect to maximizing fusion gain. At fixed bootstrap current fraction, fusion gain varies approximately as the square of the confinement multiplier, normalized beta, and major radius, and varies as the toroidal field and elongation both to the third power. For example, REBCO high-temperature superconductors (HTS) offer the potential to operate at much higher toroidal field than present fusion magnets, but HTS cables are also beginning to access winding pack current densities up to an order of magnitude higher than present technology, and smaller HTS TF magnet sizes make low-aspect-ratio HTS tokamaks potentially attractive by leveraging naturally higher normalized beta and elongation. Further, advances in kinetic stabilization and feedback control of resistive wall modes could also enable significant increases in normalized beta and fusion gain. Significant reductions in pilot plant size will also likely require increased plasma energy confinement, and control of turbulence and/or low edge recycling (for example using lithium walls) would have major impact on fusion gain. Reduced device size could also exacerbate divertor heat loads, and the impact of novel divertor solutions on pilot plant configurations is addressed. For
Toroidicity Dependence of Tokamak Edge Safety Factor and Shear
Institute of Scientific and Technical Information of China (English)
SHIBingren
2002-01-01
In large tokamak device and reactor designs, the relationship between the toroidal current and the edge safety factor is very important because this will determine the eventual device or reactor size according to MHD stability requirements. In many preliminary
Compact Ignition Tokamak Program: status of FEDC studies
Energy Technology Data Exchange (ETDEWEB)
Flanagan, C.A.
1985-01-01
Viewgraphs on the Compact Ignition Tokamak Program comprise the report. The technical areas discussed are the mechanical configuration status, magnet analysis, stress analysis, cooling between burns, TF coil joint, and facility/device layout options. (WRF)
Tokamak Start-up under Assistance of RF Waves
Institute of Scientific and Technical Information of China (English)
方瑜德
2004-01-01
To improve the start-up behavior of tokamak discharges and realize the low loop voltage start-up is required by performance of large scale, full superconductor tokamaks. In recent years, some kinds of RF wave have been used to assist the start-up and some exciting results have been gained. This paper introduce the investigation on both in physical principle and experimental research of the start-up process, in which high frequency RF waves were used to assist it.
NEOCLASSICAL TRANSPORT IN A TOKAMAK WITH ELECTRIC SHEAR
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Neoclassical transport theory for a tokamak in the presence of a large radial electric field with shear is developed using Hamiltonian formalism. Diffusion coefficients are derived in both the plateau and banana regimes where the squeezing factor in coefficients can greatly affect diffusion at the plasma edge. Rotation speeds are calculated in the scrape-off region. They are in good agreement with the measurements on the TdeV tokamak.
Phase equilibria in polydisperse nonadditive hard-sphere systems.
Paricaud, Patrice
2008-08-01
Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.
Phase equilibria in model surfactants forming Langmuir monolayers.
Ramírez, E; Santana, A; Cruz, A; López, G E
2007-12-14
The study of Langmuir monolayers has generated the attention of researchers because of their unique properties and their not well understood phase equilibrium. These monolayers exhibit interesting phase diagrams where the unusual liquid-liquid equilibrium can be observed for a single component monolayer. Monte Carlo computer simulations in the virtual Gibbs ensemble were used to obtain the phase diagram of Langmuir monolayers. The liquid-vapor and liquid-liquid phase equilibria were considered by constructing the Cailletet-Mathias phase diagrams. By using the Ising model and the rectilinear approximations the identification of the critical properties for both equilibria was determined. These critical parameters were calculated as a function of the strength of the interaction between the surfactant molecules and the aqueous subphase. As a result, we have identified the coexistence between a liquid expanded state (LES)-vapor and the liquid condensed state-LES, in agreement with experimental and theoretical evidence in the literature. We obtained a clear separation of phases and a strong dependence on the strength of the solvent used. Namely, as the interaction between the solvent and the head of the surfactant increases, the critical properties also increase. Equilibrium states were characterized by computing thermodynamic quantities as a function of temperature and solvent strength.
Stability of Hall equilibria in neutron star crusts
Marchant, Pablo; Valdivia, Juan Alejandro; Hoyos, Jaime H
2014-01-01
In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stab...
Conformational equilibria and intrinsic affinities define integrin activation.
Li, Jing; Su, Yang; Xia, Wei; Qin, Yan; Humphries, Martin J; Vestweber, Dietmar; Cabañas, Carlos; Lu, Chafen; Springer, Timothy A
2017-03-01
We show that the three conformational states of integrin α5β1 have discrete free energies and define activation by measuring intrinsic affinities for ligand of each state and the equilibria linking them. The 5,000-fold higher affinity of the extended-open state than the bent-closed and extended-closed states demonstrates profound regulation of affinity. Free energy requirements for activation are defined with protein fragments and intact α5β1 On the surface of K562 cells, α5β1 is 99.8% bent-closed. Stabilization of the bent conformation by integrin transmembrane and cytoplasmic domains must be overcome by cellular energy input to stabilize extension. Following extension, headpiece opening is energetically favored. N-glycans and leg domains in each subunit that connect the ligand-binding head to the membrane repel or crowd one another and regulate conformational equilibria in favor of headpiece opening. The results suggest new principles for regulating signaling in the large class of receptors built from extracellular domains in tandem with single-span transmembrane domains.
State-of-the-art review of phase equilibria
Energy Technology Data Exchange (ETDEWEB)
Prausnitz, J.M.
1980-03-01
High-pressure phase-equilibrium calculations using an equation of state are more sensitive to the mixing rules than to details in the effect of density or temperature on pressure. Attention must be given to the problem of how to extend equations of state to mixtures. One possible technique is provided by perturbation theory; another by superposition of chemical equilibria. At low or moderate pressures, vapor-phase corrections are often important. When specific intermolecular forces produce formation of molecular aggregates, strong deviations from ideal-gas behavior can be significant even at pressures well below 1 bar. When vapor-liquid equilibrium data are reduced using conventional expressions for the excess Gibbs energy, the resulting binary parameters tend to be partially correlated, it difficult, but no impossible, to calculate ternary liquid-liquid equilibria using binary parameters only. New models for calculating properties of liquid-phase mixtures mist allow for changes in free volume to give consideration to the effect of mixing on changes in rotational and vibrational degrees of freedom. Liquid-phase volumetric effects are also important in describing the solubilities of gases in solvent mixtures. Therefore, future liquid-phase models should incorporate a liquid-phase equation of state, either of the van der Waals type or, perhaps, as given by the direct-correlation function theory of liquids.
DIII-D Advanced Tokamak Research Overview
Energy Technology Data Exchange (ETDEWEB)
V.S. Chan; C.M. Greenfield; L.L. Lao; T.C. Luce; C.C. Petty; G.M. Staebler
1999-12-01
This paper reviews recent progress in the development of long-pulse, high performance discharges on the DIII-D tokamak. It is highlighted by a discharge achieving simultaneously {beta}{sub N}H of 9, bootstrap current fraction of 0.5, noninductive current fraction of 0.75, and sustained for 16 energy confinement times. The physics challenge has changed in the long-pulse regime. Non-ideal MHD modes are limiting the stability, fast ion driven modes may play a role in fast ion transport which limits the stored energy and plasma edge behavior can affect the global performance. New control tools are being developed to address these issues.
Vertically stabilized elongated cross-section tokamak
Sheffield, George V.
1977-01-01
This invention provides a vertically stabilized, non-circular (minor) cross-section, toroidal plasma column characterized by an external separatrix. To this end, a specific poloidal coil means is added outside a toroidal plasma column containing an endless plasma current in a tokamak to produce a rectangular cross-section plasma column along the equilibrium axis of the plasma column. By elongating the spacing between the poloidal coil means the plasma cross-section is vertically elongated, while maintaining vertical stability, efficiently to increase the poloidal flux in linear proportion to the plasma cross-section height to achieve a much greater plasma volume than could be achieved with the heretofore known round cross-section plasma columns. Also, vertical stability is enhanced over an elliptical cross-section plasma column, and poloidal magnetic divertors are achieved.
Sliding Mode Control of a Tokamak Transformer
Energy Technology Data Exchange (ETDEWEB)
Romero, J. A.; Coda, S.; Felici, F.; Moret, J. M.; Paley, J.; Sevillano, G.; Garrido, I.; Le, H. B.
2012-06-08
A novel inductive control system for a tokamak transformer is described. The system uses the flux change provided by the transformer primary coil to control the electric current and the internal inductance of the secondary plasma circuit load. The internal inductance control is used to regulate the slow flux penetration in the highly conductive plasma due to the skin effect, providing first-order control over the shape of the plasma current density profile. Inferred loop voltages at specific locations inside the plasma are included in a state feedback structure to improve controller performance. Experimental tests have shown that the plasma internal inductance can be controlled inductively for a whole pulse starting just 30ms after plasma breakdown. The details of the control system design are presented, including the transformer model, observer algorithms and controller design. (Author) 67 refs.
MHD stability limits in the TCV Tokamak
Energy Technology Data Exchange (ETDEWEB)
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation {kappa} and triangularity {delta}, with high {kappa}, and low {delta} leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The
Advantages of iron core in a tokamak
Energy Technology Data Exchange (ETDEWEB)
Bettis, E.S.; Ballou, J.K.; Becraft, W.R.; Peng, Y.K.M.; Watts, H.L.
1977-01-01
A quantitative comparison of the iron core vs air core concepts was carried out on a preliminary basis by using a representative tokamak reactor design with the following self-consistent reference parameters. In the area of plasma engineering, poloidal field and MHD equilibrium considerations with an unsaturated iron core is discussed. The question of proper poloidal field coils to maintain D-shaped plasmas of relatively high anti ..beta.. (7%) with a saturated iron core is also discussed. Estimates of the required iron core size, volt seconds, magnetic flux and its influence on force loading on the superconducting toroidal field coils are shown. Conceptual designs of the mechanical structure of an iron core device are presented. Favorable impacts on the OH power supply cost and complexity are indicated.
Dissipative nonlinear structures in tokamak plasmas
Directory of Open Access Journals (Sweden)
K. A. Razumova
2001-01-01
Full Text Available A lot of different kinds of instabilities may be developed in high temperature plasma located in a strong toroidal magnetic field (tokamak plasma. Nonlinear effects in the instability development result in plasma self-organization. Such plasma has a geometrically complicated configuration, consisting of the magnetic surfaces imbedded into each other and split into islands with various characteristic numbers of helical twisting. The self-consistency of the processes means that the transport coefficients in plasma do not depend just on the local parameters, being a function of the whole plasma configuration and of the forces affecting it. By disrupting the bonds between separate magnetic surfaces filled with islands, one can produce zones of reduced transport in the plasma, i.e. “internal thermal barriers”, allowing one essentially to increase the plasma temperature and density.
Nonlinear lower hybrid modeling in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Napoli, F.; Schettini, G. [Università Roma Tre, Dipartimento di Ingegneria, Roma (Italy); Castaldo, C.; Cesario, R. [Associazione EURATOM/ENEA sulla Fusione, Centro Ricerche Frascati (Italy)
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
A lithium deposition system for tokamak devices*
Graziul, Christopher; Majeski, Richard; Kaita, Robert; Hoffman, Daniel; Timberlake, John; Card, David
2002-11-01
The production of a lithium deposition system using commercially available components is discussed. This system is intended to provide a fresh lithium wall coating between discharges in a tokamak. For this purpose, a film 100-200 Å thick is sufficient to ensure that the plasma interacts solely with the lithium. A test system consisting of a lithium evaporator and a deposition monitor has been designed and constructed to investigate deposition rates and coverage. A Thermionics 3kW e-gun is used to rapidly evaporate small amounts of solid lithium. An Inficon XTM/2 quartz deposition monitor then measures deposition rate at varying distances, positions and angles relative to the e-gun crucible. Initial results from the test system will be presented. *Supported by US DOE contract #DE-AC02-76CH-03073
Transport Bifurcation in a Rotating Tokamak Plasma
Highcock, E G; Schekochihin, A A; Parra, F I; Roach, C M; Cowley, S C
2010-01-01
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all non-zero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.
General Tokamak Circuit Simulation Program-GTCSP
Energy Technology Data Exchange (ETDEWEB)
Matsukawa, Makoto; Miura, Yushi [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Aoyagi, Tetsuo
1997-05-01
General Tokamak Circuit Simulation Program (GTCSP) was originally developed for the design work of JT-60 Power Supply System in JAERI. Therefore the prepared models (components) to be analyzed are generator, thyristor converter and coils. This is one of the unique points of GTCSP in comparison with other conventional electric circuit analysis program, because they make a circuit from the small devices such as resister, coil, condenser, transistor and so on. However, GTCSP is also clearly conventional because it is possible to construct an electric circuit freely with the prepared components. Moreover, a similar function could be realized by addition a new component to GTCSP. This report is assumed to be used as an User Manual of the GTCSP, not only to present the development and the analytical functions. Then some useful examples are described, and how to get graphic outputs are also mentioned. (author)
Safety factor profile control in a tokamak
Bribiesca Argomedo, Federico; Prieur, Christophe
2014-01-01
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The t...
Energy Technology Data Exchange (ETDEWEB)
Caldino H, U.; Francois L, J. L., E-mail: ucaldino@outlook.com [UNAM, Facultad de Ingenieria, Departamento de Sistemas Energeticos, Paseo Cuauhnahuac 8532, 62550 Jiutepec, Morelos (Mexico)
2014-10-15
The TPM1 is a small Tokamak that belongs to the Centro de Investigacion en Ciencias Aplicadas y Tecnologia Avanzada of Instituto Politecnico Nacional (CICATA-IPN); the project is under construction. Currently it has the vacuum chamber, and is intended that the machine can operate with electric pulses of 10 ms to study the behavior of plasmas in order to provide knowledge in the field of nuclear fusion by magnetic confinement. To achieve this goal is necessary to design the toroidal field coils which operate the Tokamak. This paper presents an analysis which was performed to obtain the correct configuration of coils depending on design parameters for operation of the machine. Once determined this configuration, an analysis of electromagnetic forces present in normal machine operation on one coil was conducted, this to know the stresses in the encapsulation of the same. Considering the pulsed operation, a thickness of 5 mm is determined in the encapsulated, considering fatigue failure based on studies of fatigue failures in epoxy resins. (Author)
Characterization and scaling of the tokamak edge transport barrier
Energy Technology Data Exchange (ETDEWEB)
Schneider, Philip Adrian
2012-04-24
The high confinement regime (H-mode) in a tokamak plasma displays a remarkable edge region. On a small spatial scale of 1-2 cm the properties of the plasma change significantly. Certain parameters vary 1-2 orders of magnitude in this region, called the pedestal. Currently, there is no complete understanding of how the pedestal forms or how it is sustained. The goal of this thesis is to contribute to the theoretical understanding of the pedestal and provide scalings towards larger machines, like ITER and DEMO. A pedestal database was built with data from different tokamaks: ASDEX Upgrade, DIIID and JET. The pedestal was characterized with the same method for all three machines. This gives the maximum value, gradient and width of the pedestal in n{sub e}, T{sub e} and T{sub i}. These quantities were analysed along with quantities derived from them, such as the pressure or the confinement time. For this purpose two parameter sets were used: normalized parameters (pressure {beta}, time {nu}{sub *}, length {rho}{sub *}, shape f{sub q}) and machine parameters (size a, magnetic field B{sub t}, plasma current I{sub p}, heating P). All results are dependent on the choice of the coordinate system: normalized poloidal flux {Psi}{sub N} and real space r/a. The most significant result, which was obtained with both parameter sets, shows a different scaling of the pedestal width for the electron temperature and the electron density. The presented scalings predict that in ITER and DEMO the temperature pedestal will be appreciably wider than the density pedestal. The pedestal top scaling for the pressure reveals differences between the electron and the ion pressure. In extrapolations this results in values for T{sub e,ped} of 4 keV (ITER) and 10 keV (DEMO), but significantly lower values for the ion temperature. A two-term method was applied to use the pedestal pressure to determine the pedestal contribution to the global confinement time {tau}{sub E}. The dependencies in the
Social Interactions under Incomplete Information: Games, Equilibria, and Expectations
Yang, Chao
My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter "A Tobit Model with Social
Duong, Manh Hong; Han, The Anh
2016-12-01
In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, [Formula: see text], and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as [Formula: see text] as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.
Noori, Ehsanallah; Sadeghi, Yahya; Ghoranneviss, Mahmood
2016-10-01
In this study, magnetic measurement of poloidal fields were used to determine poloidal beta and plasma internal inductance of Damavand tokamak combination of poloidal beta and plasma internal inductance (β _p+{l_i}/{2} ), known as Shafranov parameter, was obtained experimentally in terms of normal and tangential components of the magnetic field. Plasma internal inductance and poloidal beta were obtained using parametrization method based on analytical solution of Grad-Shafranov equation (GSE) and compared with parabolic-like profile of toroidal current density approach for determination of the plasma internal inductance. Finding evolution of β _p+{l_i}/{2} and plasma internal inductance. Finding poloidal beta (Shafranov parameter and internal inductance) and using energy balance equation, thermal energy and energy confinement were determined qualitatively in terms of poloidal beta during a regular discharge of Damavand tokamak.
Relevant parameter space and stability of spherical tokamaks with a plasma center column
Lampugnani, L. G.; Garcia-Martinez, P. L.; Farengo, R.
2017-02-01
A spherical tokamak (ST) with a plasma center column (PCC) can be formed inside a simply connected chamber via driven magnetic relaxation. From a practical perspective, the ST-PCC could overcome many difficulties associated with the material center column of the standard ST reactor design. Besides, the ST-PCC concept can be regarded as an advanced helicity injected device that would enable novel experiments on the key physics of magnetic relaxation and reconnection. This is because the concept includes not only a PCC but also a coaxial helicity injector (CHI). This combination implies an improved level of flexibility in the helicity injection scheme required for the formation and sustainment phases. In this work, the parameter space determining the magnetic structure of the ST-PCC equilibria is studied under the assumption of fully relaxed plasmas. In particular, it is shown that the effect of the external bias field of the PCC and the CHI essentially depends on a single parameter that measures the relative amount of flux of these two entities. The effect of plasma elongation on the safety factor profile and the stability to the tilt mode are also analyzed. In the first part of this work, the stability of the system is explained in terms of the minimum energy principle, and relevant stability maps are constructed. While this picture provides an adequate insight into the underlying physics of the instability, it does not include the stabilizing effect of line-tying at the electrodes. In the second part, a dynamical stability analysis of the ST-PCC configurations, including the effect of line-tying, is performed by numerically solving the magnetohydrodynamic equations. A significant stability enhancement is observed when the PCC contains more than the 70% of the total external bias flux, and the elongation is not higher than two.
Lower Hybrid Wave Current Drive Efficiency on the HT-7 Tokamak
Institute of Scientific and Technical Information of China (English)
CHEN Zhong-Yong; WAN Bao-Nian; SHI Yue-Jiang; HU Li-Qun; XU Han-Dong; LI Guo-Chao
2005-01-01
@@ Lower hybrid (LH) wave current drive efficiency on our HT-7 tokamak has been investigated based on the hot electrical conductivity theory.The interaction of the residual toroidal electric field with fast electrons has been included in the determination of current drive efficiency.The LH wave power scan was performed in the plasma parameter ranges of Ip = 50-156kA, (n)e = 0.5 × 1019-1.6 × 1019 m-3, PLH = 50-350kW.The current drive efficiency is derived to be about 0.1 × 1019-0.4 × 1019 Am-2W-1 on the HT-7 tokamak, which depends on the electron density and the LH wave phase velocity.At the electron density of about 1.5 × 1019 m-3, with the LH wave parallel refraction index peaked at 1.8, the highest current drive efficiency was obtained.A more generally normalized method is introduced to analyse the experimental data, which combines all the data in one curve.The normalized parameters are independent of the plasma parameters.
CONTROL OF MHD STABILITY IN DIII-D ADVANCED TOKAMAK DISCHARGES
Energy Technology Data Exchange (ETDEWEB)
STRAIT,EJ; BIALEK,J; CHANCE,MS; CHU,MS; EDGELL,DH; FERRON,JR; GREENFIELD,CM; GAROFALO,AM; HUMPHREYS,DA; JACKSON,GL; JAYAKUMAR,RJ; JERNIGAN,TC; KIM,JS; LA HAYE,RJ; LAO,LL; LUCE,TC; MAKOWSKI,MA; MURAKAMI,M; NAVRATIL,GA; OKABAYASHI,M; PETTY,CC; REIMERDES,H; SCOVILLE,JT; TURNBULL,AD; WADE,MR; WALKER,ML; WHYTE,DG; DIII-D TEAM
2003-06-01
OAK-B135 Advanced tokamak research in DIII-D seeks to optimize the tokamak approach for fusion energy production, leading to a compact, steady state power source. High power density implies operation at high toroidal beta, {beta}{sub T}=
2{micro}{sub 0}/B{sub T}{sup 2}, since fusion power density increases roughly as the square of the plasma pressure. Steady-state operation with low recirculating power for current drive implies operation at high poloidal beta, {beta}{sub P} =
2{micro}{sub 0}/{sup 2}, in order to maximize the fraction of self-generated bootstrap current. Together, these lead to a requirement of operation at high normalized beta, {beta}{sub N} = {beta}{sub T}(aB/I), since {beta}{sub P}{beta}{sub T} {approx} 25[(1+{kappa}{sup 2})/2] ({beta}{sub N}/100){sup 2}. Plasmas with high normalized beta are likely to operate near one or more stability limits, so control of MHD stability in such plasmas is crucial.
Numbers of Relative Equilibria in the Planar Four-Vortex Problem: Some Special Cases
Tsai, Ya-Lun
2016-11-01
Three planar four-vortex problems are considered in this paper. In the (3+1) -vortex problem, we study the relative equilibria of the four point vortices when one vortex has zero vorticity and the other three with nonzero vorticities form an equilateral triangle. In the (1+3) -vortex problem, we study the limiting cases of the relative equilibria when one of the four point vortices has fixed nonzero vorticity and other vorticities approach zero. The third problem is the case of vanishing total vorticity. All problems involve two real vorticity parameters. We consider all meaningful pairs of parameters and find there can only be 4, 8, 9 or 10 relative equilibria in the (3+1) -vortex problem, and 8, 10, 12 or 14 relative equilibria in the (1+3) -vortex problem. For the case of zero total vorticity, there are 0, 1 or 2 collinear relative equilibria and 2, 3 or 4 strictly planar relative equilibria. We completely classify parameters according to the different numbers of relative equilibria. For all cases, we reduce them to the problems of counting common zeros in an open region of {{{R}}}2 for polynomial systems with two equations, two variables, and two parameters. We propose a method to count zeros for such type of systems for all parameters in an open region of R2 through symbolic computations. Therefore, all of our results are proved rigorously.
Energy Technology Data Exchange (ETDEWEB)
Vdovin, V. [NRC Kurchatov Institute Tokamak Physics Institute, Moscow (Russian Federation)
2014-02-12
The Innovative concept and 3D full wave code modeling Off-axis current drive by RF waves in large scale tokamaks, reactors FNSF-AT, ITER and DEMO for steady state operation with high efficiency was proposed [1] to overcome problems well known for LH method [2]. The scheme uses the helicons radiation (fast magnetosonic waves at high (20–40) IC frequency harmonics) at frequencies of 500–1000 MHz, propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by Helicons will help to have regimes with negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure β{sub N} > 3 (the so-called Advanced scenarios) of interest for FNSF and the commercial reactor. Modeling with full wave three-dimensional codes PSTELION and STELEC2 showed flexible control of the current profile in the reactor plasmas of ITER, FNSF-AT and DEMO [2,3], using multiple frequencies, the positions of the antennae and toroidal waves slow down. Also presented are the results of simulations of current generation by helicons in tokamaks DIII-D, T-15MD and JT-60SA [3]. In DEMO and Power Plant antenna is strongly simplified, being some analoge of mirrors based ECRF launcher, as will be shown. For spherical tokamaks the Helicons excitation scheme does not provide efficient Off-axis CD profile flexibility due to strong coupling of helicons with O-mode, also through the boundary conditions in low aspect machines, and intrinsic large amount of trapped electrons, as is shown by STELION modeling for the NSTX tokamak. Brief history of Helicons experimental and modeling exploration in straight plasmas, tokamaks and tokamak based fusion Reactors projects is given, including planned joint DIII-D – Kurchatov Institute experiment on helicons CD [1].
Vdovin, V.
2014-02-01
The Innovative concept and 3D full wave code modeling Off-axis current drive by RF waves in large scale tokamaks, reactors FNSF-AT, ITER and DEMO for steady state operation with high efficiency was proposed [1] to overcome problems well known for LH method [2]. The scheme uses the helicons radiation (fast magnetosonic waves at high (20-40) IC frequency harmonics) at frequencies of 500-1000 MHz, propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by Helicons will help to have regimes with negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure βN > 3 (the so-called Advanced scenarios) of interest for FNSF and the commercial reactor. Modeling with full wave three-dimensional codes PSTELION and STELEC2 showed flexible control of the current profile in the reactor plasmas of ITER, FNSF-AT and DEMO [2,3], using multiple frequencies, the positions of the antennae and toroidal waves slow down. Also presented are the results of simulations of current generation by helicons in tokamaks DIII-D, T-15MD and JT-60SA [3]. In DEMO and Power Plant antenna is strongly simplified, being some analoge of mirrors based ECRF launcher, as will be shown. For spherical tokamaks the Helicons excitation scheme does not provide efficient Off-axis CD profile flexibility due to strong coupling of helicons with O-mode, also through the boundary conditions in low aspect machines, and intrinsic large amount of trapped electrons, as is shown by STELION modeling for the NSTX tokamak. Brief history of Helicons experimental and modeling exploration in straight plasmas, tokamaks and tokamak based fusion Reactors projects is given, including planned joint DIII-D - Kurchatov Institute experiment on helicons CD [1].
MHD stability limits in the TCV Tokamak
Energy Technology Data Exchange (ETDEWEB)
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation {kappa} and triangularity {delta}, with high {kappa}, and low {delta} leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The
Phase Equilibria and Transition in Mixtures of a Homopolymer and a Block Copolymer. II.
1983-01-26
AD-A124 929 PHASE EQUILIBRIA AND TRANSITION IN MIXTURES OF A In- NOMOPOLYMER AND’A BLOCK..(U) CINCINNATI UNJY ON DEPT OF MATERIALS SCIENCE AND...REPORT NO. 7 v2 L Phase Equilibria and Transition in Mixtures of a Homopolymer and a Block Copolymer II. The Phase Diagram by R. J. Roe and W. C. Zin...homopolymers as in our systems. The phase equilibria at temperatures above the "pseudo-triple point" BCD can be interpreted in terms of the free energy of
Trajectory planning of tokamak flexible in-vessel inspection robot
Energy Technology Data Exchange (ETDEWEB)
Wang, Hesheng [Department of Automation, Shanghai Jiao Tong University, 200240 Shanghai (China); Key Laboratory of System Control and Information Processing, Ministry of Education of China, 200240 Shanghai (China); Chen, Weidong, E-mail: wdchen@sjtu.edu.cn [Department of Automation, Shanghai Jiao Tong University, 200240 Shanghai (China); Key Laboratory of System Control and Information Processing, Ministry of Education of China, 200240 Shanghai (China); Lai, Yinping; He, Tao [Department of Automation, Shanghai Jiao Tong University, 200240 Shanghai (China); Key Laboratory of System Control and Information Processing, Ministry of Education of China, 200240 Shanghai (China)
2015-10-15
Highlights: • A tokamak flexible in-vessel inspection robot is designed. • Two trajectory planning methods are used to ensure the full coverage of the first wall scanning. • The method is tested on a simulated platform of EAST with the flexible in-vessel inspection robot. • Experimental results show the effectiveness of the proposed algorithm. - Abstract: Tokamak flexible in-vessel inspection robot is mainly designed to carry a camera for close observation of the first wall of the vacuum vessel, which is essential for the maintenance of the future tokamak reactor without breaking the working condition of the vacuum vessel. A tokamak flexible in-vessel inspection robot is designed. In order to improve efficiency of the remote maintenance, it is necessary to design a corresponding trajectory planning algorithm to complete the automatic full coverage scanning of the complex tokamak cavity. Two different trajectory planning methods, RS (rough scanning) and FS (fine scanning), according to different demands of the task, are used to ensure the full coverage of the first wall scanning. To quickly locate the damage position, the first trajectory planning method is targeted for quick and wide-ranging scan of the tokamak D-shaped section, and the second one is for careful observation. Furthermore, both of the two different trajectory planning methods can ensure the full coverage of the first wall scanning with an optimal end posture. The method is tested on a simulated platform of EAST (Experimental Advanced Superconducting Tokamak) with the flexible in-vessel inspection robot, and the results show the effectiveness of the proposed algorithm.
Carpenter, Donald A.
2008-01-01
Confusion exists among database textbooks as to the goal of normalization as well as to which normal form a designer should aspire. This article discusses such discrepancies with the intention of simplifying normalization for both teacher and student. This author's industry and classroom experiences indicate such simplification yields quicker…
Energy Technology Data Exchange (ETDEWEB)
Rewoldt, G.; Tang, W.M. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Lao, L.L. [General Atomics, San Diego, CA (United States)
1997-03-01
The microinstability properties of discharges with negative (reversed) magnetic shear in the Tokamak Fusion Test Reactor (TFTR) and DIII-D experiments with and without confinement transitions are investigated. A comprehensive kinetic linear eigenmode calculation employing the ballooning representation is employed with experimentally measured profile data, and using the corresponding numerically computed magnetohydrodynamic (MHD) equilibria. The instability considered is the toroidal drift mode (trapped-electron-{eta}{sub i} mode). A variety of physical effects associated with differing q-profiles are explained. In addition, different negative magnetic shear discharges at different times in the discharge for TFTR and DIII-D are analyzed. The effects of sheared toroidal rotation, using data from direct spectroscopic measurements for carbon, are analyzed using comparisons with results from a two-dimensional calculation. Comparisons are also made for nonlinear stabilization associated with shear in E{sub r}/RB{sub {theta}}. The relative importance of changes in different profiles (density, temperature, q, rotation, etc.) on the linear growth rates is considered.
Study of ionic equilibria of indotricarbocyanines in aromatic hydrocarbons
Energy Technology Data Exchange (ETDEWEB)
Dyadyusha, G.G.; Ishchenko, A.A.; Derevyanko, N.A.; Tolmachev, A.I.
1982-05-01
Study of the equilibria in nonpolar solvents is very complicated by the poor solubility of the salt-like dyes. Indotricarbocyanines I and II were found to be fairly soluble in aromatic hydrocarbons for solving these problems by means of electronic spectra. In the present work, their absorption spectra were studied in benzene, toluene, and m-xylene (the absorption spectra were measured on the SF-8 spectrophotometer). It was shown that the dyes studied in these solvents have spectral bands of unusual form of polymethine dyes. At the long wave edge of the spectra of indotricarbocyanines, a distinct band appears, whose intensity is very dependent on the nature of the anion. In the case of perchlorate I, it has a lower intensity, and in the case of iodide II, the intensity is higher.
Tautomeric equilibria in solutions of 1-methyl-2-phenacylbenzimidazoles
Skotnicka, Agnieszka; Czeleń, Przemysław; Gawinecki, Ryszard
2017-04-01
Until now the susceptibility of 1-methyl-2-phenacylbenzimidazoles to the proton transfer has not been carefully examined. There only have been selective trials to recognize tautomeric equilibrium of substituted compounds. Unfortunately, conclusions of these studies are often conflicting. Therefore, the aim of this work was to analyze the influence of the factors affecting the tautomeric processes of substituted 1-methyl-2-phenacylbenzimidazoles in solutions of chloroform by spectroscopic technique of 1H and 13C NMR. Complex equilibria may only take place when molecules of tautomeric species contain multiple basic and/or acidic centres. Analysis of NMR spectra show unequivocally that 1-methyl-2-phenacylbenzimidazoles (ketimine tautomeric form) are in equilibrium with (Z)-2-(1-methyl-1H-benzo[d]imidazol-2yl)-1-phenylethenols (enolimine).
Multiple equilibria of cross-equatorial Inertial jets
Institute of Scientific and Technical Information of China (English)
CHAO JiPing; LIU Fei
2007-01-01
Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial inertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equilibria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Multiple equilibria of cross-equatorial Inertial jets
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the developed Anderson and Moore’s theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.
Complex Networks as Nash Equilibria of Navigation Games
Gulyás, András; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2014-01-01
The common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organised so that networks can perform their functions. One common function that many networks perform is targeted transport or navigation. Here with the help of game theory we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties of real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. They are navigation skeletons that we show are present in the Internet, {\\it E. coli} metabolic network, English word network, US airport network, and the Hungarian road network. The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can dramatically improve or paralyse the navigation in the network.
Navigable networks as Nash equilibria of navigation games
Gulyás, András; Bíró, József J.; Kőrösi, Attila; Rétvári, Gábor; Krioukov, Dmitri
2015-07-01
Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.
Axisymmetric equilibria of a gravitating plasma with incompressible flows
Throumoulopoulos, G N
2001-01-01
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\ll 1$, where $\\beta_0$, $\\gamma_0$, $\\delta_0$, and $\\...
Morrison, Philip J; Tronko, Natalia
2013-01-01
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {\\delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {\\delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instabili...
Phase equilibria in the Ni-Co-Ga alloy system
Energy Technology Data Exchange (ETDEWEB)
Ducher, R. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan); Kainuma, R. [Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Sendai 980-8577 (Japan)], E-mail: kainuma@tagen.tohoku.ac.jp; Ishida, K. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan)
2008-10-20
Phase equilibria among the {alpha} (A1), {alpha}' (L1{sub 2}), {beta} (B2), {delta} (Ni{sub 5}Ga{sub 3}) and {epsilon} (Ni{sub 13}Ga{sub 9}) phases at elevated temperatures and the existing composition region of the martensite phase at room temperature in the Ni-Co side of the Ni-Co-Ga system were examined by electron probe microanalysis (EPMA) using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that single-phase regions of the {alpha}, {alpha}' and {beta} phases at 700 and 1000 deg. C exist in a wide composition range parallel to Ni-Co section and that the existing region of the martensite phase at room temperature is also located over a wide range in the {beta} phase along the {beta} + {alpha} (or {alpha}') two-phase region.
Boric acid equilibria in near-critical and supercritical water
Energy Technology Data Exchange (ETDEWEB)
Wofford, W.T.; Gloyna, E.F.; Johnston, K.P. [Univ. of Texas, Austin, TX (United States)
1998-05-01
Greater knowledge of acid-base equilibria is crucial to understanding the chemistry of hydrothermal processes including oxidation of organics, corrosion, catalysis, hydrolysis reactions, crystal growth and formation, precipitation of metal complexes and steam power cycles. The pH values of aqueous solutions of boric acid and KOH were measured with the optical indicator 2-naphthol at temperatures from 300 to 380 C. The equilibrium constant K{sub b}{sup {minus}1} for the reaction B(OH){sub 3} + OH{sup {minus}} = B(OH){sub 4}{sup {minus}} was determined from the pH measurements and correlated with a modified Born model. The titration curve for the addition of HCl to sodium borate exhibits strong acid-strong base behavior even at 350 C and 24.1 MPa. At these conditions, aqueous solutions of sodium borate buffer the pH at 9.6 {+-} 0.25.
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Dynamic data evaluation for solid-liquid equilibria
DEFF Research Database (Denmark)
Cunico, Larissa; Ceriani, Roberta; Kang, Jeong Won
The accuracy and reliability of the measured data sets to be used in regression of model parameters is an important issue related to modeling of phase equilibria. It is clear that good parameters for any model cannot be obtained from low quality data. A thermodynamic consistency test for solid-liquid...... systems using a relation between the solid and liquid activity coefficients for systems containing metals [1], where the data from the two phases are given were proposed. However, as consistency tests based on the Gibbs–Duhem equation are not feasible, new consistency tests have been developed [2]. Some...... of the developed tests were based in the quality tests proposed for VLE data by Kang et al. [3] and a methodology that combines solute activity coefficients in the liquid phase at infinite dilution and a theoretically based term to account for the non-ideality in dilute solutions are discussed. In this work, case...
Settling the Complexity of Computing Two-Player Nash Equilibria
Chen, Xi; Teng, Shang-Hua
2007-01-01
We settle a long-standing open question in algorithmic game theory. We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. This is the first of a series of results concerning the complexity of Nash equilibria. In particular, we prove the following theorems: Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results demonstrate that, even in the simplest form of non-cooperative games, equilibrium computation and approximation are polynomial-time equivalent to fixed point computation. Our results also have two broad complexity implications in mathematical economics and operations res...
Extended Group Contribution Model for Polyfunctional Phase Equilibria
DEFF Research Database (Denmark)
Abildskov, Jens
-liquid equilibria from data on binary mixtures, composed of structurally simple molecules with a single functional group. More complex is the situation with mixtures composed of structurally more complicated molecules or molecules with more than one functional group. The UNIFAC method is extended to handle...... polyfunctional group situations, based on additional information on molecular structure. The extension involves the addition of second-order correction terms to the existing equation. In this way the current first-order formulation is retained. The second-order concept is developed for mixture properties based....... In chapter 4 parameters are estimated for the first-order UNIFAC model, based on which parameters are estimated for one of the second-order models described in chapter 3. The parameter estimation is based on measured binary data on around 4000 systems, covering 11 C-, H- and O-containing functional groups...
Three-dimensional magnetotail equilibria by numerical relaxation techniques
Hesse, Michael; Birn, Joachim
1993-01-01
Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.
Development of 3D ferromagnetic model of tokamak core with strong toroidal asymmetry
DEFF Research Database (Denmark)
Markovič, Tomáš; Gryaznevich, Mikhail; Ďuran, Ivan;
2015-01-01
Fully 3D model of strongly asymmetric tokamak core, based on boundary integral method approach (i.e. characterization of ferromagnet by its surface) is presented. The model is benchmarked on measurements on tokamak GOLEM, as well as compared to 2D axisymmetric core equivalent for this tokamak...
Basic Physics of Tokamak Transport Final Technical Report.
Energy Technology Data Exchange (ETDEWEB)
Sen, Amiya K.
2014-05-12
The goal of this grant has been to study the basic physics of various sources of anomalous transport in tokamaks. Anomalous transport in tokamaks continues to be one of the major problems in magnetic fusion research. As a tokamak is not a physics device by design, direct experimental observation and identification of the instabilities responsible for transport, as well as physics studies of the transport in tokamaks, have been difficult and of limited value. It is noted that direct experimental observation, identification and physics study of microinstabilities including ITG, ETG, and trapped electron/ion modes in tokamaks has been very difficult and nearly impossible. The primary reasons are co-existence of many instabilities, their broadband fluctuation spectra, lack of flexibility for parameter scans and absence of good local diagnostics. This has motivated us to study the suspected tokamak instabilities and their transport consequences in a simpler, steady state Columbia Linear Machine (CLM) with collisionless plasma and the flexibility of wide parameter variations. Earlier work as part of this grant was focused on both ITG turbulence, widely believed to be a primary source of ion thermal transport in tokamaks, and the effects of isotope scaling on transport levels. Prior work from our research team has produced and definitively identified both the slab and toroidal branches of this instability and determined the physics criteria for their existence. All the experimentally observed linear physics corroborate well with theoretical predictions. However, one of the large areas of research dealt with turbulent transport results that indicate some significant differences between our experimental results and most theoretical predictions. Latter years of this proposal were focused on anomalous electron transport with a special focus on ETG. There are several advanced tokamak scenarios with internal transport barriers (ITB), when the ion transport is reduced to
The Impact of Prophage on the Equilibria and Stability of Phage and Host
Yu, Pei; Nadeem, Alina; Wahl, Lindi M.
2016-11-01
In this paper, we present a bacteriophage model that includes prophage, that is, phage genomes that are incorporated into the host cell genome. The general model is described by an 18-dimensional system of ordinary differential equations. This study focuses on asymptotic behaviour of the model, and thus the system is reduced to a simple six-dimensional model, involving uninfected host cells, infected host cells and phage. We use dynamical system theory to explore the dynamic behaviour of the model, studying in particular the impact of prophage on the equilibria and stability of phage and host. We employ bifurcation and stability theory, centre manifold and normal form theory to show that the system has multiple equilibrium solutions which undergo a series of bifurcations, finally leading to oscillating motions. Numerical simulations are presented to illustrate and confirm the analytical predictions. The results of this study indicate that in some parameter regimes, the host cell population may drive the phage to extinction through diversification, that is, if multiple types of host emerge; this prediction holds even if the phage population is likewise diverse. This parameter regime is restricted, however, if infecting phage are able to recombine with prophage sequences in the host cell genome.
The Impact of Prophage on the Equilibria and Stability of Phage and Host
Yu, Pei; Nadeem, Alina; Wahl, Lindi M.
2017-06-01
In this paper, we present a bacteriophage model that includes prophage, that is, phage genomes that are incorporated into the host cell genome. The general model is described by an 18-dimensional system of ordinary differential equations. This study focuses on asymptotic behaviour of the model, and thus the system is reduced to a simple six-dimensional model, involving uninfected host cells, infected host cells and phage. We use dynamical system theory to explore the dynamic behaviour of the model, studying in particular the impact of prophage on the equilibria and stability of phage and host. We employ bifurcation and stability theory, centre manifold and normal form theory to show that the system has multiple equilibrium solutions which undergo a series of bifurcations, finally leading to oscillating motions. Numerical simulations are presented to illustrate and confirm the analytical predictions. The results of this study indicate that in some parameter regimes, the host cell population may drive the phage to extinction through diversification, that is, if multiple types of host emerge; this prediction holds even if the phage population is likewise diverse. This parameter regime is restricted, however, if infecting phage are able to recombine with prophage sequences in the host cell genome.
Donnet, Marcel; Bowen, Paul; Lemaître, Jacques
2009-12-15
Thermodynamic solubility calculations are normally only related to thermodynamic equilibria in solution. In this paper, we extend the use of such solubility calculations to help elucidate possible precipitation reaction pathways during the entire reaction. We also estimate the interfacial energy of particles using only solubility data by a modification of Mersmann's approach. We have carried this out by considering precipitation reactions as a succession of small quasi-equilibrium states. Thus possible equilibrium precipitation pathways can be evaluated by calculating the evolution of surface charge, particle size and/or interfacial energy during the ongoing reaction. The approach includes the use of the Kelvin's law to express the influence of particle size on the solubility constant of precipitates, the use of Nernst's law to calculate surface potentials from solubility calculations and relate this to experimentally measured zeta potentials. Calcium carbonate precipitation and zeta potential measurements of well characterised high purity calcite have been used as a model system to validate the calculated values. The clarification of the change in zeta potential on titration illustrates the power of this approach as a tool for reaction pathway prediction and hence knowledge based tailoring of precipitation reactions.
Impurity effects on trapped electron mode in tokamak plasmas
Du, Huarong; Wang, Zheng-Xiong; Dong, J. Q.
2016-07-01
The effects of impurity ions on the trapped electron mode (TEM) in tokamak plasmas are numerically investigated with the gyrokinetic integral eigenmode equation. It is shown that in the case of large electron temperature gradient ( η e ), the impurity ions have stabilizing effects on the TEM, regardless of peaking directions of their density profiles for all normalized electron density gradient R / L n e . Here, R is the major radius and L n e is the electron density gradient scale length. In the case of intermediate and/or small η e , the light impurity ions with conventional inwardly (outwardly) peaked density profiles have stabilizing effects on the TEM for large (small) R / L n e , while the light impurity ions with steep inwardly (outwardly) peaked density profiles can destabilize the TEM for small (large) R / L n e . Besides, the TEM driven by density gradient is stabilized (destabilized) by the light carbon or oxygen ions with inwardly (outwardly) peaked density profiles. In particular, for flat and/or moderate R / L n e , two independent unstable modes, corresponding respectively to the TEM and impurity mode, are found to coexist in plasmas with impurity ions of outwardly peaked density profiles. The high Z tungsten impurity ions play a stronger stabilizing role in the TEM than the low Z impurity ions (such as carbon and oxygen) do. In addition, the effects of magnetic shear and collision on the TEM instability are analyzed. It is shown that the collisionality considered in this work weakens the trapped electron response, leading to a more stable TEM instability, and that the stabilizing effects of the negative magnetic shear on the TEM are more significant when the impurity ions with outwardly peaked density profile are taken into account.
Effect of Resonant Magnetic Perturbations on 3D equilibria in the MST RFP
Munaretto, Stefano
2015-11-01
The orientation of 3D, stellarator-like equilibria in the MST RFP can now be controlled with application of an m = 1 RMP. This has led to greatly improved diagnosis, revealing enhancements in both the central electron temperature and density. Coupled to a recent advance in the V3FIT code, reconstructions of the 3D equilibria have also been dramatically improved. The RMP also inhibits the generation of high-energy >20 keV electrons that is otherwise common with the 3D state. This state occurs when the normally broad spectrum of core-resonant m = 1 tearing modes condenses, with the innermost resonant mode growing to large amplitude, reaching ~ 8% of the axisymmetric field strength. This occurs in plasmas of sufficiently large Lundquist number ~ IpTe3/2, and the duration of the state is maximized with zero applied Bt (infinite toroidal beta). As the dominant mode grows, eddy current in MST's conducting shell slows the mode's rotation. This leads to locking of the 3D structure, but with an orientation that varies randomly shot to shot, making diagnosis difficult. An m = 1 RMP can now be applied with an array of saddle coils at the vertical insulated cut in the shell. With an amplitude br/B ~ 10% and a tailored temporal waveform, the RMP can force the 3D structure into any desired orientation relative to MST's diagnostics. A recent advance in V3FIT allows calculation of the substantial helical image current flowing in MST's shell, which has in turn allowed self-consistent utilization of both external and internal (Faraday rotation) measurements of the magnetic field. The ORBIT code predicts reduced stochasticity and improved confinement of high-energy electrons within the 3D structure. The suppression of these electrons by the m = 1 RMP may reflect a change to the central magnetic topology. The generation of these electrons is unaffected by non-resonant perturbations, such as m = 3. Supported by the US DOE.
Axisymmetric equilibria with pressure anisotropy and plasma flow
Evangelias, Achilleas
2016-01-01
In this Master thesis we investigate the influence of pressure anisotropy and incompressible flow of arbitrary direction on the equilibrium properties of magnetically confined, axisymmetric toroidal plasmas. The main novel contribution is the derivation of a pertinent generalised Grad-Shafranov equation. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger-Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy, through an anisotropy function assumed to be uniform on the magnetic surfaces, and plasma flow, via the...
A Multistep Equilibria-Redox-Complexation Demonstration to Illustrate Le Chatelier's Principle.
Berger, Tomas G.; Mellon, Edward K.
1996-01-01
Describes a process that can be used to illustrate a number of chemical principles including Le Chatelier's principle, redox chemistry, equilibria versus steady state situations, and solubility of species. (JRH)
Mottez, F
2003-01-01
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.
The freedom to choose neutron star magnetic field equilibria: Table 1.
Glampedakis, Kostas; Lasky, Paul D.
2016-12-01
Our ability to interpret and glean useful information from the large body of observations of strongly magnetized neutron stars rests largely on our theoretical understanding of magnetic field equilibria. We answer the following question: is one free to arbitrarily prescribe magnetic equilibria such that fluid degrees of freedom can balance the equilibrium equations? We examine this question for various models for neutron star matter; from the simplest single-fluid barotrope to more realistic non-barotropic multifluid models with superfluid/superconducting components, muons and entropy. We do this for both axi- and non-axisymmetric equilibria, and in Newtonian gravity and general relativity. We show that, in axisymmetry, the most realistic model allows complete freedom in choosing a magnetic field equilibrium whereas non-axisymmetric equilibria are never completely arbitrary.
Modeling of Vapor-Liquid-Solid Equilibria in Acidic Aqueous Solutions
DEFF Research Database (Denmark)
Christensen, Søren Gregers; Thomsen, Kaj
2003-01-01
The phase behavior (vapor - liquid equilibria (VLE) and solid - liquid equilibria (SLE)) and thermal properties of aqueous solutions of ions like (K+, Na+, NH4+, Ca2+, Cl-) in the presence of phosphoric acid (H3PO4, H2PO4-, HPO42- ) and nitric acid (HNO3, NO3-) are described by means of the Exten......The phase behavior (vapor - liquid equilibria (VLE) and solid - liquid equilibria (SLE)) and thermal properties of aqueous solutions of ions like (K+, Na+, NH4+, Ca2+, Cl-) in the presence of phosphoric acid (H3PO4, H2PO4-, HPO42- ) and nitric acid (HNO3, NO3-) are described by means...
Tokamak blanket design study, final report
Energy Technology Data Exchange (ETDEWEB)
1980-08-01
A cylindrical module concept was developed, analyzed, and incorporated in a tokamak blanket system that includes piping systems, vacuum boundary sealing, and support structures. The design is based on the use of state-of-the-art structural materials (20% cold-worked type 316 stainless steel), lithium as the breeding material, and pressurized helium as the coolant. The module design consists of nested concentric cylinders (with an outer diameter of 10 cm) and features direct wall cooling by helium flowing between the outer (first-wall) cylinder and the inner (lithium-containing) cylinder. Each cylinder can withstand full coolant pressure, thus enhancing reliability. Results show that stainless steel is a viable material for a first wall subjected to a neutron wall loading of 4 MW/m/sup 2/ and a particle heat flux of 1 MW/m/sup 2/. Lifetime analysis shows that the first-wall design meets the goal of operating at 20-min cycles with 95% duty for 100,000 cycles. To reduce system complexity, a larger 20-cm-diam module also was analyzed for incorporation in the blanket assembly. Reliability assessment indicates that it may be possible to double the module in size from 10 to 20 cm in diameter. With a modest increase in coolant pumping power, a blanket assembly comprising 20-cm-diam modules can still achieve 100,000 operating cycles - equivalent to a 3.6-year design lifetime - with only one or two helium coolant leaks into the plasma.
Fast bolometric measurements on the TCV tokamak
Furno, I.; Weisen, H.; Mlynar, J.; Pitts, R. A.; Llobet, X.; Marmillod, Ph.; Pochon, G. P.
1999-12-01
The design and first results are presented from a bolometric diagnostic with high temporal resolution recently installed on the TCV tokamak. The system consists of two pinhole cameras viewing the plasma from above and below at the same toroidal location. Each camera is equipped with an AXUV-16ELO linear array of 16 p-n junction photodiodes, characterized by a flat spectral sensitivity from ultraviolet to x-ray energies, a high temporal response (<0.5 μs), and insensitivity to low-energy neutral particles emitted by the plasma. This high temporal resolution allows the study of transient phenomena such as fast magnetohydrodynamic (MHD) activity hitherto inaccessible with standard bolometry. In the case of purely electromagnetic radiation, good agreement has been found when comparing results from the new diagnostic with those from a standard metal foil bolometer system. This comparison has also revealed that the contribution of neutrals to the foil bolometer measurements can be extremely important under certain operating conditions, precluding the application of tomographic techniques for reconstruction of the radiation distribution.
Aspects of Tokamak toroidal magnet protection
Energy Technology Data Exchange (ETDEWEB)
Green, R.W.; Kazimi, M.S.
1979-07-01
Simple but conservative geometric models are used to estimate the potential for damage to a Tokamak reactor inner wall and blanket due to a toroidal magnet field collapse. The only potential hazard found to exist is due to the MHD pressure rise in a lithium blanket. A survey is made of proposed protection methods for superconducting toroidal magnets. It is found that the two general classifications of protection methods are thermal and electrical. Computer programs were developed which allow the toroidal magnet set to be modeled as a set of circular filaments. A simple thermal model of the conductor was used which allows heat transfer to the magnet structure and which includes the effect of temperature dependent properties. To be effective in large magnets an electrical protection system should remove at least 50% of the stored energy in the protection circuit assuming that all of the superconductor in the circuit quenches when the circuit is activated. A protection system design procedure based on this criterion was developed.
Zeeman Spectroscopy of Tokamak Edge Plasmas
Hey, J. D.; Chu, C. C.; Mertens, Ph.
2002-12-01
Zeeman spectroscopy is a valuable tool both for diagnostic purposes, and for more fundamental studies of atomic and molecular processes in the boundary region of magnetically confined fusion plasmas (B ≃ 1 to 10 T). The method works well when the Zeeman (Paschen-Back) effect plays an important, or dominant, rôle in relation to other broadening mechanisms (Doppler, Stark, resonant excitation transfer) in determining the spectral line shape. For impurity species identification and temperature determination, Zeeman spectroscopy has advantages over charge-exchange recombination spectroscopy from highly excited radiator states, since spectral features practically unique to the species under investigation are analysed. It also provides useful information on probable mechanisms of line production (e.g. sputtering mechanisms, electron impact-induced dissociative excitation from molecules in the edge plasma), and on the temperature evolution of lower charge states in the process of convection inwards or diffusion outwards from the hotter plasma interior. Where different physical processes are responsible for different sections of the line profile — especially in the case of hydrogen isotopes — Zeeman spectroscopy can provide a set of characteristic temperatures for each section. The method is introduced in both passive and active spectroscopy, and general principles of the Zeeman effect are discussed with special reference to régimes of interest for the tokamak. Relevant physical processes (sputtering mechanisms, electron impact-induced dissociative excitation from molecules in the edge plasma, and ion-atom collisional heating mechanisms) are illustrated by sample spectra.
Modelling and control of a tokamak plasma; Modelisation et commande d`un plasma de tokamak
Energy Technology Data Exchange (ETDEWEB)
Bremond, S.
1995-10-18
Vertically elongated tokamak plasmas, while attractive as regards Lawson criteria, are intrinsically instable. It is found that the open-loop instability dynamics is characterised by the relative value of two dimensionless parameters: the coefficient of inductive coupling between the vessel and the coils, and the coil damping efficiency on the plasma displacement relative to that of the vessel. Applications to Tore Supra -where the instability is due to the iron core attraction- and DIII-D are given. A counter-effect of the vessel, which temporarily reverses the effect of coil control on the plasma displacement, is seen when the inductive coupling is higher than the damping ratio. Precise control of the plasma boundary is necessary if plasma-wall interaction and/or coupling to heating antennas are to be monitored. A positional drift, of a few mm/s, which had been observed in the Tore Supra tokamak, is explained and corrected. A linear plasma shape response model is then derived from magnetohydrodynamic equilibrium calculation, and proved to be in good agreement with experimental data. An optimal control law is derived, which minimizes an integral quadratic criteria on tracking errors and energy expenditure. This scheme avoids compensating coil currents, and could render local plasma shaping more precise. (authors). 123 refs., 77 figs., 6 tabs., 4 annexes.
Energy Technology Data Exchange (ETDEWEB)
Sayer, R.O.; Peng, Y.K.M.; Strickler, D.J.; Jardin, S.C.
1990-01-01
The Tokamak Simulation Code and the TWIR postprocessor code have been used to develop credible plasma disruption scenarios for the Compact Ignition Tokamak (CIT) in order to predict the evolution of forces on CIT conducting structures and to provide results required for detailed structural design analysis. The extreme values of net radial and vertical vacuum vessel (VV) forces were found to be F{sub R}={minus}12.0 MN/rad and F{sub Z}={minus}3.0 MN/rad, respectively, for the CIT 2.1-m, 11-MA design. Net VV force evolution was found to be altered significantly by two mechanisms not noted previously. The first, due to poloidal VV currents arising from increased plasma paramagnetism during thermal quench, reduces the magnitude of the extreme F{sub R} by 15-50{percent} and modifies the distribution of forces substantially. The second effect is that slower plasma current decay rates give more severe net vertical VV loads because the current decay occurs when the plasma has moved farther from midplane than is the case for faster decay rates. 7 refs., 9 figs., 1 tab.
Prospects for pilot plants based on the tokamak, spherical tokamak and stellarator
Menard, J. E.; Bromberg, L.; Brown, T.; Burgess, T.; Dix, D.; El-Guebaly, L.; Gerrity, T.; Goldston, R. J.; Hawryluk, R. J.; Kastner, R.; Kessel, C.; Malang, S.; Minervini, J.; Neilson, G. H.; Neumeyer, C. L.; Prager, S.; Sawan, M.; Sheffield, J.; Sternlieb, A.; Waganer, L.; Whyte, D.; Zarnstorff, M.
2011-10-01
A potentially attractive next-step towards fusion commercialization is a pilot plant, i.e. a device ultimately capable of small net electricity production in as compact a facility as possible and in a configuration scalable to a full-size power plant. A key capability for a pilot-plant programme is the production of high neutron fluence enabling fusion nuclear science and technology (FNST) research. It is found that for physics and technology assumptions between those assumed for ITER and nth-of-a-kind fusion power plant, it is possible to provide FNST-relevant neutron wall loading in pilot devices. Thus, it may be possible to utilize a single facility to perform FNST research utilizing reactor-relevant plasma, blanket, coil and auxiliary systems and maintenance schemes while also targeting net electricity production. In this paper three configurations for a pilot plant are considered: the advanced tokamak, spherical tokamak and compact stellarator. A range of configuration issues is considered including: radial build and blanket design, magnet systems, maintenance schemes, tritium consumption and self-sufficiency, physics scenarios and a brief assessment of research needs for the configurations.
Mick, Jason R; Soroush Barhaghi, Mohammad; Jackman, Brock; Rushaidat, Kamel; Schwiebert, Loren; Potoff, Jeffrey J
2015-09-21
Transferrable force fields, based on n-6 Mie potentials, are presented for noble gases. By tuning the repulsive exponent, ni, it is possible to simultaneously reproduce experimental saturated liquid densities and vapor pressures with high accuracy, from the normal boiling point to the critical point. Vapor-liquid coexistence curves for pure fluids are calculated using histogram reweighting Monte Carlo simulations in the grand canonical ensemble. For all noble gases, saturated liquid densities and vapor pressures are reproduced to within 1% and 4% of experiment, respectively. Radial distribution functions, extracted from NVT and NPT Monte Carlo simulations, are in similarly excellent agreement with experimental data. The transferability of the optimized force fields is assessed through calculations of binary mixture vapor-liquid equilibria. These mixtures include argon + krypton, krypton + xenon, methane + krypton, methane + xenon, krypton + ethane, and xenon + ethane. For all mixtures, excellent agreement with experiment is achieved without the introduction of any binary interaction parameters or multi-body interactions.
Sen, WANG; Qiping, YUAN; Bingjia, XIAO
2017-03-01
Plasma control system (PCS), mainly developed for real-time feedback control calculation, plays a significant part during normal discharges in a magnetic fusion device, while the tokamak simulation code (TSC) is a nonlinear numerical model that studies the time evolution of an axisymmetric magnetized tokamak plasma. The motivation to combine these two codes for an integrated simulation is specified by the facts that the control system module in TSC is relatively simple compared to PCS, and meanwhile, newly-implemented control algorithms in PCS, before applied to experimental validations, require numerical validations against a tokamak plasma simulator that TSC can act as. In this paper, details of establishment of the integrated simulation framework between the EAST PCS and TSC are generically presented, and the poloidal power supply model and data acquisition model that have been implemented in this framework are described as well. In addition, the correctness of data interactions among the EAST PCS, Simulink and TSC is clearly confirmed during an interface test, and in a simulation test, the RZIP control scheme in the EAST PCS is numerically validated using this simulation platform. Supported by the National Magnetic Confinement Fusion Science Program of China (No. 2014GB103000) and the National Natural Science Foundation of China (No. 11205200).
Plasma Shape and Current Density Profile Control in Advanced Tokamak Operating Scenarios
Shi, Wenyu
The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion has sufficient energy density to potentially supply the world population with its increasing energy demands. The tokamak is a magnetic confinement device used to achieve controlled fusion reactions. Experimental fusion technology has now reached a level where tokamaks are able to produce about as much energy as is expended in heating the fusion fuel. The next step towards the realization of a nuclear fusion tokamak power plant is ITER, which will be capable of exploring advanced tokamak (AT) modes, characterized by a high fusion gain and plasma stability. The extreme requirements of the advanced modes motivates researchers to improve the modeling of the plasma response as well as the design of feedback controllers. This dissertation focuses on several magnetic and kinetic control problems, including the plasma current, position and shape control, and data-driven and first-principles-driven modeling and control of plasma current density profile and the normalized plasma pressure ratio betaN. The plasma is confined within the vacuum vessel by an external electromagnetic field, produced primarily by toroidal and poloidal field coils. The outermost closed plasma surface or plasma boundary is referred to as the shape of the plasma. A central characteristic of AT plasma regimes is an extreme elongated shape. The equilibrium among the electromagnetic forces acting on an elongated plasma is unstable. Moreover, the tokamak performance is improved if the plasma is located in close proximity to the torus wall, which guarantees an efficient use of available volume. As a consequence, feedback control of the plasma position and shape is necessary. In this dissertation, an Hinfinity-based, multi-input-multi-output (MIMO) controller for the National Spherical Torus Experiment (NSTX) is developed, which is used to control the plasma position, shape, and X
Energy Technology Data Exchange (ETDEWEB)
Valencia A, R
2006-07-01
As a main objective of this work, we present some experimental results obtained from studying the process of extracting those impurities created by the interaction plasma with its vessel wall in the case of Novillo tokamak. Likewise, we describe the main cleaning and conditioning techniques applied to it, fundamentally that of glow discharge cleaning at a low electron temperature (<10 eV), both in noble and reactive gases, as well as the conditioning by thin film deposits of hydrogen rich amorphous carbon (carbonization) leading to a reduction in the plasma resistivity from 8.99 x 10{sup -6} to 4.5 x 10{sup -6} {omega}-m, thus taking the Z{sub ef} value from 3.46 to 2.07 which considerably improved the operational parameters of the machine. With a view to justifying the fact that controlled nuclear fusion is a feasible alternative for the energy demand that humanity will face in the future, we review in Chapter 1 some fundamentals of the energy production by nuclear fusion reactions while, in Chapter 2, we examine two relevant plasma wall interaction processes. Our experimental array used to produce both cleaning and intense plasma discharges is described in Chapter 3 along with the associated diagnostics equipment. Chapter 4 contains a description of the vessel conditioning techniques followed in the process. Finally, we report our results in Chapter 5 while, in Chapter 6, some conclusions and remarks are presented. It is widely known that tokamak impurities are generated mainly by the plasma-wall interaction, particularly in the presence of high potentials between the plasma sheath and the limiter or wall. Given that impurities affect most adversely the plasma behaviour, understanding and controlling the impurity extraction mechanisms is crucial for optimizing the cleaning and wall conditioning discharge processes. Our study of one impurity extraction mechanism for both low and high Z in Novillo tokamak was carried out though mass spectrometry, optical emission
Solid Phase Equilibria in the Pi-Ga-As and Pt-Ga-Sb Systems
1988-07-22
OFFICE OF NAVAL RESEARCH Research Contract N00014-87-K-0014 R&T Code 413E026---01 AD-A 198 654 TECHNICAL REPORT No. 9 SOLID PHASE EQUILIBRIA IN THE...Classtcation) UNCLASSLFIED: Tech.Rept.#9 SOLID PHASE EQUILIBRIA IN T11: Pt-Ga-As AND Pt-Ga-Sb SYST’IS 12 PERSONAL AuTiOR(S) C.T. Tsai and R.S. Williats 13a TYPE
Calculation of Phase Equilibria Based on the Levenberg-Marquardt Method
Institute of Scientific and Technical Information of China (English)
Ruijie ZHANG; Lei LI; Zhongwei CHEN; Zhi HE; Wanqi JIE
2005-01-01
The Levenberg-Marquardt method, the best algorithm to obtain the least-square solution of nonlinear equations, is applied to calculate the stable phase equilibria. It can get the best combination between robustness and speed of the calculations. Its application to ternary Al-Si-Mg system is executed in detail. The calculated phase equilibria agree well with the experimental results. Furthermore, the Levenberg-Marquardt method is not sensitive to the initial values.
Thermodynamic characteristics of protolytic equilibria in aqueous solutions of glycyl peptides
Gridchin, S. N.
2016-11-01
Protolytic equilibria in aqueous solutions of glycyl-DL-serine, glycyl-DL-threonine, and glycyl-DL-valine are investigated by means of potentiometry and calorimetry. Dissociation constants and heat effects of the above dipeptides are determined. Standard thermodynamic characteristics (p K°, Δdis G°, Δdis H°, Δdis S°) of the investigated equilibria are calculated. The obtained results are compared to corresponding data on relative compounds.
Calculation of Binary Adsorption Equilibria: Hydrocarbons and Carbon Dioxide on Activated Carbon
DEFF Research Database (Denmark)
Marcussen, Lis; Krøll, A.
1999-01-01
Binary adsorption equilibria are calculated by means of a mathematical model for multicomponent mixtures combined with the SPD (Spreading Pressure Dependent) model for calculation of activity coefficients in the adsorbed phase. The model has been applied successfully for the adsorption of binary ...... mixtures of hydrocarbons and carbon dioxide on activated carbons. The model parameters have been determined, and the model has proven to be suited for prediction of adsorption equilibria in the investigated systems....
Studies of instability and transport in tokamak plasmas with very weak magnetic shear
Energy Technology Data Exchange (ETDEWEB)
Dong, J.Q.; Zhang, Y.Z. [Southwestern Inst. of Physics, Chengdu (China)]|[International Center for Theoretical Physics, Trieste (Italy); Mahajan, S.M. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1997-04-01
Ion temperature gradient (ITG or {eta}{sub i}) driven microinstabilities are studied, using kinetic theory, for tokamak plasmas with very weak (positive or negative) magnetic shear (VWS). The gradient of magnetic shear as well as the effects of parallel and perpendicular velocity shear (v{prime}{sub {parallel}} and v{prime}{sub E}) are included in the defining equations. Two eigenmodes: the double (D) and the global (G) are found to coexist. Parametric dependence of these instabilities, and of the corresponding quasilinear transport is systematically analyzed. It is shown that, in VWS plasmas, a parallel velocity shear (PVS) may stabilize or destabilize the modes, depending on the individual as well as the relative signs of PVS and of the gradient of magnetic shear. The quasilinear transport induced by the instabilities may be significantly reduced with PVS in VWS plasmas. The v{prime}{sub E} values required to completely suppress the instabilities are much lower in VWS plasmas than they are in normal plasmas. Possible correlations with tokamak experiments are discussed.
Texas Experimental Tokamak. Technical progress report, April 1990--April 1993
Energy Technology Data Exchange (ETDEWEB)
Wootton, A.J.
1993-04-01
This progress report covers the period from November 1, 1990 to April 30, 1993. During that period, TEXT was operated as a circular tokamak with a material limiter. It was devoted to the study of basic plasma physics, in particular to study of fluctuations, turbulence, and transport. The purpose is to operate and maintain TEXT Upgrade as a complete facility for applied tokamak physics, specifically to conduct a research program under the following main headings: (1) to elucidate the mechanisms of working gas, impurity, and thermal transport in tokamaks, in particular to understand the role of turbulence; (2) to study physics of the edge plasma, in particular the turbulence; (3) to study the physics or resonant magnetic fields (ergodic magnetic divertors, intra island pumping); and (4) to study the physics of electron cyclotron heating (ECRH). Results of studies in each of these areas are reported.
The Dynamic Mutation Characteristics of Thermonuclear Reaction in Tokamak
Directory of Open Access Journals (Sweden)
Jing Li
2014-01-01
Full Text Available The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given.
A control approach for plasma density in tokamak machines
Energy Technology Data Exchange (ETDEWEB)
Boncagni, Luca, E-mail: luca.boncagni@enea.it [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Pucci, Daniele; Piesco, F.; Zarfati, Emanuele [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy); Mazzitelli, G. [EURATOM – ENEA Fusion Association, Frascati Research Center, Division of Fusion Physics, Rome, Frascati (Italy); Monaco, S. [Dipartimento di Ingegneria Informatica, Automatica e Gestionale ' ' Antonio Ruberti' ' , Sapienza Università di Roma (Italy)
2013-10-15
Highlights: •We show a control approach for line plasma density in tokamak. •We show a control approach for pressure in a tokamak chamber. •We show experimental results using one valve. -- Abstract: In tokamak machines, chamber pre-fill is crucial to attain plasma breakdown, while plasma density control is instrumental for several tasks such as machine protection and achievement of desired plasma performances. This paper sets the principles of a new control strategy for attaining both chamber pre-fill and plasma density regulation. Assuming that the actuation mean is a piezoelectric valve driven by a varying voltage, the proposed control laws ensure convergence to reference values of chamber pressure during pre-fill, and of plasma density during plasma discharge. Experimental results at FTU are presented to discuss weaknesses and strengths of the proposed control strategy. The whole system has been implemented by using the MARTe framework [1].
Tokamak dust particle size and surface area measurement
Energy Technology Data Exchange (ETDEWEB)
Carmack, W.J.; Smolik, G.R.; Anderl, R.A.; Pawelko, R.J.; Hembree, P.B.
1998-07-01
The INEEL has analyzed a variety of dust samples from experimental tokamaks: General Atomics` DII-D, Massachusetts Institute of Technology`s Alcator CMOD, and Princeton`s TFTR. These dust samples were collected and analyzed because of the importance of dust to safety. The dust may contain tritium, be activated, be chemically toxic, and chemically reactive. The INEEL has carried out numerous characterization procedures on the samples yielding information useful both to tokamak designers and to safety researchers. Two different methods were used for particle characterization: optical microscopy (count based) and laser based volumetric diffraction (mass based). Surface area of the dust samples was measured using Brunauer, Emmett, and Teller, BET, a gas adsorption technique. The purpose of this paper is to present the correlation between the particle size measurements and the surface area measurements for tokamak dust.
Hybrid Method for Tokamak MHD Equilibrium Configuration Reconstruction
Institute of Scientific and Technical Information of China (English)
HE Hong-Da; DONG Jia-Qi; ZHANG Jin-Hua; JIANG Hai-Bin
2007-01-01
A hybrid method for tokamak MHD equilibrium configuration reconstruction is proposed and employed in the modified EFIT code. This method uses the free boundary tokamak equilibrium configuration reconstruction algorithm with one boundary point fixed. The results show that the position of the fixed point has explicit effects on the reconstructed divertor configurations. In particular, the separatrix of the reconstructed divertor configuration precisely passes the required position when the hybrid method is used in the reconstruction. The profiles of plasma parameters such as pressure and safety factor for reconstructed HL-2A tokamak configurations with the hybrid and the free boundary methods are compared. The possibility for applications of the method to swing the separatrix strike point on the divertor target plate is discussed.
Energy Technology Data Exchange (ETDEWEB)
Vdovin, V. L., E-mail: vdov@nfi.kiae.ru [National Research Centre ' Kurchatov Institute,' (Russian Federation)
2013-02-15
The innovative concept and 3D full-wave code modeling the off-axis current drive by radio-frequency (RF) waves in large-scale tokamaks, ITER and DEMO, for steady-state operation with high efficiency is proposed. The scheme uses the helicon radiation (fast magnetosonic waves at high (20-40) ion cyclotron frequency harmonics) at frequencies of 500-700 MHz propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by helicons, in conjunction with the bootstrap current, ensure the maintenance of a given value of the total current in the stability margin q(0) {>=} 2 and q(a) {>=} 4, and will help to have regimes with a negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure {beta}{sub N} > 3 (the so-called advanced scenarios) of interest for the commercial reactor. Modeling with full-wave three-dimensional codes PSTELION and STELEC showed flexible control of the current profile in the reactor plasmas of ITER and DEMO, using multiple frequencies, the positions of the antennae and toroidal wave slow down. Also presented are the results of simulations of current generation by helicons in the DIII-D, T-15MD, and JT-60AS tokamaks. Commercially available continuous-wave klystrons of the MW/tube range are promising for commercial stationary fusion reactors. The compact antennae of the waveguide type are proposed, and an example of a possible RF system for today's tokamaks is given. The advantages of the scheme (partially tested at lower frequencies in tokamaks) are a significant decline in the role of parametric instabilities in the plasma periphery, the use of electrically strong resonator-waveguide type antennae, and substantially greater antenna-plasma coupling.
Vdovin, V. L.
2013-02-01
The innovative concept and 3D full-wave code modeling the off-axis current drive by radio-frequency (RF) waves in large-scale tokamaks, ITER and DEMO, for steady-state operation with high efficiency is proposed. The scheme uses the helicon radiation (fast magnetosonic waves at high (20-40) ion cyclotron frequency harmonics) at frequencies of 500-700 MHz propagating in the outer regions of the plasmas with a rotational transform. It is expected that the current generated by helicons, in conjunction with the bootstrap current, ensure the maintenance of a given value of the total current in the stability margin q(0) ≥ 2 and q( a) ≥ 4, and will help to have regimes with a negative magnetic shear and internal transport barrier to ensure stability at high normalized plasma pressure β N > 3 (the so-called advanced scenarios) of interest for the commercial reactor. Modeling with full-wave three-dimensional codes PSTELION and STELEC showed flexible control of the current profile in the reactor plasmas of ITER and DEMO, using multiple frequencies, the positions of the antennae and toroidal wave slow down. Also presented are the results of simulations of current generation by helicons in the DIII-D, T-15MD, and JT-60AS tokamaks. Commercially available continuous-wave klystrons of the MW/tube range are promising for commercial stationary fusion reactors. The compact antennae of the waveguide type are proposed, and an example of a possible RF system for today's tokamaks is given. The advantages of the scheme (partially tested at lower frequencies in tokamaks) are a significant decline in the role of parametric instabilities in the plasma periphery, the use of electrically strong resonator-waveguide type antennae, and substantially greater antenna-plasma coupling.
Nie, Xiaobing; Zheng, Wei Xing
2016-03-01
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
Broer, H.; Hoveijn, I.; Lunter, G.; Vegter, G.
2003-01-01
The Birkhoff normal form procedure is a widely used tool for approximating a Hamiltonian systems by a simpler one. This chapter starts out with an introduction to Hamiltonian mechanics, followed by an explanation of the Birkhoff normal form procedure. Finally we discuss several algorithms for comput
Simulation of EAST vertical displacement events by tokamak simulation code
Qiu, Qinglai; Xiao, Bingjia; Guo, Yong; Liu, Lei; Xing, Zhe; Humphreys, D. A.
2016-10-01
Vertical instability is a potentially serious hazard for elongated plasma. In this paper, the tokamak simulation code (TSC) is used to simulate vertical displacement events (VDE) on the experimental advanced superconducting tokamak (EAST). Key parameters from simulations, including plasma current, plasma shape and position, flux contours and magnetic measurements match experimental data well. The growth rates simulated by TSC are in good agreement with TokSys results. In addition to modeling the free drift, an EAST fast vertical control model enables TSC to simulate the course of VDE recovery. The trajectories of the plasma current center and control currents on internal coils (IC) fit experimental data well.
A CONCEPT FOR NEXT STEP ADVANCED TOKAMAK FUSION DEVICE
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A concept is introduced for initiating the design study of a special class of tokamak,which has a magnetic confinement configuration intermediate between contemporary advanced tokamak and the recently established spherical torus (ST,also well known by the name "spherical tokamak").The leading design parameter in the present proposal is a dimensionless geometrical parameter, the machine aspect ratio A＝R0/a0＝2.0,where the parameters a0 and R0 denote,respectively,the plasma (equatorial) minor radius and the plasma major radius.The aim of this choice is to technologically and experimentally go beyond the aspect ratio frontier (R0/a0≈2.5) of present day tokamaks and enter a broad unexplored domain existing on the (a0,R0) parameter space in current international tokamak database,between the data region already moderately well covered by the advanced conventional tokamaks and the data region planned to be covered by STs.Plasma minor radius a0 has been chosen to be the second basic design parameter, and consequently,the plasma major radius R0 is regarded as a dependent design parameter.In the present concept,a nominal plasma minor radius a0＝1.2m is adopted to be the principal design value,and smaller values of a0 can be used for auxiliary design purposes,to establish extensive database linkage with existing tokamaks.Plasma minor radius can also be adjusted by mechanical and/or electromagnetic means to smaller values during experiments,for making suitable data linkages to existing machines with higher aspect ratios and smaller plasma minor radii.The basic design parameters proposed enable the adaptation of several confinement techniques recently developed by STs,and thereby a specially arranged central-bore region inside the envisioned tokamak torus,with retrieved space in the direction of plasma minor radius,will be available for technological adjustments and maneuverings to facilitate implementation of engineering instrumentation and real time high
Adaptive grid finite element model of the tokamak scrapeoff layer
Energy Technology Data Exchange (ETDEWEB)
Kuprat, A.P.; Glasser, A.H. [Los Alamos National Lab., NM (United States)
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Resistive demountable toroidal-field coils for tokamak reactors
Energy Technology Data Exchange (ETDEWEB)
Jassby, D.L.; Jacobsen, R.A.; Kalnavarns, J.; Masson, L.S.; Sekot, J.P.
1981-07-01
Readily demountable TF (toroidal-field) coils allow complete access to the internal components of a tokamak reactor for maintenance of replacement. The requirement of readily demountable joints dictates the use of water-cooled resistive coils, which have a host of decisive advantages over superconducting coils. Previous papers have shown that resistive TF coils for tokamak reactors can operate in the steady state with acceptable power dissipation (typically, 175 to 300 MW). This paper summarizes results of parametric studies of size optimization of rectangular TF coils and of a finite-element stress analysis, and examines several candidate methods of implementing demountable joints for rectangular coils constructed of plate segments.
Measurement of Current Profile in a Tokamak Through AC Modulation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The plasma current is modulated with an alternating current (ac) component in a frequency range of 90 Hz～900 Hz in the plateau discharge phase in the CT-6B tokamak. A plasma electric conductivity profile in a form of (1 - r2/a2)α with a parameter α, which is fitted with the experimental data, can be determined. The effects of magnetic shear in a tokamak field configuration on the current penetration are taken into account in the numerical simulation. The measurement method and obtained results are discussed.
Design and Analysis of the Thermal Shield of EAST Tokamak
Institute of Scientific and Technical Information of China (English)
XIE Han; LIAO Ziying
2008-01-01
EAST (Experimental Advanced Superconducting Tokamak) is a tokamak with superconducting toroidal and poloidal magnets operated at 4.5 K. In order to reduce the thermal load applied on the surfaces of all cryogenically cooled components and keep the heat load of the cryogenic system at a minimum, a continuous radiation shield system located between the magnet system and warm components is adopted. The main loads to which the thermal shield system is subjected are gravity, seismic, electromagnetic and thermal gradients. This study employed NASTRAN and ANSYS finite element codes to analyze the stress under a spectrum of loading conditions and combinations, providing a theoretical basis for an optimization design of the structure.
Computer simulation of transport driven current in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Nunan, W.J.; Dawson, J.M. (University of California at Los Angeles, Department of Physics, 405 Hilgard Avenue, Los Angeles, California 90024-1547 (United States))
1994-09-19
We have investigated transport driven current in tokamaks via 2+1/2 dimensional, electromagnetic, particle-in-cell simulations. These have demonstrated a steady increase of toroidal current in centrally fueled plasmas. Neoclassical theory predicts that the bootstrap current vanishes at large aspect ratio, but we see equal or greater current growth in straight cylindrical plasmas. These results indicate that a centrally fueled and heated tokamak may sustain its toroidal current, even without the seed current'' which the neoclassical bootstrap theory requires.
TIBER: Tokamak Ignition/Burn Experimental Research. Final design report
Energy Technology Data Exchange (ETDEWEB)
Henning, C.D.; Logan, B.G.; Barr, W.L.; Bulmer, R.H.; Doggett, J.N.; Johnson, B.M.; Lee, J.D.; Hoard, R.W.; Miller, J.R.; Slack, D.S.
1985-11-01
The Tokamak Ignition/Burn Experimental Research (TIBER) device is the smallest superconductivity tokamak designed to date. In the design plasma shaping is used to achieve a high plasma beta. Neutron shielding is minimized to achieve the desired small device size, but the superconducting magnets must be shielded sufficiently to reduce the neutron heat load and the gamma-ray dose to various components of the device. Specifications of the plasma-shaping coil, the shielding, coaling, requirements, and heating modes are given. 61 refs., 92 figs., 30 tabs. (WRF)
Magnetic flux reconstruction methods for shaped tokamaks
Energy Technology Data Exchange (ETDEWEB)
Tsui, Chi-Wa
1993-12-01
The use of a variational method permits the Grad-Shafranov (GS) equation to be solved by reducing the problem of solving the 2D non-linear partial differential equation to the problem of minimizing a function of several variables. This high speed algorithm approximately solves the GS equation given a parameterization of the plasma boundary and the current profile (p` and FF` functions). The author treats the current profile parameters as unknowns. The goal is to reconstruct the internal magnetic flux surfaces of a tokamak plasma and the toroidal current density profile from the external magnetic measurements. This is a classic problem of inverse equilibrium determination. The current profile parameters can be evaluated by several different matching procedures. Matching of magnetic flux and field at the probe locations using the Biot-Savart law and magnetic Green`s function provides a robust method of magnetic reconstruction. The matching of poloidal magnetic field on the plasma surface provides a unique method of identifying the plasma current profile. However, the power of this method is greatly compromised by the experimental errors of the magnetic signals. The Casing Principle provides a very fast way to evaluate the plasma contribution to the magnetic signals. It has the potential of being a fast matching method. The performance of this method is hindered by the accuracy of the poloidal magnetic field computed from the equilibrium solver. A flux reconstruction package has been implemented which integrates a vacuum field solver using a filament model for the plasma, a multi-layer perception neural network as an interface, and the volume integration of plasma current density using Green`s functions as a matching method for the current profile parameters. The flux reconstruction package is applied to compare with the ASEQ and EFIT data. The results are promising.
Fusion neutron diagnostics on ITER tokamak
Bertalot, L.; Barnsley, R.; Direz, M. F.; Drevon, J. M.; Encheva, A.; Jakhar, S.; Kashchuk, Y.; Patel, K. M.; Arumugam, A. P.; Udintsev, V.; Walker, C.; Walsh, M.
2012-04-01
ITER is an experimental nuclear reactor, aiming to demonstrate the feasibility of nuclear fusion realization in order to use it as a new source of energy. ITER is a plasma device (tokamak type) which will be equipped with a set of plasma diagnostic tools to satisfy three key requirements: machine protection, plasma control and physics studies by measuring about 100 different parameters. ITER diagnostic equipment is integrated in several ports at upper, equatorial and divertor levels as well internally in many vacuum vessel locations. The Diagnostic Systems will be procured from ITER Members (Japan, Russia, India, United States, Japan, Korea and European Union) mainly with the supporting structures in the ports. The various diagnostics will be challenged by high nuclear radiation and electromagnetic fields as well by severe environmental conditions (ultra high vacuum, high thermal loads). Several neutron systems with different sensitivities are foreseen to measure ITER expected neutron emission from 1014 up to almost 1021 n/s. The measurement of total neutron emissivity is performed by means of Neutron Flux Monitors (NFM) installed in diagnostic ports and by Divertor Neutron Flux Monitors (DNFM) plus MicroFission Chambers (MFC) located inside the vacuum vessel. The neutron emission profile is measured with radial and vertical neutron cameras. Spectroscopy is accomplished with spectrometers looking particularly at 2.5 and 14 MeV neutron energy. Neutron Activation System (NAS), with irradiation ends inside the vacuum vessel, provide neutron yield data. A calibration strategy of the neutron diagnostics has been developed foreseeing in situ and cross calibration campaigns. An overview of ITER neutron diagnostic systems and of the associated challenging engineering and integration issues will be reported.
Energy Technology Data Exchange (ETDEWEB)
Ortega C, G.; Gaytan G, E. [Instituto Tecnologico de Toluca, Instituto nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)
1998-07-01
Taking as basis some proposed methodologies by software engineering it was designed and developed a data processing system coming from the diagnostic equipment by spectroscopy, for the study of plasma impurities, during the cleaning discharges. the data acquisition is realized through an electronic interface which communicates the computer with the spectroscopy system of Novillo Tokamak. The data were obtained starting from files type text and processed for their subsequently graphic presentation. For development of this system named PRODATN (Processing of Data for Spectroscopy in Novillo Tokamak) was used the LabVIEW graphic programming language. (Author)
Energy Technology Data Exchange (ETDEWEB)
Fraboulet, D.
1996-09-17
Detection of {alpha}(3.5 MeV) fusion products will be of major importance for the achievement of self sustained discharges in fusion thermonuclear reactors. Due to their cyclotronic gyration in the confining magnetic field of a tokamak, {alpha} particles are suspected to radiate in the radio-frequency band [RF: 10-500 MHz]. Our aim is to determine whether detection of RF emission radiated from a reactor plasma can provide information concerning those fusion products. We observed experimentally that the RF emission radiated from fast ions situated in the core of the discharge is detectable with a probe located at the plasma edge. For that purpose, fast temporal acquisition of spectral power was achieved in a narrow frequency band. We also propose two complementary models for this emission. In the first one, we describe locally the energy transfer between the photon population and the plasma and we compute the radiation equilibrium taking place in the tokamak. {alpha} particles are not the unique species involved in the equilibrium and it is necessary to take into account all other species present in the plasma (Deuterium, Tritium, electrons,...). Our second model consists in the numerical resolution of the Maxwell-Vlasov with the use of a variational formulation, in which all polarizations are considered and the 4 first cyclotronic harmonics are included in a 1-D slab geometry. The development of this second model leads to the proposal for an experimental set up aiming to the feasibility demonstration of a routine diagnostic providing the central {alpha} density in a reactor. (author). 166 refs.
Liquid-liquid equilibria for ternary polymer mixtures
Energy Technology Data Exchange (ETDEWEB)
Oh, Suk Yung [Division of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791 (Korea, Republic of); Bae, Young Chan, E-mail: ycbae@hanyang.ac.kr [Division of Chemical Engineering and Molecular Thermodynamics Laboratory, Hanyang University, Seoul 133-791 (Korea, Republic of)
2011-01-24
Graphical abstract: We developed a molecular thermodynamic model for multicomponent systems and discribed the phase equilibrium for ternary polymer mixtures by using the model parameters obtained from the binary systems. Research highlights: {yields} Model parameters were obtained from the binary systems. {yields} The obtained parameters were directly used to predict the ternary data. {yields} The undetermined parameters were used to correlate the ternary data. {yields} The proposed model agreed well with the experimental data. - Abstract: A molecular thermodynamic model for multicomponent systems based on a closed-packed lattice model is presented based on two contributions; entropy and energy contribution. The calculated liquid-liquid equilibria of ternary chainlike mixtures agreed with Monte Carlo simulation results. The proposed model can satisfactorily predict Types 0, 1, 2 and 3 phase separations of the Treybal classification. The model parameters obtained from the binary systems were used to directly predict real ternary systems and the calculated results correlated well with experimental data using few adjustable parameters. Specific interactions in associated binary systems were considered using a secondary lattice.
A molecular-thermodynamic framework for asphaltene-oil equilibria
Energy Technology Data Exchange (ETDEWEB)
Wu, J.; Prausnitz, J.M. [Univ. of California, Berkeley, CA (United States). Dept. of Chemical Engineering]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.; Firoozabadi, A. [Reservoir Engineering Research Inst., Palo Alto, CA (United States)
1997-02-01
Asphaltene precipitation is a perennial problem in production and refinery of crude oils. To avoid precipitation, it is useful to predict the solubility of asphaltenes in petroleum liquids as a function of temperature, pressure and liquid-phase composition. In the molecular-thermodynamic model presented here, both asphaltenes and resins are represented by pseudo-pure components, and all other components in the solution are represented by a continuous medium which affects interactions among asphaltene and resin particles. The effect of the medium on asphaltene-asphaltene, resin-asphaltene, resin-resin pair interactions is taken into account through its density and molecular-dispersion properties. To obtain expressions for the chemical potential of asphaltene and for the osmotic pressure of an asphaltene-containing solution, the authors use the integral theory of fluids coupled with the SAFT model to allow for asphaltene aggregation and for adsorption of resin on asphaltene particles. With these expressions, a variety of experimental observations can be explained including the effects of temperature, pressure and composition on the phase behavior of asphaltene-containing fluids. For engineering application, the molecular parameters in this model must be correlated to some macroproperties of oil such as density and molecular weight. When such correlations are established, it will be possible to calculate asphaltene-precipitation equilibria at a variety of conditions for realistic systems.
Transitions of Spherical Thermohaline Circulation to Multiple Equilibria
Özer, Saadet; Şengül, Taylan
2017-06-01
The main aim of the paper is to investigate the transitions of the thermohaline circulation in a spherical shell in a parameter regime which only allows transitions to multiple equilibria. We find that the first transition is either continuous (Type-I) or drastic (Type-II) depending on the sign of the transition number. The transition number depends on the system parameters and l_c , which is the common degree of spherical harmonics of the first critical eigenmodes, and it can be written as a sum of terms describing the nonlinear interactions of various modes with the critical modes. We obtain the exact formulas of this transition number for l_c=1 and l_c=2 cases. Numerically, we find that the main contribution to the transition number is due to nonlinear interactions with modes having zero wave number and the contribution from the nonlinear interactions with higher frequency modes is negligible. In our numerical experiments we encountered both types of transition for Le1 . In the continuous transition scenario, we rigorously prove that an attractor in the phase space bifurcates which is homeomorphic to the 2l_c dimensional sphere and consists entirely of degenerate steady state solutions.
Phase equilibria in the Ni-Fe-Ga alloy system
Energy Technology Data Exchange (ETDEWEB)
Ducher, R. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan); Kainuma, R. [Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Sendai 980-8577 (Japan)], E-mail: kainuma@tagen.tohoku.ac.jp; Ishida, K. [Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aoba-yama, Sendai 980-8579 (Japan)
2008-09-08
The phase equilibria, A2/B2 and B2/L2{sub 1} (or D0{sub 3}) order-disorder transitions and martensitic transformation on the Ni-Fe side of the Ni-Fe-Ga system were examined by electron probe microanalysis (EPMA) and differential scanning calorimetric (DSC) measurement. The equilibrium compositions of interrelations mainly among the {alpha} (A2), {beta} (B2), {beta}' (L2{sub 1} or D0{sub 3}), {gamma} (A1) and {gamma}' (L1{sub 2}) phases were determined using diffusion triples which were fabricated by two-step diffusion coupling. It was confirmed that a bcc single-phase region composed of {alpha}, {beta} and {beta}' at 850-1000 deg. C exists in a wide composition range and that the critical temperature of the B2/L2{sub 1} order-disorder transformation in the Fe{sub 3}Ga-Ni{sub 3}Ga pseudo-binary section gradually increases with increasing Ni content. The existing composition region of the martensite phase at room temperature was also determined by the diffusion triple method.
Molecular equilibria and condensation sequences in carbon rich gases
Sharp, C. M.; Wasserburg, G. J.
1993-01-01
Chemical equilibria in stellar atmospheres have been investigated by many authors. Lattimer, Schramm, and Grossman presented calculations in both O rich and C rich environments and predicted possible presolar condensates. A recent paper by Cherchneff and Barker considered a C rich composition with PAH's included in the calculations. However, the condensation sequences of C bearing species have not been investigated in detail. In a carbon rich gas surrounding an AGB star, it is often assumed that graphite (or diamond) condenses out before TiC and SiC. However, Lattimer et al. found some conditions under which TiC condenses before graphite. We have performed molecular equilibrium calculations to establish the stability fields of C(s), TiC(s), and SiC(s) and other high temperature phases under conditions of different pressures and C/O. The preserved presolar interstellar dust grains so far discovered in meteorites are graphite, diamond, SiC, TiC, and possibly Al2O3.
Fokker-Planck Study of Tokamak Electron Cyclotron Resonance Heating
Institute of Scientific and Technical Information of China (English)
SHIBingren; LONGYongxing; DONGJiaqi; LIWenzhong; JIAOYiming; WANGAike
2002-01-01
In this study, we add a subroutine for describing the electron cyclotron resonant heating calculation to the Fokker-Planck code. By analyzing the wave-particle resonance condition in tokamak plasma and the fast motion of electrons along magnetic field lines, suitable quasi-linear diffusion coefficients are given.
MHD analysis of edge instabilities in the JET tokamak
Perez von Thun, Christian Pedro
2004-01-01
The aim of nuclear fusion energy research is to demonstrate the feasibility of nuclear fusion reactors as a future energy source. The tokamak is the most advanced fusion machine to date, and is most likely the first system to be converted into a reactor. An important subject of nuclear fusion resear
Disruption avoidance through active magnetic feedback in tokamak plasmas
Paccagnella, Roberto; Zanca, Paolo; Yanovskiy, Vadim; Finotti, Claudio; Manduchi, Gabriele; Piron, Chiara; Carraro, Lorella; Franz, Paolo; RFX Team
2014-10-01
Disruptions avoidance and mitigation is a fundamental need for a fusion relevant tokamak. In this paper a new experimental approach for disruption avoidance using active magnetic feedback is presented. This scheme has been implemented and tested on the RFX-mod device operating as a circular tokamak. RFX-mod has a very complete system designed for active mode control that has been proved successful for the stabilization of the Resistive Wall Modes (RWMs). In particular the current driven 2/1 mode, unstable when the edge safety factor, qa, is around (or even less than) 2, has been shown to be fully and robustly stabilized. However, at values of qa (qa > 3), the control of the tearing 2/1 mode has been proved difficult. These results suggested the idea to prevent disruptions by suddenly lowering qa to values around 2 where the tearing 2/1 is converted to a RWM. Contrary to the universally accepted idea that the tokamaks should disrupt at low qa, we demonstrate that in presence of a well designed active control system, tokamak plasmas can be driven to low qa actively stabilized states avoiding plasma disruption with practically no loss of the plasma internal energy.
Kazakhstan tokamak for material testing conceptual design and basic parameters
Energy Technology Data Exchange (ETDEWEB)
Korotkov, V.A. E-mail: korotkov@sintez.niiefa.spb.su; Azizov, E.A.; Cherepnin, Yu.S.; Dokouka, V.N.; Ya.Dvorkin, N.; Khayrutdinov, R.R.; Krylov, V.A.; Kuzmin, E.G.; Leykin, I.N.; Mineev, A.B.; Shkolnik, V.S.; Shestakov, V.P.; Shapovalov, G.V.; Tazhibaeva, I.L.; Tikhomirov, L.N.; Yagnov, V.A
2001-10-01
The construction of a special machine for plasma facing material testing under powerful and particle and heat flux deposition is necessary for progress of researches in the field of controlled fusion to industrial application. Kazakhstan tokamak for material testing (KTM) is planned as spherical tokamak with moderate-to-low aspect ratio (A=2) and high plasma and vacuum vessel elongation, that allows to reach high plasma parameters, large power-intensity at a compact arrangement of design elements and low requirements to a toroidal magnetic field. KTM tokamak is planned in order to investigate the following issues: (1) Plasma confinement in tokamak with A=2, plasma parameters and configurations working window; (2) Differed kinds of divertor plates under power flux of plasma to divertor volume; (3) Plasma-wall interaction (different materials and coating) and plasma-limiter configurations. In the paper the basic parameters of the machine are given. The design of magnet system with poloidal field coils, vacuum vessel and divertor are submitted.
Dynamic diagnostics of the error fields in tokamaks
Pustovitov, V. D.
2007-07-01
The error field diagnostics based on magnetic measurements outside the plasma is discussed. The analysed methods rely on measuring the plasma dynamic response to the finite-amplitude external magnetic perturbations, which are the error fields and the pre-programmed probing pulses. Such pulses can be created by the coils designed for static error field correction and for stabilization of the resistive wall modes, the technique developed and applied in several tokamaks, including DIII-D and JET. Here analysis is based on the theory predictions for the resonant field amplification (RFA). To achieve the desired level of the error field correction in tokamaks, the diagnostics must be sensitive to signals of several Gauss. Therefore, part of the measurements should be performed near the plasma stability boundary, where the RFA effect is stronger. While the proximity to the marginal stability is important, the absolute values of plasma parameters are not. This means that the necessary measurements can be done in the diagnostic discharges with parameters below the nominal operating regimes, with the stability boundary intentionally lowered. The estimates for ITER are presented. The discussed diagnostics can be tested in dedicated experiments in existing tokamaks. The diagnostics can be considered as an extension of the 'active MHD spectroscopy' used recently in the DIII-D tokamak and the EXTRAP T2R reversed field pinch.
Bulk Ion Heating with ICRF Waves in Tokamaks
DEFF Research Database (Denmark)
Mantsinen, M. J.; Bilato, R.; Bobkov, V. V.
2015-01-01
Heating with ICRF waves is a well-established method on present-day tokamaks and one of the heating systems foreseen for ITER. However, further work is still needed to test and optimize its performance in fusion devices with metallic high-Z plasma facing components (PFCs) in preparation of ITER a...
Feedback Control for Plasma Position on HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
LIBo; SONGXianming; LILi; LIULi; WANGMinghong; FANMingjie; CHENLiaoyuan; YAOLieying; YANGQingwei
2003-01-01
HL-2A is a tokamak with closed divertor. It had been built at the end of 2002 and began to discharge from then on. To further study plasma discharges in HL-2A, a feedback control system (FBCS) for plasma position bad been developed in 2003.
Solenoid-free plasma start-up in spherical tokamaks
Raman, R.; Shevchenko, V. F.
2014-10-01
The central solenoid is an intrinsic part of all present-day tokamaks and most spherical tokamaks. The spherical torus (ST) confinement concept is projected to operate at high toroidal beta and at a high fraction of the non-inductive bootstrap current as required for an efficient reactor system. The use of a conventional solenoid in a ST-based fusion nuclear facility is generally believed to not be a possibility. Solenoid-free plasma start-up is therefore an area of extensive worldwide research activity. Solenoid-free plasma start-up is also relevant to steady-state tokamak operation, as the central transformer coil of a conventional aspect ratio tokamak reactor would be located in a high radiation environment but would be needed only during the initial discharge initiation and current ramp-up phases. Solenoid-free operation also provides greater flexibility in the selection of the aspect ratio and simplifies the reactor design. Plasma start-up methods based on induction from external poloidal field coils, helicity injection and radio frequency current drive have all made substantial progress towards meeting this important need for the ST. Some of these systems will now undergo the final stages of test in a new generation of large STs, which are scheduled to begin operations during the next two years. This paper reviews research to date on methods for inducing the initial start-up current in STs without reliance on the conventional central solenoid.
The Effect of Recycling in the HL-1M Tokamak
Institute of Scientific and Technical Information of China (English)
ZHENGYongzhen
2002-01-01
It is often stated that even clean tokamak discharges disrupt at high density. One possibility is that such disruption result from the energy loss arising from hydrogen recycling at the edge of the plasma.this energy loss could lead to a contraction of the current channel and the production of a disruptively unstable configuration.
General Description of Ideal Tokamak MHD Instability Ⅱ
Institute of Scientific and Technical Information of China (English)
石秉仁
2002-01-01
In this subsequent study on general description of ideal tokamak MHD instability,the part Ⅱ, by using a coordinate with rectified magnetic field lines, the eigenmode equationsdescribing the low-mode-number toroidal Alfven modes (TAE and EAE) are derived through afurther expansion of the shear Alfven equation of motion.
Test particle transport in perturbed magnetic fields in tokamaks
de Rover, M.; Schilham, A.M.R.; Montvai, A.; Cardozo, N. J. L.
1999-01-01
Numerical calculations of magnetic field line trajectories in a tokamak are used to investigate the common hypotheses that (i) field lines in a chaotic field make a Gaussian random walk and (ii) that the poloidal component of the magnetic field is uniform in regions with a chaotic magnetic field. Bo
Evidence of Inward Toroidal Momentum Convection in the JET Tokamak
DEFF Research Database (Denmark)
Tala, T.; Zastrow, K.-D.; Ferreira, J.
2009-01-01
Experiments have been carried out on the Joint European Torus tokamak to determine the diffusive and convective momentum transport. Torque, injected by neutral beams, was modulated to create a periodic perturbation in the toroidal rotation velocity. Novel transport analysis shows the magnitude an...
Conceptual design of Remote Control System for EAST tokamak
Energy Technology Data Exchange (ETDEWEB)
Sun, X.Y., E-mail: xysun@ipp.ac.cn; Wang, F.; Wang, Y.; Li, S.
2014-05-15
Highlights: • A new design conception for remote control for EAST tokamak is proposed. • Rich Internet application (RIA) was selected to implement the user interface. • Some security mechanism was used to fulfill security requirement. - Abstract: The international collaboration becomes popular in tokamak research like in many other fields of science, because the experiment facilities become larger and more expensive. The traditional On-site collaboration Model that has to spend much money and time on international travel is not fit for the more frequent international collaboration. The Remote Control System (RCS), as an extension of the Central Control System for the EAST tokamak, is designed to provide an efficient and economical way to international collaboration. As a remote user interface, the RCS must integrate with the Central Control System for EAST tokamak to perform discharge control function. This paper presents a design concept delineating a few key technical issues and addressing all significant details in the system architecture design. With the aim of satisfying system requirements, the RCS will select rich Internet application (RIA) as a user interface, Java as a back-end service and Secure Socket Layer Virtual Private Network (SSL VPN) for securable Internet communication.
Tokamak Scenario Trajectory Optimization Using Fast Integrated Simulations
Urban, Jakub; Artaud, Jean-François; Vahala, Linda; Vahala, George
2015-11-01
We employ a fast integrated tokamak simulator, METIS, for optimizing tokamak discharge trajectories. METIS is based on scaling laws and simplified transport equations, validated on existing experiments and capable of simulating a full tokamak discharge in about 1 minute. Rapid free-boundary equilibrium post-processing using FREEBIE provides estimates of PF coil currents or forces. We employ several optimization strategies for optimizing key trajectories, such as Ip or heating power, of a model ITER hybrid discharge. Local and global algorithms with single or multiple objective functions show how to reach optimum performance, stationarity or minimum flux consumption. We constrain fundamental operation parameters, such as ramp-up rate, PF coils currents and forces or heating power. As an example, we demonstrate the benefit of current over-shoot for hybrid mode, consistent with previous results. This particular optimization took less than 2 hours on a single PC. Overall, we have established a powerful approach for rapid, non-linear tokamak scenario optimization, including operational constraints, pertinent to existing and future devices design and operation.
Current ramps in tokamaks: from present experiments to ITER scenarios
Imbeaux, F.; Citrin, J.; Hobirk, J.; Hogeweij, G. M. D.; Kochl, F.; Leonov, V. M.; Miyamoto, S.; Nakamura, Y.; Parail, V.; Pereverzev, G.; Polevoi, A.; Voitsekhovitch, I.; Basiuk, V.; Budny, R.; Casper, T.; Fereira, J.; Fukuyama, A.; Garcia, J.; Gribov, Y. V.; Hayashi, N.; Honda, M.; Hutchinson, I. H.; Jackson, G.; Kavin, A. A.; Kessel, C. E.; Khayrutdinov, R. R.; Labate, C.; Litaudon, X.; Lomas, P. J.; Lonnroth, J.; Luce, T.; Lukash, V. E.; Mattei, M.; Mikkelsen, D.; Nunes, I.; Peysson, Y.; Politzer, P.; Schneider, M.; Sips, G.; Tardini, G.; Wolfe, S. M.; Zhogolev, V. E.
2011-01-01
In order to prepare adequate current ramp-up and ramp-down scenarios for ITER, present experiments from various tokamaks have been analysed by means of integrated modelling in view of determining relevant heat transport models for these operation phases. A set of empirical heat transport models for
Pellet Enhanced Performance on the HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
DING Xuan-Tong; LIU Yi; ZHOU Yan; PAN Yu-Dong; CUI Zheng-Ying; HUANG Yuan; LIU Ze-Tian; SHI Zhong-Bing; JI Xiao-Quan; XIAO Wei-Wen; LIU Yong; YANG Qing-Wei; YAN Long-Wen; ZHU Gen-Liang; XIAO Zheng-Gui; LIU De-Quan; CAO Zeng; GAO Qing-Di; LONG Yong-Xing
2006-01-01
@@ Enhanced confinement has been achieved by the centre fuelling of pellet injection on the HL-2A tokamak. The energy confinement time increases from 50ms to 140ms after the pellet injection. Experimental results show that the improvement of the confinement is related to the decrease of the electron heat transport.
Sensitivity of transient synchrotron radiation to tokamak plasma parameters
Energy Technology Data Exchange (ETDEWEB)
Fisch, N.J.; Kritz, A.H.
1988-12-01
Synchrotron radiation from a hot plasma can inform on certain plasma parameters. The dependence on plasma parameters is particularly sensitive for the transient radiation response to a brief, deliberate, perturbation of hot plasma electrons. We investigate how such a radiation response can be used to diagnose a variety of plasma parameters in a tokamak. 18 refs., 13 figs.
TPX diagnostics for tokamak operation, plasma control and machine protection
Energy Technology Data Exchange (ETDEWEB)
Edmonds, P.H. [Texas Univ., Austin, TX (United States). Fusion Research Center; Medley, S.S.; Young, K.M. [Princeton Univ., NJ (United States). Plasma Physics Lab.] [and others
1995-08-01
The diagnostics for TPX are at an early design phase, with emphasis on the diagnostic access interface with the major tokamak components. Account has to be taken of the very severe environment for diagnostic components located inside the vacuum vessel. The placement of subcontracts for the design and fabrication of the diagnostic systems is in process.
Ion Temperature-Measurements in Tokamak Plasmas by Rutherford Scattering
Vanblokland, A. A. E.; Barbian, E. P.; Donne, A. J. H.; van der Grift, A. F.; Grimbergen, T. W. M.; Oyevaar, T.; Schüller, F. C.; Tammen, H. F.; Vanderven, H. W.; Vijverberg, T. F.; Dewinter, F. D. A.; Bertschinger, G.; Cosler, A.; Korten, M.
1992-01-01
A Rutherford scattering diagnostic has been applied at the TEXTOR tokamak to obtain spatially and temporally resolved information on the temperature of the bulk ions in the plasma. In the experimental setup, a helium atomic beam (30-keV, 12-mA equivalent current) passes vertically through the plasma
Evolving magnetic equilibria in anomalous turbulent transport simulations
Lee, Jungpyo; Cerfon, Antoine; Highcock, Edmund; Barnes, Michael
2014-10-01
The evolution of poloidal and toroidal magnetic fluxes in a tokamak are determined by Faraday's law in which electric field needs to be consistent with 1-D radial transports of density, temperature, and toroidal angular momentum. Consistency is required because the transport of the thermodynamic variables depends on the 2-D magnetic equilibrium that changes depending on the radial pressure profile. For neoclassical transport, consistency is achieved through a proper treatment of the parallel electric field and Ohm's law [Hinton and Hazeltine (1976), Hirshman and Jardin (1979)]. Recently, consistency for the anomalous turbulent transport has been studied analytically using a Lagrangian formulation of gyrokinetics [Sugama et al. (2014)]. In this poster, we propose a simple numerical model to evolve both the magnetic equilibrium and the radial profile of density, temperature, and toroidal angular frequency due to turbulent transport with a fixed q (safety factor) profile. The constraint of fixed q profile makes the evolution self-consistent only if the transport time scale is much smaller than the resistive current diffusion time scale. In this model, we use the transport code TRINITY coupled with the local gyrokinetic code GS2 and the q-solver version of the Grad-Shafranov code ECOM.
Design and construction of Alborz tokamak vacuum vessel system
Energy Technology Data Exchange (ETDEWEB)
Mardani, M., E-mail: mohsenmardani@gmail.com [Amirkabir University of Technology (Tehran Polytechnic), Tehran (Iran, Islamic Republic of); Amrollahi, R.; Koohestani, S. [Amirkabir University of Technology (Tehran Polytechnic), Tehran (Iran, Islamic Republic of)
2012-09-15
Highlights: Black-Right-Pointing-Pointer The Alborz tokamak is a D-shape cross section tokamak that is under construction in Amirkabir University of Technology. Black-Right-Pointing-Pointer As one of the key components for the device, the vacuum vessel can provide ultra-high vacuum and clean environment for the plasma operation. Black-Right-Pointing-Pointer A limiter is a solid surface which defines the edge of the plasma and designed to protect the wall from the plasma, localizes the plasma-surface interaction and localizes the particle recycling. Black-Right-Pointing-Pointer Structural analyses were confirmed by FEM model for dead weight, vacuum pressure and plasma disruptions loads. - Abstract: The Alborz tokamak is a D-shape cross section tokamak that is under construction in Amirkabir University of Technology. At the heart of the tokamak is the vacuum vessel and limiter which collectively are referred to as the vacuum vessel system. As one of the key components for the device, the vacuum vessel can provide ultra-high vacuum and clean environment for the plasma operation. The VV systems need upper and lower vertical ports, horizontal ports and oblique ports for diagnostics, vacuum pumping, gas puffing, and maintenance accesses. A limiter is a solid surface which defines the edge of the plasma and designed to protect the wall from the plasma, localizes the plasma-surface interaction and localizes the particle recycling. Basic structure analyses were confirmed by FEM model for dead weight, vacuum pressure and plasma disruptions loads. Stresses at general part of the VV body are lower than the structure material allowable stress (117 MPa) and this analysis show that the maximum stresses occur near the gravity support, and is about 98 MPa.
LIDAR Thomson scattering for advanced tokamaks. Final report
Energy Technology Data Exchange (ETDEWEB)
Molvik, A.W.; Lerche, R.A.; Nilson, D.G. [and others
1996-03-18
The LIDAR Thomson Scattering for Advanced Tokamaks project made a valuable contribution by combining LLNL expertise from the MFE Program: tokamak design and diagnostics, and the ICF Program and Physics Dept.: short-pulse lasers and fast streak cameras. This multidisciplinary group evaluated issues involved in achieving a factor of 20 higher high spatial resolution (to as small as 2-3 mm) from the present state of the art in LIDAR Thomson scattering, and developed conceptual designs to apply LIDAR Thomson scattering to three tokamaks: Upgraded divertor measurements in the existing DIII-D tokamak; Both core and divertor LIDAR Thomson scattering in the proposed (now cancelled) TPX; and core, edge, and divertor LIDAR Thomson scattering on the presently planned International Tokamak Experimental Reactor, ITER. Other issues were evaluated in addition to the time response required for a few millimeter spatial resolution. These include the optimum wavelength, 100 Hz operation of the laser and detectors, minimizing stray light - always the Achilles heel of Thomson scattering, and time dispersion in optics that could prevent good spatial resolution. Innovative features of our work included: custom short pulsed laser concepts to meet specific requirements, use of a prism spectrometer to maintain a constant optical path length for high temporal and spatial resolution, the concept of a laser focus outside the plasma to ionize gas and form an external fiducial to use in locating the plasma edge as well as to spread the laser energy over a large enough area of the inner wall to avoid laser ablation of wall material, an improved concept for cleaning windows between shots by means of laser ablation, and the identification of a new physics issue - nonlinear effects near a laser focus which could perturb the plasma density and temperature that are to be measured.
LONG-PULSE, HIGH-PERFORMANCE DISCHARGES IN THE DIII-D TOKAMAK
Energy Technology Data Exchange (ETDEWEB)
T.C. LUCE; M.R. WADE; P.A. POLITZER; S.L. ALLEN; M E. AUSTIN; D.R. BAKER; B.D. BRAY; D.P. BRENNAN; K.H. BURRELL; T.A. CASPER; M.S. CHU; J.D. De BOO; E.J. DOYLE; J.R. FERRON; A.M. GAROFALO; P.GOHIL; I.A. GORELOV; C.M. GREENFIELD; R.J. GROEBNER; W.W. HEIBRINK; C.-L. HSIEH; A.W. HYATT; R.JAYAKUMAR; J.E.KINSEY; R.J. LA HAYE; L.L.LAO; C.J.LASNIER; E.A. LAZARUS; A.W. LEONARD; Y.R.LIN-LIU; J.LOHR; M.A. MAKOWSKI; M.MURAKAMI; C.C.PETTY; R.I. PINSKER; R.PRATER; C.L. RETTIG; T.L. RHODES; B.W. RICE; E.J. STRAIT; T.S. TAYLOR; D.M. THOMAS; A.D. TURNBULL; J.G. WATKINS; W.P.WEST; K.-L. WONG
2000-10-01
Significant progress in obtaining high performance discharges for many energy confinement times in the DIII-D tokamak has been realized since the previous IAEA meeting. In relation to previous discharges, normalized performance {approx}10 has been sustained for >5 {tau}{sub E} with q{sub min} >1.5. (The normalized performance is measured by the product {beta}{sub N} H{sub 89} indicating the proximity to the conventional {beta} limits and energy confinement quality, respectively.) These H-mode discharges have an ELMing edge and {beta} {approx}{le} 5%. The limit to increasing {beta} is a resistive wall mode, rather than the tearing modes previously observed. Confinement remains good despite the increase in q. The global parameters were chosen to optimize the potential for fully non-inductive current sustainment at high performance, which is a key program goal for the DIII-D facility in the next two years. Measurement of the current density and loop voltage profiles indicate {approx}75% of the current in the present discharges is sustained non-inductively. The remaining ohmic current is localized near the half radius. The electron cyclotron heating system is being upgraded to replace this remaining current with ECCD. Density and {beta} control, which are essential for operating advanced tokamak discharges, were demonstrated in ELMing H-mode discharges with {beta}{sub N}H{sub 89} {approx} 7 for up to 6.3 s or {approx} 34 {tau}{sub E}. These discharges appear to be in resistive equilibrium with q{sub min} {approx} 1.05, in agreement with the current profile relaxation time of 1.8 s.
Bifurcations and selection of equilibria in a simple cosymmetric model of filtrational convection.
Govorukhin, V. N.; Yudovich, V. I.
1999-06-01
A three-dimensional set of ordinary differential equations that constitutes a simple abstract model of Darcy convection is investigated. The model reproduces a number of effects that are typical for dynamic systems with nontrivial cosymmetry. Nontrivial cosymmetry can give rise to a continuous family of equilibria where, in this case, the equilibrium stability spectrum varies along the family. The family of equilibria and its stability are examined analytically, and special bifurcations that occur in the system are investigated. It is shown that discrete and continual symmetries, called "flash symmetries," can be present in the system for certain parameter values. Computer experiments on the selection of equilibria in the symmetric and cosymmetric cases have been carried out. They showed that, for initial points that are far enough from a cycle of equilibria, the neighborhood of a single equilibrium is established in the case of cosymmetry, but all the equilibria are equivalent in the case of symmetry. The authors hope that these results, as well as the formulation of the problems and the approach to their solution, will serve as a sample in the investigation of more complex systems in mathematical physics. (c) 1999 American Institute of Physics.
ELM induced tungsten melting and its impact on tokamak operation
Coenen, J. W.; Arnoux, G.; Bazylev, B.; Matthews, G. F.; Jachmich, S.; Balboa, I.; Clever, M.; Dejarnac, R.; Coffey, I.; Corre, Y.; Devaux, S.; Frassinetti, L.; Gauthier, E.; Horacek, J.; Knaup, M.; Komm, M.; Krieger, K.; Marsen, S.; Meigs, A.; Mertens, Ph.; Pitts, R. A.; Puetterich, T.; Rack, M.; Stamp, M.; Sergienko, G.; Tamain, P.; Thompson, V.
2015-08-01
In JET-ILW dedicated melt exposures were performed using a sequence of 3MA/2.9T H-Mode JET pulses with an input power of PIN = 23 MW, a stored energy of ∼6 MJ and regular type I ELMs at ΔWELM = 0.3 MJ and fELM ∼ 30 Hz. In order to assess the risk of starting ITER operations with a full W divertor, one of the task was to measure the consequences of W transients melting due to ELMs. JET is the only tokamak able to produce transients/ ELMs large enough (>300 kJ per ELM) to facilitate melting of tungsten. Such ELMs are comparable to mitigated ELMs expected in ITER. By moving the outer strike point (OSP) onto a dedicated leading edge the base temperature was raised within ∼1 s to allow transient ELM-driven melting during the subsequent 0.5 s. Almost 1 mm (∼6 mm3) of W was moved by ∼ 150 ELMs within 5 subsequent discharges. Significant material losses in terms of ejections into the plasma were not observed. There is indirect evidence that some small droplets (∼ 80 μm) were ejected. The impact on the main plasma parameters is minor and no disruptions occurred. The W-melt gradually moved along the lamella edge towards the high field side, driven by j × B forces. The evaporation rate determined is 100 times less than expected from steady state melting and thus only consistent with transient melting during individual ELMs. IR data, spectroscopy, as well as melt modeling point to transient melting. Although the type of damage studied in these JET experiments is unlikely to be experienced in ITER, the results do strongly support the design strategy to avoid exposed edges in the ITER divertor. The JET experiments required a surface at normal incidence and considerable pre-heating to produce tungsten melting. They provide unique experimental evidence for the absence of significant melt splashing at events resembling mitigated ELMs on ITER and establish a unique experimental benchmark for the simulations being used to study transient shallow melting on ITER W
Correlation of three-liquid-phase equilibria involving ionic liquids.
Rodríguez-Escontrela, I; Arce, A; Soto, A; Marcilla, A; Olaya, M M; Reyes-Labarta, J A
2016-08-03
The difficulty in achieving a good thermodynamic description of phase equilibria is finding a model that can be extended to a large variety of chemical families and conditions. This problem worsens in the case of systems containing more than two phases or involving complex compounds such as ionic liquids. However, there are interesting applications that involve multiphasic systems, and the promising features of ionic liquids suggest that they will play an important role in many future processes. In this work, for the first time, the simultaneous correlation of liquid-liquid and liquid-liquid-liquid equilibrium data for ternary systems involving ionic liquids has been carried out. To that end, the phase diagram of the water + [P6 6 6 14][DCA] + hexane system has been determined at 298.15 K and 323.15 K and atmospheric pressure. The importance of this system lies in the possibility of using the surface active ionic liquid to improve surfactant enhanced oil recovery methods. With those and previous measurements, thirteen sets of equilibrium data for water + ionic liquid + oil ternary systems have been correlated. The isoactivity equilibrium condition, using the NRTL model, and some pivotal strategies are proposed to correlate these complex systems. Good agreement has been found between experimental and calculated data in all the regions (one triphasic and two biphasic) of the diagrams. The geometric aspects related to the Gibbs energy of mixing function obtained using the model, together with the minor common tangent plane equilibrium condition, are valuable tools to check the consistency of the obtained correlation results.
The thermodynamic fundamentals relating phase equilibria in binary and ternary systems to the thermodynamic properties of the phases are reviewed and...system demonstrate the application of the equations for extracting thermodynamic data from phase diagrams and also for the prediction of phase equilibria .
DEFF Research Database (Denmark)
Fonseca, José M.S.; von Solms, Nicolas
2012-01-01
A new apparatus for the study of high-pressure phase equilibria at low temperatures using an analytical method was designed, assembled and tested. The apparatus was specially developed for the study of multi-phase equilibria in systems containing hydrocarbons, water and hydrate inhibitors...
Isotropic-nematic phase equilibria of hard-sphere chain fluids—Pure components and binary mixtures
Oyarzun, B.; Van Westen, T.; Vlugt, T.J.H.
2015-01-01
The isotropic-nematic phase equilibria of linear hard-sphere chains and binary mixtures of them are obtained from Monte Carlo simulations. In addition, the infinite dilution solubility of hard spheres in the coexisting isotropic and nematic phases is determined. Phase equilibria calculations are
A Continuous Family of Equilibria in Ferromagnetic Media are Ground States
Su, Xifeng; de la Llave, Rafael
2017-09-01
We show that a foliation of equilibria (a continuous family of equilibria whose graph covers all the configuration space) in ferromagnetic transitive models are ground states. The result we prove is very general, and it applies to models with long range and many-body interactions. As an application, we consider several models of networks of interacting particles including models of Frenkel-Kontorova type on Z^d and one-dimensional quasi-periodic media. The result above is an analogue of several results in the calculus of variations (fields of extremals) and in PDE's. Since the models we consider are discrete and long range, new proofs need to be given. We also note that the main hypothesis of our result (the existence of foliations of equilibria) is the conclusion (using KAM theory) of several recent papers. Hence, we obtain that the KAM solutions recently established are minimizers when the interaction is ferromagnetic and transitive (these concepts are defined later).
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
A note on relative equilibria in a rotating shallow water layer
Ait Abderrahmane, Hamid
2013-05-08
Relative equilibria of two and three satellite vortices in a rotating shallow water layer have been recorded via particle image velocimetry (PIV) and their autorotation speed was estimated. This study shows that these equilibria retain the fundamental characteristics of Kelvin\\'s equilibria, and could be adequately described by the classical idealized point vortex theory. The same conclusion can also be inferred using the experimental dataset of Bergmann etÂ al.Â (J.Â FluidÂ Mech., vol. 679, 2011, pp. 415-431; J. Fluid Mech., vol. 691, 2012, pp. 605-606) if the assigned field\\'s contribution to pattern rotation is included. © 2013 Cambridge University Press.
Effect of temperature on acid-base equilibria in separation techniques. A review.
Gagliardi, Leonardo G; Tascon, Marcos; Castells, Cecilia B
2015-08-19
Studies on the theoretical principles of acid-base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid-base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid-liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simpliﬁed models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC.
Variational principles in chemical equilibria: Complex chemical systems with interacting subsystems
Zilbergleyt, B
2010-01-01
The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach the problem of complex equilibrium is solved by minimization of the system Gibbsâ free energy subject to logistic constraints. DTD demands any isolated system to comprise smaller subentities, which individual equilibria are based on the balance of internal and external thermodynamic forces, acting against them. The internal forces are equal to the subsystems thermodynamic affinities, while external forces originate from subsystems mutual interactions. Those interactions impose additional constraints on the mother system Gibbsâ free energy minimum. Basic expression of discrete thermodynamics, being multiplied by subsystems deviations from their âtrueâ thermodynamic equilibria, is naturally identical to dâAlembertâs principle. A thermodynamic ve...
Fueling studies on the lithium tokamak experiment
Lundberg, Daniel Patrick
Lithium plasma facing components reduce the flux of "recycled" particles entering the plasma edge from the plasma facing components. This results in increased external fueling requirements and provides the opportunity to control the magnitude and distribution of the incoming particle flux. It has been predicted that the plasma density profile will then be determined by the deposition profile of the external fueling, rather than dominated by the recycled particle flux. A series of experiments on the Lithium Tokamak Experiment demonstrate that lithium wall coatings facilitate control of the neutral and plasma particle inventories. With fresh lithium coatings and careful gas injection programming, over 90% of the injected particle inventory can be absorbed in the lithium wall during a discharge. Furthermore, dramatic changes in the fueling requirements and plasma parameters were observed when lithium coatings were applied. This is largely due to the elimination of water as an impurity on the plasma facing components. A Molecular Cluster Injector (MCI) was developed for the fueling of LTX plasmas. The MCI uses a supersonic nozzle, cooled to liquid nitrogen temperatures, to create the conditions necessary for molecular cluster formation. It has been predicted that molecular clusters will penetrate deeper into plasmas than gas-phase molecules via a reduced ionization cross-section and by improving the collimation of the neutral jet. Using an electron beam diagnostic, the densities of the cryogenic MCI are measured to be an order of magnitude higher than in the room-temperature jets formed with the same valve pressure. This indicates increased collimation relative to what would be expected from ideal gas dynamics alone. A systematic study of the fueling efficiencies achieved with the LTX fueling systems is presented. The fueling efficiency of the Supersonic Gas Injector (SGI) is demonstrated to be strongly dependent on the distance between the nozzle and plasma edge. The
Vacuum system of SST-1 Tokamak
Energy Technology Data Exchange (ETDEWEB)
Khan, Ziauddin, E-mail: ziauddin@ipr.res.in [Institute for Plasma Research, Near Indira Bridge, Bhat, Gandhinagar 382 428 (India); Pathan, Firozkhan; George, Siju; Semwal, Pratibha; Dhanani, Kalpesh; Paravastu, Yuvakiran; Thankey, Prashant; Ramesh, Gattu; Himabindu, Manthena; Pradhan, Subrata [Institute for Plasma Research, Near Indira Bridge, Bhat, Gandhinagar 382 428 (India)
2013-10-15
Highlights: ► Air leaks developed during ongoing SST-1 cooldown campaign were detected online using RGA. ► The presence of N{sub 2} and O{sub 2} gases with the ratio of their partial pressures with ∼3.81:1 confirmed the air leaks. ► Baking of SST-1 was done efficiently by flowing hot N{sub 2} gas in C-channels welded on inner surfaces without any problem. ► In-house fabricated demountable bull nose couplers were demonstrated for high temperature and pressure applications. ► Cryopumping effect was observed when liquid helium cooled superconducting magnets reached below 63 K. -- Abstract: Vacuum chambers of Steady State Superconducting (SST-1) Tokamak comprises of the vacuum vessel and the cryostat. The plasma will be confined inside the vacuum vessel while the cryostat houses the superconducting magnet systems (TF and PF coils), LN{sub 2} cooled thermal shields and hydraulics for these circuits. The vacuum vessel is an ultra-high (UHV) vacuum chamber while the cryostat is a high-vacuum (HV) chamber. In order to achieve UHV inside the vacuum vessel, it would be baked at 150 °C for longer duration. For this purpose, U-shaped baking channels are welded inside the vacuum vessel. The baking will be carried out by flowing hot nitrogen gas through these channels at 250 °C at 4.5 bar gauge pressure. During plasma operation, the pressure inside the vacuum vessel will be raised between 1.0 × 10{sup −4} mbar and 1.0 × 10{sup −5} mbar using piezoelectric valves and control system. An ultimate pressure of 4.78 × 10{sup −6} mbar is achieved inside the vacuum vessel after 100 h of pumping. The limitation is due to the development of few leaks of the order of 10{sup −5} mbar l/s at the critical locations of the vacuum vessel during baking which was confirmed with the presence of nitrogen gas and oxygen gas with the ratio of ∼3.81:1 indicating air leak. Similarly an ultimate vacuum of 2.24 × 10{sup −5} mbar is achieved inside the cryostat. Baking of the
Sasidevan, V
2015-01-01
The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games - namely, those of Nash equilibrium and co-action equilibrium. For the Nash equilibrium, we show that the dynamical view can provide an equilibrium refinement, selecting one equilibrium among several possibilities, thereby solving the issue of multiple equilibria that appear in some games. We illustrate in detail this dynamical perspective by considering three well known 2-person games namely the Prisoner's Dilemma, game of Chicken and the Stag-Hunt. We find that in all of these cases, co-action equilibria tends to correspond to `nicer' strategies than those corresponding to Nash equilibria.
Concept definition of KT-2, a large-aspect-ratio diverter tokamak with FWCD
Energy Technology Data Exchange (ETDEWEB)
Kim, Sung Kyoo; Chang, In Soon; Chung, Moon Kyoo; Hwang, Chul Kyoo; Lee, Kwang Won; In, Sang Ryul; Choi, Byung Ho; Hong, Bong Keun; Oh, Byung Hoon; Chung, Seung Ho; Yoon, Byung Joo; Yoon, Jae Sung; Song, Woo Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Chang, Choong Suk; Chang, Hong Yung; Choi, Duk In; Nam, Chang Heui [Korea Advanced Inst. of Science and Technology, Taejon (Korea, Republic of); Chung, Kyoo Sun [Hanyang Univ., Seoul (Korea, Republic of); Hong, Sang Heui [Seoul National Univ., Seoul (Korea, Republic of); Kang, Heui Dong [Kyungpook National Univ., Taegu (Korea, Republic of); Lee, Jae Koo [Pohang Inst. of Science and Technology, Kyungnam (Korea, Republic of)
1994-11-01
A concept definition of the KT-2 tokamak is made. The research goal of the machine is to study the `advanced tokamak` physics and engineering issues on the mid size large-aspect-ratio diverter tokamak with intense RF heating (>5 MW). Survey of the status of the research fields, the physics basis for the concept, operation scenarios, as well as machine design concept are presented. (Author) 86 refs., 17 figs., 22 tabs.
Plasma discharge in ferritic first wall vacuum vessel of the Hitachi Tokamak HT-2
Energy Technology Data Exchange (ETDEWEB)
Abe, Mitsushi; Nakayama, Takeshi; Asano, Katsuhiko; Otsuka, Michio [Hitachi Ltd., Tokyo (Japan)
1997-11-01
A tokamak discharge with ferritic material first wall was tried successfully. The Hitachi Tokamak HT-2 had a stainless steel SUS304 vacuum vessel and modified to have a ferritic plate first wall for experiments to investigate the possibility of ferritic material usage in magnetic fusion devices. The achieved vacuum pressure and times used for discharge cleaning was roughly identical with the stainless steel first wall or the original HT-2. We concluded that ferritic material vacuum vessel is possible for tokamaks. (author)
Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks
Energy Technology Data Exchange (ETDEWEB)
Hanson, James D. [Auburn University, Auburn, Alabama; Anderson, D.T. [University of Wisconsin, Madison; Cianciosa, M. [Auburn University, Auburn, Alabama; Franz, P. [EURATOM / ENEA, Italy; Harris, J. H. [Oak Ridge National Laboratory (ORNL); Hartwell, G. H. [Auburn University, Auburn, Alabama; Hirshman, Steven Paul [ORNL; Knowlton, Stephen F. [Auburn University, Auburn, Alabama; Lao, Lang L. [General Atomics, San Diego; Lazarus, Edward Alan [ORNL; Marrelli, L. [Association EURATOM ENEA Fusion, Consorzio RFX, Padua, Italy; Maurer, D. A. [Auburn University, Auburn, Alabama; Schmitt, J. C. [Princeton Plasma Physics Laboratory (PPPL); Sontag, A. C. [Oak Ridge National Laboratory (ORNL); Stevenson, B. A. [Auburn University, Auburn, Alabama; Terranova, D. [Association EURATOM ENEA Fusion, Consorzio RFX, Padua, Italy
2013-01-01
Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Canale, Eduardo A.
2015-02-01
© 2015 AIP Publishing LLC. This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1-15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree-order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization
Energy Technology Data Exchange (ETDEWEB)
Canale, Eduardo A., E-mail: ecanale@pol.una.py [Facultad Politénica, UNA, Asunción (Paraguay); Monzón, Pablo, E-mail: monzon@fing.edu.uy [School of Engineering, UDELAR, Montevideo 11300 (Uruguay)
2015-02-15
This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.
A comparison of Nash equilibria analysis and agent-based modelling for power markets
Energy Technology Data Exchange (ETDEWEB)
Krause, T.; Andersson, G. [EEH Power Systems Laboratory, ETH Zuerich, (Switzerland); Beck, E.V.; Cherkaoui, R.; Germond, A. [LRE Laboratoire de Reseaux Electriques, EPFL-STI-LRE, Lausanne (Switzerland); Ernst, D. [Universitede Liege, Institut Montefiore Batiment B28, Liege (Belgium)
2006-11-15
In this paper we compare Nash equilibria analysis and agent-based modelling for assessing the market dynamics of network-constrained pool markets. Power suppliers submit their bids to the market place in order to maximize their payoffs, where we apply reinforcement learning as a behavioral agent model. The market clearing mechanism is based on the locational marginal pricing scheme. Simulations are carried out on a benchmark power system. We show how the evolution of the agent-based approach relates to the existence of a unique Nash equilibrium or multiple equilibria in the system. Additionally, the parameter sensitivity of the results is discussed. (author)
On the non-stiffness of edge transport in L-mode tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Sauter, O.; Brunner, S.; Kim, D.; Merlo, G.; Behn, R.; Coda, S.; Duval, B. P.; Federspiel, L.; Goodman, T. P.; Karpushov, A.; Merle, A.; Team, TCV, E-mail: olivier.sauter@epfl.ch [Centre de Recherches en Physique des Plasmas, Association EURATOM-Confédération Suisse, EPFL, PPB-Ecublens, 1015 Lausanne (Switzerland); Camenen, Y. [CNRS, UMR 7345, Aix-Marseille Université, Marseille (France)
2014-05-15
Transport analyses using first-principle turbulence codes and 11/2 -D transport codes usually study radial transport properties between the tokamak plasma magnetic axis and a normalized minor radius around 0.8. In this region, heat transport shows significantly stiff properties resulting in temperature scalelength values (R∕L{sub T}) that are relatively independent of the level of the radial heat flux. We have studied experimentally in the tokamak à configuration variable [F. Hofmann et al., Plasma Phys. Controlled Fusion 36, B277 (1994)] the radial electron transport properties of the edge region, close to the last closed flux surface, namely, between ρ{sub V}=√(V/V{sub edge})=0.8 to 1. It is shown that electron transport is not stiff in this region and high R∕L{sub Te} values (∼20–40) can be attained even for L-mode confinement. We can define a “pedestal” location, already in L-mode regimes, where the transport characteristics change from constant logarithmic gradient, inside ρ{sub V} = 0.8, to constant gradient between 0.8 and 1.0. In particular, we demonstrate, with well resolved T{sub e} and n{sub e} profiles, that the confinement improvement with plasma current I{sub p}, with or without auxiliary heating, is due to this non-stiff edge region. This new result is used to explain the significant confinement improvement observed with negative triangularity, which could not be explained by theory to date. Preliminary local gyrokinetic simulations are now consistent with an edge, less stiff, region that is more sensitive to triangularity than further inside. We also show that increasing the electron cyclotron heating power increases the edge temperature inverse scalelength, in contrast to the value in the main plasma region. The dependence of confinement on density in ohmic plasmas is also studied and brings new insight in the understanding of the transition between linear and saturated confinement regimes, as well as of the density limit and
Stability analysis of tokamak plasmas; Analyse de stabilite de plasmas de tokamak
Energy Technology Data Exchange (ETDEWEB)
Bourdelle, C
2000-10-01
In a tokamak plasma, the energy transport is mainly turbulent. In order to increase the fusion reactions rate, it is needed to improve the energy confinement. The present work is dedicated to the identification of the key parameters leading to plasmas with a better confined energy in order to guide the future experiments. For this purpose, a numerical code has been developed. It calculates the growth rates characterizing the instabilities onset. The stability analysis is completed by the evaluation of the shearing rate of the rotation due to the radial electric field. When this shearing rate is greater than the growth rate the ion turbulence is fully stabilised. The shearing rate and the growth rate are determined from the density, temperature and security factor profiles of a given plasma. Three types of plasmas have been analysed. In the Radiative Improved modes of TEXTOR, high charge number ions seeding lowers the growth rates. In Tore Supra-high density plasmas, a strong magnetic shear and/or a more efficient ion heating linked to a bifurcation of the toroidal rotation direction (which is not understood) trigger the improvement of the confinement. In other Tore Supra plasmas, locally steep electron pressure gradients have been obtained following magnetic shear reversal. This locally negative magnetic shear has a stabilizing effect. In these three families of plasmas, the growth rates decrease, the confinement improves, the density and temperature profiles are steeper. This steepening induces an increase of the rotation shearing rate, which then maintains the confinement high quality. (author)
Enhanced confinement regimes and control technology in the DIII-D tokamak
Energy Technology Data Exchange (ETDEWEB)
Lohr, J.; Burrell, K.H. [General Atomics, San Diego, CA (United States); Coda, S. [Massachusetts Inst. of Tech., Cambridge, MA (United States)] [and others
1993-07-01
Advanced tokamak performance has been demonstrated in the DIII-D tokamak in a series of experiments which brought together developments in technology and improved understanding of the physical principles underlying tokamak operation. The achievement of greatly improved confinement coupled with development of new systems for real time plasma control have permitted investigation of the heretofore hidden or poorly controlled variables which together determine global confinement. These experiments, which included work in transport and control of the plasma boundary, point toward development of operationally and economically attractive reactors based on the tokamak. Some of these experiments are described.
A novel approach to linearization of the electromagnetic parameters of tokamaks with an iron core
Energy Technology Data Exchange (ETDEWEB)
Fu, P. E-mail: fupeng@mail.ipp.ac.cn; Liu, Z.Z.; Zou, J.H
2002-05-01
The equivalent model of an iron core tokamak is developed, in which the electromagnetic parameters of several pairs of coils in opposite series (PCOS) are not dependent on the saturation of the iron core during tokamak operation. With this the electromagnetic parameters of all the coils in an iron core tokamak can be linearized, As an example, the electromagnetic parameters of Hefei Super-conductive Tokamak with iron core (HT-7) are linearized, and it is in good agreement with the experimental results. The linearization approach can be applied in real time plasma control and electromagnetic analysis.
Multipoint Thomson scattering diagnostic for the ETE tokamak
Berni, L. A.; Alonso, M. P.; Oliveira, R. M.
2004-10-01
To measure the electron temperature and plasma density profiles on the Experimento Tokamak Esférico tokamak a multiplexed Thomson scattering diagnostic was implemented. The diagnostic is based on a 10 J ruby laser and a single five spectral channel filter polychromator. A collection lens with f/6.3 relay the scattered light from 23 spatial points to optical fibers. The fibers have a monotonous increasing length and are inserted into the polychromator. Between the collection lens and each fiber optic we have a microlens to match the numerical aperture and to enlarge the plasma observation volume. This work describes the project, the simulations, and the preliminary results obtained with the first four optical fibers.
Molecular emission in the edge plasma of T-10 tokamak
Energy Technology Data Exchange (ETDEWEB)
Zimin, A. M., E-mail: zimin@power.bmstu.ru [Bauman Moscow State Technical University (Russian Federation); Krupin, V. A. [National Research Centre Kurchatov Institute (Russian Federation); Troynov, V. I. [Bauman Moscow State Technical University (Russian Federation); Klyuchnikov, L. A. [National Research Centre Kurchatov Institute (Russian Federation)
2015-12-15
The experiments on recording molecular emission in the edge plasma of the T-10 tokamak are described. To obtain reliable spectra with sufficient spectral, temporal, and spatial resolution, the optical circuit is optimized for various experimental conditions. Typical spectra measured in two sections of the tokamak are shown. It is shown that, upon varying the parameters of the discharge, the molecular spectrum not only changes significantly in intensity but also undergoes a qualitative change in the rotational and vibrational structure. For a detailed analysis, we use the Fulcher-α system (d{sup 3}Π{sub u}–a{sup 3}Σ{sub g}{sup +}) of deuterium in the wavelength range from 590 to 640 nm. The rotational temperatures of ground state X{sup 1}Σ{sub g}{sup +} and upper excited state d{sup 3}Π{sub u} are estimated by the measured spectra.
Overview of ARIES-RS tokamak fusion power plant
Energy Technology Data Exchange (ETDEWEB)
Najmabadi, F. [California Univ., San Diego, CA (United States). Fusion Energy Research Program
1998-09-01
In order for fusion power to be widely accepted in the next century, it should offer advantages compared to available sources of energy. The Starlite study has examined the ability of tokamak-based power plants to compete with fusion energy sources. A set of top-level system requirements and goals for system economics, safety and waste disposal, and reliability and availability were established during extensive consultations with US electric utilities and industry representatives. Five different tokamak plasma operation modes were considered and different technology options (e.g. choice of structural material, coolant, breeder) were developed and assessed. Based on this assessment, the ARIES-RS design study was initiated to examine a power plant based on the reversed-shear mode of plasma operation, coupled to a fusion power core which uses high-performance lithium-cooled vanadium components. An overview of the ARIES-RS design is presented in this paper. (orig.) 14 refs.
Collisionless microtearing modes in hot tokamaks: Effect of trapped electrons
Energy Technology Data Exchange (ETDEWEB)
Swamy, Aditya K.; Ganesh, R., E-mail: ganesh@ipr.res.in [Institute for Plasma Research, Bhat, Gandhinagar, 382428 (India); Brunner, S.; Vaclavik, J.; Villard, L. [CRPP, EPFL, 1015 Lausanne (Switzerland)
2015-07-15
Collisionless microtearing modes have recently been found linearly unstable in sharp temperature gradient regions of large aspect ratio tokamaks. The magnetic drift resonance of passing electrons has been found to be sufficient to destabilise these modes above a threshold plasma β. A global gyrokinetic study, including both passing electrons as well as trapped electrons, shows that the non-adiabatic contribution of the trapped electrons provides a resonant destabilization, especially at large toroidal mode numbers, for a given aspect ratio. The global 2D mode structures show important changes to the destabilising electrostatic potential. The β threshold for the onset of the instability is found to be generally downshifted by the inclusion of trapped electrons. A scan in the aspect ratio of the tokamak configuration, from medium to large but finite values, clearly indicates a significant destabilizing contribution from trapped electrons at small aspect ratio, with a diminishing role at larger aspect ratios.
Tokamak resistive magnetohydrodynamic ballooning instability in the negative shear regime
Institute of Scientific and Technical Information of China (English)
Shi Bing-Ren; Lin Jian-Long; Li Ji-Quan
2007-01-01
Improved confinement of tokamak plasma with central negative shear is checked against the resistive ballooning mode. In the negative shear regime, the plasma is always unstable for purely growing resistive ballooning mode. For a simplest tokamak equilibrium model, the s-α model, characteristics of this kind of instability are fully clarified by numerically solving the high n resistive magnetohydrodynamic ballooning eigen-equation. Dependences of the growth rate on the resistivity, the absolute shear value, the pressure gradient are scanned in detail. It is found that the growth rate is a monotonically increasing function of a while it is not sensitive to the changes of the shear s, the initial phase θ0 and the resistivity parameter εR.
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%.
Operation of cryostat vacuum vessel of HT-7 superconducting tokamak
Energy Technology Data Exchange (ETDEWEB)
Yang, Y. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)]. E-mail: yangyu@ipp.ac.cn; Su, M. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)
2006-11-15
The superconducting tokamak HT-7 has been in operation for over 10 years. The safe and reliable operation of its cryostat vacuum vessel, which contains the superconducting coils is essential for each experimental run since the superconducting toroidal field coils are contained inside the vessel. In this paper, the operation is reviewed with the emphasis on the analysis on anomalous pressure rises and the corresponding solutions. It is shown that under close monitoring and timely handling, the cryostat vacuum vessel could still satisfy the requirements of the experimental operation despite of the material aging. This provides guideline for vacuum operating of HT-7. The experiences should be valuable for other superconducting projects as well, including a whole superconducting tokamak under construction, EAST.
Specification of asymmetric VDE loads of the ITER tokamak
Energy Technology Data Exchange (ETDEWEB)
Bachmann, C., E-mail: christian.bachmann@iter.org [ITER Organization CS90 046, 13067St. Paul lez Durance, Cedex (France); Sugihara, M.; Roccella, R.; Sannazzaro, G.; Gribov, Y. [ITER Organization CS90 046, 13067St. Paul lez Durance, Cedex (France); Riccardo, V.; Hender, T.C.; Gerasimov, S.N. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB (United Kingdom); Pautasso, G. [Max Planck Institute for Plasma Physics, D-85748 Garching (Germany); Belov, A.; Lamzin, E. [D.V. Efremov Institute, Scientific Technical Centre ' Sintez' (Russian Federation); Roccella, M. [L. T. Calcoli, 23087 Merate, Lecco (Italy)
2011-10-15
During asymmetric vertical displacement events (AVDEs) associated with the kink mode of the plasma two asymmetry phenomena were observed in existing tokamaks, in particular in JET . The related halo currents flowing in the passive structure were identified as the cause of asymmetric EM loads on tokamak components. The first phenomenon is a toroidal peak of the poloidal halo current that flows in the passive structure. The second phenomenon is that the toroidal plasma current is not uniform toroidally, so a toroidally non-uniform current flows in the vessel . The specification of the expected characteristics of both phenomena as well as of the consequent asymmetric loads in ITER are summarized here. The related loads are specified for likely, unlikely and extremely unlikely AVDEs.
Localized measurements of turbulence in the TORE SUPRA tokamak
Energy Technology Data Exchange (ETDEWEB)
Devynck, P.; Garbet, X.; Laviron, C.; Payan, J.; Saha, S.K. (CEA Centre d' Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France)); Gervais, F.; Hennequin, P.; Quemeneur, A.; Truc, A. (Ecole Polytechnique, 91 - Palaiseau (France))
1993-01-01
A collective infra-red laser scattering diagnostic has been installed on the TORE SUPRA tokamak for the measurement of plasma density fluctuations. For the range of wavenumbers explored (3-15) cm[sup -1], the scattering angles are very weak ([approx] 1 mrad). Consequently, the scattering signals are averaged along the whole observation chord, resulting in poor longitudinal spatial localization. However, by virtue of the pitch angle variation of the magnetic field lines in the tokamak, and of the perpendicularity of the turbulence wavevector to these field lines, it has been possible to obtain partial spatial resolution along the direction of the beam. Good agreement between the experimental and theoretical angular resolution of the diagnostic as well as the results of cross-correlation performed on the signals obtained by two simultaneous probing beams also justify this novel concept. (Author).
3D MHD disruptions simulations of tokamaks plasmas
Paccagnella, Roberto; Strauss, Hank; Breslau, Joshua
2008-11-01
Tokamaks Vertical Displacement Events (VDEs) and disruptions simulations in toroidal geometry by means of a single fluid visco-resistive magneto-hydro-dynamic (MHD) model are presented in this paper. The plasma model, implemented in the M3D code [1], is completed with the presence of a 2D homogeneous wall with finite resistivity. This allows the study of the relatively slowly growing magneto-hydro-dynamical perturbation, the resistive wall mode (RWM), which is, in this work, the main drive of the disruptions. Amplitudes and asymmetries of the halo currents pattern at the wall are also calculated and comparisons with tokamak experimental databases and predictions for ITER are given. [1] W. Park, E.V. Belova, G.Y. Fu, X.Z. Tang, H.R. Strauss, L.E. Sugiyama, Phys. Plasmas 6 (1999) 1796.
Analysis on the severe accidents in KSTAR tokamak
Energy Technology Data Exchange (ETDEWEB)
Lee, Myoung Jae; Cheong, Y. H.; Choi, Y. S.; Cheon, E. J. [PlaGen, Seoul (Korea, Republic of)
2003-11-15
The establishment of regulatory and approval systems for KSTAR (Korea Superconducting Tokamak Advanced Research) has been demanded as the facility is targeted to be completed in the year of 2005. Such establishment can be achieved by performing adequate and in-depth analyses on safety issues covering radiological and chemical hazard materials, radiation protection, high vacuum, very low temperature, etc. The loss of coolant accidents and the loss of vacuum accident in fusion facilities have been introduced with summary of simulation results that were previously reported for ITER and JET. Computer codes that are actively used for accident simulation research are examined and their main features are briefly described. It can be stated that the safety analysis is indispensable to secure the safety of workers and individual members of the public as well as to establish the regulatory and approval systems for KSTAR tokamak.
Imaging System and Plasma Imaging on HL-2A Tokamak
Institute of Scientific and Technical Information of China (English)
郑银甲; 冯震; 罗萃文; 刘莉; 李伟; 严龙文; 杨青巍; 刘永
2004-01-01
As a new diagnostic means, plasma-imaging system has been developed on the HL2A tokamak, with a basic understanding of plasma discharge scenario of the entire torus, checking the plasma position and the clearance between the plasma and the first wall during discharge. The plasma imaging system consists of (1) color video camera, (2) observation window and turn mirror,(3) viewing & collecting optics, (4) video cable, (5) Video capture card as well as PC. This paper mainly describes the experimental arrangement, plasma imaging system and detailed part in the system, along with the experimental results. Real-time monitoring of plasma discharge process,particularly distinguishing limitor and divertor configuration, the imaging system has become key diagnostic means and laid the foundation for further physical experiment on the HL-2A tokamak.
On the Production of Relativistic Runaway Electrons in Damavand Tokamak
Moslehi-Fard, Mahmoud
2013-02-01
Experimental observations in Damavand tokamak show that hard X-ray is produced by either disruption with I p 20 kA. Hard X-ray also persists from the initiation of plasma discharge to the end. Occurrence of multiple spikes in hard X-ray during the discharge is evident. The propagation of hard X-ray is attributed to runaway electrons. We observe runaway electrons in two regimes with different characteristics. Regime (RADI) is similar to the observations of other Tokamak during disruption on that the plasma current is reduced abruptly and interpreted by Dreicer theory. In the regime of RADII, hard X-ray and subsequently runaway electrons are observed from starting of plasma discharge which provides the condition that the most of runaway electrons contain the toroidal plasma current. Runaway electron beam excites whistler waves and scattered electrons in velocity space and prevent growing the runaway electrons beam.
First Neutron Spectrometry Measurement at the HL-2A Tokamak
Xi, Yuan; Xufei, Xie; Zhongjing, Chen; Xingyu, Peng; Tieshuan, Fan; Jinxiang, Chen; Xiangqing, Li; Guoliang, Yuan; Jinwei, Yang; Qingwei, Yang
2013-01-01
A compact neutron spectrometer based on the liquid scintillator is presented for the neutron energy spectrum measurement at the HL-2A tokamak. The spectrometer has been well characterized and a fast digital pulse shape discrimination software has been developed using the charge comparison method. A digitizer data acquisition system with the maximum frequency of 1 MHz can work under the high count rate environment at HL-2A. Specific radiation shielding and magnetic shielding for the spectrometerhas been designed for the neutron spectrum measurement at the HL-2A Tokamak. For the analysis of the pulse height spectrum, dedicated numerical simulation utilizing NUBEAM combining with GENESIS has been made to obtain the neutron energy spectrum, following which the transportation process from the plasma to the detector has been evaluated with Monte Carlo calculations. The distorted neutron energy spectrum has been folded with response matrix of the liquid scintillation spectrometer, and good consistency has been found...
Plasma shaping effects on tokamak scrape-off layer turbulence
Riva, Fabio; Lanti, Emmanuel; Jolliet, Sébastien; Ricci, Paolo
2017-03-01
The impact of plasma shaping on tokamak scrape-off layer (SOL) turbulence is investigated. The drift-reduced Braginskii equations are written for arbitrary magnetic geometries, and an analytical equilibrium model is used to introduce the dependence of turbulence equations on tokamak inverse aspect ratio (ε ), Shafranov’s shift (Δ), elongation (κ), and triangularity (δ). A linear study of plasma shaping effects on the growth rate of resistive ballooning modes (RBMs) and resistive drift waves (RDWs) reveals that RBMs are strongly stabilized by elongation and negative triangularity, while RDWs are only slightly stabilized in non-circular magnetic geometries. Assuming that the linear instabilities saturate due to nonlinear local flattening of the plasma gradient, the equilibrium gradient pressure length {L}p=-{p}e/{{\
Transition to subcritical turbulence in a tokamak plasma
van Wyk, F; Schekochihin, A A; Roach, C M; Field, A R; Dorland, W
2016-01-01
Unstable perturbations driven by the pressure gradient and other sources of free energy in tokamak plasmas can grow exponentially and eventually saturate nonlinearly, leading to turbulence. Recent work has shown that in the presence of sheared flows, such systems can be subcritical. This means that all perturbations are linearly stable and a transition to a turbulent state only occurs if large enough initial perturbations undergo sufficient transient growth to allow nonlinear interaction. There is, however, currently very little known about a subcritical transition to turbulence in fusion-relevant plasmas. Here we use first-principles gyrokinetic simulations of a turbulent plasma in the outer core of the Mega-Ampere Spherical Tokamak (MAST) to demonstrate that the experimentally observed state is near the transition threshold, that the turbulence in this state is subcritical, and that transition to turbulence occurs via accumulation of very long-lived, intense, finite-amplitude coherent structures, which domi...
Radial transport of toroidal angular momentum in tokamaks
Calvo, Ivan
2014-01-01
The radial flux of toroidal angular momentum is needed to determine tokamak intrinsic rotation profiles. Its computation requires knowledge of the gyrokinetic distribution functions and turbulent electrostatic potential to second-order in $\\epsilon = \\rho/L$, where $\\rho$ is the ion Larmor radius and $L$ is the variation length of the magnetic field. In this article, a complete set of equations to calculate the radial transport of toroidal angular momentum in any tokamak is presented. In particular, the $O(\\epsilon^2)$ equations for the turbulent components of the distribution functions and electrostatic potential are given for the first time without assuming that the poloidal magnetic field over the magnetic field strength is small.
A quasi-linear gyrokinetic transport model for tokamak plasmas
Casati, Alessandro
2012-01-01
The development of a quasi-linear gyrokinetic transport model for tokamak plasmas, ultimately designed to provide physically comprehensive predictions of the time evolution of the thermodynamic relevant quantities, is a task that requires tight links among theoretical, experimental and numerical studies. The framework of the model here proposed, which operates a reduction of complexity on the nonlinear self-organizing plasma dynamics, allows in fact multiple validations of the current understanding of the tokamak micro-turbulence. The main outcomes of this work stem from the fundamental steps involved by the formulation of such a reduced transport model, namely: (1) the verification of the quasi-linear plasma response against the nonlinearly computed solution, (2) the improvement of the turbulent saturation model through an accurate validation of the nonlinear codes against the turbulence measurements, (3) the integration of the quasi-linear model within an integrated transport solver.
Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments
Energy Technology Data Exchange (ETDEWEB)
Wang, W.X.; Lin, Z.; Tang, W.M.; Lee, W.W.; Ethier, S.; Lewandowski, J.L.V.; Rewoldt, G.; Hahm, T.S.; Manickam, J.
2006-01-01
A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Melt layer erosion of metallic armour targets during off-normal events in tokamaks
Bazylev, B.; Wuerz, H.
2002-12-01
Melt layer erosion by melt motion is the dominating erosion mechanism for metallic armours under high heat loads. A 1-D fluid dynamics simulation model for calculation of melt motion was developed and validated against experimental results for tungsten from the e-beam facility JEBIS and beryllium from the e-beam facility JUDITH. The driving force in each case is the gradient of the surface tension. Due to the high velocity which develops in the Be melt considerable droplet splashing occurs.
Design of geometric phase measurement in EAST Tokamak
Lan, T; Liu, J; Jie, Y X; Wang, Y L; Gao, X; Qin, H
2016-01-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
The Aneutronic Rodless Ultra Low Aspect Ratio Tokamak
Ribeiro, Celso
2016-10-01
The replacement of the metal centre-post in spherical tokamaks (STs) by a plasma centre-post (PCP, the TF current carrier) is the ideal scenario for a ST reactor. A simple rodless ultra low aspect-ratio tokamak (RULART) using a screw-pinch PCP ECR-assisted with an external solenoid has been proposed in the most compact RULART [Ribeiro C, SOFE-15]. There the solenoid provided the stabilizing field for the PCP and the toroidal electrical field for the tokamak start-up, which will stabilize further the PCP, acting as stabilizing closed conducting surface. Relative low TF will be required. The compactness (high ratio of plasma-spherical vessel volume) may provide passive stabilization and easier access to L-H mode transition. It is presented here: 1) stability analysis of the PCP (initially MHD stable due to the hollow J profile); 2) tokamak equilibrium simulations, and 3) potential use for aneutronic reactions studies via pairs of proton p and boron 11B ion beams in He plasmas. The beams' line-of-sights sufficiently miss the sources of each other, thus allowing a near maximum relative velocities and reactivity. The reactions should occur close to the PCP mid-plane. Some born alphas should cross the PCP and be dragged by the ion flow (higher momentum exchange) towards the anode but escape directly to a direct electricity converter. Others will reach evenly the vessel directly or via thermal diffusion (favourable heating by the large excursion 2a), leading to the lowest power wall load possible. This might be a potential hybrid direct-steam cycle conversion reactor scheme, nearly aneutronic, and with no ash or particle retention problems, as opposed to the D-T thermal reaction proposals.
Imaging charge exchange recombination spectroscopy on the TEXTOR tokamak
Energy Technology Data Exchange (ETDEWEB)
Howard, J [Plasma Research Laboratory, The Australian National University, Canberra 0200 (Australia); Jaspers, R [Eindhoven University of Technology, Eindhoven (Netherlands); Lischtschenko, O; Delabie, E [FOM Institute for Plasma Physics ' Rijnhuizen' , Nieuwegein (Netherlands); Chung, J [National Fusion Research Institute, Daejeon (Korea, Republic of)
2010-12-15
We describe the application of a simple spatial-heterodyne coherence-imaging filter for 2D Doppler imaging of charge exchange recombination (CXR) emission from a heating beam in the TEXTOR tokamak. Results obtained by the CXR imaging system are found to be consistent with measurements obtained using a standard multi-channel spectrometer-based system. We describe the system, indicate possible enhancements and future applications for imaging CXRS.
Imaging charge exchange recombination spectroscopy on the TEXTOR tokamak
Howard, J.; Jaspers, R.; Lischtschenko, O.; Delabie, E.; Chung, J.
2010-12-01
We describe the application of a simple spatial-heterodyne coherence-imaging filter for 2D Doppler imaging of charge exchange recombination (CXR) emission from a heating beam in the TEXTOR tokamak. Results obtained by the CXR imaging system are found to be consistent with measurements obtained using a standard multi-channel spectrometer-based system. We describe the system, indicate possible enhancements and future applications for imaging CXRS.
Multi-field plasma sandpile model in tokamaks and applications
Peng, X. D.; Xu, J. Q.
2016-08-01
A multi-field sandpile model of tokamak plasmas is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast/micro time-scale and diffusive transports on the slow/macro time-scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are taken into account simultaneously. New redistribution rules of a sand-relaxing process are defined according to the transport properties of special turbulence which allows the uphill particle transport. Applying the model, we first simulate the steady-state plasma profile self-sustained by drift wave turbulences in the Ohmic discharge of a tokamak. A scaling law as f = a q0 b + c for the relation of both center-density n ( 0 ) and electron (ion) temperatures T e ( 0 ) ( T i ( 0 ) ) with the center-safety-factor q 0 is found. Then interesting work about the nonlocal transport phenomenon observed in tokamak experiments proceeds. It is found that the core electron temperature increases rapidly in response to the edge cold pulse and inversely it decreases in response to the edge heat pulse. The results show that the nonlocal response of core electron temperature depending on the amplitudes of background plasma density and temperature is more remarkable in a range of gas injection rate. Analyses indicate that the avalanche transport caused by plasma drift instabilities with thresholds is a possible physical mechanism for the nonlocal transport in tokamaks. It is believed that the model is capable of being applied to more extensive questions occurring in the transport field.
Electromagnetic effects on rippling instability and tokamak edge fluctuations
Energy Technology Data Exchange (ETDEWEB)
Murakami, Sadayoshi; Saleem, Hamid [National Inst. for Fusion Science, Toki, Gifu (Japan)
1998-07-01
Electromagnetic effects on rippling mode are investigated as a cause of low frequency electromagnetic fluctuations in tokamak edge region. It is shown that, in a current-carrying resistive plasma, the purely growing electrostatic rippling mode can turn out to be an electromagnetic oscillatory instability. The resistivity fluctuation and temperature gradient are the main sources of this instability, which requires both parallel and perpendicular wave vectors. The Alfven waves in a coupled dispersion relation are found heavily damped in such dissipative plasmas. (author)
Heavy Neutral Beam Probe for Edge Plasma Analysis in Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Castracane, J.
2001-01-04
The Heavy Neutral Beam Probe (HNBP) developed initially with DOE funding under the Small Business Innovation Research (SBIR) program was installed on the Tokamak de Varennes (TdeV) at the CCFM. This diagnostic was designed to perform fundamental measurements of edge plasma properties. The hardware was capable of measuring electron density and potential profiles with high spatial and temporal resolution. Fluctuation spectra for these parameters were obtained with HNBP for transport studies.
HCN Laser Interferometer on the EAST Superconducting Tokamak
Institute of Scientific and Technical Information of China (English)
XU Qiang; GAO Xiang; JIE Yinxian; LIU Haiqing; SHI Nan; CHENG Yongfei; TONG Xingde
2008-01-01
A single-channel far-infrared (FIR) laser interferometer was developed to measure the line averaged electron density on the EAST tokamak. The structure of the single-channel FIR laser interferometer is described in detail. The evolution of density sawtooth oscillation was measured by means the FIR laser interferometer, and was identified by electron cyclotron emission (ECE) signals and soft X-ray intensity. The discharges with and without sawtooth were compared with each other in the Hugill diagram.
On Runaway Transport under Magnetic Turbulence in Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Castejon, F.; Equilior, S.; Rodriguez-Rodrigo, L. [CIEMAT. Madrid (Spain)
2001-07-01
The influence of magnetic turbulence on runaway transport has been studied. The evolution of runaway distribution function has been calculated using Electra a 2D code in momentum space and 1D in radius coordinate. The code considers the effect of averaging the turbulence by runaway orbits. Then Hard X-Ray emission spectrum is estimated and compared with experimental results of TJ-1 tokamak, obtaining a remarkable agreement. (Author) 15 refs.
Structural materials for large superconducting magnets for tokamaks
Energy Technology Data Exchange (ETDEWEB)
Long, C.J.
1976-12-01
The selection of structural materials for large superconducting magnets for tokamak-type fusion reactors is considered. The important criteria are working stress, radiation resistance, electromagnetic interaction, and general feasibility. The most advantageous materials appear to be face-centered-cubic alloys in the Fe-Ni-Cr system, but high-modulus composites may be necessary where severe pulsed magnetic fields are present. Special-purpose structural materials are considered briefly.
Application of advanced composites in tokamak magnet systems
Energy Technology Data Exchange (ETDEWEB)
Long, C. J.
1977-11-01
The use of advanced (high-modulus) composites in superconducting magnets for tokamak fusion reactors is discussed. The most prominent potential application is as the structure in the pulsed poloidal-field coil system, where a significant reduction in eddy currents could be achieved. Present low-temperature data on the advanced composites are reviewed briefly; they are too meager to do more than suggest a broad class of composites for a particular application.
Analysis of neutral hydrogenic emission spectra in a tokamak
Ko, J.; Chung, J.; Jaspers, R. J. E.
2015-10-01
Balmer-α radiation by the excitation of thermal and fast neutral hydrogenic particles has been investigated in a magnetically confined fusion device, or tokamak, from the Korea Superconducting Tokamak Advanced Research (KSTAR). From the diagnostic point of view, the emission from thermal neutrals is associated with passive spectroscopy and that from energetic neutrals that are usually injected from the outside of the tokamak to the active spectroscopy. The passive spectroscopic measurement for the thermal Balmer-α emission from deuterium and hydrogen estimates the relative concentration of hydrogen in a deuterium-fueled plasma and therefore, makes a useful tool to monitor the vacuum wall condition. The ratio of hydrogen to deuterium obtained from this measurement qualitatively correlates with the energy confinement of the plasma. The Doppler-shifted Balmer-α components from the fast neutrals features the spectrum of the motional Stark effect (MSE) which is an essential principle for the measurement of the magnetic pitch angle profile. Characterization of this active MSE spectra, especially with multiple neutral beam lines crossing along the observation line of sight, has been done for the guideline of the multi-ion-source heating beam operation and for the optimization of the narrow bandpass filters that are required for the polarimeter-based MSE diagnostic system under construction at KSTAR.
Preconceptual design and assessment of a Tokamak Hybrid Reactor
Energy Technology Data Exchange (ETDEWEB)
Teofilo, V.L.; Leonard, B.R. Jr.; Aase, D.T.
1980-09-01
The preconceptual design of a commercial Tokamak Hybrid Reactor (THR) power plant has been performed. The tokamak fusion driver for this hybrid is operated in the ignition mode. The D-T fusion plasma, which produces 1140 MW of power, has a major radius of 5.4 m and a minor radius of 1.0 m with an elongation of 2.0. Double null poloidal divertors are assumed for impurity control. The confining toroidal field is maintained by D-shaped Nb/sub 3/Sn superconducting magnets with a maximum field of 12T at the coil. Three blankets with four associated fuel cycle alternatives have been combined with the ignited tokamak fusion driver. The engineering, material, and balance of plant design requirements for the THR are briefly described. Estimates of the capital, operating and maintenance, and fuel cycle costs have been made for the various driver/blanket combinations and an assessment of the market penetrability of hybrid systems is presented. An analysis has been made of the nonproliferation aspects of the hybrid and its associated fuel cycles relative to fission reactors. The current and required level of technology for both the fusion and fission components of the hybrid system has been reviewed. Licensing hybrid systems is also considered.
Stability-transport modeling of the SINP tokamak discharges
Indian Academy of Sciences (India)
S Lahiri; S Mukhopadhyay; A N S Iyengar; R Pal
2001-05-01
A one-dimensional stability transport code has been developed to simulate the evolution of tokamak plasma discharges. Explicit finite-difference methods have been used to follow the temporal evolution of the electron temperature equation. The poloidal field diffusion equation has been solved at every time step. The effects of MHD instabilities have been incorporated by solving equations for MHD mixing and tearing modes as and when required. The code has been applied to follow the evolution of tokamak plasma discharges obtained in the Saha Institute of Nuclear Physics (SINP) tokamak. From these simulations, we have been able to identify the possible models of thermal conductivity, diffusion and impurity contents in these discharges. Effects of different MHD modes have been estimated. It has been found that in low discharge =1, =1 and =2, =1 modes play major role in discharge evolution. These modes are found to result in the positive jump in the loop voltage which was also observed in the experiments. Hollow current density profile and negative shear in the profile have also been found in the rising phase of a discharge.
Operation of a tokamak reactor in the radiative improved mode
Morozov, D. Kh.; Mavrin, A. A.
2016-03-01
The operation of a nuclear fusion reactor has been simulated within a model based on experimental results obtained at the TEXTOR-94 tokamak and other facilities in which quasistationary regimes were achieved with long confinement times, high densities, and absence of the edge-localized mode. The radiative improved mode of confinement studied in detail at the TEXTOR-94 tokamak is the most interesting such regime. One of the most important problems of modern tokamaks is the problem of a very high thermal load on a divertor (or a limiter). This problem is quite easily solved in the radiative improved mode. Since a significant fraction of the thermal energy is reemitted by an impurity, the thermal loading is significantly reduced. As the energy confinement time τ E at high densities in the indicated mode is significantly larger than the time predicted by the scaling of ITERH-98P(y, 2), ignition can be achieved in a facility much smaller than the ITER facility at plasma temperatures below 20 keV. The revealed decrease in the degradation of the confinement time τ E with an increase in the introduced power has been analyzed.
Microwave Imaging Reflectometer (MIR) Development for the EAST Tokamak
Domier, Calvin; Hu, Xing; Spear, Alexander; Zhu, Yilun; Xie, Jinlin; Luhmann, Neville
2016-10-01
An upgraded MIR system is being developed for the EAST tokamak based on the successful DIII-D MIR system. The EAST MIR system has 8 radial channels consisting of 8 independent probing frequencies ranging from 75 to 103 GHz, driven by fast tuning synthesizers and active frequency multipliers. There are 12 poloidal channels in the heterodyne down-conversion receiver system, with each channel corresponding to a separate poloidal position inside the tokamak. The down-conversion electronics are designed to optimize signal to noise ratio and are embedded with a microcontroller to realize remote computer control. Considerable improvements are also seen in the front-end plasma facing optics. This new optical system provides features including focusing, zoom, field curvature adjustment, and incident angle adjustment. These functions can be realized together or independently depending on the configuration setup of the large aperture lenses. This MIR system is expected to be installed on the EAST tokamak in December 2016, co-located with the Electron Cyclotron Emission Imaging (ECEI) system, to simultaneously measure electron density and temperature fluctuations. This work was supported by U.S. DOE Grant DE-FG02-99ER54531 and by the National MCF energy development program of China.
Numerical Tokamak Turbulence Calculations on the CRAY T3E
Energy Technology Data Exchange (ETDEWEB)
Lynch, V.E., Leboeuf, J.N., Carreras, B.A. [Oak Ridge National Lab., TN (United States)], Alvarez, J.D., Garcia, L. [Universidad `Carlos III` de Madrid (Spain)
1997-12-31
Full cross section calculations of ion-temperature-gradient-driven turbulence with Landau closure are being carried out as part of the Numerical Tokamak Turbulence Project, one of the U.S. Department of Energy`s Phase II Grand Challenges. To include the full cross section of a magnetic fusion device like the tokamak requires more memory and CPU time than is available on the National Energy Research Scientific Computing Center`s (NERSC`s) shared-memory vector machines such as the CRAY C90 and J90. Calculations of cylindrical multi-helicity ion-temperature-gradient-driven turbulence were completed on NERSC`s 160-processor distributed-memory CRAY T3E parallel computer with 256 Mbytes of memory per processor. This augurs well for yet more memory and CPU intensive calculations on the next-generation T3E at NERSC. This paper presents results on benchmarks with the current T3E at NERSC. Physics results pertaining to plasma confinement at the core of tokamaks subject to ion-temperature-gradient-driven-turbulence are also highlighted. Results at this resolution covering this extent of physical time were previously unattainable. Work is in progress to increase the resolution, improve the performance of the parallel code, and include toroidal geometry in these calculations in anticipation of the imminent arrival of a fully configured,512-processor, T3E-900 model.
Modeling of Anomalous Transport in Tokamaks with FACETS code
Pankin, A. Y.; Batemann, G.; Kritz, A.; Rafiq, T.; Vadlamani, S.; Hakim, A.; Kruger, S.; Miah, M.; Rognlien, T.
2009-05-01
The FACETS code, a whole-device integrated modeling code that self-consistently computes plasma profiles for the plasma core and edge in tokamaks, has been recently developed as a part of the SciDAC project for core-edge simulations. A choice of transport models is available in FACETS through the FMCFM interface [1]. Transport models included in FMCFM have specific ranges of applicability, which can limit their use to parts of the plasma. In particular, the GLF23 transport model does not include the resistive ballooning effects that can be important in the tokamak pedestal region and GLF23 typically under-predicts the anomalous fluxes near the magnetic axis [2]. The TGLF and GYRO transport models have similar limitations [3]. A combination of transport models that covers the entire discharge domain is studied using FACETS in a realistic tokamak geometry. Effective diffusivities computed with the FMCFM transport models are extended to the region near the separatrix to be used in the UEDGE code within FACETS. 1. S. Vadlamani et al. (2009) %First time-dependent transport simulations using GYRO and NCLASS within FACETS (this meeting).2. T. Rafiq et al. (2009) %Simulation of electron thermal transport in H-mode discharges Submitted to Phys. Plasmas.3. C. Holland et al. (2008) %Validation of gyrokinetic transport simulations using %DIII-D core turbulence measurements Proc. of IAEA FEC (Switzerland, 2008)
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
Energy Technology Data Exchange (ETDEWEB)
Long-Poe Ku and Allen H. Boozer
2009-06-05
If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.
Performance Projections For The Lithium Tokamak Experiment (LTX)
Energy Technology Data Exchange (ETDEWEB)
Majeski, R.; Berzak, L.; Gray, T.; Kaita, R.; Kozub, T.; Levinton, F.; Lundberg, D. P.; Manickam, J.; Pereverzev, G. V.; Snieckus, K.; Soukhanovskii, V.; Spaleta, J.; Stotler, D.; Strickler, T.; Timberlake, J.; Yoo, J.; Zakharov, L.
2009-06-17
Use of a large-area liquid lithium limiter in the CDX-U tokamak produced the largest relative increase (an enhancement factor of 5-10) in Ohmic tokamak confinement ever observed. The confinement results from CDX-U do not agree with existing scaling laws, and cannot easily be projected to the new lithium tokamak experiment (LTX). Numerical simulations of CDX-U low recycling discharges have now been performed with the ASTRA-ESC code with a special reference transport model suitable for a diffusion-based confinement regime, incorporating boundary conditions for nonrecycling walls, with fuelling via edge gas puffing. This model has been successful at reproducing the experimental values of the energy confinement (4-6 ms), loop voltage (<0.5 V), and density for a typical CDX-U lithium discharge. The same transport model has also been used to project the performance of the LTX, in Ohmic operation, or with modest neutral beam injection (NBI). NBI in LTX, with a low recycling wall of liquid lithium, is predicted to result in core electron and ion temperatures of 1-2 keV, and energy confinement times in excess of 50 ms. Finally, the unique design features of LTX are summarized.
Rai, Neeraj; Siepmann, J Ilja
2007-09-13
The explicit hydrogen version of the transferable potentials for phase equilibria (TraPPE-EH) force field is extended to benzene, pyridine, pyrimidine, pyrazine, pyridazine, thiophene, furan, pyrrole, thiazole, oxazole, isoxazole, imidazole, and pyrazole. While the Lennard-Jones parameters for carbon, hydrogen (two types), nitrogen (two types), oxygen, and sulfur are transferable for all 13 compounds, the partial charges are specific for each compound. The benzene dimer energies for sandwich, T-shape, and parallel-displaced configurations obtained for the TraPPE-EH force field compare favorably with high-level electronic structure calculations. Gibbs ensemble Monte Carlo simulations were carried out to compute the single-component vapor-liquid equilibria for benzene, pyridine, three diazenes, and eight five-membered heterocycles. The agreement with experimental data is excellent with the liquid densities and vapor pressures reproduced within 1 and 5%, respectively. The critical temperatures and normal boiling points are predicted with mean deviations of 0.8 and 1.6%, respectively.
Energy Technology Data Exchange (ETDEWEB)
Crisanti, F.; Apruzzese, G.; Frigione, D.; Kroegler, H.; Lovisetto, L.; Mazzitelli, G.; Podda, S. [ENEA, Centro Ricerche Frascati, Rome (Italy). Dip. Energia
1996-09-01
On the FTU Tokamak the plasma physics operations started on the 20/4/90. The first plasma had a plasma current Ip=0.75 MA for about a second. The experimental phase lasted until 7/7/94, when a long shut-down begun for installing the toroidal limiter in the inner side of the vacuum vessel. In these four years of operations plasma experiments have been successfully exploited, e.g. experiments of single and multiple pellet injections; full current drive up to Ip=300 KA was obtained by using waves at the frequency of the Lower Hybrid; analysis of ohmic plasma parameters with different materials (from the low Z silicon to high Z tungsten) as plasma facing element was performed. In this work a statistical analysis of the full period of operation is presented. Moreover, a comparison with the statistical data from other Tokamaks is attempted.
Energy Technology Data Exchange (ETDEWEB)
Viola, B.; Maddaluno, G.; Pericoli Ridolfini, V. [EURATOM-ENEA Association, C.R. Frascati, Via E. Fermi 45, 00044 Frascati (Rome) (Italy); Corrigan, G.; Harting, D. [Culham Centre of Fusion Energy, EURATOM-Association, Abingdon (United Kingdom); Mattia, M. [Dipartimento di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico, 00133 Roma (Italy); Zagorski, R. [Institute of Plasma Physics and Laser Microfusion-EURATOM Association, 01-497 Warsaw (Poland)
2014-06-15
The new magnetic configurations for tokamak divertors, snowflake and super-X, proposed to mitigate the problem of the power exhaust in reactors have clearly evidenced the need for an accurate and reliable modeling of the physics governing the interaction with the plates. The initial effort undertaken jointly by ENEA and IPPLM has been focused to exploit a simple and versatile modeling tool, namely the 2D TECXY code, to obtain preliminary comparison between the conventional and snowflake configurations for the proposed new device FAST that should realize an edge plasma with properties quite close to those of a reactor. The very interesting features found for the snowflake, namely a power load mitigation much larger than expected directly from the change of the magnetic topology, has further pushed us to check these results with the more sophisticated computational tool EDGE2D coupled with the neutral code module EIRENE. After a preparatory work that has been carried out in order to adapt this code combination to deal with non-conventional, single null equilibria and in particular with second order nulls in the poloidal field generated in the snowflake configuration, in this paper we describe the first activity to compare these codes and discuss the first results obtained for FAST. The outcome of these EDGE2D runs is in qualitative agreement with those of TECXY, confirming the potential benefit obtainable from a snowflake configuration. (copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Dorville, Nicolas; Belmont, Gérard; Aunai, Nicolas; Dargent, Jérémy; Rezeau, Laurence
2015-09-01
Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115-121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958-1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251-317 (1996); and F. Mottez, Phys. Plasmas 10, 1541-1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20
Energy Technology Data Exchange (ETDEWEB)
Dorville, Nicolas, E-mail: nicolas.dorville@lpp.polytechnique.fr; Belmont, Gérard; Aunai, Nicolas; Dargent, Jérémy; Rezeau, Laurence [LPP, Ecole Polytechnique, CNRS, UPMC, Université Paris Sud, Palaiseau (France)
2015-09-15
Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present
Energy Technology Data Exchange (ETDEWEB)
Kobori, Hikaru [Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan); Kasada, Ryuta, E-mail: r-kasada@iae.kyoto-u.ac.jp [Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan); Hiwatari, Ryoji [Central Research Institute of Electric Power Industry, Tokyo (Japan); Konishi, Satoshi [Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
2016-11-01
Highlights: • We incorporated the Life Cycle Analysis (LCA) of tokamak type DEMO reactor and following commercial reactors as an extension of a system code. • We calculated CO{sub 2} emissions from reactor construction, operation and decommissioning that is considered as a major environmental cost. • We found that the objective of conceptual design of the tokamak fusion power reactor is moved by changing evaluation index. • The tokamak fusion reactor can reduce CO{sub 2} emissions in the life cycle effectively by reduction of the amount involved in the replacement of internal components. • The tokamak fusion reactor achieves under 0.174$/kWh electricity cost, the tokamak fusion reactor is contestable with 1500 degrees-class LNG-fired combined cycle power plant. - Abstract: This study incorporate the Life Cycle Analysis (LCA) of tokamak type DEMO reactor and following commercial reactors as an extension of a system code to calculate CO{sub 2} emissions from reactor construction, operation and decommissioning that is considered as a major environmental cost. Competitiveness of tokamak fusion power reactors is expected to be evaluated by the cost and environmental impact represented by the CO{sub 2} emissions, compared with present and future power generating systems such as fossil, nuclear and renewables. Result indicated that (1) The objective of conceptual design of the tokamak fusion power reactor is moved by changing evaluation index. (2) The tokamak fusion reactor can reduce CO{sub 2} emissions in the life cycle effectively by reduction of the amount involved in the replacement of internal components. (3) The tokamak fusion reactor achieves under 0.174$/kWh electricity cost, the tokamak fusion reactor is contestable with 1500 degrees-class LNG-fired combined cycle power plant.
Energy Technology Data Exchange (ETDEWEB)
Lopez C, R.; Melendez L, L.; Chavez A, E.; Colunga S, S.; Valencia A, R.; Gaytan G, E
1992-07-15
The analytical procedure to carry out the establishment of the discharge in a Tokamak including: a) Ionization, b) Diffusion losses, recombination, union, drift speed, spurious fields, and c) Electric field is presented. In an experimental way a procedure settles down by means of which it is characterized the plasma, specially a new characteristic discharge parameter is settled down and it is the plasma current by the duration of the (I{sub p}t) discharge. (Author)
Phase equilibria in the Ag-Au-In system at 500°C
Ptashkina, E. A.; Romanova, A. G.; Pavlenko, A. S.; Kabanova, E. G.; Kuznetsov, V. N.
2017-02-01
Phase equilibria in Ag-Au-In system at 500°C are investigated by means of electron microscopy, electron probe microanalysis, and X-ray powder diffraction. The part of the system's isothermal cross section with an indium content of up to 50 at % is constructed.
New investigation of phase equilibria in the system Al-Cu-Si.
Ponweiser, Norbert; Richter, Klaus W
2012-01-25
The phase equilibria and invariant reactions in the system Al-Cu-Si were investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA) and electron probe micro analysis (EPMA). Isothermal phase equilibria were investigated within two isothermal sections. The isothermal section at 500 °C covers the whole ternary composition range and largely confirms the findings of previous phase diagram investigations. The isothermal section at 700 °C describes phase equilibria only in the complex Cu-rich part of the phase diagram. A new ternary compound τ was found in the region between (Al,Cu)-γ(1) and (Cu,Si)-γ and its solubility range was determined. The solubility of Al in κ-CuSi was found to be extremely high at 700 °C. In contrast, no ternary solubility in the β-phase of Cu-Al was found, although this phase is supposed to form a complete solid solution according to previous phase diagram assessments. Two isopleths, at 10 and 40 at.% Si, were investigated by means of DTA and a partial ternary reaction scheme (Scheil diagram) was constructed, based on the current work and the latest findings in the binary systems Al-Cu and Cu-Si. The current study shows that the high temperature equilibria in the Cu-rich corner are still poorly understood and additional studies in this area would be favorable.
Modelling of phase equilibria of glycol ethers mixtures using an association model
DEFF Research Database (Denmark)
Garrido, Nuno M.; Folas, Georgios; Kontogeorgis, Georgios
2008-01-01
Vapor-liquid and liquid-liquid equilibria of glycol ethers (surfactant) mixtures with hydrocarbons, polar compounds and water are calculated using an association model, the Cubic-Plus-Association Equation of State. Parameters are estimated for several non-ionic surfactants of the polyoxyethylene ...
Simulation of the high-pressure phase equilibria of hydrocarbon-water/brine systems
DEFF Research Database (Denmark)
Zuo, You-Xiang; Stenby, Erling Halfdan; Guo, Tian-Min
1996-01-01
The major objectives of this work are: (1) extend the modified Patel-Teja (MPT) equation of state proposed for aqueous electrolyte systems (Zuo and Guo, 1991) to describe the liquid-liquid and vapor-liquid-liquid equilibria of hydrocarbon-water/brine systems through introducing an unconventional ...
A numerical approach to investigate the stability of equilibria for structured population models
Breda, D.; Diekmann, O.; Maset, S.; Vermiglio, R.
2013-01-01
We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems ofVolterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved
Hommes, C.
2013-01-01
We discuss recent work on bounded rationality and learning in relation to Soros’ principle of reflexivity and stress the empirical importance of non-rational, almost selffulfilling equilibria in positive feedback systems. As an empirical example, we discuss a behavioral asset pricing model with hete
Rexwinkel, G.; Heesink, A.B.M.; Swaaij, van W.P.M.
1999-01-01
Single-solute adsorption equilibria have been measured for the adsorption of the gaseous solutes chloroform, chlorobenzene, and 1,1,1-trichloroethane onto Amberlite XAD-4 resin. For 1,1,1-trichloroethane the adsorption equilibrium has also been measured with activated carbon Norit ROW 0.8 SUPRA as a
Engwerda, Jacob
2015-01-01
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformu
Transport and Phase Equilibria Properties for Steam Flooding of Heavy Oils
Energy Technology Data Exchange (ETDEWEB)
Gabitto, Jorge; Barrufet, Maria
2001-12-18
The objectives of this research included experimental determination and rigorous modeling and computation of phase equilibria, volumetric, and transport properties of hydrocarbon/CO2/water mixtures at pressures and temperatures typical of steam injection processes for thermal recovery of heavy oils.
Liquid-liquid equilibria for binary and ternary polymer solutions with PC-SAFT
DEFF Research Database (Denmark)
Lindvig, Thomas; Michelsen, Michael Locht; Kontogeorgis, Georgios
2004-01-01
Two algorithms for evaluating liquid-liquid equilibria (LLE) for binary and ternary polymer solutions are presented. The binary algorithm provides the temperature versus concentration cloud-point curve at fixed pressure, whereas the ternary algorithm provides component 1 versus component 2...
The Representation of Highly Non-Ideal Phase Equilibria Using Computer Graphics.
Charos, Georgios N.; And Others
1986-01-01
Previous work focused on use of computer graphics in teaching thermodynamic phase equilibria for classes I and II. Extends this work to include the considerably more non-ideal phase behavior shown by classes III, IV, and V. Student and instructor response has been overwhelmingly positive about the approach. (JN)
van Bennekom, Joost G.; Winkelman, Jozef G. M.; Venderbosch, Robertus H.; Nieland, Sebastiaan D. G. B.; Heeres, Hero J.
2012-01-01
A solution method was developed to calculate the simultaneous phase and chemical equilibria in high-pressure methanol synthesis (P = 20 MPa, 463
Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion
Olaya, Maria del Mar; Reyes-Labarta, Juan A.; Serrano, Maria Dolores; Marcilla, Antonio
2010-01-01
Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…