MHD equilibrium with toroidal rotation
International Nuclear Information System (INIS)
Li, J.
1987-03-01
The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)
Problems in nonlinear resistive MHD
International Nuclear Information System (INIS)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-01-01
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1
Nonlinear evolution of MHD instabilities
International Nuclear Information System (INIS)
Bateman, G.; Hicks, H.R.; Wooten, J.W.; Dory, R.A.
1975-01-01
A 3-D nonlinear MHD computer code was used to study the time evolution of internal instabilities. Velocity vortex cells are observed to persist into the nonlinear evolution. Pressure and density profiles convect around these cells for a weak localized instability, or convect into the wall for a strong instability. (U.S.)
Proceedings of the workshop on nonlinear MHD and extended MHD
International Nuclear Information System (INIS)
1998-01-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database
Proceedings of the workshop on nonlinear MHD and extended MHD
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
MHD equilibrium of heliotron J plasmas
International Nuclear Information System (INIS)
Suzuki, Yasuhiro; Nakamura, Yuji; Kondo, Katsumi; Nakajima, Noriyoshi; Hayashi, Takaya
2004-01-01
MHD equilibria of Heliotron J plasma are investigated by using HINT code. By assuming some profiles of the current density, effects of the net toroidal currents on the magnetohydrodynamics (MHD) equilibrium are investigated. If the rotational transform can be controlled by the currents, the generation of good flux surfaces is expected. In order to study equilibria with self-consistent bootstrap current, the boozer coordinates are constructed by converged HINT equilibrium as a preliminary study. Obtained spectra are compared with ones of VMEC code and both results are consistent. (author)
Goya - an MHD equilibrium code for toroidal plasmas
International Nuclear Information System (INIS)
Scheffel, J.
1984-09-01
A description of the GOYA free-boundary equilibrium code is given. The non-linear Grad-Shafranov equation of ideal MHD is solved in a toroidal geometry for plasmas with purely poloidal magnetic fields. The code is based on a field line-tracing procedure, making storage of a large amount of information on a grid unnecessary. Usage of the code is demonstrated by computations of equi/libria for the EXTRAP-T1 device. (Author)
Compact torus theory: MHD equilibrium and stability
International Nuclear Information System (INIS)
Barnes, D.C.; Seyler, C.E.; Anderson, D.V.
1979-01-01
Field reversed theta pinches have demonstrated the production and confinement of compact toroidal configurations with surprisingly good MHD stability. In these observations, the plasma is either lost by diffusion or by the loss of the applied field or is disrupted by an n = 2 (where n is the toroidal mode number) rotating instability only after 30 to 100 MHD times, when the configuration begins to rotate rigidly above a critical speed. These experiments have led one to investigate the equilibrium, stability, and rotation of a very elongated, toroidally axisymmetric configuration with no toroidal field. Many of the above observations are explained by recent results of these investigations which are summarized
MHD equilibrium identification on ASDEX-Upgrade
International Nuclear Information System (INIS)
McCarthy, P.J.; Schneider, W.; Lakner, K.; Zehrfeld, H.P.; Buechl, K.; Gernhardt, J.; Gruber, O.; Kallenbach, A.; Lieder, G.; Wunderlich, R.
1992-01-01
A central activity accompanying the ASDEX-Upgrade experiment is the analysis of MHD equilibria. There are two different numerical methods available, both using magnetic measurements which reflect equilibrium states of the plasma. The first method proceeds via a function parameterization (FP) technique, which uses in-vessel magnetic measurements to calculate up to 66 equilibrium parameters. The second method applies an interpretative equilibrium code (DIVA) for a best fit to a different set of magnetic measurements. Cross-checks with the measured particle influxes from the inner heat shield and the divertor region and with visible camera images of the scrape-off layer are made. (author) 3 refs., 3 figs
3-D nonlinear evolution of MHD instabilities
International Nuclear Information System (INIS)
Bateman, G.; Hicks, H.R.; Wooten, J.W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed
Averaged description of 3D MHD equilibrium
International Nuclear Information System (INIS)
Medvedev, S.Yu.; Drozdov, V.V.; Ivanov, A.A.; Martynov, A.A.; Pashekhonov, Yu.Yu.; Mikhailov, M.I.
2001-01-01
A general approach by S.A.Galkin et al. in 1991 to 2D description of MHD equilibrium and stability in 3D systems was proposed. The method requires a background 3D equilibrium with nested flux surfaces to generate the metric of a Riemannian space in which the background equilibrium is described by the 2D equation of Grad-Shafranov type. The equation can be solved then varying plasma profiles and shape to get approximate 3D equilibria. In the framework of the method both planar axis conventional stellarators and configurations with spatial magnetic axis can be studied. In the present report the formulation and numerical realization of the equilibrium problem for stellarators with planar axis is reviewed. The input background equilibria with nested flux surfaces are taken from vacuum magnetic field approximately described by analytic scalar potential
Nonlinear MHD analysis for LHD plasmas
International Nuclear Information System (INIS)
Ichiguchi, K.; Nakajima, N.; Wakatani, M.; Carreras, B.A.
2003-01-01
The nonlinear behavior of the interchange modes with multi-helicity in the Large Helical Device is analyzed based on the reduced MHD equations. In the equilibrium at sufficiently low beta value, the saturation of a single mode and the following excitation of other single mode whose resonant surface is close to that of the saturated mode are slowly repeated. This sequence leads to the local deformation of the pressure profile. Increasing the beta value with the pressure profile fixed, a bursting phenomenon due to the overlap of multiple modes is observed in the kinetic energy, which results in the global reduction of the pressure profile. Increasing the beta value using the pressure profile saturated at the lower beta value suppresses the bursting behavior. This result indicates the possibility that the pressure profile is self-organized so that the LHD plasma should attain the high beta regime through a stable path. (author)
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Investigations on application of multigrid method to MHD equilibrium analysis
International Nuclear Information System (INIS)
Ikuno, Soichiro
2000-01-01
The potentiality of application for Multi-grid method to MHD equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearization of the equation, the problem is solved by use of the iterative method. Although the Red-Black SOR method or Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. The Multi-grid method is compared with the SOR method for the Poisson Problem. The results of computations show that the CPU time required for the Multi-grid method is about 1000 times as small as that for the SOR method. (author)
Measured MHD equilibrium in Alcator C
International Nuclear Information System (INIS)
Pribyl, P.A.
1986-03-01
A method of processing data from a set of partial Rogowski loops is developed to study the MHD equilibrium in Alcator C. Time dependent poloidal fields in the vicinity of the plasma are calculated from measured currents, with field penetration effects being accounted for. Fields from eddy currents induced by the plasma in the tokamak structure are estimated as well. Each of the set of twelve B/sub θ/ measurements can then be separated into a component from the plasma current and a component from currents external to the pickup loops. Harmonic solutions to Maxwell's equations in toroidal coordinates are fit to these measurements in order to infer the fields everywhere in the vacuum region surrounding the plasma. Using this diagnostic, plasma current, position, shape, and the Shafranov term Λ = β/sub p/ + l/sub i//2 - 1 may be computed, and systematic studies of these plasma parameters are undertaken for Alcator C plasmas
MHD equilibrium of toroidal fusion plasma with stationary flows
International Nuclear Information System (INIS)
Galkowski, A.
1994-01-01
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad's ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs
Energy Technology Data Exchange (ETDEWEB)
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
MHD equilibrium and stability in heliotron plasmas
Energy Technology Data Exchange (ETDEWEB)
Ichiguchi, Katsuji [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-09-01
Recent topics in the theoretical magnetohydrodynamic (MHD) analysis in the heliotron configuration are overviewed. Particularly, properties of three-dimensional equilibria, stability boundary of the interchange mode, effects of the net toroidal current including the bootstrap current and the ballooning mode stability are focused. (author)
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Outline of fast analyzer for MHD equilibrium 'FAME'
International Nuclear Information System (INIS)
Sakata, Shinya; Haginoya, Hirofumi; Tsuruoka, Takuya; Aoyagi, Tetsuo; Saito, Naoyuki; Harada, Hiroo; Tani, Keiji; Watanabe, Hideto.
1994-03-01
The FAME (Fast Analyzer for Magnetohydrodynamic (MHD) Equilibrium) system has been developed in order to provide more than 100 MHD equilibria in time series which are enough for the non-stationary analysis of the experimental data of JT-60 within about 20 minutes shot interval. The FAME is an MIMD type small scale parallel computer with 20 microprocessors which are connected by a multi-stage switching system. The maximum theoretical speed is 250 MFLOPS. For the software system of FAME, MHD equilibrium analysis code SELENE and its input data production code FBI are tuned up taking the parallel processing into consideration. Consequently, the computational performance of the FAME system becomes more than 7 times faster than the existing general purpose computer FACOM M780-10s. This report summarizes the outline of the FAME system including hardware, soft-ware and peripheral equipments. (author)
2-D skin-current toroidal-MHD-equilibrium code
International Nuclear Information System (INIS)
Feinberg, B.; Niland, R.A.; Coonrod, J.; Levine, M.A.
1982-09-01
A two-dimensional, toroidal, ideal MHD skin-current equilibrium computer code is described. The code is suitable for interactive implementation on a minicomptuer. Some examples of the use of the code for design and interpretation of toroidal cusp experiments are presented
Modified NASA-Lewis chemical equilibrium code for MHD applications
Sacks, R. A.; Geyer, H. K.; Grammel, S. J.; Doss, E. D.
1979-01-01
A substantially modified version of the NASA-Lewis Chemical Equilibrium Code was recently developed. The modifications were designed to extend the power and convenience of the Code as a tool for performing combustor analysis for MHD systems studies. The effect of the programming details is described from a user point of view.
Calculation code NIRVANA for free boundary MHD equilibrium
International Nuclear Information System (INIS)
Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa
1975-03-01
The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)
Magnetic analysis of tokamak plasma with approximate MHD equilibrium solution
International Nuclear Information System (INIS)
Moriyama, Shin-ichi; Hiraki, Naoji
1993-01-01
A magnetic analysis method for determining equilibrium configuration parameters (plasma shape, poloidal beta and internal inductance) on a non-circular tokamak is described. The feature is to utilize an approximate MHD equilibrium solution which explicitly relates the configuration parameters with the magnetic fields picked up by magnetic sensors. So this method is suitable for the real-time analysis performed during a tokamak discharge. A least-squares fitting procedure is added to the analytical algorithm in order to reduce the errors in the magnetic analysis. The validity is investigated through the numerical calculation for a tokamak equilibrium model. (author)
Numerical study of spherical Torus MHD equilibrium configuration
International Nuclear Information System (INIS)
Cheng Faying; Dong Jiaqi; Wang Aike
2003-01-01
Tokamak equilibrium code SWEQU has been modified so that it can be used for the MHD equilibrium study of low aspect ratio device. Evolution of plasma configuration in start-up phase and double-null divertor configuration in steady-state phase has been simulated using the modified code. Results show that the new code can be used not only to obtain the equilibrium configuration of spherical Torus in steady-state phase, but also to simulate the evolution of plasma in the start-up phase
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
Moawad, S. M.; Moawad
2013-10-01
The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.
On nonlinear MHD-stability of toroidal magnetized plasma
International Nuclear Information System (INIS)
Ilgisonis, V.I.; Pastukhov, V.P.
1994-01-01
The variational approach to analyze the nonlinear MHD stability of ideal plasma in toroidal magnetic field is proposed. The potential energy functional to be used is expressed in terms of complete set of independent Lagrangian invariants, that allows to take strictly into account all the restrictions inherent in the varied functions due to MHD dynamic equations. (author). 3 refs
International Nuclear Information System (INIS)
Moawad, S. M.; Ibrahim, D. A.
2016-01-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
Numerical study for determining PF coil system parameters in MHD equilibrium of KT-2 tokamak plasma
International Nuclear Information System (INIS)
Ryu, J.; Hong, S.H.; Lee, K.W.; Hong, B.G.; In, S.R.; Kim, S.K.
1995-01-01
The KT-2 is a large-aspect-ratio medium-sized divertor tokamak in the conceptual design phase and planned to be operational in 1998 at the Korea Atomic Energy Research Institute (KAERI). Plasma equilibrium in tokamak can be acquired by controlling the current of poloidal field (PF) coils in appropriate geometries and positions. In this study, the authors have performed numerical calculations to achieve the various equilibrium conditions fitting given plasma shapes and satisfying PF current limitations. Usually an ideal magnetohydrodynamic (MHD) equation is used to obtain the equilibrium solution of tokamak plasma, and it is practical to take advantage of a numerical method in solving the MHD equation because it has nonlinear source terms. Two equilibrium codes have been applied to find a double-null configuration of free-boundary tokamak plasma in KT-2: one is of the authors' own developing and the other is a free-boundary tokamak equilibrium code (FBT) that has been used mainly for the verification of developed code's results. PF coil system parameters including their positions and currents are determined for the optimization of input power required when the specifications of KT-2 tokamak are met. Then, several sets of equilibrium conditions during the tokamak operation are found to observe the changes of poloidal field currents with the passing of operation time step, and the basic stability problems related with the magnetic field structure is also considered
ORMEC: a three-dimensional MHD spectral inverse equilibrium code
International Nuclear Information System (INIS)
Hirshman, S.P.; Hogan, J.T.
1986-02-01
The Oak Ridge Moments Equilibrium Code (ORMEC) is an efficient computer code that has been developed to calculate three-dimensional MHD equilibria using the inverse spectral method. The fixed boundary formulation, which is based on a variational principle for the spectral coefficients (moments) of the cylindrical coordinates R and Z, is described and compared with the finite difference code BETA developed by Bauer, Betancourt, and Garabedian. Calculations for the Heliotron, Wendelstein VIIA, and Advanced Toroidal Facility (ATF) configurations are performed to establish the accuracy and mesh convergence properties for the spectral method. 16 refs., 13 figs
A toroidal plasma MHD equilibrium code 'EQUCIR version 1'
International Nuclear Information System (INIS)
Ninomiya, Hiromasa; Shinya, Kichiro; Kameari, Akihisa.
1980-10-01
A new free-boundary toroidal MHD equilibrium code ''EQUCIR version 1'' has been developed. The central problems approached by this code is as follows: 1) The magnetic flux distribution of a plasma at equilibrium is determined in the given external field. 2) A set of circuit equations between the plasma and the external conductors are constructed. These circuit equations and the Grad-Shafranov equation are solved self-consistently and the time evolutions of plasma equilibria and currents in external conductors are determined at the same time. 3) The currents in the external conductors are determined so that the plasma cross-section and plasma parameters are to be maintained with desired ones. It is shown that this code is very useful for study of the tokamak plasma equilibria, for design of the poloidal coil system and for investigation of experimental results. (author)
Nonlinear MHD dynamo operating at equipartition
DEFF Research Database (Denmark)
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate...
Topics on MHD equilibrium and stability in heliotron / torsatron
International Nuclear Information System (INIS)
Ichiguchi, Katsuji; Nakajima, Noriyoshi; Okamoto, Masao.
1996-10-01
Recent topics on the MHD properties with and without bootstrap current in Heliotron / Torsatron configurations are presented. In a currentless equilibrium with a large Shafranov shift, a high-n ballooning mode can be unstable even in the region with positive gradient of the rotational transform. This is because the local shear in the field line bending term can be reduced by the fact that the local enhancement of the poloidal field varies in the radial direction. Since the local curvature of the field lines depends on the label of the magnetic field line, α, in Heliotron / Torsatron, the eigenvalue ω 2 also depends on α. In the Mercier stable region, the level surfaces of ω 2 of unstable modes form spheroids in the (ψ, θ k , α) space, where ψ and θ k are the label of the flux surface and the radial wave number, while they form cylinders in tokamaks. Such high-n modes cannot be related to low-n modes in this case. In the LHD configuration, bootstrap current depends on the collisionality of the plasma. When the beta value is raised by increasing the temperature with the density fixed, the plasma becomes less collisional and the bootstrap current grows in the direction where the rotational transform is increased. On the contrary, when the beta value is raised by increasing the density with the temperature fixed, the plasma becomes more collisional. While a small amount of the current flows in the same direction as in the above sequence at low beta in this case, the direction of the current reverses at high beta equilibrium. This is because the geometrical factor in the expression of the bootstrap current in the plateau regime has opposite signature to that in the 1/ν regime. The latter equilibrium sequence is more stable in the Mercier criterion than the former one. Thus, the beta should be raised by increasing the density rather than the temperature to obtain stable high beta plasma. (author)
Neoclassical viscous stress tensor for non-linear MHD simulations with XTOR-2F
International Nuclear Information System (INIS)
Mellet, N.; Maget, P.; Meshcheriakov, D.; Lütjens, H.
2013-01-01
The neoclassical viscous stress tensor is implemented in the non-linear MHD code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), allowing consistent bi-fluid simulations of MHD modes, including the metastable branch of neoclassical tearing modes (NTMs) (Carrera et al 1986 Phys. Fluids 29 899–902). Equilibrium flows and bootstrap current from the neoclassical theory are formally recovered in this Chew–Goldberger–Low formulation. The non-linear behaviour of the new model is verified on a test case coming from a Tore Supra non-inductive discharge. A NTM threshold that is larger than with the previous model is obtained. This is due to the fact that the velocity is now part of the bootstrap current and that it differs from the theoretical neoclassical value. (paper)
A nonlinear resistive MHD-code in cylindrical geometry
International Nuclear Information System (INIS)
Jakoby, A.
1987-11-01
A computer code has been developed which solves the full compressible resistive magnetohydrodynamic (MHD) equations in cylindrical geometry. The variables are expanded in Fourier series in the poloidal and axial directions while finite differences are used in the radial direction. The time advance is accomplished by using a semi-implicit predictor-corrector-scheme. Applications to the ideal m=1 ideal kink saturation in the nonlinear regime and the subsequent decay of the singular current layer due to resistivity are presented. (orig.)
On MHD nonlinear stretching flow of Powell–Eyring nanomaterial
Directory of Open Access Journals (Sweden)
Tasawar Hayat
Full Text Available This communication addresses the magnetohydrodynamic (MHD flow of Powell–Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell–Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted. Keywords: Powell–Eyring fluid, Magnetohydrodynamics, Nanomaterial, Nonlinear stretching surface
Nonlinear MHD dynamics of tokamak plasmas on multiple time scales
International Nuclear Information System (INIS)
Kruger, S.E.; Schnack, D.D.; Brennan, D.P.; Gianakon, T.A.; Sovinec, C.R.
2003-01-01
Two types of numerical, nonlinear simulations using the NIMROD code are presented. In the first simulation, we model the disruption occurring in DIII-D discharge 87009 as an ideal MHD instability driven unstable by neutral-beam heating. The mode grows faster than exponential, but on a time scale that is a hybrid of the heating rate and the ideal MHD growth rate as predicted by analytic theory. The second type of simulations, which occur on a much longer time scale, focus on the seeding of tearing modes by sawteeth. Pressure effects play a role both in the exterior region solutions and in the neoclassical drive terms. The results of both simulations are reviewed and their implications for experimental analysis is discussed. (author)
Dynamics of nonlinear resonant slow MHD waves in twisted flux tubes
Directory of Open Access Journals (Sweden)
R. Erdélyi
2002-01-01
Full Text Available Nonlinear resonant magnetohydrodynamic (MHD waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc. The resonant behaviour of slow MHD waves is confined in a narrow dissipative layer. Using the method of simplified matched asymptotic expansions inside and outside of the narrow dissipative layer, we generalise the so-called connection formulae obtained in linear MHD for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These connection formulae for resonant MHD waves across the dissipative layer play a similar role as the well-known Rankine-Hugoniot relations connecting solutions at both sides of MHD shock waves. The key results are the nonlinear connection formulae found in dissipative cylindrical MHD which are an important extension of their counterparts obtained in linear ideal MHD (Sakurai et al., 1991, linear dissipative MHD (Goossens et al., 1995; Erdélyi, 1997 and in nonlinear dissipative MHD derived in slab geometry (Ruderman et al., 1997. These generalised connection formulae enable us to connect solutions obtained at both sides of the dissipative layer without solving the MHD equations in the dissipative layer possibly saving a considerable amount of CPU-time when solving the full nonlinear resonant MHD problem.
Nonlinear equilibrium in Tokamaks including convective terms and viscosity
International Nuclear Information System (INIS)
Martin, P.; Castro, E.; Puerta, J.
2003-01-01
MHD equilibrium in tokamaks becomes very complex, when the non-linear convective term and viscosity are included in the momentum equation. In order to simplify the analysis, each new term has been separated in type gradient terms and vorticity depending terms. For the special case in which the vorticity vanishes, an extended Grad-Shafranov type equation can be obtained. However now the magnetic surface is not isobars or current surfaces as in the usual Grad-Shafranov treatment. The non-linear convective terms introduces gradient of Bernoulli type kinetic terms . Montgomery and other authors have shown the importance of the viscosity terms in tokamaks [1,2], here the treatment is carried out for the equilibrium condition, including generalized tokamaks coordinates recently described [3], which simplify the equilibrium analysis. Calculation of the new isobar surfaces is difficult and some computation have been carried out elsewhere for some particular cases [3]. Here, our analysis is extended discussing how the toroidal current density, plasma pressure and toroidal field are modified across the midplane because of the new terms (convective and viscous). New calculations and computations are also presented. (Author)
International Nuclear Information System (INIS)
Velikhov, E.P.; Golubev, V.S.; Dykhne, A.M.
1976-01-01
The paper assesses the position in 1975 of theoretical and experimental work on the physics of a magnetohydrodynamic generator with non-equilibrium plasma conductivity. This research started at the beginning of the 1960s; as work on the properties of thermally non-equilibrium plasma in magnetic fields and also in MHD generator ducts progressed, a number of phenomena were discovered and investigated that had either been unknown in plasma physics or had remained uninvestigated until that time: ionization instability and ionization turbulence of plasma in a magnetic field, acoustic instability of a plasma with anisotropic conductivity, the non-equilibrium ionization wave and the energy balance of a non-equilibrium plasma. At the same time, it was discovered what physical requirements an MHD generator with non-equilibrium conductivity must satisfy to achieve high efficiency in converting the thermal or kinetic energy of the gas flow into electric energy. The experiments on MHD power generation with thermally non-equilibrium plasma carried out up to 1975 indicated that it should be possible to achieve conversion efficiencies of up to 20-30%. (author)
Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities
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Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.
1988-10-01
Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs
L. Braga, F.
2013-10-01
The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic (MHD) equilibrium with reversed current density (RCD) profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.
Axisymmetric MHD equilibrium solver with bicubic Hermite elements
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Luetjens, H.; Bondeson, A.; Roy, A.
1990-05-01
A numerical code solving axisymmetric magnetohydrodynamic equilibria with rectangular bicubic Hermite elements has been developed. Two test cases are used for checking the convergence rate of the solution. The mapping of the equilibrium quantities into flux coordinates for magnetohydrodynamic stability calculation is performed by a method which preserves the convergence properties of the cubic Hermite elements. Convergence studies show the behaviour of the stability results when the equilibrium mesh is varied. (author) 13 refs., 3 tabs
Multi-scale-nonlinear interactions among macro-MHD mode, micro-turbulence, and zonal flow
International Nuclear Information System (INIS)
Ishizawa, Akihiro; Nakajima, Noriyoshi
2007-01-01
This is the first numerical simulation demonstrating that macro-magnetohydrodynamic (macro-MHD) mode is exited as a result of multi-scale interaction in a quasi-steady equilibrium formed by a balance between zonal flow and micro-turbulence via reduced-two-fluid simulation. Only after obtaining the equilibrium which includes zonal flow and the turbulence caused by kinetic ballooning mode is this simulation of macro-MHD mode, double tearing mode, accomplished. In the quasi-steady equilibrium a macro-fluctuation which has the same helicity as that of double tearing mode is a part of the turbulence until it grows as a macro-MHD mode finally. When the macro-MHD grows it effectively utilize free energy of equilibrium current density gradient because of positive feedback loop between suppression of zonal flow and growth of the macro-fluctuation causing magnetic reconnection. Thus once the macro-MHD grows from the quasi-equilibrium, it does not go back. This simulation is more comparable with experimental observation of growing macro-fluctuation than traditional MHD simulation of linear instabilities in a static equilibrium. (author)
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Tsventoukh, M. M.
2010-01-01
A study is made of the convective (interchange, or flute) plasma stability consistent with equilibrium in magnetic confinement systems with a magnetic field decreasing outward and large curvature of magnetic field lines. Algorithms are developed which calculate convective plasma stability from the Kruskal-Oberman kinetic criterion and in which the convective stability is iteratively consistent with MHD equilibrium for a given pressure and a given type of anisotropy in actual magnetic geometry. Vacuum and equilibrium convectively stable configurations in systems with a decreasing, highly curved magnetic field are calculated. It is shown that, in convectively stable equilibrium, the possibility of achieving high plasma pressures in the central region is restricted either by the expansion of the separatrix (when there are large regions of a weak magnetic field) or by the filamentation of the gradient plasma current (when there are small regions of a weak magnetic field, in which case the pressure drops mainly near the separatrix). It is found that, from the standpoint of equilibrium and of the onset of nonpotential ballooning modes, a kinetic description of convective stability yields better plasma confinement parameters in systems with a decreasing, highly curved magnetic field than a simpler MHD model and makes it possible to substantially improve the confinement parameters for a given type of anisotropy. For the Magnetor experimental compact device, the maximum central pressure consistent with equilibrium and stability is calculated to be as high as β ∼ 30%. It is shown that, for the anisotropy of the distribution function that is typical of a background ECR plasma, the limiting pressure gradient is about two times steeper than that for an isotropic plasma. From a practical point of view, the possibility is demonstrated of achieving better confinement parameters of a hot collisionless plasma in systems with a decreasing, highly curved magnetic field than those
MHD Kelvin-Helmholtz instability in non-hydrostatic equilibrium
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Laghouati, Y; Bouabdallah, A; Zizi, M; Alemany, A
2007-01-01
The present work deals with the linear stability of a magnetohydrodynamic shear flow so that a stratified inviscid fluid rotating about a vertical axis when a uniform magnetic field is applied in the direction of the streaming or zonal flow. In geophysical flow, the stability of the flow is determined by taking into account the nonhydrostatic condition depending on Richardson number R i and the deviation δ from hydrostatic equilibrium. According to Stone (Stone P H 1971 J. Fluid. Mech. 45 659), it is shown that such deviation δ decreases the growth rates of three kinds of instability which can appear as geostrophic (G), symmetric (S) and Kelvin-Helmholtz (K-H) instabilities. To be specific, the evolution of the flow is therefore considered in the light of the influence of magnetic field, particularly, on K-H instability. The results of this study are presented by the linear stability of a magnetohydrodynamic, with horizontal free-shear flow of stratified fluid, subject to rotation about the vertical axis and uniform magnetic field in the zonal direction. Results are discussed and compared to previous works as Chandrasekhar (Chandrasekhar S 1961 Hydrodynamic and hydromagnetic stability (Oxford: Clarendon Press) chapter 11 pp 481-513) and Stone
Effect of bootstrap current on MHD equilibrium beta limit in heliotron plasmas
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Watanabe, K.Y.
2001-01-01
The effect of bootstrap current on the beta limit of MHD equilibria is studied systematically by an iterative calculation of MHD equilibrium and the consistent bootstrap current in high beta heliotron plasmas. The LHD machine is treated as a standard configuration heliotron with an L=2 planar axis. The effects of vacuum magnetic configurations, pressure profiles and the vertical field control method are studied. The equilibrium beta limit with consistent bootstrap current is quite sensitive to the magnetic axis location for finite beta, compared with the currentless cases. For a vacuum configuration with the magnetic axis shifted inwards in the torus, even in the high beta regimes, the bootstrap current flows to increase the rotational transform, leading to an increase in the equilibrium beta limit. On the contrary, for a vacuum configuration with the magnetic axis shifted outwards in the torus, even in the low beta regimes, the bootstrap current flows so as to reduce the rotational transform; therefore, there is an acceleration of the Shafranov shift increase as beta increases, leading to a decrease in the equilibrium beta limit. The pressure profiles and vertical field control methods influence the equilibrium beta limit through the location of the magnetic axis for finite beta. These characteristics are independent of both device parameters, such as magnetic field strength, and device size in the low collisional regime. (author)
Construction of a path of MHD equilibrium solutions by an iterative method
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Kikuchi, Fumio.
1979-09-01
This paper shows a constructive proof of the existence of a path of solutions to a nonlinear eigenvalue problem expressed by -Δu = lambda u + in Ω, and u = -1 on deltaΩ where Ω is a two-dimensional domain with a boundary deltaΩ. This problem arises from the ideal MHD equilibria in tori. The existence proof is based on the principle of contraction mappings, which is widely employed in nonlinear problems such as those associated with bifurcation phenomena. Some comments are also given on the application of the present iteration techniques to numerical method. (author)
Inclusion of pressure and flow in the KITES MHD equilibrium code
International Nuclear Information System (INIS)
Raburn, Daniel; Fukuyama, Atsushi
2013-01-01
One of the simplest self-consistent models of a plasma is single-fluid magnetohydrodynamic (MHD) equilibrium with no bulk fluid flow under axisymmetry. However, both fluid flow and non-axisymmetric effects can significantly impact plasma equilibrium and confinement properties: in particular, fluid flow can produce profile pedestals, and non-axisymmetric effects can produce islands and stochastic regions. There exist a number of computational codes which are capable of calculating equilibria with arbitrary flow or with non-axisymmetric effects. Previously, a concept for a code to calculate MHD equilibria with flow in non-axisymmetric systems was presented, called the KITES (Kyoto ITerative Equilibrium Solver) code. Since then, many of the computational modules for the KITES code have been completed, and the work-in-progress KITES code has been used to calculate non-axisymmetric force-free equilibria. Additional computational modules are required to allow the KITES code to calculate equilibria with pressure and flow. Here, the authors report on the approaches used in developing these modules and provide a sample calculation with pressure. (author)
MHD equilibrium and pressure driven instability in L=1 heliotron plasmas
International Nuclear Information System (INIS)
Nakamura, Y.; Suzuki, Y.; Yamagishi, O.; Kondo, K.; Nakajima, N.; Hayashi, T.; Monticello, D.A.; Reiman, A.H.
2003-01-01
Free boundary MHD equilibrium properties of Heliotron J are investigated by VMEC, HINT and PIES codes, and ideal MHD stability properties are studied by the Mercier criterion, the ballooning mode equation and the CAS3D global stability code. It is shown by the equilibrium calculations that the change of the plasma boundary shape is substantial in a low shear helical system even if the beta is relatively low. Preliminary comparison between PIES results and HINT results shows that the beta value at which the magnetic island begin to be perceptible is almost the same in both codes, but the island width seems to be different. From the stability analysis, good correlation is found between local and global analyses for the three dimensional(3D) or helical ballooning mode whose mode structure shows strong poloidal and toroidal mode (helical mode) coupling. In the helical ballooning mode, the Eigenmode is localized within a flux tube. It is also found that the positive shear of the rotational transform is favorable for the 3D ballooning mode stability in a low shear helical system. (author)
Experimental and theoretical studies of the effects of nonuniformities in equilibrium MHD generators
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Rosenbaum, M.; Shamma, S.E.; Louis, J.F.
1980-01-01
An experimental study of the effects of thermal and velocity nonuniformities is performed in an equilibrium plasma for a range of Hall parameters. An electrodeless MHD disk generator with radial flow is chosen as the ideal geometry for these experiments. By introducing equally spaced cold blades in the flow, it is possible to create well defined two-dimensional wake nonuniformities with strong variations of the plasma properties in the direction normal to the magnetic field and the flow. This type of nonuniformity is predicted to provide the strongest reduction of Hall coefficient and effective conductivity for high values of Hall parameter. This degradation is controlled by both the level of nonuniformities and the value of the ideal Hall parameter. The former is dependent upon the number of blades (root mean square deviation of the conductivity), and the latter is dependent upon the values of the magnetic field intensities. The results provide basic quantitative information about the effects of conductivity and velocity nonuniformities on the performance of equilibrium MHD generators over a wide range of Hall coefficients, between 2 and 7. Reduction formulae are established between the effective and ideal Hall parameters for different levels of nonuniformities intensities. Theoretical predictions are derived from a detailed two-dimensional electrodynamic analysis and a simplified engineering model based on a generalization of Rosa's layer model. These experiments validate the analytical studies and support the use of the theoretical layer models in describing the effect of boundary layers on the performance of linear generators
Implementation of a 3-D nonlinear MHD [magnetohydrodynamics] calculation on the Intel hypercube
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Lynch, V.E.; Carreras, B.A.; Drake, J.B.; Hicks, H.R.; Lawkins, W.F.
1987-01-01
The optimization of numerical schemes and increasing computer capabilities in the last ten years have improved the efficiency of 3-D nonlinear resistive MHD calculations by about two to three orders of magnitude. However, we are still very limited in performing these types of calculations. Hypercubes have a large number of processors with only local memory and bidirectional links among neighbors. The Intel Hypercube at Oak Ridge has 64 processors with 0.5 megabytes of memory per processor. The multiplicity of processors opens new possibilities for the treatment of such computations. The constraint on time and resources favored the approach of using the existing RSF code which solves as an initial value problem the reduced set of MHD equations for a periodic cylindrical geometry. This code includes minimal physics and geometry, but contains the basic three dimensionality and nonlinear structure of the equations. The code solves the reduced set of MHD equations by Fourier expansion in two angular coordinates and finite differences in the radial one. Due to the continuing interest in these calculations and the likelihood that future supercomputers will take greater advantage of parallelism, the present study was initiated by the ORNL Exploratory Studies Committee and funded entirely by Laboratory Discretionary Funds. The objectives of the study were: to ascertain the suitability of MHD calculation for parallel computation, to design and implement a parallel algorithm to perform the computations, and to evaluate the hypercube, and in particular, ORNL's Intel iPSC, for use in MHD computations
Development of the PARVMEC Code for Rapid Analysis of 3D MHD Equilibrium
Seal, Sudip; Hirshman, Steven; Cianciosa, Mark; Wingen, Andreas; Unterberg, Ezekiel; Wilcox, Robert; ORNL Collaboration
2015-11-01
The VMEC three-dimensional (3D) MHD equilibrium has been used extensively for designing stellarator experiments and analyzing experimental data in such strongly 3D systems. Recent applications of VMEC include 2D systems such as tokamaks (in particular, the D3D experiment), where application of very small (delB/B ~ 10-3) 3D resonant magnetic field perturbations render the underlying assumption of axisymmetry invalid. In order to facilitate the rapid analysis of such equilibria (for example, for reconstruction purposes), we have undertaken the task of parallelizing the VMEC code (PARVMEC) to produce a scalable and temporally rapidly convergent equilibrium code for use on parallel distributed memory platforms. The parallelization task naturally splits into three distinct parts 1) radial surfaces in the fixed-boundary part of the calculation; 2) two 2D angular meshes needed to compute the Green's function integrals over the plasma boundary for the free-boundary part of the code; and 3) block tridiagonal matrix needed to compute the full (3D) pre-conditioner near the final equilibrium state. Preliminary results show that scalability is achieved for tasks 1 and 3, with task 2 still nearing completion. The impact of this work on the rapid reconstruction of D3D plasmas using PARVMEC in the V3FIT code will be discussed. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.
Ideal MHD equilibrium of a weakly toroidal plasma column with elongated cross-section
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Heesch, E.J.M. van; Schuurman, W.
1980-07-01
Solutions are obtained of the ideal MHD equations describing the equilibrium of a weakly toroidal plasma with an elliptic cross-section surrounded by a force-free magnetic field with constant ratio between current density and magnetic field strength. The force-free field parameter causes the stagnation points to recede along the major axis of the ellipse. Above a certain value of the force-free field parameter, stagnation points do not exist, so that the compression ratio of the plasma column is no longer limited. The analysis was carried out to first order in the force-free field parameter as well as to second order for an estimate of the error
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Kelleher, W.P.
1987-01-01
In the assessment of Magnetohydrodynamic (MHD) equilibrium and Poloidal Field Coil (PFC) arrangement for toroidal axisymmetric geometry, the Grad-Shafranov equation must be solved, either analytically or numerically. Existing numerical tools have been developed primarily for mainframe usage and can prove cumbersome for screening assessments and parametric evaluations. The objective of this thesis was to develop a personal computer (PC)-based calculational tool for assessing MHD/PFC problems in a highly interactive mode, well suited for scoping studies. The approach adopted involves a two-step process: first the MHD equilibrium is calculated and then the PFC arrangement, consistent with the equilibrium, is determined in an interactive design environment. The PC-based system developed consists of two programs: (1) PCEQ, which solve the MHD equilibrium problem and (2) PFDE-SIGN, which is employed to arrive at a PFC arrangement. PCEQ provides an output file including, but not limited to, the following: poloidal beta, total beta, safety factors, q, on axis and on edge. PCEQ plots the following contours and/or profiles: flux, pressure and toroidal current density, safety factor, and ratio of plasma toroidal field to vacuum field
Nonlinear MHD-equations: symmetries, solutions and conservation laws
International Nuclear Information System (INIS)
Samokhin, A.V.
1985-01-01
To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family
Nonlinear 2D convection and enhanced cross-field plasma transport near the MHD instability threshold
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Pastukhov, V.P.; Chudin, N.V.
2003-01-01
Results of theoretical study and computer simulations of nonlinear 2D convection induced by a convective MHD instability near its threshold in FRC-like non-paraxial magnetic confinement system are presented. An appropriate closed set of weakly nonideal reduced MHD equations is derived to describe the self-consistent plasma dynamics. It is shown that the convection forms nonlinear large scale stochastic vortices (convective cells), which tend to restore and to maintain the marginally stable pressure pro e and result in an essentially nonlocal enhanced heat transport. A large amount of data on the structure of the nascent convective flows is obtained and analyzed. The computer simulations of long time plasma evolutions demonstrate such features of the resulting anomalous transport as pro e consistency, L-H transition, external transport barrier, pinch of impurities, etc. (author)
Depression of Nonlinearity in Decaying Isotropic MHD Turbulence
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Servidio, S.; Matthaeus, W. H.; Dmitruk, P.
2008-01-01
Spectral method simulations show that undriven magnetohydrodynamic turbulence spontaneously generates coherent spatial correlations of several types, associated with local Beltrami fields, directional alignment of velocity and magnetic fields, and antialignment of magnetic and fluid acceleration components. These correlations suppress nonlinearity to levels lower than what is obtained from Gaussian fields, and occur in spatial patches. We suggest that this rapid relaxation leads to non-Gaussian statistics and spatial intermittency
Kinematics of Nonlinearly Interacting MHD Instabilities in a Plasma
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Hansen, Alexander K.
2000-01-01
Plasmas play host to a wide variety of instabilities. For example, tearing instabilities use finite plasma resistivity to exploit the free energy provided by plasma currents parallel to the magnetic field to alter the magnetic topology of the plasma through a process known as reconnection. These instabilities frequently make themselves known in magnetic confinement experiments such as tokamaks and reversed field pinches (RFPs). In RFP plasmas, in fact, several tearing instabilities (modes) are simultaneously active, and are of large amplitude. Theory predicts that in addition to interacting linearly with magnetic perturbations from outside the plasma, such as field errors or as resistive wall, the modes in the RFP can interact nonlinearly with each other through a three-wave interaction. In the current work investigations of both the linear (external) and nonlinear contributions to the kinematics of the tearing modes in the Madison Symmetric Torus (MST) RFP are reported Theory predicts that tearing modes will respond only to magnetic perturbations that are spatially resonant with them, and was supported by experimental work done on tokamak devices. The results in this work verified that the theory is still applicable to the RFP, in spite of its more complicated magnetic mode structure, involving perturbations of a single poloidal mode number
Nonlinear MHD and energetic particle modes in stellarators
International Nuclear Information System (INIS)
Strauss, H.R.
2002-01-01
The M3D code has been applied to ideal, resistive, two fluid, and hybrid simulations of compact quasi axisymmetric stellarators. When beta exceeds a threshold, low poloidal mode number (m=6∼18) modes grow exponentially, clearly distinguishable from the equilibrium evolution. Simulations of NCSX have beta limits are significantly higher than the infinite mode number ballooning limits. In the presence of resistivity, these modes occur well below the ideal limit. Their growth rate scaling with resistivity is similar to tearing modes. With sufficient viscosity, the growth rate becomes slow enough to allow calculations of magnetic island evolution. Hybrid gyrokinetic simulations with energetic particles indicate that global shear Alfven TAE - like modes can be destabilized in stellarators. Computations in a two - period compact stellarator obtained a predominantly n=1 toroidal mode with about the expected TAE frequency. Work is in progress to study fast ion-driven Alfven modes in NCSX. (author)
Nonlinear MHD and energetic particle modes in stellarators
International Nuclear Information System (INIS)
Strauss, H.R.; Fu, G.Y.; Park, W.; Breslau, J.; Sugiyama, L.E.
2003-01-01
The M3D (Multi-level 3D) project carries out simulation studies of plasmas using multiple levels of physics, geometry and grid models. The M3D code has been applied to ideal, resistive, two fluid, and hybrid simulations of compact quasi axisymmetric stellarators. When β exceeds a threshold, moderate toroidal mode number (n ∼ 10) modes grow exponentially, clearly distinguishable from the equilibrium evolution. The β limits are significantly higher than the infinite mode number ballooning limits. In the presence of resistivity, these modes occur well below the ideal limit. Their growth rate scaling with resistivity is similar to tearing modes. At low resistivity, the modes couple to resistive interchanges, which are unstable in most stellarators. Two fluid simulations with M3D show that resistive modes can be stabilized by diamagnetic drift. The two fluid computations are done with a realistic value of the Hall parameter, the ratio of ion skin depth to major radius. Hybrid gyrokinetic simulations with energetic particles indicate that global shear Alfven TAE - like modes can be destabilized in stellarators. Computations in a two-period compact stellarator obtained a predominantly n=1 toroidal mode with the expected TAE frequency. It is found that TAE modes are more stable in the two-period compact stellarator that in a tokamak with the same q and pressure profiles. M3D combines a two dimensional unstructured mesh with finite element discretization in poloidal planes, and fourth order finite differencing in the toroidal direction. (author)
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Nonlinear Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations
Abbott, Stephen; Germaschewski, Kai
2014-10-01
Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
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Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
3D nonlinear MHD simulations of ultra-low q plasmas
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Bonfiglio, D.; Cappello, S.; Piovan, R.; Zanotto, L.; Zuin, M.
2008-01-01
Magnetohydrodynamic (MHD) phenomena occurring in the ultra-low safety factor (ULq) configuration are investigated by means of 3D nonlinear MHD simulations. The ULq configuration, a screw pinch characterized by the edge safety factor q edge in the interval 0 edge edge values which are about the major rational numbers, suggesting plasma self-organization. Similar behaviour is observed in experimental ULq discharges, like those recently obtained exploiting the flexibility of the RFX-mod device. The transition of q edge from a major rational number to the next one occurs together with the development of a kink deformation of the plasma column, whose stabilization yields a nearly axisymmetric state with a rather flat q profile. Numerical simulations also show that it is possible to sustain either of the two conditions, namely, the saturated kink helical configuration and the axisymmetric one, by forcing q edge at a suitable value. Finally, the effects of this MHD phenomenology on the confinement properties of ULq plasmas are discussed.
International Nuclear Information System (INIS)
Takeda, Tatsuoki
1985-01-01
In this article analyses of the MHD stabilities which govern the global behavior of a fusion plasma are described from the viewpoint of the numerical computation. First, we describe the high accuracy calculation of the MHD equilibrium and then the analysis of the linear MHD instability. The former is the basis of the stability analysis and the latter is closely related to the limiting beta value which is a very important theoretical issue of the tokamak research. To attain a stable tokamak plasma with good confinement property it is necessary to control or suppress disruptive instabilities. We, next, describe the nonlinear MHD instabilities which relate with the disruption phenomena. Lastly, we describe vectorization of the MHD codes. The above MHD codes for fusion plasma analyses are relatively simple though very time-consuming and parts of the codes which need a lot of CPU time concentrate on a small portion of the codes, moreover, the codes are usually used by the developers of the codes themselves, which make it comparatively easy to attain a high performance ratio on the vector processor. (author)
Development of a 3D non-linear implicit MHD code
International Nuclear Information System (INIS)
Nicolas, T.; Ichiguchi, K.
2016-06-01
This paper details the on-going development of a 3D non-linear implicit MHD code, which aims at making possible large scale simulations of the non-linear phase of the interchange mode. The goal of the paper is to explain the rationale behind the choices made along the development, and the technical difficulties encountered. At the present stage, the development of the code has not been completed yet. Most of the discussion is concerned with the first approach, which utilizes cartesian coordinates in the poloidal plane. This approach shows serious difficulties in writing the preconditioner, closely related to the choice of coordinates. A second approach, based on curvilinear coordinates, also faced significant difficulties, which are detailed. The third and last approach explored involves unstructured tetrahedral grids, and indicates the possibility to solve the problem. The issue to domain meshing is addressed. (author)
Extended MHD modeling of nonlinear instabilities in fusion and space plasmas
Energy Technology Data Exchange (ETDEWEB)
Germaschewski, Kai [Univ. of New Hampshire, Durham, NH (United States)
2017-11-15
A number of different sub-projects where pursued within this DOE early career project. The primary focus was on using fully nonlinear, curvilinear, extended MHD simulations of instabilities with applications to fusion and space plasmas. In particular, we performed comprehensive studies of the dynamics of the double tearing mode in different regimes and confi gurations, using Cartesian and cyclindrical geometry and investigating both linear and non-linear dynamics. In addition to traditional extended MHD involving Hall term and electron pressure gradient, we also employed a new multi-fluid moment model, which shows great promise to incorporate kinetic effects, in particular off-diagonal elements of the pressure tensor, in a fluid model, which is naturally computationally much cheaper than fully kinetic particle or Vlasov simulations. We used our Vlasov code for detailed studies of how weak collisions effect plasma echos. In addition, we have played an important supporting role working with the PPPL theory group around Will Fox and Amitava Bhattacharjee on providing simulation support for HED plasma experiments performed at high-powered laser facilities like OMEGA-EP in Rochester, NY. This project has support a great number of computational advances in our fluid and kinetic plasma models, and has been crucial to winning multiple INCITE computer time awards that supported our computational modeling.
Energy Technology Data Exchange (ETDEWEB)
Vlaykov, Dimitar G., E-mail: Dimitar.Vlaykov@ds.mpg.de [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen (Germany); Grete, Philipp [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Schmidt, Wolfram [Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg (Germany); Schleicher, Dominik R. G. [Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C (Chile)
2016-06-15
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.
Numerical simulation of MHD equilibrium configuration for the HL-2A modification
International Nuclear Information System (INIS)
Chen Qian; Wang Aike; Li Fangzhu; Zhang Jinghua
2008-01-01
Numerical simulation is employed for the HL-2A modification, which includes the optimum design of zero-field in the start-up phase, the limiter equilibrium configuration, the single/double null divertor equilibrium configuration, and the equilibrium configuration evolution from gas breakdown to current plateau. Results show that the new program can satisfy the design requirement. (authors)
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
International Nuclear Information System (INIS)
Webb, G. M.; Brio, M.; Zank, G. P.
1996-01-01
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation
Linear and nonlinear instability theory of a noble gas MHD generator
International Nuclear Information System (INIS)
Mesland, A.J.
1982-01-01
This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)
Nonlinear wave-beam kinetic equilibrium in decelerating systems
International Nuclear Information System (INIS)
Grishin, V.K.; Shaposhnikova, E.N.
1981-01-01
The equilibrium state of the wave-beam system arising during the interaction of a particle beam and excited electromagnetic wave has been investigated on the basis of the analysis of the exact polution of a non-linear self-consistent linear equation using the complete system of conservation laws. A waveguide with a dielectric filler, into which a monoenergetic particle beam magnetized in a transverse plane is continuously injected, is used as a model of an decelerating system. A dispersion equation describing the system state and expression for the evaluation of efficiency of the beam energy conversion to the field energy have been obtained. It is concluded that larae fields and high efficiency of energy conversion are achieved during the marked beam reconstruction. States with different values of current and beam velocity but similar amplitudes of a longitudinal field are possible in the system considered [ru
NON-EQUILIBRIUM HELIUM IONIZATION IN AN MHD SIMULATION OF THE SOLAR ATMOSPHERE
International Nuclear Information System (INIS)
Golding, Thomas Peter; Carlsson, Mats; Leenaarts, Jorrit
2016-01-01
The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilibrium hydrogen ionization by performing a 2D radiation-magnetohydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyα and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with local thermodynamic equilibrium (LTE) ionization shows that non-equilibrium helium ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behavior with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11–18 kK, compared to models with LTE helium ionization. We conclude that non-equilibrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region. It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed
Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem
International Nuclear Information System (INIS)
Atanasiu, C.V.; Subbotin, A.A.
1999-01-01
In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)
Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium
International Nuclear Information System (INIS)
Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho
2004-01-01
Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)
The Toshiba Blow-Down MHD Test Facility, and Experiments on Non-Equilibrium Ionization
International Nuclear Information System (INIS)
Yamamoto, Y.; Ogiwara, H.; Shioda, S.; Miyata, M.; Goto, M.; Kasahara, E.
1968-01-01
The Toshiba blow-down MHD test facility, which was constructed in 1966 and has operated successfully in many experiments, is described. Operating conditions achieved are: the working gas is helium seeded with potassium, the maximum mass flow being 80 g/sec, the maximum seed fraction 0.1%; the gas static lies between temperature 1200 and 1700°K, the static pressure between 2.0 ∼ 1.2 atm, the velocity of gas in the generator channel between 1000 and 200 m/sec; the duration is up to 30 sec; the magnetic field is 2.7 T; the impurity of working gas is below 150 ppm. (author)
Directory of Open Access Journals (Sweden)
Yahaya Shagaiya Daniel
2018-04-01
Full Text Available The combined effects of thermal stratification, applied electric and magnetic fields, thermal radiation, viscous dissipation and Joules heating are numerically studied on a boundary layer flow of electrical conducting nanofluid over a nonlinearly stretching sheet with variable thickness. The governing equations which are partial differential equations are converted to a couple of ordinary differential equations with suitable similarity transformation techniques and are solved using implicit finite difference scheme. The electrical conducting nanofluid particle fraction on the boundary is passively rather than actively controlled. The effects of the emerging parameters on the electrical conducting nanofluid velocity, temperature, and nanoparticles concentration volume fraction with skin friction, heat transfer characteristics are examined with the aids of graphs and tabular form. It is observed that the variable thickness enhances the fluid velocity, temperature, and nanoparticle concentration volume fraction. The heat and mass transfer rate at the surface increases with thermal stratification resulting to a reduction in the fluid temperature. Electric field enhances the nanofluid velocity which resolved the sticking effects caused by a magnetic field which suppressed the profiles. Radiative heat transfer and viscous dissipation are sensitive to an increase in the fluid temperature and thicker thermal boundary layer thickness. Comparison with published results is examined and presented. Keywords: MHD nanofluid, Variable thickness, Thermal radiation, Similarity solution, Thermal stratification
Energy Technology Data Exchange (ETDEWEB)
Chen, J.; Zhuang, G., E-mail: ge-zhuang@hust.edu.cn; Li, Q.; Liu, Y.; Gao, L.; Zhou, Y. N.; Jian, X.; Xiong, C. Y.; Wang, Z. J. [State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074 (China); Brower, D. L.; Ding, W. X. [Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095 (United States)
2014-11-15
A high-performance Faraday-effect polarimeter-interferometer system has been developed for the J-TEXT tokamak. This system has time response up to 1 μs, phase resolution < 0.1° and minimum spatial resolution ∼15 mm. High resolution permits investigation of fast equilibrium dynamics as well as magnetic and density perturbations associated with intrinsic Magneto-Hydro-Dynamic (MHD) instabilities and external coil-induced Resonant Magnetic Perturbations (RMP). The 3-wave technique, in which the line-integrated Faraday angle and electron density are measured simultaneously by three laser beams with specific polarizations and frequency offsets, is used. In order to achieve optimum resolution, three frequency-stabilized HCOOH lasers (694 GHz, >35 mW per cavity) and sensitive Planar Schottky Diode mixers are used, providing stable intermediate-frequency signals (0.5–3 MHz) with S/N > 50. The collinear R- and L-wave probe beams, which propagate through the plasma poloidal cross section (a = 0.25–0.27 m) vertically, are expanded using parabolic mirrors to cover the entire plasma column. Sources of systematic errors, e.g., stemming from mechanical vibration, beam non-collinearity, and beam polarization distortion are individually examined and minimized to ensure measurement accuracy. Simultaneous density and Faraday measurements have been successfully achieved for 14 chords. Based on measurements, temporal evolution of safety factor profile, current density profile, and electron density profile are resolved. Core magnetic and density perturbations associated with MHD tearing instabilities are clearly detected. Effects of non-axisymmetric 3D RMP in ohmically heated plasmas are directly observed by polarimetry for the first time.
Two-Fluid and Resistive Nonlinear Simulations of Tokamak Equilibrium, Stability, and Reconnection
International Nuclear Information System (INIS)
Jardin, S.; Sovinec, C.; Breslau, J.; Ferraro, N.; Hudson, S.; King, J.; Kruger, S.; Ramos, J.; Schnack, D.
2008-01-01
The NIMROD and M3D/M3D-C1 codes now each have both a resistive MHD and a two-fluid (2F) capability including gyroviscosity and Hall terms. We describe: (1) a nonlinear 3D verification test in the resistive MHD regime in which the two codes are in detailed agreement, (2) new studies that illuminate the effect of two-fluid physics on spontaneous rotation in tokamaks, (3) studies of nonlinear reconnection in regimes of relevance to fusion plasmas with peak nonlinear reconnection rates that are essentially independent of the resistivity, and (4) linear two-fluid tearing mode calculations including electron mass that agree with analytic studies over a wide range of parameter regimes
Sauer, K.; Dubinin, E.; Baumgärtel, K.
1998-09-01
The characteristic scale of the Martian magnetosheath is less than the pick-up gyroradius of oxygen ions. This leads to admissible differential motion of protons and heavies and a strong coupling between both ion fluids. 2D bi-ion MHD simulations reveal many new interesting features in such Large Larmour Radius systems. The formation of an ion-composition boundary, which separates both plasmas, and structuring of the transition from proton dominated plasma of the solar wind origin to massive planetary plasma are the main features of the interaction. A comprehensive multi-instrument study of Martian plasma environment and the comparison with theoretical modelling initiated in the framework of the Visiting Science Programme of the International Space Science Institute (ISSI) in Bern (Switzerland) gives confirmation that Mars interacts with the solar wind like a comet which has a outgassing rate near to that of Grigg-Skjellerup. The results may also be relevant for small bodies which are surrounded by a neutral gas atmosphere (icy moons, asteroids, Mercury).
Equilibrium and stability MHD in the magnetic confinement for thermonuclear fusion
International Nuclear Information System (INIS)
Otero, Dino; Proto, A.N.
1979-08-01
A survey of the mayor systems for magnetic confinement of plasmas is made. The basic concepts are reviewed briefly. The equilibrium and stability conditions for open systems (mirrors, magnetic wells, Z and Theta-pinches), for toroidal axisymmetric (Z-Pinch, Screw-Pinch, Belt-Pinch and Tokamak) and toroidal non-axisymmetric systems (High-β Stellarator and low-β Theta-Pinch) are discussed. A comparative analysis between the diferent systems is made. In the conclusions, the author's opinions about future developments in the field are included. (author) [es
A MHD equilibrium code 'EQUCIR version 2' applicable to up-down asymmetric toroidal plasma
International Nuclear Information System (INIS)
Shinya, Kichiro; Ninomiya, Hiromasa
1981-01-01
Computer code EQUCIR version 2, which can analyse tokamak plasma equilibrium without assuming up-down symmetry with respect to the mid-plane, has been developed. This code is essentially the same as EQUCIR version 1 which has already been reported and can deal with only symmetrical plasma with respect to the mid-plane. Because data input stream is slightly different from version 1 physical background of the change and the method of calculation are explained. Data input manual for the different points is also summarized. The code has been applied to the analysis of INTOR single-null divertor plasmas and to the design of hybrid poloidal coils resulting in useful and powerful means for the design. (author)
Sun, P. J.; Li, Y. D.; Ren, Y.; Zhang, X. D.; Wu, G. J.; Xu, L. Q.; Chen, R.; Li, Q.; Zhao, H. L.; Zhang, J. Z.; Shi, T. H.; Wang, Y. M.; Lyu, B.; Hu, L. Q.; Li, J.; The EAST Team
2018-01-01
In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence (k\\perpρi˜2{-}5.2 ) and the MHD mode (toroidal mode number m = -1 , poloidal mode number n = 1 ) are measured simultaneously, using a four-channel tangential CO2 laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.
Route analysis for MHD equilibria
International Nuclear Information System (INIS)
Kikuchi, Fumio; Aizawa, Tatsuhiko
1982-01-01
In Tokamak facilities which are promising in nuclear fusion reactor development, the plasma in the core is often described by MHD approximation. Specifically, since an axisymmetric torus is approximately assumed as the first wall (shell) shape in actual Tokamak facilities, the Grad-Shafranov equation to be satisfied by an axisymmetric equilibrium solution for ideal MHD fluid must be solved, and the characteristics of its solution must be clarified. This paper shows the outline of the numerical calculation which employs both the incremental method taking the particular incremental nodal point values as the control parameters and the interaction method in accordance with Newton method at the same time, the analysis objective being a non-linear eigenvalue problem dealing the boundary of plasma region with surrounding vacuum region as the free boundary. Next, the detailed route analysis of the equilibrium solution is performed, utilizing the above numerical calculation technique, to clarify the effect of shell shape on the behaviour of the equilibrium solution. As the shape of the shell, a rectangular section torus, which have a notch depression at a part of the shell inner boundary, is considered. In the paper, the fundamental MHD equation and its approximate solution by the finite element method, the behaviour of plasma equilibrium solution in a shell having a notch, and the effect of notch shapes on plasma behaviour are described. This analysis verifies the effectiveness of the calculation method. (Wakatsuki, Y.)
Existence of nash equilibrium in competitive nonlinear pricing games with adverse selection
Monteiro, P. K.
2003-01-01
We show that for a large class of competitive nonlinear pricing games with adverse selection, the property of better-reply security is naturally satisfied - thus, resolving via a result due to Reny (1999) the issue of existence of Nash equilibrium for a large class of competitive nonlinear pricing games.
MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness
Directory of Open Access Journals (Sweden)
T. Hayat
Full Text Available This research explores the magnetohydrodynamic (MHD boundary layer flow of Powell-Eyring nanofluid past a non-linear stretching sheet of variable thickness. An electrically conducting fluid is considered under the characteristics of magnetic field applied transverse to the sheet. The mathematical expressions are accomplished via boundary layer access, Brownian motion and thermophoresis phenomena. The flow analysis is subjected to a recently established conditions requiring zero nanoparticles mass flux. Adequate transformations are implemented for the reduction of partial differential systems to the ordinary differential systems. Series solutions for the governing nonlinear flow of momentum, temperature and nanoparticles concentration have been executed. Physical interpretation of numerous parameters is assigned by graphical illustrations and tabular values. Moreover the numerical data of drag coefficient and local heat transfer rate are executed and discussed. It is investigated that higher wall thickness parameter results in the reduction of velocity distribution. Effects of thermophoresis parameter on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of thermophoresis parameter. Keywords: MHD, Variable thicked surface, Powell-Eyring nanofluid, Zero mass flux conditions
Energy Technology Data Exchange (ETDEWEB)
Hong, Sang Hee; Kang, Kyung Doo; Ryu, Ji Myung; Kim, Deok Kyu; Chung, TaeKyun; Chung, Mo Se [Seoul National University, Seoul (Korea, Republic of); Cho, Su Won [Kyungki University, Suwon (Korea, Republic of)
1995-08-01
In the present project for developing the numerical codes of 2-D MHD equilibrium, edge plasma transport and neutral particle transport for the tokamak plasmas, we computed the MHD equilibria of single and double null configurations and determined the external coil currents and the plasma parameters used for operation and control data. Also we numerically acquired the distributions of edge plasma parameters in poloidal and radial directions= and the design-related values according to the various operating conditions using the developed plasma transport code. Furthermore, a neutral particle transport code for the edge region is developed and them used for the analysis of the neutral particle behavior yielding the source terms in the fluid transport equations, and expected to supply the input parameters for the edge plasma transport code. 53 refs., 12 tabs., 44 figs. (author)
Punctuated equilibrium in a non-linear system of action
J.S. Timmermans (Jos)
2008-01-01
textabstractColeman's equilibrium model of social development, the Linear System of Action, is extended to cover the dynamics of societal transitions. The model implemented has the characteristics of a dissipative system. A variation and selection algorithm favoring the retention of relatively
Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D
Energy Technology Data Exchange (ETDEWEB)
King, J. D., E-mail: kingjd@fusion.gat.com [Oak Ridge Institute for Science Education, Oak Ridge, Tennessee 37830-8050 (United States); General Atomics, P.O. Box 85608, San Diego, California 92816-5608 (United States); Strait, E. J.; Ferraro, N. M.; Lanctot, M. J.; Paz-Soldan, C.; Turnbull, A. D. [General Atomics, P.O. Box 85608, San Diego, California 92816-5608 (United States); Lazerson, S. A.; Logan, N. C.; Park, J.-K.; Nazikian, R.; Okabayashi, M. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Haskey, S. R. [Plasma Research Laboratory, Research School of Physical Sciences and Engineering, The Australia National University, Canberra, Australian Capital Territory 0200 (Australia); Hanson, J. M. [Columbia University, 2960 Broadway, New York, New York 10027 (United States); Liu, Yueqiang [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB (United Kingdom); Shiraki, D. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States)
2015-07-15
DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics (MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidal mode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. These tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. Scans of the applied poloidal spectrum and edge safety factor confirm that low-pressure, n = 1 non-axisymmetric tokamak equilibria are determined by a single, dominant, stable eigenmode. However, at higher beta, near the ideal kink mode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.
Fast non-linear extraction of plasma equilibrium parameters using a neural network mapping
International Nuclear Information System (INIS)
Lister, J.B.; Schnurrenberger, H.
1990-07-01
The shaping of non-circular plasmas requires a non-linear mapping between the measured diagnostic signals and selected equilibrium parameters. The particular configuration of Neural Network known as the multi-layer perceptron provides a powerful and general technique for formulating an arbitrary continuous non-linear multi-dimensional mapping. This technique has been successfully applied to the extraction of equilibrium parameters from measurements of single-null diverted plasmas in the DIII-D tokamak; the results are compared with a purely linear mapping. The method is promising, and hardware implementation is straightforward. (author) 15 refs., 7 figs
Fast non-linear extraction of plasma equilibrium parameters using a neural network mapping
International Nuclear Information System (INIS)
Lister, J.B.; Schnurrenberger, H.
1991-01-01
The shaping of non-circular plasmas requires a non-linear mapping between the measured diagnostic signals and selected equilibrium parameters. The particular configuration of neural network known as the multilayer perceptron provides a powerful and general technique for formulating an arbitrary continuous non-linear multi-dimensional mapping. This technique has been successfully applied to the extraction of equilibrium parameters from measurements of single-null diverted plasmas in the DIII-D tokamak; the results are compared with a purely linear mapping. The method is promising, and hardware implementation is straightforward. (author). 17 refs, 8 figs, 2 tab
MHD pilot industrial applications
International Nuclear Information System (INIS)
Freeman, M.; Riviere-Wekstein, G.
1994-01-01
MHD industrial applications (and their historical developments) are sketched in the fields of nuclear fission, nuclear fusion and marine vehicles propelling. Nuclear fission projects resulted in promising prototypes between 1972 and 1980, especially for liquid-metal MHD generators. All of them have been stopped by the scientific policies of the governments. Nuclear fusion projects used mainly the equilibrium plasma of tokamak type reactors; some military projects used pulsed plasma to perform pulsed MHD generators. Marine vehicle propelling is the most advanced field. By june 1992, the japanese sea-going boat 'Yamato 1' was sailing with two MHD propellers. A few months later, the building of 'Yamato 2' has begun
Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Liu, Yunqi; Gong, Yungui [School of Physics, Huazhong University of Science and Technology,Wuhan, Hubei 430074 (China); Wang, Bin [IFSA Collaborative Innovation Center, Department of Physics and Astronomy, Shanghai Jiao Tong University,Shanghai 200240 (China)
2016-02-17
We study the non-equilibrium condensation process in a holographic superconductor with nonlinear corrections to the U(1) gauge field. We start with an asymptotic Anti-de-Sitter(AdS) black hole against a complex scalar perturbation at the initial time, and solve the dynamics of the gravitational systems in the bulk. When the black hole temperature T is smaller than a critical value T{sub c}, the scalar perturbation grows exponentially till saturation, the final state of spacetime approaches to a hairy black hole. In the bulk theory, we find the clue of the influence of nonlinear corrections in the gauge filed on the process of the scalar field condensation. We show that the bulk dynamics in the non-equilibrium process is completely consistent with the observations on the boundary order parameter. Furthermore we examine the time evolution of horizons in the bulk non-equilibrium transformation process from the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent and event horizons show that the original AdS black hole configuration requires more time to finish the transformation to become a hairy black hole if there is nonlinear correction to the electromagnetic field. We generalize our non-equilibrium discussions to the holographic entanglement entropy and find that the holographic entanglement entropy can give us further understanding of the influence of the nonlinearity in the gauge field on the scalar condensation.
Non-linear neutron star oscillations viewed as deviations from an equilibrium state
International Nuclear Information System (INIS)
Sperhake, U
2002-01-01
A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)
Directory of Open Access Journals (Sweden)
Wubshet Ibrahim
2015-12-01
Full Text Available Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined. The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic (MHD stagnation point flow past a stretching sheet with convective heating. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered. The nanoparticle fractions on the boundary are considered to be passively controlled. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. Prandtl number Pr, velocity ratio parameter A, magnetic parameter M, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Moreover, the problem is governed by temperature ratio parameter (Nr=TfT∞ and radiation parameter Rd. Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt number −θ′(0 decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase. Furthermore, radiation has a positive effect on temperature and concentration profiles.
Fellner, Klemens; Tang, Bao Quoc
2018-06-01
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.
International Nuclear Information System (INIS)
Nakamura, Y.; Matsumoto, T.; Wakatani, M.; Ichiguchi, K.; Garcia, L.; Carreras, B.A.
1995-04-01
A particular configuration of the LHD stellarator with an unusually flat pressure profile has been chosen to be a test case for comparison of the MHD stability property predictions of different three-dimensional and averaged codes for the purpose of code comparison and validation. In particular, two relatively localized instabilities, the fastest growing modes with toroidal mode number n = 2 and n = 3 were studied using several different codes, with the good agreement that has been found providing justification for the use of any of them for equilibria of the type considered
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.
The CHEASE code for toroidal MHD equilibria
International Nuclear Information System (INIS)
Luetjens, H.
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 Ψ. 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
Annual progress on DoE Grant for Nonlinear and Nonideal MHD
International Nuclear Information System (INIS)
Callen, J. D.
2002-01-01
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects
A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium
International Nuclear Information System (INIS)
Beretta, G.P.
1986-01-01
This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications
Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage
Khrapov, Sergey; Khoperskov, Alexander
2018-03-01
A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.
International Nuclear Information System (INIS)
Hoelzl, M; Merkel, P; Lackner, K; Strumberger, E; Huijsmans, G T A; Aleynikova, K; Liu, F; Atanasiu, C; Nardon, E; Fil, A; McAdams, R; Chapman, I
2014-01-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described
Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM.
Rashidi, Mohammad Mehdi; Freidoonimehr, Navid; Momoniat, Ebrahim; Rostami, Behnam
2015-01-01
In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.
Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM.
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
Full Text Available In the current article, a combination of the differential transform method (DTM and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1, dimensionless axial magnetic force strength parameter (N2, dimensionless tangential magnetic force strength parameter (N3, and magnetic Reynolds number (Rem are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.
Directory of Open Access Journals (Sweden)
Mohammed Almakki
2017-07-01
Full Text Available The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.
Directory of Open Access Journals (Sweden)
Ricardo A. da Mota Silveira
Full Text Available AbstractThis paper presents a nonlinear stability analysis of piles under bilateral contact constraints imposed by a geological medium (soil or rock. To solve this contact problem, the paper proposes a general numerical methodology, based on the finite element method (FEM. In this context, a geometrically nonlinear beam-column element is used to model the pile while the geological medium can be idealized as discrete (spring or continuum (Winkler and Pasternak foundation elements. Foundation elements are supposed to react under tension and compression, so during the deformation process the structural elements are subjected to bilateral contact constraints. The errors along the equilibrium paths are minimized and the convoluted nonlinear equilibrium paths are made traceable through the use of an updated Lagrangian formulation and a Newton-Raphson scheme working with the generalized displacement technique. The study offers stability analyses of three problems involving piles under bilateral contact constraints. The analyses show that in the evaluation of critical loads a great influence is wielded by the instability modes. Also, the structural system stiffness can be highly influenced by the representative model of the soil.
International Nuclear Information System (INIS)
Strickler, D.J.; Galambos, J.D.; Peng, Y.K.M.
1989-03-01
Two versions of the Fusion Engineering Design Center (FEDC) free-boundary equilibrium code designed to computer the poloidal field (PF) coil current distribution of elongated, magnetically limited tokamak plasmas are demonstrated and applied to the systems analysis of the impact of plasma elongation on the design point of the International Thermonuclear Experimental Reactor (ITER). These notes were presented at the ITER Specialists' Meeting on the PF Coil System and Operational Scenario, held at the Max Planck Institute for Plasma Physics in Garching, Federal Republic of Germany, May 24--27, 1988. 8 refs., 6 figs., 4 tabs
Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Sanchez, R.; Tribaldos, V.; Geiger, J.
2018-02-01
The recently developed free-plasma-boundary version of the SIESTA MHD equilibrium code (Hirshman et al 2011 Phys. Plasmas 18 062504; Peraza-Rodriguez et al 2017 Phys. Plasmas 24 082516) is used for the first time to study scenarios with considerable bootstrap currents for the Wendelstein 7-X (W7-X) stellarator. Bootstrap currents in the range of tens of kAs can lead to the formation of unwanted magnetic island chains or stochastic regions within the plasma and alter the boundary rotational transform due to the small shear in W7-X. The latter issue is of relevance since the island divertor operation of W7-X relies on a proper positioning of magnetic island chains at the plasma edge to control the particle and energy exhaust towards the divertor plates. Two scenarios are examined with the new free-plasma-boundary capabilities of SIESTA: a freely evolving bootstrap current one that illustrates the difficulties arising from the dislocation of the boundary islands, and a second one in which off-axis electron cyclotron current drive (ECCD) is applied to compensate the effects of the bootstrap current and keep the island divertor configuration intact. SIESTA finds that off-axis ECCD is indeed able to keep the location and phase of the edge magnetic island chain unchanged, but it may also lead to an undesired stochastization of parts of the confined plasma if the EC deposition radial profile becomes too narrow.
Directory of Open Access Journals (Sweden)
M. Farooq
Full Text Available This article studies MHD double stratified stagnation point flow of Carreau fluid towards a non linear stretchable surface with radiation. Features of heat and mass transfer are evaluated by using convective boundary conditions. Resulting nonlinear problems are solved and studied for the velocity, temperature and concentration fields. Heat and mass transfer rates in addition to skin friction are discussed. Besides this for the verification of the present findings, the results of presented analysis have been compared with the available works in particular situations and reasonable agreement is noted. Keywords: Convective boundary condition, Thermal radiation, Double stratification, Stagnation point flow
Nonlinear equilibrium structure of thin currents sheets: influence of electron pressure anisotropy
Directory of Open Access Journals (Sweden)
L. M. Zelenyi
2004-01-01
Full Text Available Thin current sheets represent important and puzzling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magnetospheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a collapsing MHD solution with a plane singularity. Being potential sites of effective energy accumulation, these structures have received a good deal of attention during the last decade, especially after the launch of the multiprobe CLUSTER mission which is capable of resolving their 3D features. Many theoretical models of thin current sheet dynamics, including the well-known current sheet bifurcation, have been developed recently. A self-consistent 1D analytical model of thin current sheets in which the tension of the magnetic field lines is balanced by the ion inertia rather than by the plasma pressure gradients was developed earlier. The influence of the anisotropic electron population and of the corresponding electrostatic field that acts to restore quasi-neutrality of the plasma is taken into account. It is assumed that the electron motion is fluid-like in the direction perpendicular to the magnetic field and fast enough to support quasi-equilibrium Boltzmann distribution along the field lines. Electrostatic effects lead to an interesting feature of the current density profile inside the current sheet, i.e. a narrow sharp peak of electron current in the very center of the sheet due to fast curvature drift of the particles in this region. The corresponding magnetic field profile becomes much steeper near the neutral plane although the total cross-tail current is in all cases dominated by the ion contribution. The dependence of electrostatic effects on the ion to electron temperature ratio, the curvature of the magnetic field lines, and the average electron magnetic moment is also analyzed. The implications of these effects on the fine structure of thin current sheets
Non-linear quantum critical dynamics and fluctuation-dissipation ratios far from equilibrium
Energy Technology Data Exchange (ETDEWEB)
Zamani, Farzaneh [Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden (Germany); Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, 01187 Dresden (Germany); Ribeiro, Pedro [CeFEMA, Instituto Superior Tcnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Russian Quantum Center, Novaya Street 100 A, Skolkovo, Moscow Area, 143025 (Russian Federation); Kirchner, Stefan, E-mail: stefan.kirchner@correlated-matter.com [Center for Correlated Matter, Zhejiang University, Hangzhou, Zhejiang 310058 (China)
2016-02-15
Non-thermal correlations of strongly correlated electron systems and the far-from-equilibrium properties of phases of condensed matter have become a topical research area. Here, an overview of the non-linear dynamics found near continuous zero-temperature phase transitions within the context of effective temperatures is presented. In particular, we focus on models of critical Kondo destruction. Such a quantum critical state, where Kondo screening is destroyed in a critical fashion, is realized in a number of rare earth intermetallics. This raises the possibility of experimentally testing for the existence of fluctuation-dissipation relations far from equilibrium in terms of effective temperatures. Finally, we present an analysis of a non-interacting, critical reference system, the pseudogap resonant level model, in terms of effective temperatures and contrast these results with those obtained near interacting quantum critical points. - Highlights: • Critical Kondo destruction explains the unusual properties of quantum critical heavy fermion compounds. • We review the concept of effective temperatures in models of critical Kondo destruction. • We compare effective temperatures found near non-interacting and fully interacting fixed points. • A comparison with non-interacting quantum impurity models is presented.
Energy Technology Data Exchange (ETDEWEB)
1981-11-01
Program accomplishments in a continuing effort to demonstrate the feasibility of direct coal-fired, closed-cycle MHD power generation are reported. This volume contains the following appendices: (A) user's manual for 2-dimensional MHD generator code (2DEM); (B) performance estimates for a nominal 30 MW argon segmented heater; (C) the feedwater cooled Brayton cycle; (D) application of CCMHD in an industrial cogeneration environment; (E) preliminary design for shell and tube primary heat exchanger; and (F) plant efficiency as a function of output power for open and closed cycle MHD power plants. (WHK)
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Jusoh, Rahimah; Nazar, Roslinda
2018-04-01
The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.
Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.
2018-02-01
The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.
MHD simulations on an unstructured mesh
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.
1996-01-01
We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right
Three-scale expansion of the solution of MHD and Reynolds equations for tokamak
International Nuclear Information System (INIS)
Maslov, V.P.; Omel'yanov, G.A.
1994-01-01
An asymptotic solution of the magnetohydrodynamic equations is constructed. The three scales asymptotic solution describes the non-linear evolution of small, rapidly varying perturbations of equilibrium. It is shown, that an anisotropic coherent structure appears in the linear nonstability situation, and the structures evolution directs to energy interaction between high-frequency and low-frequency waves. The closed system of MHD Reynolds equations for anisotropic structure is derived
Mathematical and numerical study of nonlinear boundary problems related to plasma physics
International Nuclear Information System (INIS)
Sermange, M.
1982-06-01
After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr
Mahanthesh, B.; Gireesha, B. J.; Shehzad, S. A.; Rauf, A.; Kumar, P. B. Sampath
2018-05-01
This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed.
Generation of sheet currents by high frequency fast MHD waves
Energy Technology Data Exchange (ETDEWEB)
Núñez, Manuel, E-mail: mnjmhd@am.uva.es
2016-07-01
The evolution of fast magnetosonic waves of high frequency propagating into an axisymmetric equilibrium plasma is studied. By using the methods of weakly nonlinear geometrical optics, it is shown that the perturbation travels in the equatorial plane while satisfying a transport equation which enables us to predict the time and location of formation of shock waves. For plasmas of large magnetic Prandtl number, this would result into the creation of sheet currents which may give rise to magnetic reconnection and destruction of the original equilibrium. - Highlights: • Regular solutions of quasilinear hyperbolic systems may evolve into shocks. • The shock location is found for high frequency fast MHD waves. • The result is applied to static axisymmetric equilibria. • The previous process may lead to the formation of sheet currents and destruction of the equilibrium.
Perturbed solutions of fixed boundary MHD equilibria
International Nuclear Information System (INIS)
Portone, A.
2004-01-01
In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Sommariva, C.; Nardon, E.; Beyer, P.; Hoelzl, M.; Huijsmans, G. T. A.; van Vugt, D.; Contributors, JET
2018-01-01
In order to contribute to the understanding of runaway electron generation mechanisms during tokamak disruptions, a test particle tracker is introduced in the JOREK 3D non-linear MHD code, able to compute both full and guiding center relativistic orbits. Tests of the module show good conservation of the invariants of motion and consistency between full orbit and guiding center solutions. A first application is presented where test electron confinement properties are investigated in a massive gas injection-triggered disruption simulation in JET-like geometry. It is found that electron populations initialised before the thermal quench (TQ) are typically not fully deconfined in spite of the global stochasticity of the magnetic field during the TQ. The fraction of ‘survivors’ decreases from a few tens down to a few tenths of percent as the electron energy varies from 1 keV to 10 MeV. The underlying mechanism for electron ‘survival’ is the prompt reformation of closed magnetic surfaces at the plasma core and, to a smaller extent, the subsequent reappearance of a magnetic surface at the edge. It is also found that electrons are less deconfined at 10 MeV than at 1 MeV, which appears consistent with a phase averaging effect due to orbit shifts at high energy.
Directory of Open Access Journals (Sweden)
Xijun Liu
2013-01-01
Full Text Available The nonlinear dynamic behavior of rain-wind-induced vibration of inclined cable is investigated with the consideration of the equilibrium position of the moving rivulet. The partial differential governing equations of three-degree-of-freedom on the model of rain-wind-induced cable vibration are established, which are proposed for describing the nonlinear interactions among the in-plane, out-of-plane vibration of the cable and the oscillation of the moving rivulet. The Galerkin method is applied to discretize the partial differential governing equations. The approximately analytic solution is obtained by using the method of averaging. The unique correspondence between the wind and the equilibrium position of the rivulet is ascertained. The presence of rivulet at certain positions on the surface of cable is then proved to be one of the trigger for wind-rain-induced cable vibration. The nonlinear dynamic phenomena of the inclined cable subjected to wind and rain turbulence are then studied by varying the parameters including mean wind velocity, Coulomb damping force, damping ratio, the span length, and the initial tension of the inclined cable on the model. The jump phenomenon is also observed which occurs when there are multiple solutions in the system.
Numerical computation of MHD equilibria
International Nuclear Information System (INIS)
Atanasiu, C.V.
1982-10-01
A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)
International Nuclear Information System (INIS)
Brassier, Stephane
1998-01-01
The Magnetohydrodynamic (MHD) equations represent the coupling between fluid dynamics equations and Maxwell's equations. We consider here a new MHD model with two temperatures. A Roe scheme is first constructed in the one dimensional case, for a multi-species model and a general equation of state. The multidimensional case is treated thanks to the Powell approach. The notion of Roe-Powell matrix, generalization of the notion of Roe matrix for multidimensional MHD, allows us to develop an original scheme on a curvilinear grid. We focus on a second part on the modelling of a Plasma Opening Switch (POS). A front-tracking method is first set up, in order to correctly handle the deformation of the front between the vacuum and the plasma. Besides, by taking into account a general Ohm's law, we have to deal with the Hall effect, which leads to nonlinear transport equations with discontinuous coefficients. Several numerical schemes are proposed and tested on a variety of test cases. This work has allowed us to construct an industrial MHD code, intended to handle complex flows and in particular to correctly simulate the behaviour of the POS. (author) [fr
Energy Technology Data Exchange (ETDEWEB)
1981-11-01
Program accomplishments in a continuing effort to demonstrate the feasibility of direct coal fired, closed cycle, magnetohydrodynamic power generation are detailed. These accomplishments relate to all system aspects of a CCMHD power generation system including coal combustion, heat transfer to the MHD working fluid, MHD power generation, heat and cesium seed recovery and overall systems analysis. Direct coal firing of the combined cycle has been under laboratory development in the form of a high slag rejection, regeneratively air cooled cyclone coal combustor concept, originated within this program. A hot bottom ceramic regenerative heat exchanger system was assembled and test fired with coal for the purposes of evaluating the catalytic effect of alumina on NO/sub x/ emission reduction and operability of the refractory dome support system. Design, procurement, fabrication and partial installation of a heat and seed recovery flow apparatus was accomplished and was based on a stream tube model of the full scale system using full scale temperatures, tube sizes, rates of temperature change and tube geometry. Systems analysis capability was substantially upgraded by the incorporation of a revised systems code, with emphasis on ease of operator interaction as well as separability of component subroutines. The updated code was used in the development of a new plant configuration, the Feedwater Cooled (FCB) Brayton Cycle, which is superior to the CCMHD/Steam cycle both in performance and cost. (WHK)
Directory of Open Access Journals (Sweden)
Junaid Ahmad Khan
2018-03-01
Full Text Available Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail. Keywords: Stretchable boundary, Thermal radiation, Chemical reaction, Mathematical modeling, Non-linear differential system, Mass transfer
Khan, Junaid Ahmad; Mustafa, M.
2018-03-01
Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail.
A theorem for non-linear stability to tearing modes
International Nuclear Information System (INIS)
Avinash, K.
1992-12-01
Within the reduced MHD approximation it is shown that dJ z /dΨ≤0 [J z is z component of the current density and Ψ is the helical flux] is a sufficient condition for the equilibrium to be non-linearly stable to tearing mode. It is further shown that this is also a sufficient condition for an equilibrium to be axisymmetric, hence helical equilibrium consistent with this condition cannot be constructed. However a class of axisymmetric equilibrium with hollow current profile is shown to satisfy the stability criterion. (author). 16 refs, 2 figs
Özdural, A.R.; Alkan, A.; Kerkhof, P.J.A.M.
2004-01-01
In this work a new mathematical model, based on non-equilibrium conditions, describing the dynamic adsorption of proteins in columns packed with spherical adsorbent particles is used to study the performance of chromatographic systems. Simulations of frontal chromatography, including axial
Directory of Open Access Journals (Sweden)
A. Fournier
2007-01-01
Full Text Available Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system – some version being currently under construction – the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow
Energy Technology Data Exchange (ETDEWEB)
Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)
1996-12-31
We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.
3D simulation studies of tokamak plasmas using MHD and extended-MHD models
International Nuclear Information System (INIS)
Park, W.; Chang, Z.; Fredrickson, E.; Fu, G.Y.
1996-01-01
The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-β disruption studies in reversed shear plasmas using the MHD level MH3D code, ω *i stabilization and nonlinear island saturation of TAE mode using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D ++ code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree which agree well with experimental data
Energy Technology Data Exchange (ETDEWEB)
Hong, Sang Hee; Lim, Ki Hang; Kang, Kyung Doo; Ryu, Ji Myung; Kim, Duk Kyu [Seoul National University, Seoul (Korea, Republic of); Cho, Soo Won [Kyungki Unviersity, Suwon (Korea, Republic of)
1995-08-01
In the present project for developing the numerical codes of 2-DMHD equilibrium, edge plasma transport and neutral particle transport for the tokamak plasmas, we compute the plasma equilibrium of double null type and calculate the external coil currents and the plasma parameters used for operation and control data. Also the numerical algorithm is developed to analyse the behavior of edge plasmas in poloidal and radial directions and the programming and debugging of a 2-D transport code are completed. Furthermore, a neutral particle transport code for the edge region is developed and then used for the analysis of the neutral transport phenomena giving the sources in the fluid equations, and expected to supply the input parameters for the edge plasma transport code. 34 refs., 5 tabs., 28 figs. (author)
Harrigan, T P
1996-01-01
A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistance is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but a high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.
International Nuclear Information System (INIS)
Rabajante, Jomar Fajardo; Talaue, Cherryl Ortega
2015-01-01
Graphical abstract: Display Omitted -- Highlights: •Properties of n-dimensional decision model of competitive interaction networks. •Graphical technique for component-wise and steady state stability analysis. •Search for parameter conditions that control equilibrium switching. •Illustrations of multi-stable systems and repressilators. -- Abstract: Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n-dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior
Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido
2011-01-01
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confi...
Directory of Open Access Journals (Sweden)
El-Khamsa Guechi
2016-09-01
Full Text Available Potato peel (PP was used as a biosorbent to remove malachite green (MG from aqueous solution under various operating conditions. The effect of the experimental parameters such as initial dye concentration, biosorbent dose, initial pH, stirring speed, temperature, ionic strength and biosorbent particle size was investigated through a number of batch sorption experiments. The sorption kinetic uptake for MG by PP at various initial dye concentrations was analyzed by non-linear method using pseudo-first, pseudo-second and pseudo-nth order models. It was found that the pseudo-nth order kinetic model was the best applicable model to describe the sorption kinetic data and the order n of sorption reaction was calculated in the range from 0.71 to 2.71. Three sorption isotherms namely the Langmuir, Freundlich and Redlich–Peterson isotherms in their non-linear forms were applied to the biosorption equilibrium data. Both the Langmuir and Redlich–Peterson models were found to fit the sorption isotherm data well, but the Redlich–Peterson model was better. Thermodynamic parameters show that the sorption process of MG is endothermic and more effective process at high temperatures. The results revealed that PP is very effective for the biosorption of MG from aqueous solutions.
Neoclassical MHD descriptions of tokamak plasmas
International Nuclear Information System (INIS)
Callen, J.D.; Kim, Y.B.; Sundaram, A.K.
1988-01-01
Considerable progress has been made in extending neoclassical MHD theory and in exploring the linear instabilities, nonlinear behavior and turbulence models it implies for tokamak plasmas. The areas highlighted in this paper include: extension of the neoclassical MHD equations to include temperature-gradient and heat flow effects; the free energy and entropy evolution implied by this more complete description; a proper ballooning mode formalism analysis of the linear instabilities; a new rippling mode type instability; numerical simulation of the linear instabilities which exhibit a smooth transition from resistive ballooning modes at high collisionality to neoclassical MHD modes at low collisionality; numerical simulation of the nonlinear growth of a single helicity tearing mode; and a Direct-Interaction-Approximation model of neoclassical MHD turbulence and the anomalous transport it induces which substantially improves upon previous mixing length model estimates. 34 refs., 2 figs
A pseudo-equilibrium thermodynamic model of information processing in nonlinear brain dynamics.
Freeman, Walter J
2008-01-01
Computational models of brain dynamics fall short of performance in speed and robustness of pattern recognition in detecting minute but highly significant pattern fragments. A novel model employs the properties of thermodynamic systems operating far from equilibrium, which is analyzed by linearization near adaptive operating points using root locus techniques. Such systems construct order by dissipating energy. Reinforcement learning of conditioned stimuli creates a landscape of attractors and their basins in each sensory cortex by forming nerve cell assemblies in cortical connectivity. Retrieval of a selected category of stored knowledge is by a phase transition that is induced by a conditioned stimulus, and that leads to pattern self-organization. Near self-regulated criticality the cortical background activity displays aperiodic null spikes at which analytic amplitude nears zero, and which constitute a form of Rayleigh noise. Phase transitions in recognition and recall are initiated at null spikes in the presence of an input signal, owing to the high signal-to-noise ratio that facilitates capture of cortex by an attractor, even by very weak activity that is typically evoked by a conditioned stimulus.
Magnetohydrodynamic (MHD) power generation
International Nuclear Information System (INIS)
Chandra, Avinash
1980-01-01
The concept of MHD power generation, principles of operation of the MHD generator, its design, types, MHD generator cycles, technological problems to be overcome, the current state of the art in USA and USSR are described. Progress of India's experimental 5 Mw water-gas fired open cycle MHD power generator project is reported in brief. (M.G.B.)
Free-boundary perturbed MHD equilibria
International Nuclear Information System (INIS)
Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
Directory of Open Access Journals (Sweden)
M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
3D equilibrium codes for mirror machines
International Nuclear Information System (INIS)
Kaiser, T.B.
1983-01-01
The codes developed for cumputing three-dimensional guiding center equilibria for quadrupole tandem mirrors are discussed. TEBASCO (Tandem equilibrium and ballooning stability code) is a code developed at LLNL that uses a further expansion of the paraxial equilibrium equation in powers of β (plasma pressure/magnetic pressure). It has been used to guide the design of the TMX-U and MFTF-B experiments at Livermore. Its principal weakness is its perturbative nature, which renders its validity for high-β calculation open to question. In order to compute high-β equilibria, the reduced MHD technique that has been proven useful for determining toroidal equilibria was adapted to the tandem mirror geometry. In this approach, the paraxial expansion of the MHD equations yields a set of coupled nonlinear equations of motion valid for arbitrary β, that are solved as an initial-value problem. Two particular formulations have been implemented in computer codes developed at NYU/Kyoto U and LLNL. They differ primarily in the type of grid, the location of the lateral boundary and the damping techniques employed, and in the method of calculating pressure-balance equilibrium. Discussions on these codes are presented in this paper. (Kato, T.)
MHD instabilities in heliotron/torsatron
International Nuclear Information System (INIS)
Wakatani, Masahiro; Nakamura, Yuji; Ichiguchi, Katsuji
1992-01-01
Recent theoretical results on MHD instabilities in heliotron/torsatron are reviewed. By comparing the results with experimental data in Heliotron E, Heliotron DR and ATF, it is pointed out that resistive interchange modes are the most crucial instabilities, since the magnetic hill occupies a substantial region of the plasma column. Development of three-dimensional MHD equilibrium codes has made significant progress. By applying the local stability criteria shown by D 1 (ideal MHD mode) and D R (resistive MHD mode) to the equilibria given by the three-dimensional codes such as BETA and VMEC, stability thresholds for the low n ideal modes or the low n resistive modes may be estimated with resonable accuracy, where n is a toroidal mode number. (orig.)
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
3D simulation studies of tokamak plasmas using MHD and extended-MHD models
International Nuclear Information System (INIS)
Park, W.; Chang, Z.; Fredrickson, E.; Fu, G.Y.; Pomphrey, N.; Sugiyama, L.E.
1997-01-01
The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-β disruption studies in reversed shear plasmas using the MHD level MH3D code, ω *i stabilization and nonlinear island rotation studies using the two-fluid level MH3D-T code, studies of nonlinear saturation of TAE modes using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D ++ code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree well with experimental data
Resistive MHD studies of high-β-tokamak plasmas
International Nuclear Information System (INIS)
Lynch, V.E.; Carreras, B.A.; Hicks, H.R.; Holmes, J.A.; Garcia, L.
1981-01-01
Numerical calculations have been performed to study the MHD activity in high-β tokamaks such as ISX-B. These initial value calculations built on earlier low β techniques, but the β effects create several new numerical issues. These issues are discussed and resolved. In addition to time-stepping modules, our system of computer codes includes equilibrium solvers (used to provide an initial condition) and output modules, such as a magnetic field line follower and an X-ray diagnostic code. The transition from current driven modes at low β to predominantly pressure driven modes at high β is described. The nonlinear studies yield X-ray emissivity plots which are compared with experiment
Scaling, Intermittency and Decay of MHD Turbulence
International Nuclear Information System (INIS)
Lazarian, A.; Cho, Jungyeon
2005-01-01
We discuss a few recent developments that are important for understanding of MHD turbulence. First, MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong non-linear coupling of compressible and incompressible motions along MHD cascade is not tenable. Alfven, slow and fast modes of MHD turbulence follow their own cascades and exhibit degrees of anisotropy consistent with theoretical expectations. Second, the fast decay of turbulence is not related to the compressibility of fluid. Rates of decay of compressible and incompressible motions are very similar. Third, viscosity by neutrals does not suppress MHD turbulence in a partially ionized gas. Instead, MHD turbulence develops magnetic cascade at scales below the scale at which neutrals damp ordinary hydrodynamic motions. Forth, density statistics does not exhibit the universality that the velocity and magnetic field do. For instance, at small Mach numbers the density is anisotropic, but it gets isotropic at high Mach numbers. Fifth, the intermittency of magnetic field and velocity are different. Both depend on whether the measurements are done in a local system of reference oriented along the local magnetic field or in the global system of reference related to the mean magnetic field
Gampp, H; Maeder, M; Zuberbühler, A D; Kaden, T A
1980-06-01
A microprocessor-controlled potentiometric titration apparatus for equilibrium studies is described. The microprocessor controls the stepwise addition of reagent, monitors the pH until it becomes constant and stores the constant value. The data are recorded on magnetic tape by a cassette recorder with an RS232 input-output interface. A non-linear least-squares program based on Marquardt's modification of the Newton-Gauss method is discussed and its performance in the calculation of equilibrium constants is exemplified. An HP 9821 desk-top computer accepts the data from the magnetic tape recorder. In addition to a fully automatic fitting procedure, the program allows manual adjustment of the parameters. Three examples are discussed with regard to performance and reproducibility.
Bifurcation theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
Energy Technology Data Exchange (ETDEWEB)
Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)
2017-05-15
Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)
Ideal MHD stability and characteristics of edge localized modes on CFETR
Li, Ze-Yu; Chan, V. S.; Zhu, Yi-Ren; Jian, Xiang; Chen, Jia-Le; Cheng, Shi-Kui; Zhu, Ping; Xu, Xue-Qiao; Xia, Tian-Yang; Li, Guo-Qiang; Lao, L. L.; Snyder, P. B.; Wang, Xiao-Gang; the CFETR Physics Team
2018-01-01
Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R = 5.7 m, B T = 5 T) derived from multi-code integrated modeling, with key parameters {{β }N},{{β }T},{{β }p} varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a = 1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R = 6.6 m, B T = 6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.
MHD stability, operational limits and disruptions
International Nuclear Information System (INIS)
1999-01-01
The present physics understandings of magnetohydrodynamic (MHD) stability of tokamak plasmas, the threshold conditions for onset of MHD instability, and the resulting operational limits on attainable plasma pressure (beta limit) and density (density limit), and the consequences of plasma disruption and disruption related effects are reviewed and assessed in the context of their application to a future DT burning reactor prototype tokamak experiment such as ITER. The principal considerations covered within the MHD stability and beta limit assessments are (i) magnetostatic equilibrium, ideal MHD stability and the resulting ideal MHD beta limit; (ii) sawtooth oscillations and the coupling of sawtooth activity to other types of MHD instability; (iii) neoclassical island resistive tearing modes and the corresponding limits on beta and energy confinement; (iv) wall stabilization of ideal MHD instabilities and resistive wall instabilities; (v) mode locking effects of non-axisymmetric error fields; (vi) edge localized MHD instabilities (ELMs, etc.); and (vii) MHD instabilities and beta/pressure gradient limits in plasmas with actively modified current and magnetic shear profiles. The principal considerations covered within the density limit assessments are (i) empirical density limits; (ii) edge power balance/radiative density limits in ohmic and L-mode plasmas; and (iii) edge parameter related density limits in H-mode plasmas. The principal considerations covered in the disruption assessments are (i) disruption causes, frequency and MHD instability onset; (ii) disruption thermal and current quench characteristics; (iii) vertical instabilities (VDEs), both before and after disruption, and plasma and in-vessel halo currents; (iv) after disruption runaway electron formation, confinement and loss; (v) fast plasma shutdown (rapid externally initiated dissipation of plasma thermal and magnetic energies); (vi) means for disruption avoidance and disruption effect mitigation; and
Agarwal, Shilpi; Rana, Puneet
2016-04-01
In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter λ_1 inhibits whereas the strain retardation parameter λ_2 exhibits heat transfer utilizing Al2O3 nanofluids.
Directory of Open Access Journals (Sweden)
Rajesh Ramaswamy
2011-01-01
Full Text Available Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM or fluorescence-correlation spectroscopy (FCS to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido
2011-01-28
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
Ogorodnikov, I N; Isaenko, L I; Zinin, E I; Kruzhalov, A V
2000-01-01
The paper presents the results of a study of the LiB sub 3 O sub 5 and Li sub 2 B sub 4 O sub 7 crystals by the use of the luminescent spectroscopy with the sub-nanosecond time resolution under excitation of the high-power synchrotron radiation. The commonness in the origin of the non-equilibrium processes in these crystals as well as the observed differences in the luminescence manifestations is discussed.
Energy Technology Data Exchange (ETDEWEB)
Ogorodnikov, I.N. E-mail: ogo@dpt.ustu.ru; Pustovarov, V.A.; Isaenko, L.I.; Zinin, E.I.; Kruzhalov, A.V
2000-06-21
The paper presents the results of a study of the LiB{sub 3}O{sub 5} and Li{sub 2}B{sub 4}O{sub 7} crystals by the use of the luminescent spectroscopy with the sub-nanosecond time resolution under excitation of the high-power synchrotron radiation. The commonness in the origin of the non-equilibrium processes in these crystals as well as the observed differences in the luminescence manifestations is discussed.
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)
Module description of TOKAMAK equilibrium code MEUDAS
International Nuclear Information System (INIS)
Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa
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)
HIDENEK: an implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas
International Nuclear Information System (INIS)
Tanaka, Motohiko.
1993-05-01
An advanced 'kinetic-MHD' simulation method and its applications to plasma physics are given in this lecture. This method is quite suitable for studying strong nonlinear, kinetic processes associated with large space-scale, low-frequency electromagnetic phenomena of plasmas. A full set of the Maxwell equations, and the Newton-Lorentz equations of motion for particle ions and guiding-center electrons are adopted. In order to retain only the low-frequency waves and instabilities, implicit particle-field equations are derived. The present implicit-particle method is proved to reproduce the MHD eigenmodes such as Alfven, magnetosonic and kinetic Alfven waves in a thermally near-equilibrium plasma. In the second part of the lecture, several physics applications are shown. These include not only the growth of the instabilities of beam ions against the background plasmas and helical kink of the current, but they also demonstrate nonlinear results such as pitch-angle scattering of the ions. Recent progress in the simulation of the Kelvin-Helmholtz instability is also presented with a special emphasis on the mixing of plasma particles. (author)
Directory of Open Access Journals (Sweden)
P. P. Hallan
2008-01-01
Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.
Numerical study of the axisymmetric ideal MHD stability of Extrap
International Nuclear Information System (INIS)
Benda, M.
1993-04-01
A numerical study of the free-boundary axisymmetric (n=0) ideal magnetohydrodynamical (MHD) motions of the Extrap device is presented. The dependence of stability on current profiles in the plasma and currents in the external conductors is investigated. Results are shown for linear growth-rates and nonlinear saturation amplitudes and their dependence on plasma radius as well as on the conducting shell radius. A method combined of two different algorithms has been developed and tested. The interior region of the plasma is simulated by means of a Lagrangian Finite Element Method (FEM) for ideal magnetohydrodynamics, The method is based on a nonlinear radiation principle for the Lagrangian description of ideal MHD. The Boundary Element Method (BEM) is used together with the Lagrangian FEM to simulate nonlinear motion of an ideal MHD plasma behaviour in a vacuum region under the influence of external magnetic fields. 31 refs
International Nuclear Information System (INIS)
Luehrmann, L.; Noseck, U.
1996-03-01
While the verification report on CHET1 primarily focused on aspects such as the correctness of algorithms with respect to the modeling of advection, dispersion and diffusion, the report in hand is intended to primarily deal with nonlinear sorption and numerical sorption modeling. Another aspect discussed is the correct treatment of decay within established radioactive decay chains. First, the physical fundamentals are explained of the processes determining the radionuclide transport in the cap rock, and hence are the basis of the program discussed. The numeric algorithms the CHET2 code is based are explained, showing the details of realisation and the function of the various defaults and corrections. The iterative coupling of transport and sorption computation is illustrated by means of a program flowchart. Furthermore, the actvities for verification of the program are explained, as well as qualitative effects of computations assuming concentration-dependent sorption. The computation of the decay within decay chains is verified, and application programming using nonlinear sorption isotherms as well as the entire process of transport calculations with CHET2 are shown. (orig./DG) [de
Vertical field and equilibrium calculation in ETE
International Nuclear Information System (INIS)
Montes, Antonio; Shibata, Carlos Shinya.
1996-01-01
The free-boundary MHD equilibrium code HEQ is used to study the plasma behaviour in the tokamak ETE, with optimized compensations coils and vertical field coils. The changes on the equilibrium parameters for different plasma current values are also investigated. (author). 5 refs., 4 figs., 2 tabs
International Nuclear Information System (INIS)
Paraschiv, I.; Bauer, B. S.; Lindemuth, I. R.; Makhin, V.
2010-01-01
The effect of sheared axial flow on the Z-pinch sausage instability has been examined with two-dimensional magnetohydrodynamic simulations. Diffuse Bennett equilibria in the presence of axial flows with parabolic and linear radial profiles have been considered, and a detailed study of the linear and nonlinear development of small perturbations from these equilibria has been performed. The consequences of both single-wavelength and random-seed perturbations were calculated. It was found that sheared flows changed the internal m=0 mode development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to small amplitudes and only long wavelengths continued to grow. Full stability was obtained for supersonic plasma flows.
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
Investigation of equilibrium, global modes and microinstabilities in the stellarator W7-AS
International Nuclear Information System (INIS)
Weller, A.; Anton, M.; Brakel, R.
1999-01-01
Equilibrium and stability properties in the WENDELSTEIN 7-AS stellarator are investigated experimentally and compared with theoretical predictions for particular cases. The topology of equilibrium magnetic surfaces and of global MHD modes is inferred from X-ray tomography. The predicted effects of externally driven currents and internal currents on the equilibrium surfaces could be confirmed experimentally. In particular the reduced Shafranov shift due to reduced Pfirsch-Schlueter currents in W7-AS could be verified. Up to the maximum accessible β ((β) ∼ 2%) plasmas can be confined without significant deterioration by pressure driven MHD-activity. However, global modes in the stable MHD spectrum such as global and toroidal Alfven eigenmodes (GAE, TAE) can be destabilised by energetic ions from neutral beam heating. These instabilities appear as very coherent low frequency modes (≤ 40 kHz) in the lower β regime without significant impact on the global confinement. At medium β very strong particle driven MHD modes with frequencies up to the range of 500 kHz can be observed. These modes can show nonlinear behaviour including periodic bursting and frequency chirping in combination with significant plasma energy losses. With increasing β Alfven modes are widely stable, because under these conditions the damping relative to the particle drive is increased. Besides the global mode activity small scale turbulent structures have been investigated in the plasma core and at the edge. The measured data of electron temperature, density and magnetic fluctuations do not yet allow to assess turbulence driven transport fluxes. However, correlations with the global confinement have been found, and the measured amplitudes are in the range expected to be relevant for anomalous transport. The observed dependence of the confinement on the edge rotational transform and magnetic shear can be explained in terms of enhanced transport at rational surfaces, however, the underlying
Investigation of equilibrium, global modes and microinstabilities in the stellarator W7-AS
International Nuclear Information System (INIS)
Weller, A.; Anton, M.; Brakel, R.
2001-01-01
Equilibrium and stability properties in the WENDELSTEIN 7-AS stellarator are investigated experimentally and compared with theoretical predictions for particular cases. The topology of equilibrium magnetic surfaces and of global MHD modes is inferred from X-ray tomography. The predicted effects of externally driven currents and internal currents on the equilibrium surfaces could be confirmed experimentally. In particular the reduced Shafranov shift due to reduced Pfirsch-Schlueter currents in W7-AS could be verified. Up to the maximum accessible β ( ∼2%) plasmas can be confined without significant deterioration by pressure driven MHD-activity. However, global modes in the stable MHD spectrum such as global and toroidal Alfven eigenmodes (GAE, TAE) can be destabilised by energetic ions from neutral beam heating. These instabilities appear as very coherent low frequency modes (≤40 kHz) in the lower β regime without significant impact on the global confinement. At medium β very strong particle driven MHD modes with frequencies up to the range of 500 kHz can be observed. These modes can show nonlinear behaviour including periodic bursting and frequency chirping in combination with significant plasma energy losses. With increasing β Alfven modes are widely stable, because under these conditions the damping relative to the particle drive is increased. Besides the global mode activity small scale turbulent structures have been investigated in the plasma core and at the edge. The measured data of electron temperature, density and magnetic fluctuations do not yet allow to assess turbulence driven transport fluxes. However, correlations with the global confinement have been found, and the measured amplitudes are in the range expected to be relevant for anomalous transport. The observed dependence of the confinement on the edge rotational transform and magnetic shear can be explained in terms of enhanced transport at rational surfaces, however, the underlying
Formation, structure, and stability of MHD intermediate shocks
International Nuclear Information System (INIS)
Wu, C.C.
1990-01-01
Contrary to the usual belief that MHD intermediate shocks are extraneous, the author has recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear wave steepening from continuous waves. In this paper, the formation, structure and stability of intermediate shocks in dissipative MHD are considered in detail. The differences between the conventional theory and his are pointed out and clarified. He shows that all four types of intermediate shocks can be formed from smooth waves. He also shows that there are free parameters in the structure of the intermediate shocks, and that these parameters are related to the shock stability. In addition, he shows that a rotational discontinuity can not exist with finite width, indicate how this is related to the existence of time-dependent intermediate shocks, and show why the conventional theory is not a good approximation to dissipative MHD solutions whenever there is rotation in magnetic field
Fuchs, Matthias
2017-08-01
The nature of the glass transition is one of the frontier questions in Statistical Physics and Materials Science. Highly cooperative structural processes develop in glass-forming melts exhibiting relaxational dynamics which is spread out over many decades in time. While considerable progress has been made in recent decades towards understanding dynamical slowing-down in quiescent systems, the interplay of glassy dynamics with external fields reveals a wealth of novel phenomena yet to be explored. This special issue focuses on recent results obtained by the Research Unit FOR 1394 `Nonlinear response to probe vitrification' which was funded by the German Science Foundation (DFG). In the projects of the research unit, strong external fields were used in order to gain insights into the complex structural and transport phenomena at the glass transition under far-from-equilibrium conditions. This aimed inter alia to test theories of the glass transition developed for quiescent systems by pushing them beyond their original regime. Combining experimental, simulational, and theoretical efforts, the eight projects within the FOR 1394 measured and determined aspects of the nonlinear response of supercooled metallic, polymeric, and silica melts, of colloidal dispersions, and of ionic liquids. Applied fields included electric and mechanic fields, and forced active probing (`micro-rheology'), where a single probe is forced through the glass-forming host. Nonlinear stress-strain and force-velocity relations as well as nonlinear dielectric susceptibilities and conductivities were observed. While the physical manipulation of melts and glasses is interesting in its own right, especially technologically, the investigations performed by the FOR 1394 suggest to use the response to strong homogeneous and inhomogeneous fields as technique to explore on the microscopic level the cooperative mechanisms in dense melts of strongly interacting constituents. Questions considered concern the
International Nuclear Information System (INIS)
Dokhane, A.; Henning, D.; Chawla, R.; Rizwan-Uddin
2003-01-01
BWR stability analysis at PSI, as at other research centres, is usually carried out employing complex system codes. However, these do not allow a detailed investigation of the complete manifold of all possible solutions of the associated nonlinear differential equation set. A novel analytical, reduced order model for BWR stability has been developed at PSI, in several successive steps. In the first step, the thermal-hydraulic model was used for studying the thermal-hydraulic instabilities. A study was then conducted of the one-channel nuclear-coupled thermal-hydraulic dynamics in a BWR by adding a simple point kinetic model for neutron kinetics and a model for the fuel heat conduction dynamics. In this paper, a two-channel nuclear-coupled thermal-hydraulic model is introduced to simulate the out-of phase oscillations in a BWR. This model comprises three parts: spatial mode neutron kinetics with the fundamental and fist azimuthal modes; fuel heat conduction dynamics; and thermal-hydraulics model. This present model is an extension of the Karve et al. model i.e., a drift flux model is used instead of the homogeneous equilibrium model for two-phase flow, and lambda modes are used instead of the omega modes for the neutron kinetics. This two-channel model is employed in stability and bifurcation analyses, carried out using the bifurcation code BIFDD. The stability boundary (SB) and the nature of the Poincare-Andronov-Hopf bifurcation (PAF-B) are determined and visualized in a suitable two-dimensional parameter/state space. A comparative study of the homogeneous equilibrium model (HEM) and the drift flux model (DFM) is carried out to investigate the effects of the DFM parameters the void distribution parameter C 0 and the drift velocity V gi -on the SB, the nature of PAH bifurcation, and on the type of oscillation mode (in-phase or out-of-phase). (author)
Three-dimensional plasma equilibrium near a separatrix
International Nuclear Information System (INIS)
Reiman, A.H.; Pomphrey, N.; Boozer, A.H.
1988-08-01
The limiting behavior of a general three-dimensional MHD equilibrium near a separatrix is calculated explicitly. No expansions in β or assumptions about island widths are made. Implications of the results for the numerical calculation of such equilibria, are discussed, as well as for issues concerning the existence of three-dimensional MHD equilibria. 16 refs., 2 figs
Helical axis stellarator equilibrium model
International Nuclear Information System (INIS)
Koniges, A.E.; Johnson, J.L.
1985-02-01
An asymptotic model is developed to study MHD equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two-dimensional generalized partial differential equation of the Grad-Shafranov type. A stellarator-expansion free-boundary equilibrium code is modified to solve the helical-axis equations. The expansion model is used to predict the equilibrium properties of Asperators NP-3 and NP-4. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift
Evolution of the MHD sheet pinch
International Nuclear Information System (INIS)
Matthaeus, W.H.; Montgomery, D.
1979-01-01
A magnetohydrodynamic (MHD) problem of recurrent interest for both astrophysical and laboratory plasmas is the evolution of the unstable sheet pinch, a current sheet across which a dc magnetic field reverses sign. The evolution of such a sheet pinch is followed with a spectral-method, incompressible, two-dimensional, MHD turbulence code. Spectral diagnostics are employed, as are contour plots of vector potential (magnetic field lines), electric current density, and velocity stream function (velocity streamlines). The nonlinear effect which seems most important is seen to be current filamentation: the concentration of the current density onto sets of small measure near a mgnetic X point. A great deal of turbulence is apparent in the current distribution, which, for high Reynolds numbers, requires large spatial grids (greater than or equal to (64) 2 ). 11 figures, 1 table
Petrick, Michael; Pierson, Edward S.; Schreiner, Felix
1980-01-01
According to the present invention, coal combustion gas is the primary working fluid and copper or a copper alloy is the electrodynamic fluid in the MHD generator, thereby eliminating the heat exchangers between the combustor and the liquid-metal MHD working fluids, allowing the use of a conventional coalfired steam bottoming plant, and making the plant simpler, more efficient and cheaper. In operation, the gas and liquid are combined in a mixer and the resulting two-phase mixture enters the MHD generator. The MHD generator acts as a turbine and electric generator in one unit wherein the gas expands, drives the liquid across the magnetic field and thus generates electrical power. The gas and liquid are separated, and the available energy in the gas is recovered before the gas is exhausted to the atmosphere. Where the combustion gas contains sulfur, oxygen is bubbled through a side loop to remove sulfur therefrom as a concentrated stream of sulfur dioxide. The combustor is operated substoichiometrically to control the oxide level in the copper.
HINT computation of LHD equilibrium with zero rotational transform surface
International Nuclear Information System (INIS)
Kanno, Ryutaro; Toi, Kazuo; Watanabe, Kiyomasa; Hayashi, Takaya; Miura, Hideaki; Nakajima, Noriyoshi; Okamoto Masao
2004-01-01
A Large Helical Device equilibrium having a zero rotational transform surface is studied by using the three dimensional MHD equilibrium code, HINT. We find existence of the equilibrium but with formation of the two or three n=0 islands composing a homoclinic-type structure near the center, where n is a toroidal mode number. The LHD equilibrium maintains the structure, when the equilibrium beta increases. (author)
The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical?
International Nuclear Information System (INIS)
Wu, C.C.
1988-01-01
Contrary to the usual belief that MHD intermediate shocks are extraneous, the authors have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, he clarifies the differences between the conventional view and the results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms his results. In addition, the study shows that there exists a larger class of shocklike solutions in the time-dependent dissiaptive MHD equations than are given by the MHD Rankine-Hugoniot relations. it also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models
MHD stability analyses of a tokamak plasma by time-dependent codes
International Nuclear Information System (INIS)
Kurita, Gen-ichi
1982-07-01
The MHD properties of a tokamak plasma are investigated by using time evolutional codes. As for the ideal MHD modes we have analyzed the external modes including the positional instability. Linear and nonlinear ideal MHD codes have been developed. Effects of the toroidicity and conducting shell on the external kink mode are studied minutely by the linear code. A new rezoning algorithm is devised and it is successfully applied to express numerically the axisymmetric plasma perturbation in a cylindrical geometry. As for the resistive MHD modes we have developed nonlinear codes on the basis of the reduced set of the resistive MHD equations. By using the codes we have studied the major disruption processes and properties of the low n resistive modes. We have found that the effects of toroidicity and finite poloidal beta are very important. Considering the above conclusion we propose a new scenario of the initiation of the major disruption. (author)
International Nuclear Information System (INIS)
Lapillonne, X.; Brunner, S.; Dannert, T.; Jolliet, S.; Marinoni, A.; Villard, L.; Goerler, T.; Jenko, F.; Merz, F.
2009-01-01
In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set [Dimits et al., Phys. Plasmas 7, 969 (2000)], significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-α or a magnetohydrodynamic (MHD) equilibrium. Similar disagreements have been reported previously [Redd et al., Phys. Plasmas 6, 1162 (1999)]. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-α model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order ε (ε=a/R is the inverse aspect ratio, a the minor radius and R the major radius). An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite ε, low β MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order ε inconsistencies in the s-α model, coincidentally compensating finite ρ * effects in the global calculations, where ρ * =ρ s /a with ρ s the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate ρ * →0 limit in the latter case.
Thermosolutal MHD flow and radiative heat transfer with viscous ...
African Journals Online (AJOL)
This paper investigates double diffusive convection MHD flow past a vertical porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic ...
Temperature oscillating regimes in Tore Supra diagnosed by MHD activity
International Nuclear Information System (INIS)
Maget, P.; Imbeaux, F.; Giruzzi, G.; Udintsev, V.S.; Huysmans, G.T.A.; Segui, J.-L.; Goniche, M.; Moreau, Ph.; Sabot, R.; Garbet, X.
2006-01-01
This paper describes what we can learn on the regimes of spontaneous electron temperature oscillations discovered in Tore Supra from the analysis of MHD activity. Since the first observations of this oscillating behaviour of plasma equilibrium, and its interpretation as a predator-prey system involving lower hybrid waves power deposition and electron confinement, analysis of MHD modes has confirmed the reality of safety factor profile oscillations. This points towards the importance of rational values of the safety factor in the transition to transport barriers in reversed magnetic shear plasmas
O'Connell, R.; Forest, C. B.; Plard, F.; Kendrick, R.; Lovell, T.; Thomas, M.; Bonazza, R.; Jensen, T.; Politzer, P.; Gerritsen, W.; McDowell, M.
1997-11-01
A MHD experiment is being constructed which will have the possibility of showing dynamo action: the self--generation of currents from fluid motion. The design allows sufficient experimental flexibility and diagnostic access to study a variety of issues central to dynamo theory, including mean--field electrodynamics and saturation (backreaction physics). Initially, helical flows required for dynamo action will be driven by propellers embedded in liquid sodium. The flow fields will first be measured using laser doppler velocimetry in a water experiment with an identical fluid Reynolds number. The magnetic field evolution will then be predicted using a MHD code, replacing the water with sodium; if growing magnetic fields are found, the experiment will be repeated with sodium.
International Nuclear Information System (INIS)
Falgarone, Edith; Rieutord, Michel; Richard, Denis; Zahn, Jean-Paul; Dauchot, Olivier; Daviaud, Francois; Dubrulle, Berengere; Laval, Jean-Philippe; Noullez, Alain; Bourgoin, Mickael; Odier, Philippe; Pinton, Jean-Francois; Leveque, Emmanuel; Chainais, Pierre; Abry, Patrice; Mordant, Nicolas; Michel, Olivier; Marie, Louis; Chiffaudel, Arnaud; Daviaud, Francois; Petrelis, Francois; Fauve, Stephan; Nore, C.; Brachet, M.-E.; Politano, H.; Pouquet, A.; Leorat, Jacques; Grapin, Roland; Brun, Sacha; Delour, Jean; Arneodo, Alain; Muzy, Jean-Francois; Magnaudet, Jacques; Braza, Marianna; Boree, Jacques; Maurel, S.; Ben, L.; Moreau, J.; Bazile, R.; Charnay, G.; Lewandowski, Roger; Laveder, Dimitri; Bouchet, Freddy; Sommeria, Joel; Le Gal, P.; Eloy, C.; Le Dizes, S.; Schneider, Kai; Farge, Marie; Bottausci, Frederic; Petitjeans, Philippe; Maurel, Agnes; Carlier, Johan; Anselmet, Fabien
2001-05-01
This publication gathers extended summaries of presentations proposed during two days on astrophysics and magnetohydrodynamics (MHD). The first session addressed astrophysics and MHD: The cold interstellar medium, a low ionized turbulent plasma; Turbulent convection in stars; Turbulence in differential rotation; Protoplanetary disks and washing machines; gravitational instability and large structures; MHD turbulence in the sodium von Karman flow; Numerical study of the dynamo effect in the Taylor-Green eddy geometry; Solar turbulent convection under the influence of rotation and of the magnetic field. The second session addressed the description of turbulence: Should we give up cascade models to describe the spatial complexity of the velocity field in a developed turbulence?; What do we learn with RDT about the turbulence at the vicinity of a plane surface?; Qualitative explanation of intermittency; Reduced model of Navier-Stokes equations: quickly extinguished energy cascade; Some mathematical properties of turbulent closure models. The third session addressed turbulence and coherent structures: Alfven wave filamentation and formation of coherent structures in dispersive MHD; Statistical mechanics for quasi-geo-strophic turbulence: applications to Jupiter's coherent structures; Elliptic instabilities; Physics and modelling of turbulent detached unsteady flows in aerodynamics and fluid-structure interaction; Intermittency and coherent structures in a washing machine: a wavelet analysis of joint pressure/velocity measurements; CVS filtering of 3D turbulent mixing layer using orthogonal wavelets. The last session addressed experimental methods: Lagrangian velocity measurements; Energy dissipation and instabilities within a locally stretched vortex; Study by laser imagery of the generation and breakage of a compressed eddy flow; Study of coherent structures of turbulent boundary layer at high Reynolds number
Elms: MHD Instabilities at the transport barrier
Energy Technology Data Exchange (ETDEWEB)
Huysmans, G.T.A
2005-07-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER.
Elms: MHD Instabilities at the transport barrier
International Nuclear Information System (INIS)
Huysmans, G.T.A.
2005-01-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
Analysis of the plasma magnetohydrodynamic equilibrium in iron core transformer Tokamak HL-1M
International Nuclear Information System (INIS)
Chen Xiaoguang; Yuan Baoshan
1992-01-01
The physical and mathematical model are presented on the problem of MHD equilibrium with the self consistent in iron core transformer HL-1M. Calculation and analysis for the plasma equilibrium of the stable boundary and free boundary are shown respectively, in an axisymmetric equilibrium model of two dimensions. First, a variation formulation of the problem is written and the equations of the poloided flux ψ are solved by a finite element method; the Picard and Newton algorithms are tested for the non-linearities. The plasma boundary and the magnetic surfaces are being simulated, with the currents in the coils, the total plasma current, its current density function and the magnetic permeability of the iron being the data for the problem; a certain number of the characteristic parameter of the equilibrium configuration is calculated. Secondly, a simple method of calculation is adopted in the determination of equilibrium fields and currents in iron core HL-1M tokamak device. In the plasma equilibrium, the magnetic effect of the air gaps in the iron core and the iron magnetic shielded plate are considered in HL-1M device. Reliable data are provided for designing and constructing the poloidal field system of HL-1M device. A good computer code is constructed, which may be useful in operating on analysis for the future device
Iqbal, Z.; Mehmood, Zaffar; Ahmad, Bilal
2018-05-01
This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.
International Nuclear Information System (INIS)
1991-10-01
The current MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. Essential elements of the current program include: (1) develop technical and environmental data for the integrated MHD topping cycle system through POC testing (1,000 hours); (2) develop technical and environmental data for the integrated MHD bottoming cycle sub system through POC testing (4,000 hours); (3) design, construct, and operate a seed regeneration POC facility (SRPF) capable of processing spent seed materials from the MHD bottoming cycle; (4) prepare conceptual designs for a site specific MHD retrofit plant; and (5) continue system studies and supporting research necessary for system testing. The current MHD program continues to be directed toward coal fired power plant applications, both stand-alone and retrofit. Development of a plant should enhance the attractiveness of MHD for applications other than electrical power. MHD may find application in electrical energy intensive industries and in the defense sector
International Nuclear Information System (INIS)
Petit, J.P.
1995-01-01
Jean-Pierre PETIT, one of the best MHD specialists, is telling this technology story and he is insisting on its military consequences. Civil MHD is only one iceberg emerged part, including a lot of leader technologies, interesting he defense. 3 notes
MHD turbulent dynamo in astrophysics: Theory and numerical simulation
Chou, Hongsong
2001-10-01
This thesis treats the physics of dynamo effects through theoretical modeling of magnetohydrodynamic (MHD) systems and direct numerical simulations of MHD turbulence. After a brief introduction to astrophysical dynamo research in Chapter 1, the following issues in developing dynamic models of dynamo theory are addressed: In Chapter 2, nonlinearity that arises from the back reaction of magnetic field on velocity field is considered in a new model for the dynamo α-effect. The dependence of α-coefficient on magnetic Reynolds number, kinetic Reynolds number, magnetic Prandtl number and statistical properties of MHD turbulence is studied. In Chapter 3, the time-dependence of magnetic helicity dynamics and its influence on dynamo effects are studied with a theoretical model and 3D direct numerical simulations. The applicability of and the connection between different dynamo models are also discussed. In Chapter 4, processes of magnetic field amplification by turbulence are numerically simulated with a 3D Fourier spectral method. The initial seed magnetic field can be a large-scale field, a small-scale magnetic impulse, and a combination of these two. Other issues, such as dynamo processes due to helical Alfvénic waves and the implication and validity of the Zeldovich relation, are also addressed in Appendix B and Chapters 4 & 5, respectively. Main conclusions and future work are presented in Chapter 5. Applications of these studies are intended for astrophysical magnetic field generation through turbulent dynamo processes, especially when nonlinearity plays central role. In studying the physics of MHD turbulent dynamo processes, the following tools are developed: (1)A double Fourier transform in both space and time for the linearized MHD equations (Chapter 2 and Appendices A & B). (2)A Fourier spectral numerical method for direct simulation of 3D incompressible MHD equations (Appendix C).
Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime
Zhu, Ping; Yan, Xingting; Huang, Wenlong
2017-10-01
Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.
International Nuclear Information System (INIS)
1968-01-01
Proceedings of a Symposium on Magnetohydrodynamic Electrical Power Generation held by the IAEA at Warsaw, 24-30 July 1968. The meeting was attended by some 300 participants from 21 countries and three international organizations. In contrast to the Symposium held two years ago, much more emphasis was placed on the economic aspects of using MHD generators in large-scale power generation. Among closed- cycle systems, the prospects of linking an ultra-high-temperature reactor with an MHD generator were explored, and the advantages gained by having a liquid-metal generator as a 'topper' in a conventional steam generating plant were presented. Comments were made about the disproportionate effect of end and boundary conditions in experimental MHD generators on the main plasma parameters, and estimates were made of the interrelationship to be expected in real generators. The estimates will have to await confirmation until results are obtained on large-scale prototype MHD systems. Progress in materials research, in design and construction of auxiliary equipment such as heat exchangers, supercooled magnets (which are- now commercially available), etc., is accompanied by sophisticated ideas of plant design. The Proceedings are complemented by three Round Table Discussions in which chosen experts from various countries discuss the outlook for closed-cycle gas, closed-cycle liquid-metal and open-cycle MHD, and give their views as to the most fruitful course to follow to achieve economic full-scale power generation. Contents: (Vol. I) 1. Closed-Cycle MHD with Gaseous Working Fluids: (a) Diagnostics (3 papers); (b) Steady-state non-equilibrium ionization (8 papers); (c) Transient non-equilibrium ionization (7 papers); (d) Pre-ionization and gas discharge (4 papers); (e) Fields and flow in MHD channels (10 papers); (0 Instabilities (8 papers); (g) Generator design and performance studies (6 papers); (Vol. II) (h) Shock waves (6 papers); (i) Power generation experiments (13 papers
Sub-grid-scale effects on short-wave instability in magnetized hall-MHD plasma
International Nuclear Information System (INIS)
Miura, H.; Nakajima, N.
2010-11-01
Aiming to clarify effects of short-wave modes on nonlinear evolution/saturation of the ballooning instability in the Large Helical Device, fully three-dimensional simulations of the single-fluid MHD and the Hall MHD equations are carried out. A moderate parallel heat conductivity plays an important role both in the two kinds of simulations. In the single-fluid MHD simulations, the parallel heat conduction effectively suppresses short-wave ballooning modes but it turns out that the suppression is insufficient in comparison to an experimental result. In the Hall MHD simulations, the parallel heat conduction triggers a rapid growth of the parallel flow and enhance nonlinear couplings. A comparison between single-fluid and the Hall MHD simulations reveals that the Hall MHD model does not necessarily improve the saturated pressure profile, and that we may need a further extension of the model. We also find by a comparison between two Hall MHD simulations with different numerical resolutions that sub-grid-scales of the Hall term should be modeled to mimic an inverse energy transfer in the wave number space. (author)
3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations
International Nuclear Information System (INIS)
Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.
1983-01-01
Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)
3D MHD simulations of pellet injection and disruptions in tokamak plasmas
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.
2001-01-01
Nonlinear MHD simulation results of pellet injection show that MHD forces can accelerate large pellets, injected on the high field side of a tokamak, to the plasma center. Magnetic reconnection can produce a reverse shear q profile. Ballooning instability caused by pellets is also reduced by high field side injection. Studies are also reported of the current quench phase of disruptions, which can cause 3D halo currents and runaway electrons. (author)
3D MHD simulations of pellet injection and disruptions in tokamak plasmas
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.
1999-01-01
Nonlinear MHD simulation results of pellet injection show that MHD forces can accelerate large pellets, injected on the high field side of a tokamak, to the plasma center. Magnetic reconnection can produce a reverse shear q profile. Ballooning instability caused by pellets is also reduced by high field side injection. Studies are also reported of the current quench phase of disruptions, which can cause 3D halo currents and runaway electrons. (author)
MHD channel performance for potential early commercial MHD power plants
International Nuclear Information System (INIS)
Swallom, D.W.
1981-01-01
The commercial viability of full and part load early commercial MHD power plants is examined. The load conditions comprise a mass flow of 472 kg/sec in the channel, Rosebud coal, 34% by volume oxygen in the oxidizer preheated to 922 K, and a one percent by mass seeding with K. The full load condition is discussed in terms of a combined cycle plant with optimized electrical output by the MHD channel. Various electrical load parameters, pressure ratios, and magnetic field profiles are considered for a baseload MHD generator, with a finding that a decelerating flow rate yields slightly higher electrical output than a constant flow rate. Nominal and part load conditions are explored, with a reduced gas mass flow rate and an enriched oxygen content. An enthalpy extraction of 24.6% and an isentropic efficiency of 74.2% is predicted for nominal operation of a 526 MWe MHD generator, with higher efficiencies for part load operation
Resistive MHD studies of TFTR discharges
International Nuclear Information System (INIS)
Hughes, M.H.; Phillips, M.W.; Sabbagh, S.A.; Budny, R.V.
1991-01-01
MHD instabilities, thought to be resistive in character, are frequently observed in the supershot operating regime of TFTR (var-epsilon β p ≤ 0.7). These instabilities are always accompanied by substantial degradation of the confinement. Similarly of interest are recent experiments at much larger β p (var-epsilon β p ≤ 1.6), achieved through ramping the current during the beam heating phase of the discharge. In this latter regime the confinement can exceed three times the corresponding L-mode value and the β value normalized to I/aB can be as large as 4.7. Representative discharges from each of these operating regimes have been analyzed using a linear resistive MHD stability code with equilibrium pressure and q profiles obtained initially from the TRANSP analysis code. The main difference between the two types of discharge, as far as stability is concerned is shown to be the shape of the current density profile. The sensitivity to the assumed parameters is discussed. 1 ref
A civil engineering approach to ideal MHD
International Nuclear Information System (INIS)
Jensen, V.O.
1992-01-01
It is well known that a magnetic field can be conceived as a medium where an isotropic compressive stress, B 2 /2μ 0 , is superimposed on a tensile stress, B 2 /μ 0 , parallel to the lines of force. When a stationary ideal MHD plasma is present in the magnetic field, the particle pressure adds to the magnetic stresses to form a combined stress tensor. Calculations of plasma equilibria based on this concept are very similar to calculations in civil engineering of static structures based on compressive, tensile, and shear stresses. Therefore the very simple physical pictures known from civil engineering when used in plasma physics provide simple physical understanding and facilitate the physical interpretation of the results. In an earlier paper the concept was used to derive and discuss the equilibrium equations for θ-, Z-, and screw pinches and the Grad-Shafranov shift in a tokamak plasma with circular cross sections of the flux surfaces. Here the concept is used to discuss the virial theorem and to obtain a simple physical interpretation of this theorem. We also reconsider the Grad-Shafranov shift in a tokamak plasma and show that a situation where all flux surfaces have circular cross sections cannot be an exact solution to the ideal MHD equations. (author) 3 refs., 3 figs
Directory of Open Access Journals (Sweden)
Katalin Martinás
2007-02-01
Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.
Equilibrium calculations and mode analysis
International Nuclear Information System (INIS)
Herrnegger, F.
1987-01-01
The STEP asymptotic stellarator expansion procedure was used to study the MHD equilibrium and stability properties of stellarator configurations without longitudinal net-current, which also apply to advanced stellarators. The effects of toroidal curvature and magnetic well, and the Shafranov shift were investigated. A classification of unstable modes in toroidal stellarators is given. For WVII-A coil-field configurations having a β value of 1% and a parabolic pressure profile, no free-boundary modes are found. This agrees with the experimental fact that unstable behavior of the plasma column is not observed for this parameter range. So a theoretical β-limit for stability against ideal MHD modes can be estimated by mode analysis for the WVII-A device
Magnetic levitation and MHD propulsion
Energy Technology Data Exchange (ETDEWEB)
Tixador, P [CNRS/CRTBT-LEG, 38 - Grenoble (France)
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried our in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ..) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. (orig.).
Magnetic levitation and MHD propulsion
International Nuclear Information System (INIS)
Tixador, P.
1994-01-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried our in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ..) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. (orig.)
Ideal MHD properties for proposed noncircular tokamaks
International Nuclear Information System (INIS)
Helton, F.J.; Greene, J.M.
1986-01-01
We obtain Double Dee, TFXC-C, Big Dee, and JET equlibria which are optimized with respect to both shape and current profile for stability to ideal MHD modes. With a wall reasonably far from the plasma surface we find that the external kink constrains q 1 to be above two, where q 1 is the plasma surface value of the safety factor, and the ballooning mode limits the value of β. Then a relevant stable β value for the Double Dee reactor design is over 7%. Such a Double Dee equilibrium is not in a separated second stability region and thus does not have a problem with accessibility. A relevant stable β value for the TFCX-C reactor design is over 6%. Equivalent relevant stable β values for the Big Dee (17%) and JET (7%) are included for calibration purposes. We compare these relevant stable β values with the β's determined by two recent scaling laws
Magnetic stresses in ideal MHD plasmas
DEFF Research Database (Denmark)
Jensen, V.O.
1995-01-01
The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma...... and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem...... and the Shafranov shift. The method had pedagogical merits as it simplifies the calculations, improves the physical understanding and facilitates an assessment of the approximations made in the calculations....
Equilibrium 𝛽-limits in classical stellarators
Loizu, J.; Hudson, S. R.; Nührenberg, C.; Geiger, J.; Helander, P.
2017-12-01
A numerical investigation is carried out to understand the equilibrium -limit in a classical stellarator. The stepped-pressure equilibrium code (Hudson et al., Phys. Plasmas, vol. 19 (11), 2012) is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high . Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed (Taylor, Rev. Mod. Phys., vol. 58 (3), 1986, pp. 741-763), the former is shown to maintain good flux surfaces up to the equilibrium -limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium -limit, is shown to develop regions of magnetic islands and chaos at sufficiently high , thereby providing a `non-ideal -limit'. Perhaps surprisingly, however, the value of at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg (Ideal MHD, 2014, Cambridge University Press) and derive a new prediction for the non-ideal equilibrium -limit above which chaos emerges.
Experimental rigs for MHD studies
International Nuclear Information System (INIS)
Venkataramani, N.; Jayakumar, R.; Iyer, D.R.; Dixit, N.S.
1976-01-01
An MHD experimental rig is a miniature MHD installation consisting of basic equipments necessary for specific investigations. Some of the experimental rigs used in the investigations being carried out at the Bhabha Atomic Research Centre, Bombay (India) are dealt with. The experiments included diagnostics and evaluation of materials in seeded combustion plasmas and argon plasmas. The design specifications, schematics and some of the results of the investigations are also mentioned. (author)
1990-10-01
The current magnetohydrodynamic MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. The public meetings were followed by the formulation of a June 1984 Coal-Fired MHD Preliminary Transition and Program Plan. This plan focused on demonstrating the proof-of-concept (POC) of coal-fired MHD electric power plants by the early 1990s. MHD test data indicate that while there are no fundamental technical barriers impeding the development of MHD power plants, technical risk remains. To reduce the technical risk three key subsystems (topping cycle, bottoming cycle, and seed regeneration) are being assembled and tested separately. The program does not require fabrication of a complete superconducting magnet, but rather the development and testing of superconductor cables. The topping cycle system test objectives can be achieved using a conventional iron core magnet system already in place at a DOE facility. Systems engineering-derived requirements and analytical modeling to support scale-up and component design guide the program. In response to environmental, economic, engineering, and utility acceptance requirements, design choices and operating modes are tested and refined to provide technical specifications for meeting commercial criteria. These engineering activities are supported by comprehensive and continuing systems analyses to establish realistic technical requirements and cost data. Essential elements of the current program are to: develop technical and environmental data for the integrated MHD topping cycle and bottoming cycle systems through POC testing (1000 and 4000 hours, respectively); design, construct, and operate a POC seed regeneration system capable of processing spent seed materials from the MHD bottoming cycle; prepare conceptual designs for a site specific MHD retrofit plant; and continue supporting research necessary for system testing.
Equilibrium reconstruction in the TCA/Br tokamak
International Nuclear Information System (INIS)
Sa, Wanderley Pires de
1996-01-01
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)
Bifurcation of plasma cylinder equilibrium into a stationary helical flow with magnetic islands
International Nuclear Information System (INIS)
Gubarev, V.F.; Dmitrenko, A.G.; Fesenko, A.I.
1985-01-01
Introduction of the low-hydrodynamic viscosity into the system of nonlinear MHD-equations enabled to use the bifurcation theory for the investigation into nonlinear phenomena connected with a tearing mode. The existance of a stable stationary helical flow with magnetic islands in the vicinity of a neutral curve is established. Fransfer from an axisymmetric equilibrium of a plasma cylinder to a helical one takes place only under soft conditions at both sides of the neutral curve. This result confirms the fact that the tearing mode, actually, is not an instability and may be con sidered only as a reason of formation of equilibrium with splitted magnetic surfaces. Really, changing the q 0 parameter (q 0 is the value proportional to a value of stability margin) at the plasma filament boundary a plasma equilibrium is attained corresponding to a stable branch of the bifurcation curve. In this case, a stable branch of the bifurcation curve corresponds to a helical stationary flow with magnetic islands in the instabwility region determined from the linear theory
Determination of gross plasma equilibrium from magnetic multipoles
Energy Technology Data Exchange (ETDEWEB)
Kessel, C.E.
1986-05-01
A new approximate technique to determine the gross plasma equilibrium parameters, major radius, minor radius, elongation and triangularity for an up-down symmetric plasma is developed. It is based on a multipole representation of the externally applied poloidal magnetic field, relating specific terms to the equilibrium parameters. The technique shows reasonable agreement with free boundary MHD equilibrium results. The method is useful in dynamic simulation and control studies.
Determination of gross plasma equilibrium from magnetic multipoles
International Nuclear Information System (INIS)
Kessel, C.E.
1986-05-01
A new approximate technique to determine the gross plasma equilibrium parameters, major radius, minor radius, elongation and triangularity for an up-down symmetric plasma is developed. It is based on a multipole representation of the externally applied poloidal magnetic field, relating specific terms to the equilibrium parameters. The technique shows reasonable agreement with free boundary MHD equilibrium results. The method is useful in dynamic simulation and control studies
Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency
Energy Technology Data Exchange (ETDEWEB)
Lakhin, V.P. [NRC “Kurchatov Institute”, Moscow (Russian Federation); Sorokina, E.A., E-mail: sorokina.ekaterina@gmail.com [NRC “Kurchatov Institute”, Moscow (Russian Federation); Peoples' Friendship University of Russia, Moscow (Russian Federation)
2014-01-24
The geodesic acoustic eigenmode for tokamak equilibrium with the maximum of local GAM frequency is found analytically in the frame of MHD model. The analysis is based on the asymptotic matching technique.
International Nuclear Information System (INIS)
Scheffel, J.
1984-03-01
The linear Grad-Shafranov equation for a toroidal, axisymmetric plasma is solved analytically. Exact solutions are given in terms of confluent hyper-geometric functions. As an alternative, simple and accurate WKBJ solutions are presented. With parabolic pressure profiles, both hollow and peaked toroidal current density profiles are obtained. As an example the equilibrium of a z-pinch with a square-shaped cross section is derived.(author)
International Nuclear Information System (INIS)
Ishizawa, A.; Nakajima, N.
2007-01-01
Micro-turbulence and macro-magnetohydrodynamic (macro-MHD) instabilities can appear in plasma at the same time and interact with each other in a plasma confinement. The multi-scale-nonlinear interaction among micro-turbulence, double tearing instability and zonal flow is investigated by numerically solving a reduced set of two-fluid equations. It is found that the double tearing instability, which is a macro-MHD instability, appears in an equilibrium formed by a balance between micro-turbulence and zonal flow when the double tearing mode is unstable. The roles of the nonlinear and linear terms of the equations in driving the zonal flow and coherent convective cell flow of the double tearing mode are examined. The Reynolds stress drives zonal flow and coherent convective cell flow, while the ion diamagnetic term and Maxwell stress oppose the Reynolds stress drive. When the double tearing mode grows, linear terms in the equations are dominant and they effectively release the free energy of the equilibrium current gradient
Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics
International Nuclear Information System (INIS)
Nakamura, T.K.M.; Hayashi, D.; Fujimoto, M.; Shinohara, I.
2004-01-01
We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed
Linear ideal MHD stability calculations for ITER
International Nuclear Information System (INIS)
Hogan, J.T.
1988-01-01
A survey of MHD stability limits has been made to address issues arising from the MHD--poloidal field design task of the US ITER project. This is a summary report on the results obtained to date. The study evaluates the dependence of ballooning, Mercier and low-n ideal linear MHD stability on key system parameters to estimate overall MHD constraints for ITER. 17 refs., 27 figs
Nonlinear dynamics of non-equilibrium holes in p-type modulation-doped GaInNAs/GaAs quantum wells
Directory of Open Access Journals (Sweden)
Amann Andreas
2011-01-01
Full Text Available Abstract Nonlinear charge transport parallel to the layers of p-modulation-doped GaInNAs/GaAs quantum wells (QWs is studied both theoretically and experimentally. Experimental results show that at low temperature, T = 13 K, the presence of an applied electric field of about 6 kV/cm leads to the heating of the high mobility holes in the GaInNAs QWs, and their real-space transfer (RST into the low-mobility GaAs barriers. This results in a negative differential mobility and self-generated oscillatory instabilities in the RST regime. We developed an analytical model based upon the coupled nonlinear dynamics of the real-space hole transfer and of the interface potential barrier controlled by space-charge in the doped GaAs layer. Our simulation results predict dc bias-dependent self-generated current oscillations with frequencies in the high microwave range.
Gyrokinetic Magnetohydrodynamics and the Associated Equilibrium
Lee, W. W.; Hudson, S. R.; Ma, C. H.
2017-10-01
A proposed scheme for the calculations of gyrokinetic MHD and its associated equilibrium is discussed related a recent paper on the subject. The scheme is based on the time-dependent gyrokinetic vorticity equation and parallel Ohm's law, as well as the associated gyrokinetic Ampere's law. This set of equations, in terms of the electrostatic potential, ϕ, and the vector potential, ϕ , supports both spatially varying perpendicular and parallel pressure gradients and their associated currents. The MHD equilibrium can be reached when ϕ -> 0 and A becomes constant in time, which, in turn, gives ∇ . (J|| +J⊥) = 0 and the associated magnetic islands. Examples in simple cylindrical geometry will be given. The present work is partially supported by US DoE Grant DE-AC02-09CH11466.
Sawtooth oscillations as MHD relaxation process in a plasma
International Nuclear Information System (INIS)
Yoshida, Zensho; Inoue, Nobuyuki; Ogawa, Yuichi
1992-01-01
The sawtooth oscillation in a tokamak plasma is a spontaneous relaxation process accompanying global instabilities which behave to reduce the internal magnetic energy. This phenomenon has a similarity to the MHD relaxation processes in Reversed Field Pinch (RFP) and Ultra Low Q (ULQ) plasmas. The self-stabilizing effect of instabilities with m (poloidal mode number) = 1 results in an increase in the central safety factor q(0). Nonlinear dynamics of m = 1 instabilities has been discussed both for global and local modes. The latter appears when a pitch minimum exists in the plasma, and is relevant to the compound sawtooth oscillation. The MHD relaxation is a restructuring process of the plasma current profile that is competitive with the resistive diffusion. (author)
MHD activity triggered by monster sawtooth crashes on Tore Supra
International Nuclear Information System (INIS)
Maget, P; Artaud, J-F; Eriksson, L-G; Huysmans, G; Lazaros, A; Moreau, P; Ottaviani, M; Segui, J-L; Zwingmann, W
2005-01-01
The crash of monster sawteeth in Tore Supra ion cyclotron resonance heated plasmas is observed to trigger long-lived magneto hydrodynamic (MHD) activity, dominated by a (m = 3, n = 2) magnetic perturbation at the edge. This phenomenon is reminiscent of the triggering of neoclassical tearing modes, although in Tore Supra the MHD activity decays and eventually vanishes. It can be explained by the linear destabilization of the (3, 2) mode as the current sheet developed in the non-linear stage of the internal kink relaxation gets closer to q = 3/2. However, the lifetime of the (3, 2) island is longer than the period of linear instability. We find that the neoclassical drive is essential for explaining the observed lifetime and width of the island, although the overall dynamics is controlled by the relaxation of the current profile on a resistive time scale
Characteristics of MHD stability of high beta plasmas in LHD
International Nuclear Information System (INIS)
Sato, M.; Nakajima, N.; Watanabe, K.Y.; Todo, Y.; Suzuki, Y.
2012-11-01
In order to understand characteristics of the MHD stability of high beta plasmas obtained in the LHD experiments, full MHD simulations have been performed for the first time. Since there is a magnetic hill in a plasma peripheral region, the ballooning modes extending into the plasma peripheral region with a chaotic magnetic field are destabilized. However, in the nonlinear phase, the core region comes under the in influence of the instabilities and the central pressure decreases. There is a tendency that modes are suppressed as the beta value and/or magnetic Reynolds number increase, which is consistent with a result that high beta plasmas enter the second stable region of the ideal ballooning modes as beta increases and remaining destabilized ballooning modes are considered to be resistive type. (author)
MHD simulation of Columbia HBT
International Nuclear Information System (INIS)
Li, X.L.
1987-01-01
The plasma of Columbia High Beta Tokamak (HBT) is studied numerically by using the two dimensional resistive MHD model. The main object of this work is to understand the high beta formation process of HBT plasma and to compare the simulation with the experiments. 21 refs., 48 figs., 2 tabs
Stabilities of MHD rotational discontinuities
International Nuclear Information System (INIS)
Wang, S.
1984-11-01
In this paper, the stabilities of MHD rotational discontinuities are analyzed. The results show that the rotational discontinuities in an incompressible magnetofluid are not always stable with respect to infinitesimal perturbation. The instability condition in a special case is obtained. (author)
MHD stability of tandem mirrors
International Nuclear Information System (INIS)
Poulsen, P.; Molvik, A.; Shearer, J.
1982-01-01
The TMX-Upgrade experiment was described, and the manner in which various plasma parameters could be affected was discussed. The initial analysis of the MHD stability of the tandem mirror was also discussed, with emphasis on the negative tandem configuration
MHD Integrated Topping Cycle Project
Energy Technology Data Exchange (ETDEWEB)
1992-01-01
The overall objective of the project is to design and construct prototypical hardware for an integrated MHD topping cycle, and conduct long duration proof-of-concept tests of integrated system at the US DOE Component Development and Integration Facility in Butte, Montana. The results of the long duration tests will augment the existing engineering design data base on MHD power train reliability, availability, maintainability, and performance, and will serve as a basis for scaling up the topping cycle design to the next level of development, an early commercial scale power plant retrofit. The components of the MHD power train to be designed, fabricated, and tested include: A slagging coal combustor with a rated capacity of 50 MW thermal input, capable of operation with an Eastern (Illinois {number sign}6) or Western (Montana Rosebud) coal, a segmented supersonic nozzle, a supersonic MHD channel capable of generating at least 1.5 MW of electrical power, a segmented supersonic diffuser section to interface the channel with existing facility quench and exhaust systems, a complete set of current control circuits for local diagonal current control along the channel, and a set of current consolidation circuits to interface the channel with the existing facility inverter.
Exponential Growth of Nonlinear Ballooning Instability
International Nuclear Information System (INIS)
Zhu, P.; Hegna, C. C.; Sovinec, C. R.
2009-01-01
Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.
Magnetic levitation and MHD propulsion
Tixador, P.
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried out in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ...) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. Depuis quelques années nous assistons à un redémarrage de programmes concernant la lévitation et la propulsion supraconductrices. Différents systèmes supraconducteurs de lévitation et de propulsion seront décrits en examinant plus particulièrement l'aspect électromagnétique. Quelques programmes à travers le monde seront abordés. Les trains à sustentation magnétique pourraient constituer un nouveau mode de transport terrestre à vitesse élevée (500 km/h) pour le 21^e siècle. Les japonais n'ont cessé de s'intéresser à ce système avec bobine supraconductrice. Ils envisagent un stade préindustriel avec la construction d'une ligne de 43 km. En 1991 un programme américain pour une durée de six ans a été lancé pour évaluer les performances des systèmes à lévitation pour le transport aux Etats Unis. La MHD (Magnéto- Hydro-Dynamique) présente des avantages intéressants pour la propulsion navale et un regain d'intérêt apparaît à l'heure actuelle. Le japon se situe là encore à la pointe des d
Variational Integration for Ideal MHD with Built-in Advection Equations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Burby, J. W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-08-05
Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
Lower hybrid wave current ramp-up and plasma equilibrium
International Nuclear Information System (INIS)
Gong Xueyu
1996-01-01
Questions on lower hybrid driven current and plasma equilibrium are studied. With the induced electric field taken into account, a system of self-consistent equations is obtained. This theory has been applied to some moments of the current ramp-up phase for the Tokamak Engineering Test Breeder (TETB) to study the lower hybrid current drive and MHD equilibrium. So, better electron current and safety factor profiles are obtained
User's manual for the FLORA equilibrium and stability code
International Nuclear Information System (INIS)
Freis, R.P.; Cohen, B.I.
1985-01-01
This document provides a user's guide to the content and use of the two-dimensional axisymmetric equilibrium and stability code FLORA. FLORA addresses the low-frequency MHD stability of long-thin axisymmetric tandem mirror systems with finite pressure and finite-larmor-radius effects. FLORA solves an initial-value problem for interchange, rotational, and ballooning stability
Several hundred megawatt MHD units
International Nuclear Information System (INIS)
Pishchikov, S.; Pinkhasik, D.; Sidorov, V.
1978-01-01
The features are described of the future MHD unit U-25 tested at the Institute of High Temperatures of the Academy of Sciences of the USSR. The attainable thermal load of the combustion chamber is 290x10 6 kJ/m 3 .h. Three types of channel were tested, i.e., the Faraday channel divided into sections with modular insulating walls, the diagonal channel without metal body, and an improved Faraday channel with an output of 20 MW. The described MHD generator is equipped with an inverter which transforms direct current into alternating current, continuously adjusts the load from no-load operation to short-circuit connection and maintains the desired electrical voltage independently of the changes in loading. A new technique of connecting and disconnecting the oxygen equipment was developed which considerably reduces the time of start-up and shut-down. Natural gas is used for heating the air heaters. All equipment used in the operation of the MHD generator is remote controlled by computer or manually. (J.B.)
Several hundred megawatt MHD units
Energy Technology Data Exchange (ETDEWEB)
Pishchikov, S; Pinkhasik, D; Sidorov, V
1978-07-01
The features are described of the future MHD unit U-25 tested at the Institute of High Temperatures of the Academy of Sciences of the USSR. The attainable thermal load of the combustion chamber is 290x10/sup 6/ kJ/m/sup 3/.h. Three types of channel were tested, i.e., the Faraday channel divided into sections with modular insulating walls, the diagonal channel without metal body, and an improved Faraday channel with an output of 20 MW. The described MHD generator is equipped with an inverter which transforms direct current into alternating current, continuously adjusts the load from no-load operation to short-circuit connection and maintains the desired electrical voltage independently of the changes in loading. A new technique of connecting and disconnecting the oxygen equipment was developed which considerably reduces the time of start-up and shut-down. Natural gas is used for heating the air heaters. All equipment used in the operation of the MHD generator is remote controlled by computer or manually.
The structure of ideal MHD Alfven modes
International Nuclear Information System (INIS)
Turnbull, A.D.; Chu, M.S.; Lao, L.L.; Greene, J.M.; Strait, E.J.; Chance, M.S.
1991-01-01
Continuum Alfven modes have undergone a resurgence in interest with the recent realization that so-called Toroidicity-Induced Alfven Eigenmodes (TAE modes) can be destabilized either by energetic beam ions in a strongly heated plasma or by alpha particles in a burning plasma. The GATO Ideal MHD Stability code, which minimizes the potential energy according to a variational formulation, has now been modified to isolate and calculate stable continuum eigenmodes. The existence of the TAE mode and its associated gap has been verified, using this code, for a circular cross-section, finite aspect ratio equilibrium. Moreover, the eigenfrequencies and eigenmodes obtained from this variational calculation are found to be in extremely good quantitative agreement with those obtained from the non-variational NOVA code. A systematic survey of the stable continuum has further revealed a surprising diversity in the structure of the continuum Alfven modes; the logarithmic singularity can be so broad, in some cases, as to occupy the whole cross-section. This has important implications for heating experiments which aim to locally excite the plasma by rf waves in the Alfven frequency range. The structure of several representative examples is discussed. The Alfven continuum, in general, and the TAE mode and its associated gap, in particular, are also found to be strongly modified by cross-sectional shaping. The dependence of the spectrum on various shaping factors is explored
Energy Technology Data Exchange (ETDEWEB)
Anon.
1984-12-15
From 3-6 September the First International Workshop on Local Equilibrium in Strong Interaction Physics took place in Bad-Honnef at the Physics Centre of the German Physical Society. A number of talks covered the experimental and theoretical investigation of the 'hotspots' effect, both in high energy particle physics and in intermediate energy nuclear physics.
African Journals Online (AJOL)
context of antimicrobial therapy in malnutrition. Dialysis has in the past presented technical problems, being complicated and time-consuming. A new dialysis system based on the equilibrium technique has now become available, and it is the principles and practical application of this apparatus (Kontron Diapack; Kontron.
van Damme, E.E.C.
2000-01-01
An outcome in a noncooperative game is said to be self-enforcing, or a strategic equilibrium, if, whenever it is recommended to the players, no player has an incentive to deviate from it.This paper gives an overview of the concepts that have been proposed as formalizations of this requirement and of
Ismail, M.S.
2014-01-01
We introduce a new concept which extends von Neumann and Morgenstern's maximin strategy solution by incorporating `individual rationality' of the players. Maximin equilibrium, extending Nash's value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that
Advanced energy utilization MHD power generation
International Nuclear Information System (INIS)
2008-01-01
The 'Technical Committee on Advanced Energy Utilization MHD Power Generation' was started to establish advanced energy utilization technologies in Japan, and has been working for three years from June 2004 to May 2007. This committee investigated closed cycle MHD, open cycle MHD, and liquid metal MHD power generation as high-efficiency power generation systems on the earth. Then, aero-space application and deep space exploration technologies were investigated as applications of MHD technology. The spin-off from research and development on MHD power generation such as acceleration and deceleration of supersonic flows was expected to solve unstart phenomena in scramjet engine and also to solve abnormal heating of aircrafts by shock wave. In addition, this committee investigated researches on fuel cells, on secondary batteries, on connection of wind power system to power grid, and on direct energy conversion system from nuclear fusion reactor for future. The present technical report described results of investigations by the committee. (author)
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
International Nuclear Information System (INIS)
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
International Nuclear Information System (INIS)
Yvars, M.
1979-10-01
The materials considered for the insulating walls of a M.H.D. converter are Al 2 O 3 , and the calcium or strontium zirconates. For the conducting walls electricity conducting oxides are being considered such as ZrO 2 or CrO 3 La essentially. The principle of M.H.D. systems is recalled, the materials considered are described as is their behaviour in the corrosive atmospheres of M.H.D. streams [fr
Intermittency in MHD turbulence and coronal nanoflares modelling
Directory of Open Access Journals (Sweden)
P. Veltri
2005-01-01
Full Text Available High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD. The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.
Ideal MHD B limits in the BIG DEE tokamak
International Nuclear Information System (INIS)
Helton, F.J.; Bernard, L.C.; Greene, J.M.
1983-01-01
Using D-D reactions, tokamak reactors become economically attractive when B (the ratio of volume averaged pressure to magnetic pressure) exceeds 5 percent. Ideal MID instabilities are of great concern because they have the potential to limit B below this range and so extensive studies have been done to determine ideal MHD B limits. As B increases with inverse aspect ratio, elongation and triangularity, the Doublet III upgrade machine -- BIG DEE -- is particularly suited to study the possibility of very high B. The authors have done computations to determine ideal MHD B limits for various plasma shapes and elongations in BIG DEE. They have determined that for q at the plasma surface greater than 2, B is limited by the ballooning mode if the wall is reasonably close to the plasma surface (d/a < 1.5 where d and a are the wall and plasma radii respectively). On the other hand, for q at the plasma surface less than 2, the n=1 external kink is unstable even with a wall close by. Thus, relevant values of limiting B can be obtained by assuming that the external kink limits the value of q at the limiter to a value greater than 2 and that the ballooning modes limit B. Under this assumption, a relevant B limit for the BIG DEE would be over 18%. For such an equilibrium, the wall position necessary to stabilize the n=1 and n=2 modes is 2a and the equilibrium is stable for n=3
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
On MHD waves, fire-hose and mirror instabilities in anisotropic plasmas
Directory of Open Access Journals (Sweden)
L.-N. Hau
2007-09-01
Full Text Available Temperature or pressure anisotropies are characteristic of space plasmas, standard magnetohydrodynamic (MHD model for describing large-scale plasma phenomena however usually assumes isotropic pressure. In this paper we examine the characteristics of MHD waves, fire-hose and mirror instabilities in anisotropic homogeneous magnetized plasmas. The model equations are a set of gyrotropic MHD equations closed by the generalized Chew-Goldberger-Low (CGL laws with two polytropic exponents representing various thermodynamic conditions. Both ions and electrons are allowed to have separate plasma beta, pressure anisotropy and energy equations. The properties of linear MHD waves and instability criteria are examined and numerical examples for the nonlinear evolutions of slow waves, fire-hose and mirror instabilities are shown. One significant result is that slow waves may develop not only mirror instability but also a new type of compressible fire-hose instability. Their corresponding nonlinear structures thus may exhibit anticorrelated density and magnetic field perturbations, a property used for identifying slow and mirror mode structures in the space plasma environment. The conditions for nonlinear saturation of both fire-hose and mirror instabilities are examined.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
Chen, Junjie; Li, Guoqiang; Qian, Jinping; Liu, Zixi
2012-11-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta βN limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power Pt increases as the toroidal magnetic field BT or the normalized beta βN is increased.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
International Nuclear Information System (INIS)
Chen Junjie; Li Guoqiang; Qian Jinping; Liu Zixi
2012-01-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta β N limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power P t increases as the toroidal magnetic field B T or the normalized beta β N is increased. (magnetically confined plasma)
Simulation of the MHD stabilities of the experiment on HL-2A tokamak by GATO code
International Nuclear Information System (INIS)
Pan Wei; Chen Liaoyuan; Dong Jiaqi; Shen Yong; Zhang Jinhua
2009-01-01
The ideal two-dimensional MHD stabilities code, GATO, has been successfully immigrated to the high-performance computing system of HL-2A and used to the simulation study of the ideal MHD stabilities of the plasmas produced by one of the pellets injection experiments on HL-2A tokamak. The EFIT code was used to reconstruct the equilibrium configures firstly and the GATO was used to compute their MHD stabilities secondly whose source data were obtained by the NO.4050 discharge of the experiments on HL-2A, and finally by analyzing these results the preliminary conclusion was devised that the confinement performance of the plasma was improved because of the stabilization effect of the anti-sheared configures created by the pellets injection. (authors)
MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!
Goedbloed, J. P.
2018-01-01
The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an ‘intuitive’ description based on the energy principle that is very misleading for most astrophysical plasmas. The ‘intuitive’ picture almost directly singles out the dominant stabilizing field line bending energy of the Alfvén waves and, consequently, concentrates on expansion schemes that minimize that contribution. This happens when the wave vector {{k}}0 of the perturbations, on average, is perpendicular to the magnetic field {B}. Hence, all macroscopic instabilities of tokamaks (kinks, interchanges, ballooning modes, ELMs, neoclassical tearing modes, etc) are characterized by satisfying the condition {{k}}0 \\perp {B}, or nearly so. In contrast, some of the major macroscopic instabilities of astrophysical plasmas (the Parker instability and the magneto-rotational instability) occur when precisely the opposite condition is satisfied: {{k}}0 \\parallel {B}. How do those instabilities escape from the dominance of the stabilizing Alfvén wave? The answer to that question involves, foremost, the recognition that MHD spectral theory of waves and instabilities of laboratory plasmas could be developed to such great depth since those plasmas are assumed to be in static equilibrium. This assumption is invalid for astrophysical plasmas where rotational and gravitational accelerations produce equilibria that are at best stationary, and the associated spectral theory is widely, and incorrectly, believed to be non-self adjoint. These complications are addressed, and cured, in the theory of the Spectral Web, recently developed by the author. Using this method, an extensive survey of instabilities of astrophysical plasmas demonstrates how the Alfvén wave is pushed into insignificance under these conditions to give rise to a host of instabilities that do not
Chau, Nancy H.
2009-01-01
This paper presents a capability-augmented model of on the job search, in which sweatshop conditions stifle the capability of the working poor to search for a job while on the job. The augmented setting unveils a sweatshop equilibrium in an otherwise archetypal Burdett-Mortensen economy, and reconciles a number of oft noted yet perplexing features of sweatshop economies. We demonstrate existence of multiple rational expectation equilibria, graduation pathways out of sweatshops in complete abs...
MHD stability properties of a system of reduced toroidal MHD equations
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1993-01-01
A system of reduced toroidal magneto-hydrodynamic (MHD) equations is derived from a general scalar representation of the complete MHD system, using an ordering in terms of the inverse aspect ratio ε of a toroidal plasma. It is shown that the energy principle for the reduced equations is identical with the usual energy principle of the complete MHD system, to the appropriate order in ε. Thus, the reduced equations have the same ideal MHD stability limits as the full MHD equations. (authors). 6 refs
Stability analysis of resistive MHD modes via a new numerical matching technique
International Nuclear Information System (INIS)
Furukawa, M.; Tokuda, S.; Zheng, L.-J.
2009-01-01
Full text: Asymptotic matching technique is one of the principal methods for calculating linear stability of resistive magnetohydrodynamics (MHD) modes such as tearing modes. In applying the asymptotic method, the plasma region is divided into two regions: a thin inner layer around the mode-resonant surface and ideal MHD regions except for the layer. If we try to solve this asymptotic matching problem numerically, we meet practical difficulties. Firstly, the inertia-less ideal MHD equation or the Newcomb equation has a regular singular point at the mode-resonant surface, leading to the so-called big and small solutions. Since the big solution is not square-integrable, it needs sophisticated treatment. Even if such a treatment is applied, the matching data or the ratio of small solution to the big one, has been revealed to be sensitive to local MHD equilibrium accuracy and grid structure at the mode-resonant surface by numerical experiments. Secondly, one of the independent solutions in the inner layer, which should be matched onto the ideal MHD solution, is not square-integrable. The response formalism has been adopted to resolve this problem. In the present paper, we propose a new method for computing the linear stability of resistive MHD modes via matching technique, where the plasma region is divided into ideal MHD regions and an inner region with finite width. The matching technique using an inner region with finite width was recently developed for ideal MHD modes in cylindrical geometry, and good performance was shown. Our method extends this idea to resistive MHD modes. In the inner region, the low-beta reduced MHD equations are solved, and the solution is matched onto the solution of the Newcomb equation by using boundary conditions such that the parallel electric field vanishes properly as approaching the computational boundaries. If we use the inner region with finite width, the practical difficulties raised above can be avoided from the beginning. Figure
Non-equilibrium in flowing atmospheric plasmas
International Nuclear Information System (INIS)
Haas, J.C.M. de.
1986-01-01
This thesis deals with the fundamental aspects of two different plasmas applied in technological processes. The first one is the cesium seeded argon plasma in a closed cycle Magnetohydrodynamic (MHD) generator, the second is the thermal argon plasma in a cascade arc with an imposed flow. In Chapter 2 the influence of non-equilibrium on the mass and energy balances of a plasma is worked out. The general theory presented there can be applied to both the plasma in an MHD generator and to the cascade arc with imposed flow. Introductions to these plasmas are given in the Chapters 3 and 6 respectively. These chapters are both followed by two chapters which treat the theoretical and the experimental investigations. The results are summarized in Chapter 9. (Auth.)
Design of MHD generator systems
International Nuclear Information System (INIS)
Buende, R.; Raeder, J.
1975-01-01
By assessment of the influence of the combustion efficiency on the electric output of the MHD generator, it can be shown that the construction and efficiency of the generator strongly depend on these parameters. The solutions of this system of equations are discussed. Following a derivation of criteria and boundary conditions of the design and a determination of the specific construction costs of individual system components, it is shown how the single design parameters influence the operational characteristics of such a system, especially the output, efficiency and energy production costs. (GG/LH) [de
Axisymmetric MHD stable sloshing ion distributions
International Nuclear Information System (INIS)
Berk, H.L.; Dominguez, N.; Roslyakov, G.V.
1986-07-01
The MHD stability of a sloshing ion distribution is investigated in a symmetric mirror cell. Fokker-Planck calculations show that stable configurations are possible for ion injection energies that are at least 150 times greater than the electron temperture. Special axial magnetic field profiles are suggested to optimize the favorable MHD properties
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Luca Anderlini; Daniele Terlizzese
2009-01-01
We build a simple model of trust as an equilibrium phenomenon, departing from standard "selfish" preferences in a minimal way. Agents who are on the receiving end of an other to transact can choose whether to cheat and take away the entire surplus, taking into account a "cost of cheating." The latter has an idiosyncratic component (an agent's type), and a socially determined one. The smaller the mass of agents who cheat, the larger the cost of cheating suffered by those who cheat. Depending o...
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.
Computational studies in tokamak equilibrium and transport
International Nuclear Information System (INIS)
Braams, B.J.
1986-01-01
This thesis is concerned with some problems arising in the magnetic confinement approach to controlled thermonuclear fusion. The work address the numerical modelling of equilibrium and transport properties of a confined plasma and the interpretation of experimental data. The thesis is divided in two parts. Part 1 is devoted to some aspects of the MHD equilibrium problem, both in the 'direct' formulation (given an equation for the plasma current, the corresponding equilibrium is to be determined) and in the 'inverse' formulation (the interpretation of measurements at the plasma edge). Part 2 is devoted to numerical studies of the edge plasma. The appropriate Navier-Stokes system of fluid equations is solved in a two-dimensional geometry. The main interest of this work is to develop an understanding of particle and energy transport in the scrape-off layer and onto material boundaries, and also to contribute to the conceptual design of the NET/INTOR tokamak reactor experiment. (Auth.)
PIXIE3D: An efficient, fully implicit, parallel, 3D extended MHD code for fusion plasma modeling
International Nuclear Information System (INIS)
Chacon, L.
2007-01-01
PIXIE3D is a modern, parallel, state-of-the-art extended MHD code that employs fully implicit methods for efficiency and accuracy. It features a general geometry formulation, and is therefore suitable for the study of many magnetic fusion configurations of interest. PIXIE3D advances the state of the art in extended MHD modeling in two fundamental ways. Firstly, it employs a novel conservative finite volume scheme which is remarkably robust and stable, and demands very small physical and/or numerical dissipation. This is a fundamental requirement when one wants to study fusion plasmas with realistic conductivities. Secondly, PIXIE3D features fully-implicit time stepping, employing Newton-Krylov methods for inverting the associated nonlinear systems. These methods have been shown to be scalable and efficient when preconditioned properly. Novel preconditioned ideas (so-called physics based), which were prototypes in the context of reduced MHD, have been adapted for 3D primitive-variable resistive MHD in PIXIE3D, and are currently being extended to Hall MHD. PIXIE3D is fully parallel, employing PETSc for parallelism. PIXIE3D has been thoroughly benchmarked against linear theory and against other available extended MHD codes on nonlinear test problems (such as the GEM reconnection challenge). We are currently in the process of extending such comparisons to fusion-relevant problems in realistic geometries. In this talk, we will describe both the spatial discretization approach and the preconditioning strategy employed for extended MHD in PIXIE3D. We will report on recent benchmarking studies between PIXIE3D and other 3D extended MHD codes, and will demonstrate its usefulness in a variety of fusion-relevant configurations such as Tokamaks and Reversed Field Pinches. (Author)
Steady convection in MHD Benard problem with Hall effects
Directory of Open Access Journals (Sweden)
Lidia Palese
2017-10-01
Full Text Available In this paper we apply some variants of the classical energy method to study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting fully ionized fluid in a horizontal layer heated from below. The classical L^2 norm, too weak to highlight some stabilizing or unstabilizing effects, can be used to dominate the nonlinear terms. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem, in terms of some independent scalar fields. In such a way, if the principle of exchange of stabilities holds, we obtain the coincidence of linear and nonlinear stability bounds.
MHD (Magnetohydrodynamics) recovery and regeneration
Energy Technology Data Exchange (ETDEWEB)
McIlroy, R. A. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Probert, P. B. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Lahoda, E. J. [Westinghouse Electric Corp., Pittsburgh, PA (United States); Swift, W. M. [Argonne National Lab. (ANL), Argonne, IL (United States); Jackson, D. M. [Univ. of Tennessee Space Inst. (UTSI), Tullahoma, TN (United States); Prasad, J. [Univ. of Tennessee Space Inst. (UTSI), Tullahoma, TN (United States); Martin, J. [Hudson Engineering (United States); Rogers, C. [Hudson Engineering (United States); Ho, K. K. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Senary, M. K. [Babcock and Wilcox Co., Alliance, OH (United States). Research Center; Lee, S. [Univ. of Akron, OH (United States)
1988-10-01
A two-phase program investigating MHD seed regeneration is described. In Phase I, bench scale experiments were carried out to demonstrate the technical feasibility of a proposed Seed Regeneration Process. The Phase I data has been used for the preliminary design of a Proof-of-Concept (POC) plant which will be built and tested in Phase II. The Phase I data will also be used to estimate the costs of a 300 Mw(t) demonstration plant for comparison with other processes. The Seed Regeneration Process consists of two major subprocesses; a Westinghouse Dry Reduction process and a modified Tampella (sulfur) Recovery process. The Westinghouse process reduces the recovered spent seed (i.e., potassium sulfate) to potassium polysulfide in a rotary kiln. The reduction product is dissolved in water to form green liquor, clarified to remove residual coal ash, and sent to the Tampella sulfur release system. The sulfur is released using carbon dioxide from flue gas in a two stage reaction. The sulfur is converted to elemental sulfur as a marketable by product. The potassium is crystallized from the green liquor and dried to the anhydrous form for return to the MHD unit.
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.
Finite-element semi-discretization of linearized compressible and resistive MHD
International Nuclear Information System (INIS)
Kerner, W.; Jakoby, A.; Lerbinger, K.
1985-08-01
The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)
Influence of external 3D magnetic fields on helical equilibrium and plasma flow in RFX-mod
International Nuclear Information System (INIS)
Piovesan, P; Bonfiglio, D; Bonomo, F; Cappello, S; Carraro, L; Cavazzana, R; Gobbin, M; Marrelli, L; Martin, P; Martines, E; Momo, B; Piron, L; Puiatti, M E; Soppelsa, A; Valisa, M; Zanca, P; Zaniol, B
2011-01-01
A spontaneous transition to a helical equilibrium with an electron internal transport barrier is observed in RFX-mod as the plasma current is raised above 1 MA (Lorenzini R et al 2009 Nature Phys. 5 570). The helical magnetic equilibrium can be controlled with external three-dimensional (3D) magnetic fields applied by 192 active coils, providing proper helical boundary conditions either rotating or static. The persistence of the helical equilibrium is strongly increased in this way. A slight reduction in the energy confinement time of about 15% is observed, likely due to the increased plasma-wall interaction associated with the finite radial magnetic field imposed at the edge. A global helical flow develops in these states and is expected to play a role in the helical self-organization. In particular, its shear may contribute to the ITB formation and is observed to increase with the externally applied radial field. The possible origins of this flow, from nonlinear visco-resistive magnetohydrodynamic (MHD) and/or ambipolar electric fields, will be discussed.
de Oliveira, Mário J
2017-01-01
This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Néel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This new edit...
Generation of compressible modes in MHD turbulence
Energy Technology Data Exchange (ETDEWEB)
Cho, Jungyeon [Chungnam National Univ., Daejeon (Korea); Lazarian, A. [Univ. of Wisconsin, Madison, WI (United States)
2005-05-01
Astrophysical turbulence is magnetohydrodynamic (MHD) in nature. We discuss fundamental properties of MHD turbulence and in particular the generation of compressible MHD waves by Alfvenic turbulence and show that this process is inefficient. This allows us to study the evolution of different types of MHD perturbations separately. We describe how to separate MHD fluctuations into three distinct families: Alfven, slow, and fast modes. We find that the degree of suppression of slow and fast modes production by Alfvenic turbulence depends on the strength of the mean field. We review the scaling relations of the modes in strong MHD turbulence. We show that Alfven modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfven modes. However, fast modes exhibit isotropy and a scaling similar to that of acoustic turbulence both in high and low {beta} plasmas. We show that our findings entail important consequences for star formation theories, cosmic ray propagation, dust dynamics, and gamma ray bursts. We anticipate many more applications of the new insight to MHD turbulence and expect more revisions of the existing paradigms of astrophysical processes as the field matures. (orig.)
Validation of equilibrium tools on the COMPASS tokamak
Energy Technology Data Exchange (ETDEWEB)
Urban, J., E-mail: urban@ipp.cas.cz [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Appel, L.C. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Artaud, J.F. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Faugeras, B. [Laboratoire J.A. Dieudonné, UMR 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02 (France); Havlicek, J. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic); Komm, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Lupelli, I. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Peterka, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic)
2015-10-15
Highlights: • Three equilibrium codes—EFIT++, FREEBIE and VacTH—have been successfully set up and validated on COMPASS. • FREEBIE can predictively calculate the equilibrium and corresponding poloidal field coil currents. • EFIT++ can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. • VacTH is a promising tool for real time plasma shape reconstruction. • Optimized parameters are estimated for EFIT++ and VacTH by a statistical analysis. - Abstract: Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code (Appel et al., 2006), the free-boundary equilibrium code FREEBIE (Artaud and Kim, 2012), and a rapid plasma boundary reconstruction code VacTH (Faugeras et al., 2014). We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated.
Stability of a two-volume MRxMHD model in slab geometry
Tuen, Li Huey
Ideal MHD models are known to be inadequate to describe various physical attributes of a toroidal field with non-continuous symmetry, such as magnetic islands and stochastic regions. Motivated by this omission, a new variational principle MRXMHD was developed; rather than include an infinity of magnetic flux surfaces, MRxMHD has a finite number of flux surfaces, and thus supports partial plasma relaxation. The model comprises of relaxed plasma regions which are separated by nested ideal MHD interfaces (flux surfaces), and can be encased in a perfectly conducting wall. In each region the pressure is constant, but can jump across interfaces. The field and field pitch, or rotational transform, can also jump across the interfaces. Unlike ideal MHD, MRxMHD plasmas can support toroidally non-axisymmetric confined magnetic fields, magnetic islands and stochastic regions. In toroidally non-axisymmetric plasma, the existence of interfaces in MRxMHD is contingent on the irrationality of the rotational transform of flux surfaces. That is, the KAM theorem shows that invariant tori (flux surfaces) continue to exist for sufficiently small perturbations to an integrable system (which describes flux surfaces), provided that the rotational transform is sufficiently irrational. Building upon the MRxMHD stability model, we study the effects of irrationality of the rotational transform at interfaces in MRxMHD on plasma stability. We present an MRxMHD equilibrium model to investigate the effects of magnetic field pitch within the plasma and across the aforementioned flux surfaces within a chosen geometry. In this model, it is found that the 2D system stability conditions are dependent on the interface and resonant surface magnetic field pitch at minimised energy states, and the stability of a system as a function of magnetic field pitch destabilises at particular values of magnetic field pitch. We benchmark the treatment of a two-volume system, along with the calculations for
Global MHD Modelling of the ISM - From large towards small scale turbulence
de Avillez, M.; Breitschwerdt, D.
2005-06-01
Dealing numerically with the turbulent nature and non-linearity of the physical processes involved in the ISM requires the use of sophisticated numerical schemes coupled to HD and MHD mathematical models. SNe are the main drivers of the interstellar turbulence by transferring kinetic energy into the system. This energy is dissipated by shocks (which is more efficient) and by molecular viscosity. We carried out adaptive mesh refinement simulations (with a finest resolution of 0.625 pc) of the turbulent ISM embedded in a magnetic field with mean field components of 2 and 3 μG. The time scale of our run was 400 Myr, sufficiently long to avoid memory effects of the initial setup, and to allow for a global dynamical equilibrium to be reached in case of a constant energy input rate. It is found that the longitudinal and transverse turbulent length scales have a time averaged (over a period of 50 Myr) ratio of 0.52-0.6, almost similar to the one expected for isotropic homogeneous turbulence. The mean characteristic size of the larger eddies is found to be ˜ 75 pc in both runs. In order to check the simulations against observations, we monitored the OVI and HI column densities within a superbubble created by the explosions of 19 SNe having masses and velocities of the stars that exploded in vicinity of the Sun generating the Local Bubble. The model reproduces the FUSE absorption measurements towards 25 white dwarfs of the OVI column density as function of distance and of N(HI). In particular for lines of sight with lengths smaller than 120 pc it is found that there is no correlation between N(OVI) and N(HI).
Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD
Ferraro, N. M.
2015-11-01
The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. This research was supported by US DOE contracts DE-FG02-95ER54309, DE-FC02-04ER54698 and DE-AC52-07NA27344.
MHD intermediate shock discontinuities: Pt. 1
International Nuclear Information System (INIS)
Kennel, C.F.; Blandford, R.D.; Coppi, P.
1989-01-01
Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic. (author)
Liquid metal MHD generator systems
International Nuclear Information System (INIS)
Satyamurthy, P.; Dixit, N.S.; Venkataramani, N.; Rohatgi, V.K.
1985-01-01
Liquid Metal MHD (LMMHD) Generator Systems are becoming increasingly important in space and terrestrial applications due to their compactness and versatility. This report gives the current status and economic viability of LMMHD generators coupled to solar collectors, fast breeder reactors, low grade heat sources and conventional high grade heat sources. The various thermodynamic cycles in the temperatures range of 100degC-2000degC have been examined. The report also discusses the present understanding of various loss mechanisms inherent in LMMHD systems and the techniques for overcoming these losses. A small mercury-air LMMHD experimental facility being set up in Plasma Physics Division along with proposals for future development of this new technology is also presented in this report. (author)
Eigenvalue problem and nonlinear evolution of kink modes in a toroidal plasma
International Nuclear Information System (INIS)
Ogino, T.; Takeda, S.; Sanuki, H.; Kamimura, T.
1979-04-01
The internal kink modes of a cylindrical plasma are investigated by a linear eigen value problem and their nonlinear evolution is studied by 3-dimensional MHD simulation based on the rectangular column model under the fixed boundary condition. The growth rates in two cases, namely uniform and diffused current profiles are analyzed in detail, which agree with the analytical estimation by Shafranov. The time evolution of the m = 1 mode showed that q > 1 is satisfied at the relaxation time (q safety factor), a stable configuration like a horse shoe (a new equilibrium) was formed. Also, the time evolution of the pressure p for the m = 2 mode showed that a stable configuration like a pair of anchors was formed. (author)
Calculation of three-dimensional MHD equilibria with islands and stochastic regions
International Nuclear Information System (INIS)
Reiman, A.; Greenside, H.
1986-08-01
A three-dimensional MHD equilibrium code is described that does not assume the existence of good surfaces. Given an initial guess for the magnetic field, the code proceeds by calculating the pressure-driven current and then by updating the field using Ampere's law. The numerical algorithm to solve the magnetic differential equation for the pressure-driven current is described, and demonstrated for model fields having islands and stochastic regions. The numerical algorithm which solves Ampere's law in three dimensions is also described. Finally, the convergence of the code is illustrated for a particular stellarator equilibrium with no large islands
Equilibrium of the kink source experiment
International Nuclear Information System (INIS)
Marklin, G.
1985-01-01
The kink source experiment (KSX) was conceived of as a method of injecting helicity into a spheromak making special use of the m = 1 helical Taylor state. It has a Z pinch as a helicity generating source, connected to a flux conserver through an entrance region. Since the entrance region is a long (length > diameter) cyclinder, the magnetic field should be close to the helical Taylor state, which is the minimum energy configuration of a magnetized plasma in an infinite cylinder with no net flux. This paper will be concerned with modeling the actual fields in the entrance region of the KSX using zero-beta ideal MHD equilibrium theory
The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media
DEFF Research Database (Denmark)
Ghsemi, E; Soleimani, S; Barari, Amin
2012-01-01
The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...
A dissipative model of plasma equilibrium in toroidal systems
International Nuclear Information System (INIS)
Wobig, H.
1985-10-01
In order to describe a steady-state plasma equilibrium in tokamaks, stellarators or other non-axisymmetric configurations, the model of ideal MHD with isotropic plasma pressure is widely used. The ideal MHD - model of a toroidal plasma equilibrium requires the existence of closed magnetic surfaces. Several numerical codes have been developed in the past to solve the three-dimensional equilibrium problem, but so far no existence theorem for a solution has been proved. Another difficulty is the formation of magnetic islands and field line ergodisation, which can only be described in terms of ideal MHD if the plasma pressure is constant in the ergodic region. In order to describe the formation of magnetic islands and ergodisation of surfaces properly, additional dissipative terms have to be incorporated to allow decoupling of the plasma and magnetic field. In a collisional plasma viscosity and inelastic collisions introduce such dissipative processes. In the model used a friction term proportional to the velocity v vector of the plasma is included. Such a term originates from charge exchange interaction of the plasma with a nuetral background. With these modifications, the equilibrium problem reduces to a set of quasilinear elliptic equations for the pressure, the electric potential and the magnetic field. The paper deals with an existence theorem based on the Fixed - Point method of Schauder. It can be shown that a self-consistent and unique equilibrium exists if the friction term is large and the plasma pressure is sufficiently low. The essential role of the dissipative terms is to remove the singularities of the ideal MHD model on rational magnetic surfaces. The problem has a strong similarity to Benard cell convection, and consequently similar behaviour such as bifurcation and exchange of stability are expected. (orig./GG)
Boundary modulation effects on MHD instabilities in Heliotrons
International Nuclear Information System (INIS)
Nakajima, N.; Hudson, S.R.; Hegna, C.C.; Nakamura, Y.
2005-01-01
In three-dimensional configurations, the confinement region is surrounded by the stochastic magnetic field lines related to magnetic islands or separatrix, leading to the fact that the plasma-vacuum boundary is not so definite compared with tokamaks that the various modulations of the plasma-vacuum boundary will be induced around the stochastic region by a large Shafranov shift of the whole plasma, in especially high-β operations. To examine such the modulation effects of the plasma boundary on MHD instabilities, high-β plasmas allowing a large Shafranov shift are considered in the inward-shifted LHD configurations with the vacuum magnetic axis R ax of 3.6m, for which previous theoretical analyses indicate that pressure-driven modes are significantly more unstable compared with experimental observations. It is shown that the boundary modulation due to a free motion of the equilibrium plasma has not only significant stabilizing effects on ideal MHD instabilities, but also characteristics consistent to experimental observations. (author)
Computational modeling of neoclassical and resistive MHD tearing modes in tokamaks
International Nuclear Information System (INIS)
Gianakon, T.A.; Hegna, C.C.; Callen, J.D.
1996-01-01
Numerical studies of the nonlinear evolution of MHD-type tearing modes in three-dimensional toroidal geometry with neoclassical effects are presented. The inclusion of neoclassical physics introduces an additional free-energy source for the nonlinear formation of magnetic islands through the effects of a bootstrap current in Ohm's law. The neoclassical tearing mode is demonstrated to be destabilized in plasmas which are otherwise Δ' stable, albeit once an island width threshold is exceeded. The plasma pressure dynamics and neoclassical tearing growth is shown to be sensitive to the choice of the ratio of the parallel to perpendicular diffusivity (Χ parallel/Χ perpendicular). The study is completed with a demonstration and theoretical comparison of the threshold for single helicity neoclassical MHD tearing modes, which is described based on parameter scans of the local pressure gradient, the ratio of perpendicular to parallel pressure diffusivities Χ perpendicular/Χ parallel, and the magnitude of an initial seed magnetic perturbation
Quantum chaos theory and the spectrum of ideal-MHD instabilities in toroidal plasmas
International Nuclear Information System (INIS)
Dewar, Robert L.; Carolin, Nuehrenberg; Tatsuno, Tomoya
2004-01-01
In a fully 3-D system such as a stellarator, the toroidal mode number n ceases to be a good quantum number - all ns within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD (magnetohydrodynamic) instabilities ceases to exist unless MHD is modified (regularized) by introducing a short-perpendicular-wavelength cutoff. Attempts to use ray tracing to estimate the regularized MHD spectrum fail due to the occurrence of chaotic ray trajectories. In quantum chaos theory, strong chaos in the semiclassical limit leads to eigenvalue statistics the same as those of a suitable ensemble of random matrices. For instance, the probability distribution function for the separation between neighboring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in separable systems, showing that a signature of quantum chaos is level repulsion. In order to determine whether eigenvalues of the regularized MHD problem obey the same statistics as those of the Schroedinger equation in both the separable 1-D case and the chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a Suydam-unstable cylindrical (1-D) equilibrium using Mathematica and a Mercier-unstable (3-D) equilibrium using the CAS3D code. In the 1-D case, we find that the unregularized Suydam-approximation spectrum has an anomalous peak at zero eigenvalue separation. On the other hand, regularization by restricting the domain of κsub(perpendicular) recovers the expected Poissonian distribution. In the 3-D case we find strong evidence of level repulsion within mode families, but mixing mode families produces Poissonian statistics. (author)
Characteristics of laminar MHD fluid hammer in pipe
International Nuclear Information System (INIS)
Huang, Z.Y.; Liu, Y.J.
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
Modeling of Nonlinear Beat Signals of TAE's
Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin
2012-03-01
Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core
On accelerated flow of MHD powell-eyring fluid via homotopy analysis method
Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul
2017-09-01
The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.
MHD flow layer formation at boundaries of magnetic islands in tokamak plasmas
International Nuclear Information System (INIS)
Jiaqi Dong; Yongxing Long; Zongze Mou; Jinhua Zhang
2005-01-01
Non-linear development of double tearing modes induced by electron viscosity is numerically simulated. MHD flow layers are demonstrated to merge in the development of the modes. The sheared flows are shown to lie just at the boundaries of the magnetic islands, and to have sufficient levels required for internal transport barrier (ITB) formation. Possible correlation between the layer formation and triggering of experimentally observed ITBs, preferentially formed in proximities of rational flux surfaces of low safety factors, is discussed. (author)
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
MHD-Vlasov simulation of the toroidal Alfven eigenmode
International Nuclear Information System (INIS)
Todo, Y.; Sato, T.; Watanabe, K.; Watanabe, T.H.; Horiuchi, R.
1994-11-01
A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a full-MHD fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n = 2 mode develops and saturates at the level of 1.8x10 -3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TEA mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite-amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated. (author)
MHD pressure drop in ducts with imperfectly insulating coatings
International Nuclear Information System (INIS)
Malang, S.; Buehler, L.
1994-08-01
Liquid metal cooled blankets in fusion tokamak's are feasible only with electrically insulating coatings at the coolant channel walls. The requirements of such coatings are investigated and a simple analytical model is developed to determine the influence of imperfections in the coatings on the magneto-hydrodynamic pressure drop. This model is compared with the results of a 3D-MHD code based on the core flow approach. Both methods are in good agreement as long as the imperfections do not increase the pressure drop by more than 20%. The analytical model over-estimates the pressure drop for values larger than 20%. The importance of self-healing of coatings in case of cracking or flaking is quantified and an equation for the equilibrium conditions between the generation of imperfection and the healing of such spots is provided
Equilibrium: two-dimensional configurations
International Nuclear Information System (INIS)
Anon.
1987-01-01
In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7
International Nuclear Information System (INIS)
Ishizawa, A.; Nakajima, N.
2007-01-01
This is the first numerical simulation demonstrating that a macromagnetohydrodynamic (macro-MHD) mode is excited as a result of multi-scale interaction in a quasi-steady equilibrium formed by a balance between microturbulence and zonal flow based on a reduced two-fluid model. This simulation of a macro-MHD mode, a double tearing mode, is accomplished in a reversed shear equilibrium that includes zonal flow and turbulence due to kinetic ballooning modes. In the quasi-steady equilibrium, a macroscale fluctuation that has the same helicity as the double tearing mode is a part of the turbulence. After a certain period of time, the macro-MHD mode begins to grow. It effectively utilizes free energy of the equilibrium current density gradient and is destabilized by a positive feedback loop between zonal flow suppression and magnetic island growth. Thus, once the macro-MHD appears from the quasi-equilibrium, it continues to grow steadily. This simulation is more comparable with experimental observations of growing macro-MHD activity than earlier MHD simulations starting from linear macroinstabilities in a static equilibrium
International Nuclear Information System (INIS)
Dunn, P.F.
1978-01-01
The basic features of the two-phase liquid-metal MHD energy conversion under development at Argonne National Laboratory are presented. The results of system studies on the Rankine-cycle and the open-cycle coal-fired cycle options are discussed. The liquid-metal MHD experimental facilities are described in addition to the system's major components, the generator, mixer and nozzle-separator-diffuser
MHD stability analysis of helical system plasmas
International Nuclear Information System (INIS)
Nakamura, Yuji
2000-01-01
Several topics of the MHD stability studies in helical system plasmas are reviewed with respect to the linear and ideal modes mainly. Difference of the method of the MHD stability analysis in helical system plasmas from that in tokamak plasmas is emphasized. Lack of the cyclic (symmetric) coordinate makes an analysis more difficult. Recent topic about TAE modes in a helical system is also described briefly. (author)
Observation of finite-β MHD phenomena in Tokamaks
International Nuclear Information System (INIS)
McGuire, K.M.
1985-01-01
Stable high beta plasmas are required for the tokamak to attain an economical fusion reactor. Recently, intense neutral beam heating experiments in tokamaks have shown new effects on plasma stability and confinement associated with high beta plasmas. The observed spectrum of MHD fluctuations at high beta is clearly dominated by the n = 1 mode when the q = 1 surface is in the plasma. The m/n = 1/1 mode drives other n = 1 modes through toroidal coupling and n > 1 modes through nonlinear coupling. On PDX, with near perpendicular injection, a resonant interaction between the n = 1 internal kink and the trapped fast ions results in loss of beam particles and heating power. Key parameters in the theory are the value of qsub(o) and the injection angle. High frequency broadband magnetic fluctuations have been observed on ISX-B and D-III and a correlation with the deterioration of plasma confinement was reported. During enhanced confinement (H-mode) discharges in divertor plasmas two new edge instabilities were observed, both localized radially near the separatrix. By assembling results from the different tokamak experiments, it is found that the simple theoretical ideal MHD beta limit has not been exceeded
Investigations on high speed MHD liquid flow
International Nuclear Information System (INIS)
Yamasaki, Takasuke; Kamiyama, Shin-ichi.
1982-01-01
Lately, the pressure drop problem of MHD two-phase flow in a duct has been investigated theoretically and experimentally in conjunction with the problems of liquid metal MHD two-phase flow power-generating cycle or of liquid metal boiling two-phase flow in the blanket of a nuclear fusion reactor. Though many research results have been reported so far for MHD single-phase flow, the hydrodynamic studies on high speed two-phase flow are reported only rarely, specifically the study dealing with the generation of cavitation is not found. In the present investigation, the basic equation was derived, analyzing the high speed MHD liquid flow in a diverging duct as the one-dimensional flow of homogeneous two-phase fluid of small void ratio. Furthermore, the theoretical solution for the effect of magnetic field on cavitation-generating conditions was tried. The pressure distribution in MHD flow in a duct largely varies with load factor, and even if the void ratio is small, the pressure distribution in two-phase flow is considerably different from that in single-phase flow. Even if the MHD two-phase flow in a duct is subsonic flow at the throat, the critical conditions may be achieved sometimes in a diverging duct. It was shown that cavitation is more likely to occur as magnetic field becomes more intense if it is generated downstream of the throat. This explains the experimental results qualitatively. (Wakatsuki, Y.)
Nonlinearly driven harmonics of Alfvén modes
Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.
2014-01-01
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Nonlinearly driven harmonics of Alfvén modes
Energy Technology Data Exchange (ETDEWEB)
Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
2014-01-15
In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.
Aerospace Applications of Non-Equilibrium Plasma
Blankson, Isaiah M.
2016-01-01
Nonequilibrium plasma/non-thermal plasma/cold plasmas are being used in a wide range of new applications in aeronautics, active flow control, heat transfer reduction, plasma-assisted ignition and combustion, noise suppression, and power generation. Industrial applications may be found in pollution control, materials surface treatment, and water purification. In order for these plasma processes to become practical, efficient means of ionization are necessary. A primary challenge for these applications is to create a desired non-equilibrium plasma in air by preventing the discharge from transitioning into an arc. Of particular interest is the impact on simulations and experimental data with and without detailed consideration of non-equilibrium effects, and the consequences of neglecting non-equilibrium. This presentation will provide an assessment of the presence and influence of non-equilibrium phenomena for various aerospace needs and applications. Specific examples to be considered will include the forward energy deposition of laser-induced non-equilibrium plasmoids for sonic boom mitigation, weakly ionized flows obtained from pulsed nanosecond discharges for an annular Hall type MHD generator duct for turbojet energy bypass, and fundamental mechanisms affecting the design and operation of novel plasma-assisted reactive systems in dielectric liquids (water purification, in-pipe modification of fuels, etc.).
Equilibrium and stability of a rotating plasma
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1979-01-01
The author considers the equilibrium and stability of a rotating plasma. The kinetic equations for ions and electrons supplemented with the Maxwell equations and the appropriate boundary conditions are used. Two different models for the rotating plasma are considered: the equilibrium of a 'fast' rotating plasma (Magneto Hydrodynamic ordering) and the stability of a slowly rotating, 'weakly' unstable plasma (Finite Larmor Radius ordering). A striking difference between these orderings is the fact that, regarding the stability of the plasma, for a F.L.R. plasma viscosity effects due to the finite Larmor radius are important, whereas in a M.H.D. plasma they are negligible (at least to the required order). (Auth.)
MHD simulations of coronal dark downflows considering thermal conduction
Zurbriggen, E.; Costa, A.; Esquivel, A.; Schneiter, M.; Cécere, M.
2017-10-01
While several scenarios have been proposed to explain supra-arcade downflows (SADs) observed descending through turbulent hot regions, none of them have systematically addressed the consideration of thermal conduction. The SADs are known to be voided cavities. Our model assumes that SADs are triggered by bursty localized reconnection events that produce non-linear waves generating the voided cavity. These subdense cavities are sustained in time because they are hotter than their surrounding medium. Due to the low density and large temperature values of the plasma we expect the thermal conduction to be an important process. Our main aim here is to study if it is possible to generate SADs in the framework of our model considering thermal conduction. We carry on 2D MHD simulations including anisotropic thermal conduction, and find that if the magnetic lines envelope the cavities, they can be isolated from the hot environment and be identified as SADs.
Thought analysis on self-organization theories of MHD plasma
International Nuclear Information System (INIS)
Kondoh, Yoshiomi; Sato, Tetsuya.
1992-08-01
A thought analysis on the self-organization theories of dissipative MHD plasma is presented to lead to three groups of theories that lead to the same relaxed state of ∇ x B = λB, in order to find an essential physical picture embedded in the self-organization phenomena due to nonlinear and dissipative processes. The self-organized relaxed state due to the dissipation by the Ohm loss is shown to be formulated generally as the state such that yields the minimum dissipation rate of global auto-and/or cross-correlations between two quantities in j, B, and A for their own instantaneous values of the global correlations. (author)
Tearing mode dynamics and sawtooth oscillation in Hall-MHD
Ma, Zhiwei; Zhang, Wei; Wang, Sheng
2017-10-01
Tearing mode instability is one of the most important dynamic processes in space and laboratory plasmas. Hall effects, resulted from the decoupling of electron and ion motions, could cause the fast development and perturbation structure rotation of the tearing mode and become non-negligible. We independently developed high accuracy nonlinear MHD code (CLT) to study Hall effects on the dynamic evolution of tearing modes with Tokamak geometries. It is found that the rotation frequency of the mode in the electron diamagnetic direction is in a good agreement with analytical prediction. The linear growth rate increases with increase of the ion inertial length, which is contradictory to analytical solution in the slab geometry. We further find that the self-consistently generated rotation largely alters the dynamic behavior of the double tearing mode and the sawtooth oscillation. National Magnetic Confinement Fusion Science Program of China under Grant No. 2013GB104004 and 2013GB111004.
Hayat, Tasawar; Akram, Javaria; Alsaedi, Ahmed; Zahir, Hina
2018-03-01
Endoscopic and homogeneous-heterogeneous reactions in MHD peristalsis of Ree-Eyring fluid are addressed. Mathematical modeling and analysis have been performed by utilizing cylindrical coordinates. Nonlinear thermal radiation is present. Impact of slip boundary conditions on temperature and velocity on outer tube are taken into consideration. Lubrication approach is employed. The nonlinear system is executed numerically for solutions of velocity, temperature and concentration. Graphical results are obtained to predict physical interpretation of various embedded parameters. It is noted that homogeneous and heterogeneous reactions affect the concentration alternatively. Moreover Brinkman number rises the temperature and heat transfer coefficient whereas thermal slip drops temperature and heat transfer rate.
International Nuclear Information System (INIS)
Jiang, Shixiao W; Lu, Haihao; Zhou, Douglas; Cai, David
2016-01-01
Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β -Fermi–Pasta–Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems. (paper)
MHD diffuser model test program
Energy Technology Data Exchange (ETDEWEB)
Idzorek, J J
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment.
MHD diffuser model test program
International Nuclear Information System (INIS)
Idzorek, J.J.
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment
MHD waveguides in space plasma
International Nuclear Information System (INIS)
Mazur, N. G.; Fedorov, E. N.; Pilipenko, V. A.
2010-01-01
The waveguide properties of two characteristic formations in the Earth's magnetotail-the plasma sheet and the current (neutral) sheet-are considered. The question of how the domains of existence of different types of MHD waveguide modes (fast and slow, body and surface) in the (k, ω) plane and their dispersion properties depend on the waveguide parameters is studied. Investigation of the dispersion relation in a number of particular (limiting) cases makes it possible to obtain a fairly complete qualitative pattern of all the branches of the dispersion curve. Accounting for the finite size of perturbations across the wave propagation direction reveals new additional effects such as a change in the critical waveguide frequencies, the excitation of longitudinal current at the boundaries of the sheets, and a change in the symmetry of the fundamental mode. Knowledge of the waveguide properties of the plasma and current sheets can explain the occurrence of preferred frequencies in the low-frequency fluctuation spectra in the magnetotail. In satellite observations, the type of waveguide mode can be determined from the spectral properties, as well as from the phase relationships between plasma oscillations and magnetic field oscillations that are presented in this paper.
Transfer equations for spectral densities of inhomogeneous MHD turbulence
International Nuclear Information System (INIS)
Tu, C.-Y.; Marsch, E.
1990-01-01
On the basis of the dynamic equations governing the evolution of magnetohydrodynamic fluctuations expressed in terms of Elsaesser variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented describing the evolutions of the energy spectrum e ± and of the residual energy spectra e R and e S of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e ± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for e R the triple correlations do not correspond to an 'energy' conserving process, but also represent a nonlinear source term for e R . If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations. (author)
Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods
Energy Technology Data Exchange (ETDEWEB)
Shadid, J N; Pawlowski, R P; Banks, J W; Chacon, L; Lin, P T; Tuminaro, R S
2009-06-03
This paper presents an initial study that is intended to explore the development of a scalable fully-implicit stabilized unstructured finite element (FE) capability for low-Mach-number resistive MHD. The discussion considers the development of the stabilized FE formulation and the underlying fully-coupled preconditioned Newton-Krylov nonlinear iterative solver. To enable robust, scalable and efficient solution of the large-scale sparse linear systems generated by the Newton linearization, fully-coupled algebraic multilevel preconditioners are employed. Verification results demonstrate the expected order-of-acuracy for the stabilized FE discretization of a 2D vector potential form for the steady and transient solution of the resistive MHD system. In addition, this study puts forth a set of challenging prototype problems that include the solution of an MHD Faraday conduction pump, a hydromagnetic Rayleigh-Bernard linear stability calculation, and a magnetic island coalescence problem. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.
Effect of Equilibrium Current Profiles on External Kink Modes in Tokamaks
International Nuclear Information System (INIS)
Liu Chao; Liu Yue; Ma Zhaoshuai
2014-01-01
Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the external kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height, width and position of the current bumps on external kink modes are analyzed. The flat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks
Nonequilibrium fluctuations in micro-MHD effects on electrodeposition
International Nuclear Information System (INIS)
Aogaki, Ryoichi; Morimoto, Ryoichi; Asanuma, Miki
2010-01-01
In copper electrodeposition under a magnetic field parallel to electrode surface, different roles of two kinds of nonequilibrium fluctuations for micro-magnetohydrodynamic (MHD) effects are discussed; symmetrical fluctuations are accompanied by the suppression of three dimensional (3D) nucleation by micro-MHD flows (the 1st micro-MHD effect), whereas asymmetrical fluctuations controlling 2D nucleation yield secondary nodules by larger micro-MHD flows (the 2nd micro-MHD effect). Though the 3D nucleation with symmetrical fluctuations is always suppressed by the micro-MHD flows, due to the change in the rate-determining step from electron transfer to mass transfer, the 2D nucleation with asymmetrical fluctuations newly turns unstable, generating larger micro-MHD flows. As a result, round semi-spherical deposits, i.e., secondary nodules are yielded. Using computer simulation, the mechanism of the 2nd micro-MHD effect is validated.
Solving free-plasma-boundary problems with the SIESTA MHD code
Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.
2017-10-01
SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.
Magnetohydrodynamic equilibrium and stability of spheromak with spheroidal plasma-vacuum interface
International Nuclear Information System (INIS)
Kaneko, Shobu; Kamitani, Atsushi; Takimoto, Akio.
1985-05-01
The analytic solutions to the Grad-Shafranov equation are obtained for a prolate and an oblate spheroidal plasma by using Hill's vortex model. Effects of a toroidal magnetic field Bsub(phi) on the MHD equilibrium configurations are investigated by using these analytic solutions. When Bsub(phi) is larger than that of the force-free configuration, the spheroidal plasmas in a vacuum magnetic field are shown to be unable in the MHD equilibrium. The several physical quantities on the equilibrium configuration are evaluated. The spheromak plasma is proved to be unstable if dp/d psi not equal 0 and d 2 V/d psi 2 >= 0 on the magnetic axis. Here p is the pressure and V(psi) the volume surrounded by a magnetic surface of psi=const. The equilibrium configurations of the spheroidal plasmas by using Hill's vortex model are shown to satisfy the above conditions, i.e., to be unstable. (author)
Magnetohydrodynamic equilibrium and stability of spheromak with spheroidal plasma-vacuum interface
International Nuclear Information System (INIS)
Kaneko, Shobu; Kamitani, Atsushi; Takimoto, Akio
1985-01-01
The analytic solutions to the Grad-Shafranov equation are obtained for a prolate and an oblate spheroidal plasma by using Hill's vortex model. Effects of a toroidal magnetic field Bsub(phi) on the MHD equilibrium configurations are investigated by using these analytic solutions. When Bsub(phi) is stronger than that of the force-free configuration, the spheroidal plasmas in a vacuum magnetic field are shown to be unable in the MHD equilibrium. The several physical quantities on the equilibrium configuration are evaluated. The spheromak plasma is proved to be unstable if dp/d psi not equal 0 and d 2 V/d psi 2 >= 0 on the magnetic axis. Here p is the pressure and V(psi) the volume surrounded by a magnetic surface of psi = const. The equilibrium configurations of the spheroidal plasmas by using Hill's vortex model are shown to satisfy the above conditions, i.e., to be unstable. (author)
International Nuclear Information System (INIS)
Ivanov, A. A.; Martynov, A. A.; Medvedev, S. Yu.; Poshekhonov, Yu. Yu.
2015-01-01
In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (with arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented
Equilibrium optimization code OPEQ and results of applying it to HT-7U
International Nuclear Information System (INIS)
Zha Xuejun; Zhu Sizheng; Yu Qingquan
2003-01-01
The plasma equilibrium configuration has a strong impact on the confinement and MHD stability in tokamaks. For designing a tokamak device, it is an important issue to determine the sites and currents of poloidal coils which have some constraint conditions from physics and engineering with a prescribed equilibrium shape of the plasma. In this paper, an effective method based on multi-variables equilibrium optimization is given. The method can optimize poloidal coils when the previously prescribed plasma parameters are treated as an object function. We apply it to HT-7U equilibrium calculation, and obtain good results
Influence of slag-seed interaction on MHD generator performance
International Nuclear Information System (INIS)
Luongo, C.A.; Kruger, C.M.
1984-01-01
An overview of past work in the field of slag/seed interaction is presented. The ideal solution model for the slag and its failure to lead to accurate predictions are discussed. The non-ideal solution model is introduced. Data on potassium vapor pressure over slags taken at the National Bureau of Standards and Montana State University were compiled and compared. Large disagreement between these sources was observed. The shortcomings of the complete thermodynamic equilibrium models led to over predictions in the fraction of seed lost to the slag. A model including non-equilibrium effects is introduced. The heat/mass transfer analogy is invoked to calculate the mass transfer rate of potassium towards the slag. Using typical conditions for a large MHD generator, an integral method is used to evaluate the potassium concentration boundary layer thickness. The calculations are performed with the slag runoff (ash rejection) as a parameter. The increase in boundary layer resistance due to potassium depletion is calculated
Method of operating a MHD power plant
International Nuclear Information System (INIS)
Wysk, S.R.
1982-01-01
A fossil fuel is burned substoichiometrically in the combustor of a mhd power plant to produce a high temperature, fuelrich product gas. The product gas is passed through a mhd channel to generate electricity. A reducing agent, preferably natural gas or hydrocarbon, is injected into the fuelrich product gas leaving the mhd generator; and the resulting mixture is held at a temperature in the range of 950 to 1500 0 C for about 1 second to permit the reducing agent to decompose a portion of the nitrogen oxides formed in the combustor. The fuel-rich product gas then passes thru an afterburner wherein combustion is completed and any excess reducing agent is consumed
Numerical study of MHD supersonic flow control
Ryakhovskiy, A. I.; Schmidt, A. A.
2017-11-01
Supersonic MHD flow around a blunted body with a constant external magnetic field has been simulated for a number of geometries as well as a range of the flow parameters. Solvers based on Balbas-Tadmor MHD schemes and HLLC-Roe Godunov-type method have been developed within the OpenFOAM framework. The stability of the solution varies depending on the intensity of magnetic interaction The obtained solutions show the potential of MHD flow control and provide insights into for the development of the flow control system. The analysis of the results proves the applicability of numerical schemes, that are being used in the solvers. A number of ways to improve both the mathematical model of the process and the developed solvers are proposed.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1992-01-01
Theoretical predictions were compared with available data from JET on the threshold unstable MHD activity in toroidal confinement devices. In particular, questions arising as to Hartmans number and the selection of a kinematic viscosity are discussed
Investigations of MHD activity in ASDEX discharges
International Nuclear Information System (INIS)
Stambaugh, R.; Gernhardt, J.; Klueber, O.; Wagner, F.
1984-06-01
This report makes a strong attempt to relate some specific observations of MHD activity in ADEX discharges to observations made on the Doublet III and PDX tokamaks and to theoretical work on high β MHD modes at GA and PPPL. Three topics are discussed. The first topic is the detailed analysis of the time history of MHD activity in a β discharge. The β limit discharge in ASDEX is identified as a discharge in which, during constant neutral beam power, β reaches a maximum and then decreases, often to a lower steady level if the heating pulse is long enough. During the L phase of this discharge, the MHD activity observed in the B coils is both a continuous and bursting coupled m >= 1 mode of the 'fishbone' type. When β is rising in the H phase, this mode disappears; only ELMs are present. At βsub(max), a different mode appears, the m=2, n=1 tearing mode, which grows rapidly as β decreases. The second topic is the very new observation of the fishbone-like mode in a discharge heated by combined neutral beam and ion cyclotron heating power. The mode characteristics are modulated by sawtooth oscillations in a manner consistent with the importance of q(0) in the stability of this mode. The third topic is the search for ELM precursors in discharges designed to have no other competing and complicating MHD activity. In these cases nonaxisymmetric precursors to the Hsub(α) spike were observed. Hence, it appears that an MHD mode, rather than an energy balance problem, must be the origin of the ELM. (orig./GG)
Algorithm and exploratory study of the Hall MHD Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Gardiner, Thomas Anthony
2010-01-01
This report is concerned with the influence of the Hall term on the nonlinear evolution of the Rayleigh-Taylor (RT) instability. This begins with a review of the magnetohydrodynamic (MHD) equations including the Hall term and the wave modes which are present in the system on time scales short enough that the plasma can be approximated as being stationary. In this limit one obtains what are known as the electron MHD (EMHD) equations which support two characteristic wave modes known as the whistler and Hall drift modes. Each of these modes is considered in some detail in order to draw attention to their key features. This analysis also serves to provide a background for testing the numerical algorithms used in this work. The numerical methods are briefly described and the EMHD solver is then tested for the evolution of whistler and Hall drift modes. These methods are then applied to study the nonlinear evolution of the MHD RT instability with and without the Hall term for two different configurations. The influence of the Hall term on the mixing and bubble growth rate are analyzed.
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Generalized MHD for numerical stability analysis of high-performance plasmas in tokamaks
International Nuclear Information System (INIS)
Mikhailovskii, A.B.
1998-01-01
A set of generalized magnetohydrodynamic (MHD) equations is formulated to accommodate the effects associated with high ion and electron temperatures in high-performance plasmas in tokamaks. The effects of neoclassical bootstrap current, neoclassical ion viscosity, the ion finite Larmor radius effect and electron and ion drift effects are taken into account in two-fluid MHD equations together with gyroviscosity, parallel viscosity, electron parallel inertia and collisionless ion heat flux. The ion velocity is identified as the plasma velocity, while the electron velocity is expressed in terms of the plasma velocity and electric current. Ion and electron momentum equations are combined to give the plasma momentum equation. The perpendicular (with respect to the equilibrium magnetic field) ion momentum equation is used as perpendicular Ohm's law and the parallel electron momentum equation - as parallel Ohm's law. Perpendicular Ohm's law allows for the Hall and ion drift effects. Parallel Ohm's law includes the electron drift effect, collisionless skin effect and bootstrap current. In addition, both perpendicular and parallel Ohm's laws contain the resistivity. Due to the quasineutrality condition, the ions and electrons are characterized by the same number density which is described by the ion continuity equation. On the other hand, the ion and electron temperatures are allowed to be different. The ion temperature is described by the ion energy equation allowing for the oblique heat flux, in addition to the perpendicular ion heat flux. The electron temperature is determined by the condition of high parallel electron heat conductivity. The ion and electron parallel viscosities are represented in a form valid for all the collisionality regimes (Pfirsch-Schluter, plateau, and banana). An optimized form of the generalized MHD equations is then represented in terms of the toroidal coordinate system used in the JET equilibrium and stability codes. The derived equations
MHD deceleration of fusion reaction products
International Nuclear Information System (INIS)
Chow, S.; Bohachevsky, I.O.
1979-04-01
The feasibility of magnetohydrodynamic (MHD) deceleration of fuel pellet debris ions exiting from an inertial confinement fusion (ICF) reactor cavity is investigated using one-dimensional flow equations. For engineering reasons, induction-type devices are emphasized; their performance characteristics are similar to those of electrode-type decelerators. Results of the analysis presented in this report indicate that MHD decelerators can be designed within conventional magnet technology to not only decelerate the high-energy fusion pellet debris ions but also to produce some net electric power in the process
Safety and reliability in superconducting MHD magnets
International Nuclear Information System (INIS)
Laverick, C.; Powell, J.; Hsieh, S.; Reich, M.; Botts, T.; Prodell, A.
1979-07-01
This compilation adapts studies on safety and reliability in fusion magnets to similar problems in superconducting MHD magnets. MHD base load magnet requirements have been identified from recent Francis Bitter National Laboratory reports and that of other contracts. Information relevant to this subject in recent base load magnet design reports for AVCO - Everett Research Laboratories and Magnetic Corporation of America is included together with some viewpoints from a BNL workshop on structural analysis needed for superconducting coils in magnetic fusion energy. A summary of design codes used in large bubble chamber magnet design is also included
Gravitational instability in isotropic MHD plasma waves
Cherkos, Alemayehu Mengesha
2018-04-01
The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.
MHD power station with coal gasification
International Nuclear Information System (INIS)
Brzozowski, W.S.; Dul, J.; Pudlik, W.
1976-01-01
A description is given of the proposed operating method of a MHD-power station including a complete coal gasification into lean gas with a simultaneous partial gas production for the use of outside consumers. A comparison with coal gasification methods actually being used and full capabilities of power stations heated with coal-derived gas shows distinct advantages resulting from applying the method of coal gasification with waste heat from MHD generators working within the boundaries of the thermal-electric power station. (author)
PHYSICAL PERFORMANCE AND BODY COMPOSITION IN MAINTENANCE HEMODIALYSIS (MHD PATIENTS
Directory of Open Access Journals (Sweden)
M Zhang
2012-06-01
Conclusions: These findings indicate that adult MHD pts had a higher % body fat. Measures of physical performance were markedly reduced in MHD pts as compared to Normals. Physical performance in MHD, measured especially by 6-MW, correlated negatively with some measures of body composition, particularly with LBMI.
Closed cycle MHD specialist meeting. Progress report, 1971--1972
International Nuclear Information System (INIS)
Rietjens, L.H.
1972-04-01
Abstracts of the conference papers on closed cycle MHD research are presented. The general areas of discussion are the following: results on closed cycle experiments; plasma properties, and instabilities and stabilization in nonequilibrium plasmas; loss mechanisms, current distributions, electrode effects, boundary layers, and gas dynamic effects; and design concepts of large MHD generators, and nuclear MHD power plants. (GRA)
Modeling TAE Response To Nonlinear Drives
Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin
2012-10-01
Experiment has detected the Toroidal Alfven Eigenmodes (TAE) with signals at twice the eigenfrequency.These harmonic modes arise from the second order perturbation in amplitude of the MHD equation for the linear modes that are driven the energetic particle free energy. The structure of TAE in realistic geometry can be calculated by generalizing the linear numerical solver (AEGIS package). We have have inserted all the nonlinear MHD source terms, where are quadratic in the linear amplitudes, into AEGIS code. We then invert the linear MHD equation at the second harmonic frequency. The ratio of amplitudes of the first and second harmonic terms are used to determine the internal field amplitude. The spatial structure of energy and density distribution are investigated. The results can be directly employed to compare with experiments and determine the Alfven wave amplitude in the plasma region.
International Nuclear Information System (INIS)
Shiraishi, J.; Aiba, N.; Miyato, N.; Yagi, M.
2014-01-01
Toroidal rotation effects are self-consistently taken into account not only in the linear magnetohydrodynamic (MHD) stability analysis but also in the equilibrium calculation. The MHD equilibrium computation is affected by centrifugal force due to the toroidal rotation. To study the toroidal rotation effects on resistive wall modes (RWMs), a new code has been developed. The RWMaC modules, which solve the electromagnetic dynamics in vacuum and the resistive wall, have been implemented in the MINERVA code, which solves the Frieman–Rotenberg equation that describes the linear ideal MHD dynamics in a rotating plasma. It is shown that modification of MHD equilibrium by the centrifugal force significantly reduces growth rates of RWMs with fast rotation in the order of M 2 = 0.1 where M is the Mach number. Moreover, it can open a stable window which does not exist under the assumption that the rotation affects only the linear dynamics. The rotation modifies the equilibrium pressure gradient and current density profiles, which results in the change of potential energy including rotational effects. (paper)
MHD simulation of high wavenumber ballooning-like modes in LHD
International Nuclear Information System (INIS)
Miura, H.; Nakajima, N.
2008-10-01
Dynamical growths of high-wavenumber ballooning modes are studied through full-3D nonlinear MHD simulations of the Large Helical Device. The growths of the ballooning modes are identified by studying the growth rates and the radial profiles of the Fourier coefficients of fluctuation variables. The mechanisms to weaken the growth of instability, such as the local fattening of the pressure and the energy release to the parallel kinetic energy, are found being insufficient to suppress the high-wavenumber ballooning modes. Consequently, the mean pressure profile is totally modified when the evolutions of the ballooning modes are saturated. The numerical results reveal that we need some mechanisms which do not originate from an ideal MHD to achieve a mild, saturated behaviors beyond the growths of unstable high ballooning modes in the helical device. The parallel heat conductivity is proposed as one of possible non-ideal mechanisms. (author)
International Nuclear Information System (INIS)
Gordin, V.A.
1998-01-01
First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)
Scaling Optimization of the SIESTA MHD Code
Seal, Sudip; Hirshman, Steven; Perumalla, Kalyan
2013-10-01
SIESTA is a parallel three-dimensional plasma equilibrium code capable of resolving magnetic islands at high spatial resolutions for toroidal plasmas. Originally designed to exploit small-scale parallelism, SIESTA has now been scaled to execute efficiently over several thousands of processors P. This scaling improvement was accomplished with minimal intrusion to the execution flow of the original version. First, the efficiency of the iterative solutions was improved by integrating the parallel tridiagonal block solver code BCYCLIC. Krylov-space generation in GMRES was then accelerated using a customized parallel matrix-vector multiplication algorithm. Novel parallel Hessian generation algorithms were integrated and memory access latencies were dramatically reduced through loop nest optimizations and data layout rearrangement. These optimizations sped up equilibria calculations by factors of 30-50. It is possible to compute solutions with granularity N/P near unity on extremely fine radial meshes (N > 1024 points). Grid separation in SIESTA, which manifests itself primarily in the resonant components of the pressure far from rational surfaces, is strongly suppressed by finer meshes. Large problem sizes of up to 300 K simultaneous non-linear coupled equations have been solved on the NERSC supercomputers. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.
Simulation study of MHD relaxation and reconnection processes in RFP plasma
International Nuclear Information System (INIS)
Kusano, Kanya; Kunimoto, Kaito; Suzuki, Yoshio; Tamano, Teruo; Sato, Tetsuya
1991-01-01
The authors have studied several nonlinear processes in RFP plasma through the use of 3D MHD simulations. In particular, they have shed light on: (1) dynamo and self-sustainment in reversed-field pinch (RFP), (2) phase locking process in MHD relaxation, and (3) the heating and acceleration in magnetic reconnection process. First, the contributions of the kink (m = 1) mode (linearly unstable) and of the m = 0 mode (driven by nonlinear coupling) to the dynamo are qualitatively evaluated using a high accuracy simulation. It is found that, if the free energy to drive kink instabilities is as small as that in the actual experimental plasma, the m = 0 modes, driven nonlinearly, play a more important role for the flux generation than the kink modes. Secondly, numerical simulations of the self-sustainment process in a RFP are performed. It is confirmed that the self-sustainment process is a coherent oscillating process composed of the MHD relaxation and the resistive diffusion processes. Toroidal phase locking process of kink modes is numerically observed in simulations of self-reversal and self-sustainment processes. It has characteristics similar to the slinky mode observed in the OHTE experiment. A detailed investigation reveals that nonlinear coupling between the most unstable two kink modes governs the entire dynamics in all kink modes and leads to the phase locking process. They find that reconnection can accelerate plasma over a local Alfven speed. This is a result of the fact that the magnetic field in the downstream area plays a similar role to de Laval nozzle. They also investigate the heating mechanisms in reconnection process. It is revealed that the viscous heating rate is as large as the joule heating rate in the reconnection process. This result implies that the viscous heating in the reconnection process is an important candidate for the mechanism to explain the RFP experiments where the ion temperatures is higher than the electron temperature
Risk premia in general equilibrium
DEFF Research Database (Denmark)
Posch, Olaf
This paper shows that non-linearities can generate time-varying and asymmetric risk premia over the business cycle. These (empirical) key features become relevant and asset market implications improve substantially when we allow for non-normalities in the form of rare disasters. We employ explici......'s effective risk aversion.......This paper shows that non-linearities can generate time-varying and asymmetric risk premia over the business cycle. These (empirical) key features become relevant and asset market implications improve substantially when we allow for non-normalities in the form of rare disasters. We employ explicit...... solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. We find that the curvature of the policy functions affects the risk premium through controlling the individual...
CREATE-NL+: A robust control-oriented free boundary dynamic plasma equilibrium solver
Energy Technology Data Exchange (ETDEWEB)
Albanese, R. [Ass. EURATOM/ENEA/CREATE, Universita’ di Napoli “Federico II”, Naples (Italy); Ambrosino, R. [Ass. EURATOM/ENEA/CREATE, Universita’ di Napoli “Parthenope”, Naples (Italy); Mattei, M., E-mail: massimiliano.mattei@unina2.it [Ass. EURATOM/ENEA/CREATE, Seconda Universita’ di Napoli, Naples (Italy)
2015-10-15
CREATE-NL+ is a FEM (Finite Elements Method) solver of the free boundary dynamic plasma equilibrium problem, i.e. the MHD (Magneto Hydro Dynamics) time evolution of 2D axisymmetric plasmas in toroidal nuclear fusion devices, including eddy currents in the passive structures, and feedback control laws for current, position and shape control. This is an improved version of the CREATE-NL code developed in 2002 which was validated on JET and used for the design of the XSC (eXtreme Shape Controller), and for simulation studies on many existing and future tokamaks. A significant improvement was the use of a robust numerical scheme for the calculation of the Jacobian matrix within the Newton based scheme for the solution of the FEM nonlinear algebraic equations. The improved capability of interfacing with other codes, and a general decrease of the computational burden for the simulation of long pulses with small time steps makes this code a flexible tool for the design and testing of magnetic control in a tokamak.
CREATE-NL+: A robust control-oriented free boundary dynamic plasma equilibrium solver
International Nuclear Information System (INIS)
Albanese, R.; Ambrosino, R.; Mattei, M.
2015-01-01
CREATE-NL+ is a FEM (Finite Elements Method) solver of the free boundary dynamic plasma equilibrium problem, i.e. the MHD (Magneto Hydro Dynamics) time evolution of 2D axisymmetric plasmas in toroidal nuclear fusion devices, including eddy currents in the passive structures, and feedback control laws for current, position and shape control. This is an improved version of the CREATE-NL code developed in 2002 which was validated on JET and used for the design of the XSC (eXtreme Shape Controller), and for simulation studies on many existing and future tokamaks. A significant improvement was the use of a robust numerical scheme for the calculation of the Jacobian matrix within the Newton based scheme for the solution of the FEM nonlinear algebraic equations. The improved capability of interfacing with other codes, and a general decrease of the computational burden for the simulation of long pulses with small time steps makes this code a flexible tool for the design and testing of magnetic control in a tokamak.
International Nuclear Information System (INIS)
Parkin, E. R.; Bicknell, G. V.
2013-01-01
Global three-dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when nonlinear motions—perhaps triggered by the onset of turbulence—upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure P >bar = 0.034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23-35 cells per scale height (in the vertical direction).
MHD stability of vertically asymmetric tokamak equilibria
International Nuclear Information System (INIS)
Dalhed, H.E.; Grimm, R.C.; Johnson, J.L.
1981-03-01
The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in β becomes important for reactor operation
Principal characteristics of SFC type MHD generator
International Nuclear Information System (INIS)
Kayukawa, Naoyuki; Oikawa, Shun-ichi; Aoki, Yoshiaki; Seidou, Tadashi; Okinaka, Noriyuki
1988-01-01
This paper describes the experimental and analytical results obtained for an MHD channel with a two dimensionally shaped magnetic field configuration called 'the SFC-type'. The power generating performance was examined under various load conditions and B-field intensities with a 2 MWt shock tunnel MHD facility. It is demonstrated that the power output performance and the enthalpy extraction scaling law of the conventional uniform B-field MHD generator (UFC-type) were significantly improved by the SFC-design of the spatial distribution of the magnetic field. The arcing processes were also examined by a high speed camera and the post-test observation of arc spot traces on electrodes. Further, the characteristic frequencies of each of the so-called micro and constricted arcs were clarified by spectral analyses. The critical current densities, which define the transient conditions of each from the diffuse-to micro arc, and from the micro-to constricted arc modes could be clearly obtained by the present spectral analysis method. We also investigated the three-dimensional behavior under strong magnetic field based on the coupled electrical and hydrodynamical equations for both of the middle scale SFC-and UFC-type generators. Finally, it is concluded from the above mentioned various aspects that the shaped 2-D magnetic field design will offer a most useful means for the realization of a compact, high efficiency and a long duration open-cycle MHD generator. (author)
On the stability of dissipative MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-04-01
The global stability of stationary equilibria of dissipative MHD is studied uisng the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian system with the full dissipative operators are given. The case of the two-fluid isentropic flow is discussed. (orig.)
MHD Ballooning Instability in the Plasma Sheet
International Nuclear Information System (INIS)
Cheng, C.Z.; Zaharia, S.
2003-01-01
Based on the ideal-MHD model the stability of ballooning modes is investigated by employing realistic 3D magnetospheric equilibria, in particular for the substorm growth phase. Previous MHD ballooning stability calculations making use of approximations on the plasma compressibility can give rise to erroneous conclusions. Our results show that without making approximations on the plasma compressibility the MHD ballooning modes are unstable for the entire plasma sheet where beta (sub)eq is greater than or equal to 1, and the most unstable modes are located in the strong cross-tail current sheet region in the near-Earth plasma sheet, which maps to the initial brightening location of the breakup arc in the ionosphere. However, the MHD beq threshold is too low in comparison with observations by AMPTE/CCE at X = -(8 - 9)R(sub)E, which show that a low-frequency instability is excited only when beq increases over 50. The difficulty is mitigated by considering the kinetic effects of ion gyrorad ii and trapped electron dynamics, which can greatly increase the stabilizing effects of field line tension and thus enhance the beta(sub)eq threshold [Cheng and Lui, 1998]. The consequence is to reduce the equatorial region of the unstable ballooning modes to the strong cross-tail current sheet region where the free energy associated with the plasma pressure gradient and magnetic field curvature is maximum
Model for ICRF fast wave current drive in self-consistent MHD equilibria
International Nuclear Information System (INIS)
Bonoli, P.T.; Englade, R.C.; Porkolab, M.; Fenstermacher, M.E.
1993-01-01
Recently, a model for fast wave current drive in the ion cyclotron radio frequency (ICRF) range was incorporated into the current drive and MHD equilibrium code ACCOME. The ACCOME model combines a free boundary solution of the Grad Shafranov equation with the calculation of driven currents due to neutral beam injection, lower hybrid (LH) waves, bootstrap effects, and ICRF fast waves. The equilibrium and current drive packages iterate between each other to obtain an MHD equilibrium which is consistent with the profiles of driven current density. The ICRF current drive package combines a toroidal full-wave code (FISIC) with a parameterization of the current drive efficiency obtained from an adjoint solution of the Fokker Planck equation. The electron absorption calculation in the full-wave code properly accounts for the combined effects of electron Landau damping (ELD) and transit time magnetic pumping (TTMP), assuming a Maxwellian (or bi-Maxwellian) electron distribution function. Furthermore, the current drive efficiency includes the effects of particle trapping, momentum conserving corrections to the background Fokker Planck collision operator, and toroidally induced variations in the parallel wavenumbers of the injected ICRF waves. This model has been used to carry out detailed studies of advanced physics scenarios in the proposed Tokamak Physics Experiment (TPX). Results are shown, for example, which demonstrate the possibility of achieving stable equilibria at high beta and high bootstrap current fraction in TPX. Model results are also shown for the proposed ITER device
Surface currents on the plasma-vacuum interface in MHD equilibria
Hanson, James
2017-10-01
The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the interface. While this surface current may be small in MHD equilibrium, it is readily computed in terms of the magnetic potentials in both the interior and exterior regions, evaluated on the surface. If only the external magnetic potential is known (as in VMEC), then the surface current can be computed from the discontinuity of the tangential field across the interface. Examples of the surface current for VMEC equilibria will be shown for a zero-pressure stellarator equilibrium. Field-line following of the vacuum magnetic field shows magnetic islands within the plasma region.
Equilibrium Droplets on Deformable Substrates: Equilibrium Conditions.
Koursari, Nektaria; Ahmed, Gulraiz; Starov, Victor M
2018-05-15
Equilibrium conditions of droplets on deformable substrates are investigated, and it is proven using Jacobi's sufficient condition that the obtained solutions really provide equilibrium profiles of both the droplet and the deformed support. At the equilibrium, the excess free energy of the system should have a minimum value, which means that both necessary and sufficient conditions of the minimum should be fulfilled. Only in this case, the obtained profiles provide the minimum of the excess free energy. The necessary condition of the equilibrium means that the first variation of the excess free energy should vanish, and the second variation should be positive. Unfortunately, the mentioned two conditions are not the proof that the obtained profiles correspond to the minimum of the excess free energy and they could not be. It is necessary to check whether the sufficient condition of the equilibrium (Jacobi's condition) is satisfied. To the best of our knowledge Jacobi's condition has never been verified for any already published equilibrium profiles of both the droplet and the deformable substrate. A simple model of the equilibrium droplet on the deformable substrate is considered, and it is shown that the deduced profiles of the equilibrium droplet and deformable substrate satisfy the Jacobi's condition, that is, really provide the minimum to the excess free energy of the system. To simplify calculations, a simplified linear disjoining/conjoining pressure isotherm is adopted for the calculations. It is shown that both necessary and sufficient conditions for equilibrium are satisfied. For the first time, validity of the Jacobi's condition is verified. The latter proves that the developed model really provides (i) the minimum of the excess free energy of the system droplet/deformable substrate and (ii) equilibrium profiles of both the droplet and the deformable substrate.
Parameter Estimation for a Computable General Equilibrium Model
DEFF Research Database (Denmark)
Arndt, Channing; Robinson, Sherman; Tarp, Finn
2002-01-01
We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of non-linear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...
Parameter Estimation for a Computable General Equilibrium Model
DEFF Research Database (Denmark)
Arndt, Channing; Robinson, Sherman; Tarp, Finn
We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of nonlinear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...
Numerical studies of the MHD spectrum of an elliptic plasma column
International Nuclear Information System (INIS)
Chance, M.S.; Greene, J.M.; Grimm, R.C.; Johnson, J.L.
1976-05-01
A numerical procedure is described for determining the MHD spectrum associated with small perturbations about an analytic equilibrium. This configuration has magnetic flux surfaces which are nested similar elliptical cylinders generated by a uniform axial current. Since the system is periodic, it models the essential features of a toroid. The code is used to study the properties of modes in the continuous shear Alfven and slow acoustic spectra as well as the discrete modes associated with the fast magnetosonic waves and kinks. Modes where the interchange criterion is violated, or nearly violated, are investigated
Multi-scale MHD analysis of heliotron plasma in change of background field
International Nuclear Information System (INIS)
Ichiguchi, K.; Sakakibara, S.; Ohdachi, S.; Carreras, B.A.
2012-11-01
A partial collapse observed in the Large Helical Device (LHD) experiments shifting the magnetic axis inwardly with a real time control of the background field is analyzed with a magnetohydrodynamics (MHD) numerical simulation. The simulation is carried out with a multi-scale simulation scheme. In the simulation, the equilibrium also evolves including the change of the pressure and the rotational transform due to the perturbation dynamics. The simulation result agrees with the experiments qualitatively, which shows that the mechanism is attributed to the destabilization of an infernal-like mode. The destabilization is caused by the change of the background field through the enhancement of the magnetic hill. (author)
MHD convective flow of magnetite-Fe3O4 nanoparticles by curved stretching sheet
Directory of Open Access Journals (Sweden)
Tasawar Hayat
Full Text Available Present work is devoted to convective flow of ferrofluid due to non linear stretching curved sheet. Electrically conducting fluid is considered in the presence of uniform magnetic field. Nanofluid comprises water and magnetite-Fe3O4 as nanoparticles. Thermal radiation and heat generation/absorption are explained. Homotopy concept is utilized for the development of solutions. Highly nonlinear partial differential systems are reduced into the nonlinear ordinary differential system. Impact of non-dimensional radius of curvature and power law index on the physical quantities like fluid pressure, velocity and temperature field are examined. Computations for surface shear stress and heat transfer rate also analyzed. Keywords: MHD nanofluid, Thermal radiation, Porous medium, Convective boundary conditions, Non-linear curved stretching sheet
On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion
Throumoulopoulos, George N.; Tasso, Henri
2002-11-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).
Stability calculations for MHD magnets
International Nuclear Information System (INIS)
Turner, L.R.; Wang, S.T.; Harrang, J.
1978-01-01
When a cryostable composite conductor carrying current experiences a heat input from a mechanical perturbation, a normal region develops which initially propagates and then either collapses or continues to propagate. A computer model has been devised to study this phenomenon. The model incorporates initial or continuing heat input from mechanical perturbations, heat conducted to the neighboring elements of the conductor and, if appropriate, heat conducted through insulation to neighboring turns. Heat is transferred to the helium coolant according to a specified heat transfer coefficient. If the element of conductor is in a normal or current-sharing state, resistive heating also occurs. The (unstable) equilibrium state of heat generation and conduction has been studied; results agree with those of a static calculation. The model has been validated against experimental measurements of response to heat pulses. The model suffers from uncertainties in transient heat transfer to the helium, but even more from uncertainties in the perturbing heat pulse which the magnet might be expected to suffer
The stability of Z-pinches with equilibrium flows
International Nuclear Information System (INIS)
Howell, D.F.
1999-01-01
According to Ideal Magnetohydrodynamic (MHD) theory the Z-pinch is an inherently unstable magnetic configuration. However it is possible that there exist regimes of operation whereby the predicted instabilities may be reduced or even eliminated. We must look to effects normally ignored in the Ideal MHD model in order to predict such regimes. In this thesis various non-ideal effects will be studied, namely the inclusion of equilibrium flow and finite Larmor radius effects. Astrophysical jets, for example those seen to be emitted from active galactic nuclei, are seen to persist for a greater time than suggested by Ideal MHD before the onset of instabilities. It is postulated that one of the contributing factors to this enhanced stability is the presence of a sheared axial flow. In this thesis we study the stability properties of the Z-pinch where flow is present in the equilibrium. It is found that a sheared axial flow generally has a stabilising effect, the degree of which is determined by the equilibrium and flow profiles, but that absolute stability cannot be achieved due to the onset of the Kelvin-Helmholtz instability. The effect of adding rotation has also been studied. It is found that adding rotation changes the equilibrium density profiles from the static case, and that it always has a destabilising effect. Another postulated method of stabilising the Z-pinch is by increasing the ratio of the ion Larmor radius to the pinch radius, and it is seen to have a stabilising effect for some equilibria in the collisionless regime. In this thesis we study the effects of increasing the Larmor radius in the collisional regime using the Hall fluid model. It is found that for free boundary modes the stability properties are unchanged for experimentally realistic values of the Larmor radius, but for fixed boundary modes a small stabilising effect is noted for some equilibria. (author)
Observation of SOL Current Correlated with MHD Activity in NBI-heated DIII-D Tokamak Discharges
International Nuclear Information System (INIS)
Takahashi, H.; Fredrickson, E.D.; Schaffer, M.J.; Austin, M.E.; Evans, T.E.; Lao, L.L.; Watkins, J.G.
2004-01-01
This work investigates the potential roles played by the scrape-off-layer current (SOLC) in MHD activity of tokamak plasmas, including effects on stability. SOLCs are found during MHD activity that are: (1) slowly growing after a mode-locking-like event, (2) oscillating in the several kHz range and phase-locked with magnetic and electron temperature oscillations, (3) rapidly growing with a sub-ms time scale during a thermal collapse and a current quench, and (4) spiky in temporal behavior and correlated with spiky features in Da signals commonly identified with the edge localized mode (ELM). These SOLCs are found to be an integral part of the MHD activity, with a propensity to flow in a toroidally non-axisymmetric pattern and with magnitude potentially large enough to play a role in the MHD stability. Candidate mechanisms that can drive these SOLCs are identified: (a) toroidally non-axisymmetric thermoelectric potential, (b) electromotive force (EMF) from MHD activity, and (c) flux swing, both toroidal and poloidal, of the plasma column. An effect is found, stemming from the shear in the field line pitch angle, that mitigates the efficacy of a toroidally non-axisymmetric SOLC to generate a toroidally non-axisymmetric error field. Other potential magnetic consequences of the SOLC are identified: (i) its error field can introduce complications in feedback control schemes for stabilizing MHD activity and (ii) its toroidally non-axisymmetric field can be falsely identified as an axisymmetric field by the tokamak control logic and in equilibrium reconstruction. The radial profile of a SOLC observed during a quiescent discharge period is determined, and found to possess polarity reversals as a function of radial distance
Ion exchange equilibrium constants
Marcus, Y
2013-01-01
Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and
Some effects of MHD activity on impurity transport in the PBX tokamak
International Nuclear Information System (INIS)
Ida, K.; Fonck, R.J.; Hulse, R.A.; LeBlanc, B.
1985-10-01
The effects of MHD activity on intrinsic impurity transport are studied in ohmic discharges of the Princeton Beta Experiment (PBX) by measuring of the Z/sub eff/ profile from visible bremsstrahlung radiation and the spectral line intensities from ultraviolet spectroscopy. A diffusive/convective transport model, including an internal disruption model, is used to simulate the data. The Z/sub eff/ profile with no MHD activity is fitted with a strong inward convection, characterized by a peaking parameter c/sub v/ (= -a 2 v/2rD) = 11 (3.5, +4.5). At the onset of MHD activity (a large m = 1 n = 1 oscillation followed by sawteeth), this strongly peaked profile is flattened and subsequently reaches a new quasi-equilibrium shape. This profile is characterized by reduced convection [c/sub v/ = 3.6 (-1.1, +1.6), D = 1.4 (-0.7, +5.6) x 10 4 cm 2 /s], in addition to the particle redistribution which accompanies the sawtooth internal disruptions. 10 figs
Quantity Constrained General Equilibrium
Babenko, R.; Talman, A.J.J.
2006-01-01
In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values.In case of price restrictions a general equilibrium may not exist and rationing on net demands or supplies is needed to clear the markets.In
A study on the fusion reactor - Development of MHD stability and transport code for KT-2 tokamak
Energy Technology Data Exchange (ETDEWEB)
Lee, Jae Koo; Shin, Kyo Jin [Pohang University of Science and Tecnology, Pohang (Korea, Republic of)
1996-08-01
MHD Stability analyses for KT-2 Tokamak were carried out by using CART (Resistive 3-D) Code. Linear Growth rates and linear perturbed eigen function of both N=0 axisymmetric mode and N=1 kink modes of highly elongated tokamak plasmas, in the presence of a conducting wall at various distances are computed and linear and nonlinear evolution of N=0 axisymmetric modes are simulated. 26 refs., 25 figs. (author)
Equilibrium of high beta plasma in closed magnetic line system (MBT)
International Nuclear Information System (INIS)
Gesso, H.; Shiina, S.; Saito, K.; Nogi, Y.; Osaniai, Y.; Yoshimura, H.; Todoroki, J.; Hamada, S.; Nihon Univ., Tokyo. Atomic Energy Research Inst.)
1985-01-01
The beta effects on the plasma equilibrium in Modified Bumpy Torus (MBT) sector, which is an asymmetric closed line system with l = 0 and fairly large l = +- 1 field distortions, are studied. For this purpose, the equilibrium of high beta plasma produced by theta-pinch is compared with that of betaless plasma numerically calculated from the measured magnetic field profiles in device. The equilibrium condition depends weakly on beta value, but the plasma cross-section is vertically elongated as the beta value increases. The m = 1 long wavelength MHD instability is not observed during the observation time of approx. 15 μs. These experimental results are compared with MHD theory based on the new ordering taking the finiteness of l = +- 1 field distortion (deltasub(+-1) > or approx. 1) into account, which suggests significant stabilizing effects due to self formation of magnetic well and also due to the conducting wall. (author)
Neoclassical MHD equilibria with ohmic current
International Nuclear Information System (INIS)
Tokuda, Shinji; Takeda, Tatsuoki; Okamoto, Masao.
1989-01-01
MHD equilibria of tokamak plasmas with neoclassical current effects (neoclassical conductivity and bootstrap current) were calculated self-consistently. Neoclassical effects on JFT-2M tokamak plasmas, sustained by ohmic currents, were studied. Bootstrap currents flow little for L-mode type equilibria because of low attainable values of poloidal beta, β J . H-mode type equilibria give bootstrap currents of 30% ohmic currents for β J attained by JFT-2M and 100% for β J ≥ 1.5, both of which are sufficient to change the current profiles and the resultant MHD equilibria. Neoclassical conductivity which has roughly half value of the classical Spitzer conductivity brings peaked ohmic current profiles to yield low safety factor at the magnetic axis. Neoclassical conductivity reduces the value of effective Z(Z eff ) which is necessary to give the observed one-turn voltage but it needs impurities accumulating at the center when such peaked current profiles are not observed. (author)
Regular shock refraction in planar ideal MHD
International Nuclear Information System (INIS)
Delmont, P; Keppens, R
2010-01-01
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest, in planar ideal (magneto)hydrodynamics. In the hydrodynamical case, 3 signals arise and the interface becomes Richtmyer-Meshkov unstable due to vorticity deposition on the shocked contact. In the magnetohydrodynamical case, on the other hand, when the normal component of the magnetic field does not vanish, 5 signals will arise. The interface then typically remains stable, since the Rankine-Hugoniot jump conditions in ideal MHD do not allow for vorticity deposition on a contact discontinuity. We present an exact Riemann solver based solution strategy to describe the initial self similar refraction phase. Using grid-adaptive MHD simulations, we show that after reflection from the top wall, the interface remains stable.
Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif
2018-06-01
The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.
Energy Technology Data Exchange (ETDEWEB)
Berk, Herbert L.
2018-02-15
The study of this project focused on developing a reduced nonlinear model to describe chirping processes in a fusion plasma. A successful method was developed with results clear enough to allow an analytic theory to be developed that replicates the long term response of a nonlinear phase space structure immersed in the MHD continnuum.
Impulsive relaxation process in MHD driven reconnection
International Nuclear Information System (INIS)
Kitabata, H.; Hayashi, T.; Sato, T.
1997-01-01
Compressible magnetohydrodynamic (MHD) simulation is carried out in order to investigate energy relaxation process of the driven magnetic reconnection in an open finite system through a long time calculation. It is found that a very impulsive energy release occurs in an intermittent fashion through magnetic reconnection for a continuous magnetic flux injection on the boundary. We focus our attention on the detailed process in the impulsive phase, which is the reconnection rate is remarkably enhanced up. (author)
MHD simulations on an unstructured mesh
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.
1998-01-01
Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D
Hopes for commercial use of MHD
International Nuclear Information System (INIS)
1968-01-01
Magnetohydrodynamics (MHD) is the study of the motion of fluids and gases in magnetic fields. After 25 years of theoretical and experimental work, it seems commercially promising for a new type of power station, where heat would be converted directly into electricity by generators without moving parts. Nuclear reactors would be well suited as the heat sources. At an Agency symposium in Warsaw in July it was felt that international cooperation is essential to develop the technique for industrial use. (author)
MHD instability studies in ISX-B
International Nuclear Information System (INIS)
Pare, V.K.; Dunlap, J.L.; Navarro, A.P.; Burris, R.D.
1979-01-01
MHD instabilities in Ohmically and beam heated ISX-B plasmas have been studied using collimated x-ray and Mirnov loop diagnostics. The diagnostic systems will be described and the instability signals will be illustrated for a variety of discharges. The latter will include those observed in connection with low and high β operation, density clamping, pellet injection, and deliberate introduction of toroidal field ripple
Status report on the Indian MHD programme
International Nuclear Information System (INIS)
Ambasankaran, C.
1978-03-01
MHD programme in India, which has been started recently as a collaborative effort by the Bhabha Atomic Research Centre and Bharat Heavy Electricals Ltd., with the technical consultation provided by the High Temperature Institute, Moscow, is described. The basic considerations which led to the launching of this project and the details of the experimental plant for R and D work are spelt out. (K.B.)
Statistical Theory of the Ideal MHD Geodynamo
Shebalin, J. V.
2012-01-01
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the
Directory of Open Access Journals (Sweden)
M. Jayachandra Babu
2017-12-01
Full Text Available The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate. Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newtonâs methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration are conversed (in three cases. By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate. Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. Keywords: MHD, Cattaneo-Christov heat flux, Thermal relaxation, Thermophoresis, Brownian motion
Energetic particle effects on global MHD modes
International Nuclear Information System (INIS)
Cheng, C.Z.
1990-01-01
The effects of energetic particles on MHD type modes are studied by analytical theories and the nonvariational kinetic-MHD stability code (NOVA-K). In particular we address the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ''fishbone'' internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral-beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n=1 internal kink mode in the hot particle beat space exists even in the absence of core ion finite Larmor radius effect (finite ω *i ). On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 23 refs., 5 figs
Magnetohydrodynamic (MHD) simulation of solar prominence formation
International Nuclear Information System (INIS)
Bao, J.
1987-01-01
Formation of Kippenhahn-Schluter type solar prominences by chromospheric mass injection is studied via numerical simulation. The numerical model is based on a two-dimensional, time-dependent magnetohydrodynamic (MHD) theory. In addition, an analysis of gravitational thermal MHD instabilities related to condensation is performed by using the small-perturbation method. The conclusions are: (1) Both quiescent and active-region prominences can be formed by chromospheric mass injection, provided certain optimum conditions are satisfied. (2) Quiescent prominences cannot be formed without condensation, though enough mass is supplied from chromosphere. The mass of a quiescent prominence is composed of both the mass injected from the chromosphere and the mass condensed from the corona. On the other hand, condensation is not important to active region prominence formation. (3) In addition to channeling and supporting effects, the magnetic field plays another important role, i.e. containing the prominence material. (4) In the model cases, prominences are supported by the Lorentz force, the gas-pressure gradient and the mass-injection momentum. (5) Due to gravity, more MHD condensation instability modes appear in addition to the basic condensation mode
Sensitivity of ITER MHD global stability to edge pressure gradients
International Nuclear Information System (INIS)
Hogan, J.T.; Martynov, A.
1994-01-01
In view of the preliminary nature of boundary models for reactor tokamaks, the sensitivity to edge gradients of the global mode MHD stability of the ITER EDA configuration has been examined. The POLAR-2D equilibrium and TORUS stability codes developed by the Keldysh Institute have been used. Transport-related profiles from the PRETOR transport code (developed by the ITER Joint Central Team) and axisymmetric equilibria for these profiles from the TEQ code (L.D. Pearlstein, LLNL) were taken as a starting point for the study. These baseline profiles are found to have quite high global stability limits, in the range g(Troyon) = 4-5. The major focus of this study is to examine global mode stability assuming small variations about the baseline profiles, changing the pressure gradients near the boundary. Such changes can be expected with an improved boundary model. Reduced stability limits are found in such cases, and unstable cases with g = 2-3 are found. Thus, the assumption of ITER stability limits higher than g = 2 must be treated with caution
Stability of ideal MHD configurations. I. Realizing the generality of the G operator
Keppens, R.; Demaerel, T.
2016-12-01
A field theoretical approach, applied to the time-reversible system described by the ideal magnetohydrodynamic (MHD) equations, exposes the full generality of MHD spectral theory. MHD spectral theory, which classified waves and instabilities of static or stationary, usually axisymmetric or translationally symmetric configurations, actually governs the stability of flowing, (self-)gravitating, single fluid descriptions of nonlinear, time-dependent idealized plasmas, and this at any time during their nonlinear evolution. At the core of this theory is a self-adjoint operator G , discovered by Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] in its application to stationary (i.e., time-independent) plasma states. This Frieman-Rotenberg operator dictates the acceleration identified by a Lagrangian displacement field ξ , which connects two ideal MHD states in four-dimensional space-time that share initial conditions for density, entropy, and magnetic field. The governing equation reads /d 2 ξ d t 2 = G [ ξ ] , as first noted by Cotsaftis and Newcomb [Nucl. Fusion, Suppl. Part 2, 447 and 451 (1962)]. The time derivatives at left are to be taken in the Lagrangian way, i.e., moving with the flow v. Physically realizable displacements must have finite energy, corresponding to being square integrable in the Hilbert space of displacements equipped with an inner product rule, for which the G operator is self-adjoint. The acceleration in the left-hand side features the Doppler-Coriolis operator v . ∇ , which is known to become an antisymmetric operator when restricting attention to stationary equilibria. Here, we present all derivations needed to get to these insights and connect results throughout the literature. A first illustration elucidates what can happen when self-gravity is incorporated and presents aspects that have been overlooked even in simple uniform media. Ideal MHD flows, as well as Euler flows, have essentially 6 + 1 wave types, where the 6 wave modes
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2017-04-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
MHD power generation for the synthetic-fuels industry
International Nuclear Information System (INIS)
Jones, M.S. Jr.
1982-01-01
The integration of open cycle MHD with various processes for the recovery of hydrocarbons for heavy oil deposits, oil sands, and oil shales are examined along with its use in producing medium Btu gas, synthetic natural gas and solvent refined coal. The major features of the MHD cycle which are of interest are: (a) the ability to produce hydrogen through the shift reaction by introducing H 2 O into the substoichiometric combustion product flow exiting the MHD diffuser, (b) the use of high temperature waste heat in the MHD exhaust, and (c) the ability of the seed in the MHD flow to remove sulfur from the combustion products. Therefore the use of the MHD cycle allows coal to be used in an environmentally acceptable manner in place of hydrocarbons which are now used to produce process heat and hydrogen. The appropriate plant sizes are in the range of 25 to 50 MWe and the required MHD generator enthalpy extraction efficiencies are low. Sale of electricity produced, over and above that used in the process, can provide a revenue stream which can improve the economics of the hydrocarbon processing. This, coupled with the replacement of coal for hydrocarbons in certain phases of the process, should improve the overall economics, while not requiring a high level of performance by the MHD components. Therefore, this area should be an early target of opportunity for the commercialization of MHD
MHD power plants - a reality of the 80's
International Nuclear Information System (INIS)
Pishchikov, S.
1981-01-01
A 300 MW MHD generator and a conventional turbogenerator of the same capacity will be used for the first MHD power block assembly projected in the USSR. The power plant's own consumption will not exceed 12% and the availability will be approximately 50%. Compared with a conventional power generating unit of a capacity of 500 MW the projected unit will provide fuel savings of at least 23%. The project is based on almost seven years long experience with the U-25 experimental MHD facility. Similar to the U-25, the MHD power plant projected will be fired with natural gas. (B.S.)
MHD power plants - a reality of the 80's
Energy Technology Data Exchange (ETDEWEB)
Pishchikov, S
1981-02-01
A 300 MW MHD generator and a conventional turbogenerator of the same capacity will be used for the first MHD power block assembly projected in the USSR. The power plant's own consumption will not exceed 12% and the availability will be approximately 50%. Compared with a conventional power generating unit of a capacity of 500 MW the projected unit will provide fuel savings of at least 23%. The project is based on almost seven years long experience with the U-25 experimental MHD facility. Similar to the U-25, the MHD power plant projected will be fired with natural gas.
Investigation of physico-chemical processes in hypervelocity MHD-gas acceleration wind tunnels
International Nuclear Information System (INIS)
Alfyorov, V.I.; Dmitriev, L.M.; Yegorov, B.V.; Markachev, Yu.E.
1995-01-01
The calculation results for nonequilibrium physicochemical processes in the circuit of the hypersonic MHD-gas acceleration wind tunnel are presented. The flow in the primary nozzle is shown to be in thermodynamic equilibrium at To=3400 K, Po=(2∼3)x10 5 Pa, M=2 used in the plenum chamber. Variations in the static pressure due to oxidation reaction of Na, K are pointed out. The channels of energy transfer from the electric field to different degrees of freedom of an accelerated gas with Na, K seeds are considered. The calculation procedure for gas dynamic and kinetic processes in the MHD-channel using measured parameters is suggested. The calculated results are compared with the data obtained in a thermodynamic gas equilibrium assumption. The flow in the secondary nozzle is calculated under the same assumptions and the gas parameters at its exit are evaluated. Particular attention is given to the influence of seeds on flows over bodies. It is shown that the seeds exert a very small influence on the flow behind a normal shock wave. The seeds behind an oblique shock wave accelerate deactivation of vibrations of N 2 , but this effect is insignificant
Discharges in the inlet region of a noble gas MHD generator
International Nuclear Information System (INIS)
Borghi, C.A.
1982-01-01
In this work the onset of the development of the non-equilibrium conductivity in the entrance region of a noble gas MHD generator is investigated both theoretically and experimentally. At low electron densities the discharge seems to be affected by a non-Maxwellian electron distribution. In Chapter II a self-consistent model of a stationary discharge in an Ar-Cs mixture at atmospheric pressure, is set up. It includes the possibility of deviations from a Maxwellian electron energy distribution. The model allows to calculate at what discharge parameters deviations from the Maxwellian electron distribution will become important. In Chapter III the relaxation of the plasma to a new equilibrium situation following a sudden change in the electron thermal energy is calculated by a model which can take radiation and a non-Maxwellian distribution into account. In Chapter IV an Ar-Cs discharge experiment is described with plasma parameters similar to those present in the entrance region of the generator. The ionization relaxation process in a noble gas MHD generator is experimentally studied and described in Chapter V. In this chapter the relaxation ionization region with and without pre-ionization is investigated. Current voltage characteristics are obtained by varying the applied voltage or the external load. The results are confronted with the theoretical results of the non-Maxwellian model developed in Chapter II. Conclusions of this work are drawn in Chapter VI. (Auth.)
Extended MHD Turbulence and Its Applications to the Solar Wind
Abdelhamid, Hamdi M.; Lingam, Manasvi; Mahajan, Swadesh M.
2016-10-01
Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k\\lt 1/{λ }I), Hall (1/{λ }I\\lt k\\lt 1/{λ }e), and electron inertia (k\\gt 1/{λ }e) regimes; k is the wavenumber and {λ }s=c/{ω }{ps} is the skin depth of species “s.” In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of -11/3 and -13/3 are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately -4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard “dissipation” range paradigm.
Brignole, Esteban Alberto
2013-01-01
Traditionally, the teaching of phase equilibria emphasizes the relationships between the thermodynamic variables of each phase in equilibrium rather than its engineering applications. This book changes the focus from the use of thermodynamics relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. Phase Equilibrium Engineering presents a systematic study and application of phase equilibrium tools to the development of chemical processes. The thermodynamic modeling of mixtures for process development, synthesis, simulation, design and
International Nuclear Information System (INIS)
Balter, H.S.
1994-01-01
This work studies the behaviour of radionuclides when it produce a desintegration activity,decay and the isotopes stable creation. It gives definitions about the equilibrium between activity of parent and activity of the daughter, radioactive decay,isotope stable and transient equilibrium and maxim activity time. Some considerations had been given to generators that permit a disgregation of two radioisotopes in equilibrium and its good performance. Tabs
Equilibrium state of colliding electron beams
Directory of Open Access Journals (Sweden)
R. L. Warnock
2003-10-01
Full Text Available We study a nonlinear integral equation that is a necessary condition on the equilibrium phase-space distribution function of stored, colliding electron beams. It is analogous to the Haïssinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in 1 degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove the existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, as would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.
MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!
Goedbloed, J. P.
2018-01-01
The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an 'intuitive' description based on the energy principle that is very misleading for
MHD limits in non-inductive tokamak plasmas: simulations and comparison to experiments on Tore Supra
International Nuclear Information System (INIS)
Maget, P.; Huysmans, G.; Ottaviani, M.; Garbet, X.; Moreau, Ph.; Segui, J.-L.; Luetjens, H.
2008-01-01
Non-inductive tokamak discharges with a flat or hollow current profile are prone to the triggering of large tearing modes when the minimum of the safety factor is just below a low order rational. This issue is of particular importance for discussing the optimal safety factor for MHD modes avoidance in Steady-State reactor plasmas. Different non-linear regimes of such magnetic configurations in Tore Supra are studied using the full MHD code XTOR. Numerical simulations show that the non-linear stage of the Double-Tearing Mode (DTM) is governed by the full reconnection model, but a single tearing mode in a low magnetic shear configuration can have a similar impact on the confinement. The different regimes observed experimentally are recovered in the simulations: a small amplitude (2,1) DTM for close resonant surfaces as seen in Tore Supra, a sawtooth-like behaviour of the (2,1) Double-Tearing Mode as first seen in TFTR, or a large amplitude (2,1) tearing mode that severely degrades the energy confinement, as reported in Tore Supra, JET or DIII-D. Situations where q min ≅1.5 with a stable n = 1 mode, as seen in Tore Supra longest discharges, seem to put specific constraints on the MHD model that is used. Indeed, curvature stabilisation without transport terms as could explain linear stability, but such effect vanishes in presence of heat transport. Electron diamagnetic rotation effect is investigated as a possible mechanism for n = 1 mode stabilization.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect
Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.
2017-09-01
This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.
Subsonic Constant-Area MHD Generator Experiments with the CNEN Blow-Down Loop Facility
Energy Technology Data Exchange (ETDEWEB)
Bertolini, E.; Gasparotto, M.; Gay, P.; Toschi, R. [Laboratorio Conversione Diretta, CNEN, Frascati (Italy)
1968-11-15
The design of the facility, described at the Salzburg Symposium, was somewhat modified following the results of the commissioning tests; the changes were mainly concerned with the thermal insulation, duct materials and caesium recovery system. The facility went into full operation in March 1967 and since then two series of MHD experiments, a total of twenty-six runs, have been performed. During the MHD runs the facility has been working mostly under the following operating conditions: stagnation temperature 1500 to 1800 Degree-Sign K; stagnation pressure-1 to 3 atm. abs.; mass How 50 to 150 g/sec; seeding 2 to 5 at.%- ; magnetic field 0 to 45 k G; Mach number 0.4 to 0.8; Hall parameter up to 6. The main purpose of the experiments was to study the performance of relatively small generators (cross-section 3 x 5 cm{sup 2}, length 8-20 cm) both when the non-equilibrium ionization is expected to be negligible and when it should be, in a very idealized model, relevant. As a first step, efforts were made to ascertain whether any of the unsatisfactory results reported in Salzburg, both for equilibrium and non-equilibrium generators, stemmed not from the basic functioning principle of an MHD small-scale generator but rather from some inadequacy of the experimental apparatus. Therefore particular attention was paid to: ceasium vaporization and mixing with helium; plasma insulation from ground; electrical insulation from ground and from each other of those electrically conductive parts of the facility which may, during the functioning, come into contact with the plasma; temperature control of the duct; purity level; duct materials; measurement system and control. In the equilibrium regime the Faraday field measured is very close to the ideal value and it reaches 80 V/cm (400 volts between electrodes); the Hall field still remains below the ideal value uB{beta}L (50% at {beta} = 3). The maximum Hall field was about 35 V/cm for a corresponding voltage of 600 V. Preionization
MHD dynamo action in space plasmas
International Nuclear Information System (INIS)
Faelthammar, C.G.
1984-05-01
Electric currents are now recognized to play a major role in the physical process of the Earths magnetosphere as well as in distant astrophysical plasmas. In driving these currents MHD dynamos as well as generators of a thermoelectric nature are important. The primary source of power for the Earths magnetospheric process is the solar wind, which supplies a voltage of the order of 200 kV across the magnetosphere. The direction of the large-scale solar wind electric field varies of many different time scales. The power input to the magnetosphere is closely correlated with the direction of the large-scale solar wind electric field in such a fashion as to mimick the response of a half-wave rectifier with a down-to-dusk conduction direction. Behind this apparently simple response there are complex plasma physical processes that are still very incompletely understood. They are intimately related to auroras, magnetic storms, radiation belts and changes in magnetospheric plasma populations. Similar dynamo actions should occur at other planets having magnetospheres. Recent observations seem to indicate that part of the power input to the Earths magnetosphere comes through MHD dynamo action of a forced plasma flow inside the flanks of the magnetopause and may play a role in other parts of the magnetosphere, too. An example of a cosmical MHD connected to a solid load is the corotating plasma of Jupiters inner magnetosphere, sweeping past the plants inner satelites. In particular the electric currents thereby driven to and from the satellite Io have attracted considerable interest.(author)
Annular MHD Physics for Turbojet Energy Bypass
Schneider, Steven J.
2011-01-01
The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).
Phase Coherence of Large Amplitude MHD Waves in the Earth's Foreshock: Geotail Observations
International Nuclear Information System (INIS)
Hada, Tohru; Koga, Daiki; Yamamoto, Eiko
2003-01-01
Large amplitude MHD turbulence is commonly found in the earth's foreshock region. It can be represented as a superposition of Fourier modes with characteristic frequency, amplitude, and phase. Nonlinear interactions between the Fourier modes are likely to produce finite correlation among the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in quasi-linear theories) or they have a finite coherence. However, naive inspection of wave phases does not reveal anything, as the wave phase is sensitively related to the choice of origin of the coordinate, which should be arbitrary. Using a method based on a surrogate data technique and a fractal analysis, we analyzed Geotail magnetic field data to evaluate the phase coherence among the MHD waves in the earth's foreshock region. We show that the correlation of wave phases does exist, indicating that the nonlinear interactions between the waves is in progress. Furthermore, by introducing an index to represent the degree of the phase coherence, we discuss that the wave phases become more coherent as the turbulence amplitude increases, and also as the propagation angle of the most dominant wave mode becomes oblique. Details of the analysis as well as implications of the present results to transport processes of energetic particles will be discussed
MHD simulations of molybdenum X-pinches
International Nuclear Information System (INIS)
Ivanenkov, G.V.; Stepnevski, V.
2002-01-01
One investigates into compression of molybdenum X-pinches applying numerical MHD-models with parabolic and conical initial geometry. The second model describing plasma axial motion in greater detail offers a real geometry of a discharge and is applicable to loads characterized by higher masses in contrast to the first one. Both models enabled to describe all basic phases of compression including origination of a minidiode, occurrence of a narrow neck, microexplosion of a hot point and origination of shock waves followed by sausage instability [ru
MHD oxidant intermediate temperature ceramic heater study
Carlson, A. W.; Chait, I. L.; Saari, D. P.; Marksberry, C. L.
1981-09-01
The use of three types of directly fired ceramic heaters for preheating oxygen enriched air to an intermediate temperature of 1144K was investigated. The three types of ceramic heaters are: (1) a fixed bed, periodic flow ceramic brick regenerative heater; (2) a ceramic pebble regenerative heater. The heater design, performance and operating characteristics under conditions in which the particulate matter is not solidified are evaluated. A comparison and overall evaluation of the three types of ceramic heaters and temperature range determination at which the particulate matter in the MHD exhaust gas is estimated to be a dry powder are presented.
MHD power conversion employing liquid metals
International Nuclear Information System (INIS)
Houben, J.W.M.A.; Massee, P.
1969-02-01
The work performed in the field of MHD generation of electricity by means of liquid metals is described. It is shown that the study of two-phase flows is essential in this topic of research; two-phase flows are therefore described. Two types of generators which can be utilized with liquid metals have been studied. The results of this study are described. A short survey of the prospects of other liquid metal systems which emerge from a study of the literature is given. Finally, conclusions are drawn concerning possibilities for further investigation
Kleppe, J.; Borm, P.E.M.; Hendrickx, R.L.P.
2008-01-01
Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up
International Nuclear Information System (INIS)
Huysmans, G.
1998-03-01
One of the aims of the JET, the Joint European Torus, project is to optimise the maximum fusion performance as measured by the neutron rate. At present, two different scenarios are developed at JET to achieve the high performance the so-called Hot-Ion H-mode scenario and the more recent development of the Optimised Shear scenario. Both scenarios have reached similar values of the neutron rate in Deuterium plasmas, up to 5 10 17 neutrons/second. Both scenarios are characterised by a transport barrier, i.e., a region in the plasma where the confinement is improved. The Hot-Ion H-mode has a transport barrier at the plasma boundary just inside the separatrix, an Optimised Shear plasma exhibits a transport barrier at about mid radius. Associated with the improved confinement of the transport barriers are locally large pressure gradients. It is these pressure gradients which, either directly or indirectly, can drive MHD instabilities. The instabilities limit the maximum performance. In the optimised shear scenario a global MHD instability leads to a disruptive end of the discharge. In the Hot-Ion H-mode plasmas, so-called Outer Modes can occur which are localised at the plasma boundary and lead to a saturation of the plasma performance. In this paper, two examples of the MHD instabilities are discussed and identified by comparing the experimentally observed modes with theoretical calculations from the ideal MHD code MISHKA-1. Also, the MHD stability boundaries of the two scenarios are presented. Section 3 contains a discussion of the mode observed just before the disruption
Technical support for open-cycle MHD program
Energy Technology Data Exchange (ETDEWEB)
None
1978-05-01
The support program for open-cycle MHD at Argonne National Lab is developing the analytical tools needed to investigate the performance of the major components in the combined-cycle MHD/steam power system. The analytical effort is centered on the primary components of the system that are unique to MHD and also on the integration of these analytical representations into a model of the entire power producing system. The present project activities include modeling of the combustor, MHD channel, slag separator, and the high-temperature air preheater. In addition, these models are combined into a complete system model, which is at present capable of carrying out optimizations of the entire system on either thermodynamic efficiency or with less confidence, cost of electrical power. Also, in support of the open-cycle program, considerable effort has gone into the formulation of a CDIF Test Plan and a National MHD Test Program.
Priority pollutant analysis of MHD-derived combustion products
Parks, Katherine D.
An important factor in developing Magnetohydrodynamics (MHD) for commercial applications is environmental impact. Consequently, an effort was initiated to identify and quantify any possible undesirable minute chemical constituents in MHD waste streams, with special emphasis on the priority pollutant species. This paper discusses how priority pollutant analyses were used to accomplish the following goals at the University of Tennessee Space Institute (UTSI): comparison of the composition of solid combustion products collected from various locations along a prototypical MHD flow train during the firing of Illinois No. 6 and Montana Rosebud coals; comparison of solid waste products generated from MHD and conventional power plant technologies; and identification of a suitable disposal option for various MHD derived combustion products. Results from our ongoing research plans for gas phase sampling and analysis of priority pollutant volatiles, semi-volatiles, and metals are discussed.
Preliminary results of MHD stability in HL-1 tokamak
International Nuclear Information System (INIS)
Zheng Yongzhen; Ma Tengcai; Xiao Zhenggui Cai Renfang
1987-01-01
In this paper, MHD activities of HL-1 tokamak plasma are studied with Fourier transform and correlatio analysis. The poloidal modes m = 1, 2, 3,4 and toroidal modes n of MHD magnetic fluctuation signals are detected. Methods for suppressing MHD instabilities are suggested and tested, after MHD instabilities are studied in HL-1. The effects of MHD characteristics in the beginning stage of discharge on the whole process of discharge are analyzed. The disruption, in HL-1 device could be divided into three kinds: internal disruption, minor disruption and major disruption. The result shows that HL-1 will have a better operation condition if internal disruption appears. In is end, the stable operation region of HL-1 tokamak is also given
Energy Technology Data Exchange (ETDEWEB)
NONE
1970-07-01
Compiled are the results of studies conducted in fiscal 1970 on MHD (magnetohydrodynamic) power generation. In the operation test and modification of the 1000kW-class MHD power generator, modification is carried out involving the combustion system, seed collecting method, and power generation channel, and reviews through experiments are conducted about the analysis and control of the boundary layer structure. In the operation test of the MHD power generator designed for prolonged operation, a test operation for resistance to heat and seeds continues more than 100 hours using a cold wall type power generation channel constituted of water cooled ceramics, and the ceramics are analyzed for failure and loss. Studies are also conducted involving MHD power generator heat exchangers, seed collecting methods, electrode materials for MHD power generators, heat-resistant materials for MHD power generators, thermal performance rating for MHD power plants, etc. In the research and development of superconductive electromagnets, superconductive electromagnets are developed and tested for 1000kW-class MHD power generators, and studies are conducted on turbine type helium liquefiers, superinsulated superconductive electromagnetic field generators, etc. (NEDO)
Vlahos, Loukas; Archontis, Vasilis; Isliker, Heinz
We consider 3D nonlinear MHD simulations of an emerging flux tube, from the convection zone into the corona, focusing on the coronal part of the simulations. We first analyze the statistical nature and spatial structure of the electric field, calculating histograms and making use of iso-contour visualizations. Then test-particle simulations are performed for electrons, in order to study heating and acceleration phenomena, as well as to determine HXR emission. This study is done by comparatively exploring quiet, turbulent explosive, and mildly explosive phases of the MHD simulations. Also, the importance of collisional and relativistic effects is assessed, and the role of the integration time is investigated. Particular aim of this project is to verify the quasi- linear assumptions made in standard transport models, and to identify possible transport effects that cannot be captured with the latter. In order to determine the relation of our results to Fermi acceleration and Fokker-Planck modeling, we determine the standard transport coefficients. After all, we find that the electric field of the MHD simulations must be downscaled in order to prevent an un-physically high degree of acceleration, and the value chosen for the scale factor strongly affects the results. In different MHD time-instances we find heating to take place, and acceleration that depends on the level of MHD turbulence. Also, acceleration appears to be a transient phenomenon, there is a kind of saturation effect, and the parallel dynamics clearly dominate the energetics. The HXR spectra are not yet really compatible with observations, we have though to further explore the scaling of the electric field and the integration times used.
Equilibrium and non equilibrium in fragmentation
International Nuclear Information System (INIS)
Dorso, C.O.; Chernomoretz, A.; Lopez, J.A.
2001-01-01
Full text: In this communication we present recent results regarding the interplay of equilibrium and non equilibrium in the process of fragmentation of excited finite Lennard Jones drops. Because the general features of such a potential resemble the ones of the nuclear interaction (fact that is reinforced by the similarity between the EOS of both systems) these studies are not only relevant from a fundamental point of view but also shed light on the problem of nuclear multifragmentation. We focus on the microscopic analysis of the state of the fragmenting system at fragmentation time. We show that the Caloric Curve (i e. the functional relationship between the temperature of the system and the excitation energy) is of the type rise plateau with no vapor branch. The usual rise plateau rise pattern is only recovered when equilibrium is artificially imposed. This result puts a serious question on the validity of the freeze out hypothesis. This feature is independent of the dimensionality or excitation mechanism. Moreover we explore the behavior of magnitudes which can help us determine the degree of the assumed phase transition. It is found that no clear cut criteria is presently available. (Author)
Is Current Account of Turkey Sustainable ? Evidence from Nonlinear Unit Root Tests
Directory of Open Access Journals (Sweden)
Serkan Taştan
2015-09-01
Full Text Available In this paper, current account sustainability of Turkey is analyzed in a nonlinear framework. Various nonlinear unit root tests have been used to test for structural break, sign and size nonlinearity. We have tested structural break and size nonlinearity separately and structural break-sign and size-sign nonlinearities simultaneously. Only considering the size nonlinearity, we have found that the current account of Turkey is sustainable. Thus, the size nonlinearity, in other words the speed of reversion to equilibrium, is essential for the current account sustainability of Turkey. We have also found that the speed of adjustment towards equilibrium is symmetric, while considering size and sign nonlinearities simultaneously.
Chemical Principles Revisited: Chemical Equilibrium.
Mickey, Charles D.
1980-01-01
Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)
Equilibrium and non-equilibrium phenomena in arcs and torches
Mullen, van der J.J.A.M.
2000-01-01
A general treatment of non-equilibrium plasma aspects is obtained by relating transport fluxes to equilibrium restoring processes in so-called disturbed Bilateral Relations. The (non) equilibrium stage of a small microwave induced plasma serves as case study.
International Nuclear Information System (INIS)
Krebs, Isabel
2017-01-01
kept from decreasing below unity by flux pumping. A detailed analysis of this flux pumping mechanism is presented, and it is discussed under which conditions the mechanism is able to sustain itself. This includes a linear stability analysis of an equilibrium with low central magnetic shear and a central q∼1. Furthermore, a step towards more realistic simulations of Hybrid discharges has been made by performing 3D nonlinear MHD simulations based on ASDEX Upgrade geometry in which some features of the current ramp-up phase in realistic Hybrid discharges are imitated. Although in the framework of single-fluid MHD and with the used parameters it is not expected that all features of realistic sawtooth cycles are reproduced, the reconnection events obtained in the simulations share some of their characteristics and two interesting phenomena are found for specific sets of parameters. First, in some cases, the reconnection process during these sawtooth-like events does not complete but stops and reverses. And second, in one case the sawtooth-like reconnection events are separated by quiescent phases showing similar characteristics as the sawtooth-free stationary states.
Energy Technology Data Exchange (ETDEWEB)
Krebs, Isabel
2017-08-08
kept from decreasing below unity by flux pumping. A detailed analysis of this flux pumping mechanism is presented, and it is discussed under which conditions the mechanism is able to sustain itself. This includes a linear stability analysis of an equilibrium with low central magnetic shear and a central q∼1. Furthermore, a step towards more realistic simulations of Hybrid discharges has been made by performing 3D nonlinear MHD simulations based on ASDEX Upgrade geometry in which some features of the current ramp-up phase in realistic Hybrid discharges are imitated. Although in the framework of single-fluid MHD and with the used parameters it is not expected that all features of realistic sawtooth cycles are reproduced, the reconnection events obtained in the simulations share some of their characteristics and two interesting phenomena are found for specific sets of parameters. First, in some cases, the reconnection process during these sawtooth-like events does not complete but stops and reverses. And second, in one case the sawtooth-like reconnection events are separated by quiescent phases showing similar characteristics as the sawtooth-free stationary states.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
Comparison of two-dimensional and three-dimensional MHD equilibrium and stability codes
International Nuclear Information System (INIS)
Herrnegger, F.; Merkel, P.; Johnson, J.L.
1986-02-01
Stability results obtained with the fully three-dimensional magnetohydrodynamic code BETA, the helically invariant code HERA, and the asymptotic stellarator expansion code STEP agree well for a straight l = 2, M = 5 stellarator model. This good agreement between the BETA and STEP codes persists as toroidal curvature is introduced. This validation provides justification for confidence in work with these models. 20 refs., 11 figs
Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems
International Nuclear Information System (INIS)
Meyer-Spasche, R.
1975-12-01
It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de
Finite-β stabilization of a diffuse helical l = MHD equilibrium
International Nuclear Information System (INIS)
Herrnegger, F.; Nuehrenberg, J.
1975-04-01
The stability of helically symmetric finite-β, l = 1 magnetohydrostatic equilibria with arbitrary pressure profile and vanishing longitudinal current is investigated by means of Mercier's criterion, a sufficient criterion by Lortz, Rebhan and Spies, and Shafranov's condition for a high-β magnetic well. The new finite-β effects are that 1) a magnetic well is created throughout the plasma region for 0.2 approximately [de
Economic comparison of MHD equilibrium options for advanced steady state tokamak power plants
International Nuclear Information System (INIS)
Ehst, D.A.; Kessel, C.E.; Jardin, S.C.; Krakowski, R.A.; Bathke, C.G.; Mau, T.K.; Najmabadi, F.
1998-01-01
Progress in theory and in tokamak experiments leads to questions of the optimal development path for commercial tokamak power plants. The economic prospects of future designs are compared for several tokamak operating modes: (high poloidal beta) first stability, second stability and reverse shear. Using a simplified economic model and selecting uniform engineering performance parameters, this comparison emphasizes the different physics characteristics - stability and non- inductive current drive - of the various equilibria. The reverse shear mode of operation is shown to offer the lowest cost of electricity for future power plants. (author)
Partial chemical equilibrium in fluid dynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.
1980-01-01
An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates omega-dot/sub s/ for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the omega-dot/sub s/ are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions with transport equations for the basic components of which these species are composed. The second system retains the usual species transport equations, but eliminates the nonlinear algebraic equilibrium constraint conditions by deriving an explicit expression for the omega-dot/sub s/. Both systems are specialized to the case of an ideal gas mixture. Considerations involved in solving these equation systems numerically are discussed briefly
MHD stability limits in the TCV Tokamak
International Nuclear Information System (INIS)
Reimerdes, H.
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 κ and triangularity δ, with high κ, and low δ 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 observed decrease
DIAGNOSIS OF FINANCIAL EQUILIBRIUM
Directory of Open Access Journals (Sweden)
SUCIU GHEORGHE
2013-04-01
Full Text Available The analysis based on the balance sheet tries to identify the state of equilibrium (disequilibrium that exists in a company. The easiest way to determine the state of equilibrium is by looking at the balance sheet and at the information it offers. Because in the balance sheet there are elements that do not reflect their real value, the one established on the market, they must be readjusted, and those elements which are not related to the ordinary operating activities must be eliminated. The diagnosis of financial equilibrium takes into account 2 components: financing sources (ownership equity, loaned, temporarily attracted. An efficient financial equilibrium must respect 2 fundamental requirements: permanent sources represented by ownership equity and loans for more than 1 year should finance permanent needs, and temporary resources should finance the operating cycle.
Equilibrium statistical mechanics
Mayer, J E
1968-01-01
The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t
Computing Equilibrium Chemical Compositions
Mcbride, Bonnie J.; Gordon, Sanford
1995-01-01
Chemical Equilibrium With Transport Properties, 1993 (CET93) computer program provides data on chemical-equilibrium compositions. Aids calculation of thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93/PC is version of CET93 specifically designed to run within 640K memory limit of MS-DOS operating system. CET93/PC written in FORTRAN.
MHD generator performance analysis for the Advanced Power Train study
Pian, C. C. P.; Hals, F. A.
1984-01-01
Comparative analyses of different MHD power train designs for early commercial MHD power plants were performed for plant sizes of 200, 500, and 1000 MWe. The work was conducted as part of the first phase of a planned three-phase program to formulate an MHD Advanced Power Train development program. This paper presents the results of the MHD generator design and part-load analyses. All of the MHD generator designs were based on burning of coal with oxygen-enriched air preheated to 1200 F. Sensitivities of the MHD generator design performance to variations in power plant size, coal type, oxygen enrichment level, combustor heat loss, channel length, and Mach number were investigated. Basd on these sensitivity analyses, together with the overall plant performance and cost-of-electricity analyses, as well as reliability and maintenance considerations, a recommended MHD generator design was selected for each of the three power plants. The generators for the 200 MWe and 500 MWe power plant sizes are supersonic designs. A subsonic generator design was selected for the 1000 MWe plant. Off-design analyses of part-load operation of the supersonic channel selected for the 200 MWe power plant were also conductd. The results showed that a relatively high overall net plant efficiency can be maintained during part-laod operation with a supersonic generator design.
Measurement of nonlinear mode coupling of tearing fluctuations
International Nuclear Information System (INIS)
Assadi, S.; Prager, S.C.; Sidikman, K.L.
1992-03-01
Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum
Energy Technology Data Exchange (ETDEWEB)
Blackburn, P E
1977-12-01
Fortran IV computer codes have been written to calculate the equilibrium partial pressures of the gaseous phase and the quantity and composition of the condensed phases in the open-cycle MHD system. The codes are based on temperature-dependent equilibrium constants, mass conservation, the mass action law, and assumed ideal solution of compounds in each of two condensed phases. It is assumed that the phases are an oxide-silicate phase and a sulfate-carbonate-hydroxide phase. Calculations are iterated for gas and condensate concentrations while increasing or decreasing the total moles of elements, but keeping mole ratios constant, to achieve the desired total pressure. During iteration the oxygen partial pressure is incrementally changed. The decision to increase or decrease the oxygen pressure in this process depends on comparison of the oxygen content calculated in the gas and condensate phases with the initial amount of oxygen in the ash, coal, seed, and air. This process, together with a normalization step, allows the elements to converge to their initial quantities. Two versions of the computer code have been written. GASCON calculates the equilibrium gas partial pressures and the quantity and composition of the condensed phases in steps of thirteen temperature and pressure combinations in which the condensate is removed after each step, simulating continuous slag removal from the MHD system. MHDGAS retains the condensate for each step, simulating flow of condensate (and gas) through the MHD system.
Energy Technology Data Exchange (ETDEWEB)
None
1979-01-01
Progress is reported on the following tasks: characterization of coal for open-cycle MHD power generation systems; compressive creep and strength studies of MHD preheater materials; preparation of coals for utilization in direct coal-fired MHD generation; characterization of volatile matter in coal; MHD materials evaluation; operability of the Moderate Temperature Slag Flow Facility; slag-seed equilibria and separations related to the MHD system; thermionic emission of coal and electrode materials; MHD instrumentation, consolidated inversion simulator, and data acquisition; combined MHD-steam plant cycle analysis and control; and slag physical properties - electrical and thermal conductivity. (WHK)
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Mechanism of power generation - the MHD way
International Nuclear Information System (INIS)
Rangachari, S.; Ramash, V.R.; Subramanian, C.K.
1975-01-01
The basic physical principles of magnetohydrodynamics and the application of this principle for power generation (direct energy conversion) are explained. A magnetohydrodynamic generator (MHDG) is described both in the Faraday and Hall modes. The advantages of the Faraday mode and the Hall mode for different geometries of the generator are mentioned. The conductor used is a fluid - an ionised gas (plasma) or a liquid metal at high temperature. The difficulties in maintaining high temperature and high velocity for the gas and very low temperature at the same time side by side for superconducting magnets to produce a strong magnetic field, are pointed out. The most commonly used gas is purified air. The advantages of MHD generators and the present power crisis have compelled further research in this field in spite of the high costs involved. (A.K.)
MHD simulation of the Bastille day event
Energy Technology Data Exchange (ETDEWEB)
Linker, Jon, E-mail: linkerj@predsci.com; Torok, Tibor; Downs, Cooper; Lionello, Roberto; Titov, Viacheslav; Caplan, Ronald M.; Mikić, Zoran; Riley, Pete [Predictive Science Inc., 9990 Mesa Rim Road, Suite 170, San Diego CA, USA 92121 (United States)
2016-03-25
We describe a time-dependent, thermodynamic, three-dimensional MHD simulation of the July 14, 2000 coronal mass ejection (CME) and flare. The simulation starts with a background corona developed using an MDI-derived magnetic map for the boundary condition. Flux ropes using the modified Titov-Demoulin (TDm) model are used to energize the pre-event active region, which is then destabilized by photospheric flows that cancel flux near the polarity inversion line. More than 10{sup 33} ergs are impulsively released in the simulated eruption, driving a CME at 1500 km/s, close to the observed speed of 1700km/s. The post-flare emission in the simulation is morphologically similar to the observed post-flare loops. The resulting flux rope that propagates to 1 AU is similar in character to the flux rope observed at 1 AU, but the simulated ICME center passes 15° north of Earth.
The Biermann catastrophe of numerical MHD
Graziani, C.; Tzeferacos, P.; Lee, D.; Lamb, D. Q.; Weide, K.; Fatenejad, M.; Miller, J.
2016-05-01
The Biermann Battery effect is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Unfortunately, direct implementation of the Biermann effect in MHD codes is known to produce unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this convergence breakdown is due to naive discretization, which fails to account for the fact that discretized irrotational vector fields have spurious solenoidal components that grow without bound near a discontinuity. We show that careful consideration of the kinetics of ion viscous shocks leads to a formulation of the Biermann effect that gives rise to a convergent algorithm. We note a novel physical effect a resistive magnetic precursor in which Biermann-generated field in the shock “leaks” resistively upstream. The effect appears to be potentially observable in experiments at laser facilities.
Two dimensional MHD flows between porous boundaries
International Nuclear Information System (INIS)
Gratton, F.T.
1994-01-01
Similarity solutions of dissipative MHD equations representing conducting fluids injected through porous walls and flowing out in both directions from the center of the channel, are studied as a function of four non dimensional parameters, Reynolds number R e , magnetic Reynolds number R m , Alfvenic Mach number, M A , and pressure gradient coefficient, C. The effluence is restrained by an external magnetic field normal to the walls. When R m m >>1, the solution may model a collision of plasmas of astrophysical interest. In this case the magnetic field lines help to drive the outflow acting jointly with the pressure gradient. The law for C as a function of the other parameters is given for several asymptotic limits. (author). 3 refs, 6 figs
International Nuclear Information System (INIS)
Berger, D.; Bernard, L.C.; Gruber, R.; Troyon, F.
1980-01-01
The Lausanne ideal MHD stability code ERATO is used to investigate spectral properties of Solovev's equilibrium at small aspect ratios. Two different elongations are considered. Both free and rigid boundary models are computed and compared. Modes characterized by a large radial extension have been found which appear to be due to coupling of m=1 and m=2 modes due to toricity. The internal modes spectrum is compared with the predictions of the full Mercier criterion, taking into account its spatial dependence, and with the ballooning modes stability criterion. (Auth.)
The Stellar IMF from Isothermal MHD Turbulence
Haugbølle, Troels; Padoan, Paolo; Nordlund, Åke
2018-02-01
We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 M ⊙ and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfvén velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.
Resonant MHD modes with toroidal coupling
International Nuclear Information System (INIS)
Connor, J.W.; Hastie, R.J.; Taylor, J.B.
1990-07-01
This is part 2 of a study of resonant perturbations, such as resistive tearing and ballooning modes, in a torus. These are described by marginal ideal mhd equations in the regions between resonant surfaces; matching across these surfaces provides the dispersion relation. In part 1 we described how all the necessary information from the ideal mhd calculations could be represented by a so-called E-matrix. We also described the calculation of this E-matrix for tearing modes (even parity in perturbed magnetic field) in a large aspect ratio torus. There the toroidal modes comprise coupled cylinder tearing modes and the E-matrix is a generalization of the familiar Δ' quantity in a cylinder. In the present paper we discuss resistive ballooning, or twisting-modes, which have odd-parity in perturbed magnetic field. We show that, unlike the tearing modes, these odd-parity modes are instrinsically toroidal and are not directly related to the odd-parity modes in a cylinder. This is evident from the analysis of the high-n limit in ballooning-space, where a transition from a stable Δ' to an unstable Δ' occurs for the twisting mode when the ballooning effect exceeds the interchange effect, which can occur even at large aspect ratio (as in a tokamak). Analysis of the high-n limit in coordinate space, rather than ballooning space, clarifies this singular behaviour and indicates how one may define twisting-mode Δ'. It also yields a prescription for treating low-n twisting modes and a method for calculating an E-matrix for resistive ballooning modes in a large aspect ratio tokamak. The elements of this matrix are given in terms of cylindrical tearing mode solutions
Energy Technology Data Exchange (ETDEWEB)
NONE
1980-03-01
Examination was conducted in detail on an MHD generation system by coal combustion, with the results reported. Concerning a gas table calculation program in coal combustion, it was prepared assuming 100% slag removal ratio in the combustor as the primary approximation. A combustor for MHD generation needs to efficiently burn fuel using high temperature pre-heated air as the oxidant, to fully dissociate/electrolytically dissociate seed, and to supply to the generation channel a high speed combustion gas plasma having a high electrical conductivity which is required for MHD generation. This year, an examination was conducted on technological problems in burning coal in an MHD combustor. As for the NOx elimination system in an MHD generation plant, an examination was made if the method studied so far in MHD generation using heavy oil as the fuel is applicable to coal. Also investigated and reviewed were various characteristics, change in physical properties, recovery method, etc., in a mixed state of seed and slag in the case of coal combustion MHD. (NEDO)
Energy Technology Data Exchange (ETDEWEB)
NONE
1969-07-01
Compiled are the results of studies conducted in fiscal 1969 on MHD (magnetohydrodynamic) power generation. In the operation test and modification of the 1,000kW-class MHD power generator, the operation test continues from the preceding fiscal year using high-temperature air as oxidant, and the growth of boundary layer in the channel is determined. In the operation test of the MHD power generator designed for prolonged operation, insulation walls, electrode materials, and structures capable of prolonged operation are developed and tested. In the research of MHD power generator heat exchangers, studies are made about the bulkhead type and heat accumulator types (stationary type, rotary type, and falling-grain type). In addition, studies are conducted about seed collecting methods, MHD power generator electrode materials, heat-resisting insulators, and thermal performance rating. In the research and development of superconductive electromagnets, studies are conducted about superconductive electromagnets for 1kW MHD power generators, ferromagnetic superconductive electromagnets for 1,000kW-class MHD power generators, 45-kilogauss col type superconductive electromagnets, turbine type helium liquefier, high current density col type superconductive electromagnets, superinsulated magnetic field generators, etc. (NEDO)
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
Alpha-Driven MHD and MHD-Induced Alpha Loss in TFTR DT Experiments
Chang, Zuoyang
1996-11-01
Theoretical calculation and numerical simulation indicate that there can be interesting interactions between alpha particles and MHD activity which can adversely affect the performance of a tokamak reactor (e.g., ITER). These interactions include alpha-driven MHD, like the toroidicity-induced-Alfven-eigenmode (TAE) and MHD induced alpha particle losses or redistribution. Both phenomena have been observed in recent TFTR DT experiments. Weak alpha-driven TAE activity was observed in a NBI-heated DT experiment characterized by high q0 ( >= 2) and low core magnetic shear. The TAE mode appears at ~30-100 ms after the neutral beam turning off approximately as predicted by theory. The mode has an amplitude measured by magnetic coils at the edge tildeB_p ~1 mG, frequency ~150-190 kHz and toroidal mode number ~2-3. It lasts only ~ 30-70 ms and has been seen only in DT discharges with fusion power level about 1.5-2.0 MW. Numerical calculation using NOVA-K code shows that this type of plasma has a big TAE gap. The calculated TAE frequency and mode number are close to the observation. (2) KBM-induced alpha particle loss^1. In some high-β, high fusion power DT experiments, enhanced alpha particle losses were observed to be correlated to the high frequency MHD modes with f ~100-200 kHz (the TAE frequency would be two-times higher) and n ~5-10. These modes are localized around the peak plasma pressure gradient and have ballooning characteristics. Alpha loss increases by 30-100% during the modes. Particle orbit simulations show the added loss results from wave-particle resonance. Linear instability analysis indicates that the plasma is unstable to the kinetic MHD ballooning modes (KBM) driven primarily by strong local pressure gradients. ----------------- ^1Z. Chang, et al, Phys. Rev. Lett. 76 (1996) 1071. In collaberation with R. Nazikian, G.-Y. Fu, S. Batha, R. Budny, L. Chen, D. Darrow, E. Fredrickson, R. Majeski, D. Mansfield, K. McGuire, G. Rewoldt, G. Taylor, R. White, K
Influence of hot beam ions on MHD ballooning modes in tokamaks
International Nuclear Information System (INIS)
Rewoldt, G.; Tang, W.M.
1984-07-01
It has recently been proposed that the presence of high energy ions from neutral beam injection can have a strong stabilizing effect on kinetically-modified ideal MHD ballooning modes in tokamaks. In order to assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a new beam-driven mode is found to occur with a growth rate comparable in magnitude to the growth rate of the MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions
Particle orbits and non-ideal MHD stability of Z-pinches
International Nuclear Information System (INIS)
Faghihi, M.
1987-01-01
Particle orbits in a linear EXTRAP vacuum magnetic field configuration are computed. The results indicate that, with an applied electric field along the axis, the particles starting near the magnetic stagnation line would gain substantial energy in the 'free fall', and are the most efficient ones to participate in the ionization process. The acquired energy depends on the electric field strength; the required value of the field is determined. The influence of the pressure anisotropy on the small wavelength internal kink (m=1) mode instability in a Z-pinch, using a generalization of Freidbergs perpendicular MHD model, is investigated. It is found that the stability criterion can not be fulfilled without violation of the fire hose stability condition. This investigation is also performed using the double-adiabatic theory. A finite Larmor radius treatment of the small wavelength kink instabilities for a Z-pinch geometry is presented. It is shown that, when the gyroviscosity is included in the perpendicular MHD model, exponentially growing Alfven waves are predicted even in a homogeneous static equilibrium with isotropic plasma pressure. The Hall effect in the incompressible Hall fluid model is considered. It is found that the Hall parameter reduces the growth rates of the kink modes, but it does not yield complete stabilization (author)
Particle orbits and non-ideal MHD stability of Z-pinches
Energy Technology Data Exchange (ETDEWEB)
Faghihi, M.
1987-01-01
Particle orbits in a linear EXTRAP vacuum magnetic field configuration are computed. The results indicate that, with an applied electric field along the axis, the particles starting near the magnetic stagnation line would gain substantial energy in the 'free fall', and are the most efficient ones to participate in the ionization process. The acquired energy depends on the electric field strength; the required value of the field is determined. The influence of the pressure anisotropy on the small wavelength internal kink (m=1) mode instability in a Z-pinch, using a generalization of Freidbergs perpendicular MHD model, is investigated. It is found that the stability criterion can not be fulfilled without violation of the fire hose stability condition. This investigation is also performed using the double-adiabatic theory. A finite Larmor radius treatment of the small wavelength kink instabilities for a Z-pinch geometry is presented. It is shown that, when the gyroviscosity is included in the perpendicular MHD model, exponentially growing Alfven waves are predicted even in a homogeneous static equilibrium with isotropic plasma pressure. The Hall effect in the incompressible Hall fluid model is considered. It is found that the Hall parameter reduces the growth rates of the kink modes, but it does not yield complete stabilization
Influence of hot beam ions on MHD ballooning modes in tokamaks
International Nuclear Information System (INIS)
Rewoldt, G.; Tang, W.M.
1984-01-01
It has recently been proposed that the presence of high-energy ions from neutral-beam injection can have a strong stabilizing effect on kinetically modified ideal-MHD ballooning modes in tokamaks. To assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a different, beam-driven root of the mode equations is found to occur with a growth rate comparable in magnitude to the growth rate of the usual MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions. (author)
Dependence of ideal MHD kink and ballooning modes on plasma shape and profiles in tokamaks
International Nuclear Information System (INIS)
Todd, A.M.M.; Manickam, J.; Okabayashi, M.; Chance, M.S.; Grimm, R.C.; Greene, J.M.; Johnson, J.L.
1978-08-01
Extensive numerical studies of ideal MHD instabilities have been carried out to gain insight into the parametric dependence of critical β's in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate for both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that for aspect ratio R/a approximately equal to 3, critical β's are of the order of 2% for circular cross sections and 5% for plasmas with elongation K approximately equal to 2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical β as a function of toroidal mode number n. We conclude that the infinite-n analytic ballooning theory provides a sufficient condition for ideal MHD internal mode stability. Low-n free boundary modes appear to set a lower limit
Equilibrium and nonequilibrium solvation and solute electronic structure
International Nuclear Information System (INIS)
Kim, H.J.; Hynes, J.T.
1990-01-01
When a molecular solute is immersed in a polar and polarizable solvent, the electronic wave function of the solute system is altered compared to its vacuum value; the solute electronic structure is thus solvent-dependent. Further, the wave function will be altered depending upon whether the polarization of the solvent is or is not in equilibrium with the solute charge distribution. More precisely, while the solvent electronic polarization should be in equilibrium with the solute electronic wave function, the much more sluggish solvent orientational polarization need not be. We call this last situation non-equilibrium solvation. We outline a nonlinear Schroedinger equation approach to these issues
Spectroscopic measurement of the MHD dynamo in the MST reversed field pinch
Energy Technology Data Exchange (ETDEWEB)
Chapman, James Tharp [Univ. of Wisconsin, Madison, WI (United States)
1998-09-01
The author has directly observed the coupling of ion velocity fluctuations and magnetic field fluctuations to produce an MHD dynamo electric field in the interior of the MST reversed field pinch. Chord averaged ion velocity fluctuations were measured with a fast spectroscopic diagnostic which collects line radiation from intrinsic carbon impurities simultaneously along two lines of sight. The chords employed for the measurements resolved long wavelength velocity fluctuations of several km/s at 8-20 kHz as tiny, fast Doppler shifts in the emitted line profile. During discrete dynamo events the velocity fluctuations, like the magnetic fluctuations, increase dramatically. The toroidal and poloidal chords with impact parameters of 0.3 a and 0.6 a respectively, resolved fluctuation wavenumbers with resonance surfaces near or along the lines of sight indicating a radial velocity fluctuation width for each mode which spans only a fraction of the plasma radius. The phase between the measured toroidal velocity fluctuations and the magnetic fluctuations matches the predictions of resistive MHD while the poloidal velocity fluctuations exhibit a phase consistent with the superposition of MHD effects and the advection of a mean flow gradient past the poloidal line of sight. Radial velocity fluctuations resolved by a chord through the center of the plasma were small compared to the poloidal and toroidal fluctuations and exhibited low coherence with the magnetic fluctuations. The ensembled nonlinear product of the ion velocity fluctuations and fluctuations in the magnetic field indicates a substantial dynamo electric field which peaks during the periods of spontaneous flux generation.
Spectroscopic measurement of the MHD dynamo in the MST reversed field pinch
International Nuclear Information System (INIS)
Chapman, J.T.
1998-09-01
The author has directly observed the coupling of ion velocity fluctuations and magnetic field fluctuations to produce an MHD dynamo electric field in the interior of the MST reversed field pinch. Chord averaged ion velocity fluctuations were measured with a fast spectroscopic diagnostic which collects line radiation from intrinsic carbon impurities simultaneously along two lines of sight. The chords employed for the measurements resolved long wavelength velocity fluctuations of several km/s at 8--20 kHz as tiny, fast Doppler shifts in the emitted line profile. During discrete dynamo events the velocity fluctuations, like the magnetic fluctuations, increase dramatically. The toroidal and poloidal chords with impact parameters of 0.3 a and 0.6 a respectively, resolved fluctuation wavenumbers with resonance surfaces near or along the lines of sight indicating a radial velocity fluctuation width for each mode which spans only a fraction of the plasma radius. The phase between the measured toroidal velocity fluctuations and the magnetic fluctuations matches the predictions of resistive MHD while the poloidal velocity fluctuations exhibit a phase consistent with the superposition of MHD effects and the advection of a mean flow gradient past the poloidal line of sight. Radial velocity fluctuations resolved by a chord through the center of the plasma were small compared to the poloidal and toroidal fluctuations and exhibited low coherence with the magnetic fluctuations. The ensembled nonlinear product of the ion velocity fluctuations and fluctuations in the magnetic field indicates a substantial dynamo electric field which peaks during the periods of spontaneous flux generation
Energy Technology Data Exchange (ETDEWEB)
NONE
1990-07-01
Experimental disk MHD facilities are predesigned, and commercial-scale (1,000 MWt) MHD/steam systems are investigated. The predesigns of the disk MHD facilities indicate that enthalpy extraction is 8.7% for a 10 MWt open cycle MHD generator, and increases to 37% for a 5 MWt closed cycle MHD generator. Commercial (1,000 MWt) MHD/steam systems are studied for 4 types. Of these types, the open cycle disk MHD generator shows the lowest efficiency of 42.8%, while the closed cycle disk MHD generator the highest efficiency of 50.0%. The open cycle linear generator, although showing an efficiency of 49.4%, may be the lowest-cost type, when the necessary heat source, heat exchangers and the like are taken into consideration. For the design of superconducting magnet, it is necessary to further investigate whether the one for the test facility is applicable to the commercial systems. (NEDO)
Modeling of LH current drive in self-consistent elongated tokamak MHD equilibria
International Nuclear Information System (INIS)
Blackfield, D.T.; Devoto, R.S.; Fenstermacher, M.E.; Bonoli, P.T.; Porkolab, M.; Yugo, J.
1989-01-01
Calculations of non-inductive current drive typically have been used with model MHD equilibria which are independently generated from an assumed toroidal current profile or from a fit to an experiment. Such a method can lead to serious errors since the driven current can dramatically alter the equilibrium and changes in the equilibrium B-fields can dramatically alter the current drive. The latter effect is quite pronounced in LH current drive where the ray trajectories are sensitive to the local values of the magnetic shear and the density gradient. In order to overcome these problems, we have modified a LH simulation code to accommodate elongated plasmas with numerically generated equilibria. The new LH module has been added to the ACCOME code which solves for current drive by neutral beams, electric fields, and bootstrap effects in a self-consistent 2-D equilibrium. We briefly describe the model in the next section and then present results of a study of LH current drive in ITER. 2 refs., 6 figs., 2 tabs
International Nuclear Information System (INIS)
Kelleher, W.P.; Steiner, D.
1989-01-01
A personal-computer (PC)-based calculational approach assesses magnetohydrodynamic (MHD) equilibrium and poloidal field (PF) coil arrangement in a highly interactive mode, well suited for tokamak scoping studies. The system developed involves a two-step process: the MHD equilibrium is calculated and then a PF coil arrangement, consistent with the equilibrium is determined in an interactive design environment. In this paper the approach is used to examine four distinctly different toroidal configurations: the STARFIRE rector, a spherical torus (ST), the Big Dee, and an elongated tokamak. In these applications the PC-based results are benchmarked against those of a mainframe code for STARFIRE, ST, and Big Dee. The equilibrium and PF coil arrangement calculations obtained with the PC approach agree within a few percent with those obtained with the mainframe code
Mapping Isobaric Aging onto the Equilibrium Phase Diagram.
Niss, Kristine
2017-09-15
The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case-challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single structural parameter, referred to as an effective temperature.
Mapping Isobaric Aging onto the Equilibrium Phase Diagram
DEFF Research Database (Denmark)
Niss, Kristine
2017-01-01
The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts...... of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case—challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium...... states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single...
Conversion software for ANSYS APDL 2 FLUENT MHD magnetic file
International Nuclear Information System (INIS)
Ghita, G.; Ionescu, S.; Prisecaru, I.
2016-01-01
The present paper describes the improvements made to the conversion software for ANSYS APDL 2 FLUENT MHD Magnetic File which is able to extract the data from ANSYS APDL file and write down a file containing the magnetic field data in FLUENT magneto hydro dynamics (MHD) format. The MHD module has some features for the uniform and non uniform magnetic field but it is limited for sinusoidal or pulsed, square wave, having a fixed duty cycle of 50%. The present software, ANSYS APDL 2 FLUENT MHD Magnetic File, suffered major modifications in comparison with the last one. The most important improvement consists in a new graphical interface, which has 3D graphical interface for the input file but also for the output file. Another improvement has been made for processing time, the new version is two times faster comparing with the old one. (authors)
Numerical Simulation of 3D Viscous MHD Flows
National Research Council Canada - National Science Library
Golovachov, Yurii P; Kurakin, Yurii A; Schmidt, Alexander A; Van Wie, David M
2003-01-01
.... Flows in hypersonic intakes are considered. Preliminary results showed that local MHD interaction in the inlet part of the intake model was the most effective for control over plasma flow field...
Diagnostic development and support of MHD (magnetohydrodynamics) test facilities
Energy Technology Data Exchange (ETDEWEB)
1989-07-01
Mississippi State University (MSU) is developing diagnostic instruments for Magnetohydrodynamics (MHD) power train data acquisition and for support of MHD component development test facilities. Microprocessor-controlled optical instruments, initially developed for HRSR support, are being refined, and new systems to measure temperatures and gas-seed-slag stream characteristics are being developed. To further data acquisition and analysis capabilities, the diagnostic systems are being interfaced with MHD Energy Center computers. Technical support for the diagnostic needs of the national MHD research effort is being provided. MSU personnel will also cooperate with government agencies and private industries to improve the transformation of research and development results into processes, products and services applicable to their needs.
Unsteady MHD free convective flow past a vertical porous plate ...
African Journals Online (AJOL)
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International Journal of Engineering, Science and Technology .... dimensional MHD boundary layer on the body with time varying temperature. ... flow of an electrically conducting fluid past an infinite vertical porous flat plate coinciding with.
Generalized similarity method in unsteady two-dimensional MHD ...
African Journals Online (AJOL)
user
International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.
Combined effects of radiation and chemical reaction on MHD flow ...
African Journals Online (AJOL)
(2016) have studied unsteady MHD flow in porous media over exponentially accelerated plate ... boundary layer flow of heat and mass transfer over a moving vertical plate with suction. ... flow considering free convection over a porous plate.
Todo, Y.; Berk, H. L.; Breizman, B. N.
2012-03-01
A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δBm/n/B ~ 5 × 10-3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δBm/n/B ~ 2 × 10-3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.
Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas
International Nuclear Information System (INIS)
Shen Yong; Dong Jiaqi; He Hongda; Turnbull, A. D.
2009-01-01
Magnetohydrodynamic (MHD) n = 1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q 0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of β c N = 2.56 for a typical HL-2A discharge with a plasma current I p = 0.245 MA, and the scaling of β c N ∼constant is confirmed. (magnetically confined plasma)
Eberl, Gérard
2016-08-01
The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.
Kuiroukidis, Ap.; Throumoulopoulos, G. N.
2015-08-01
We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).
Electrode materials for an open-cycle MHD generator channel
International Nuclear Information System (INIS)
Telegin, G.P.; Romanov, A.I.; Akopov, F.A.; Gokhshtejn, Ya.P.; Rekov, A.I.
1983-01-01
The results of investigations, technological developments and tests of high temperature materials for MHD electrodes on the base of zirconium dioxide, stabilized with oxides of calcium, yttrium, neodymium, and dioxide of cerium, chromites, tamping masses from stabilized dioxide of zirconium, cermets are considered. It is established that binary and ternary solutions on the base of zirconium dioxide and alloyed chromites are the perspective materials for the MHD electrodes on pure fuel
Equilibrium shoreface profiles
DEFF Research Database (Denmark)
Aagaard, Troels; Hughes, Michael G
2017-01-01
Large-scale coastal behaviour models use the shoreface profile of equilibrium as a fundamental morphological unit that is translated in space to simulate coastal response to, for example, sea level oscillations and variability in sediment supply. Despite a longstanding focus on the shoreface...... profile and its relevance to predicting coastal response to changing environmental conditions, the processes and dynamics involved in shoreface equilibrium are still not fully understood. Here, we apply a process-based empirical sediment transport model, combined with morphodynamic principles to provide......; there is no tuning or calibration and computation times are short. It is therefore easily implemented with repeated iterations to manage uncertainty....
Badia, Santiago; Martín, Alberto F.; Planas, Ramon
2014-10-01
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
A review on application of MHD theory to plasma boundary problems in tokamaks
International Nuclear Information System (INIS)
Itoh, Kimitaka.
1992-08-01
A survey is made on the problems of the edge plasmas, to which the analyses based on the MHD theory have been successfully applied. Also discussed are the efforts to extend the model equation to more general (and important as well) problems such as H-mode physics. An overview is first made on the advantages of the MHD picture, and the necessary supplementary physics are examined. Next, one- and two-dimensional models of the spatial structure of the edge plasma is discussed. The results on the stationary structure, both analytical and numerical, are reviewed: Typical example as well as the scaling law are shown. The instabilities associated with edge plasma is next reviewed. The surface kink mode, ballooning mode, interchange mode, resistive interchange mode and thermal instability are discussed. Role of the geometry such as the location of the X-point is studied. Influences of the atomic processes, and those of the radial electric field are also discussed. The analysis of the H-mode transition physics is finally discussed. The boundary plasma is a nonlinear media which possesses the possibility for bifurcation in which the radial electric field plays a key role. The model of the ion viscosity is also studied. Transition physics is developed. Analysis on the self-generating oscillation is shown and the relation with ELMs is discussed. After reviewing these problems, several comments are made to what directions the study can be deepened. (author) 53 refs
On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Lin, Paul T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shadid, John N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States). Department of Mathematics and Statistics,; Tsuji, Paul H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-11-01
Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered in an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.
Present state of research and development of MHD power generation
International Nuclear Information System (INIS)
Ikeda, Shigeru
1978-01-01
MHD power generation can obtain electric energy directly from the heat energy of high speed plasma flow, and the power generating plant of 1 million kW can be realized by this method. When the MHD power generation method is combined before conventional thermal power generation method, the thermal efficiency can be raised to about 60% as compared with 38% in thermal power generation plants. The research and development of MHD power generation are in progress in USA and USSR. The research and development in Japan are in the second stage now after the first stage project for 10 years, and the Mark 7 generator with 100 kW electric output for 200 hr continuous operation is under construction. The MHD power generation is divided into three types according to the conductive fluids used, namely combustion type for thermal power generation, unequilibrated type and liquid metal type for nuclear power generation. The principle of MHD power generation and the constitution of the plant are explained. In Japan, the Mark 2 generator generated 1,180 kW for 1 min in 1971, and the Mark 3 generator generated 1.9 kW continuously for 110 hr in 1967. The MHD generator with superconducting magnet succeeded in 1969 to generate 25 kW for 6 min. The second stage project aimes at collecting design data and obtaining operational experience for the construction of 10 MW class pilot plant, and the Mark 7 and 8 generators are planned. (Kako, I.)
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Electromagnetic properties of a modular MHD thruster
Kom, C. H.; Brunet, Y.
1999-04-01
The magnetic field of an annular MHD thruster made of independent superconducting modules has been studied with analytical and numerical methods. This configuration allows to obtain large magnetized volumes and high induction levels with rapidly decreasing stray fields. When some inductors are out of order, the thruster remains still operational, but the stray fields increase in the vicinity of the failure. For given structural materials and superconductors, it is possible to determine the size of the conductor in order to reduce the electromagnetic forces and the peak field supported by the conductors. For an active field of 10 T in a 6 m ray annular active channel of a thruster with 24 modules, the peak field is exactly 15.6 T in the Nb3Sn conductors and the structure has to sustain 10^8 N/m forces. The necessity to place some magnetic or superconducting shield is discussed, particularly when the thruster is in a degraded regime. Nous présentons une étude analytique et numérique du champ magnétique d'un propulseur MHD naval annulaire, constitué de secteurs inducteurs supraconducteurs. Cette configuration nécessite des champs magnétiques élevés dans des volumes importants, et permet une décroissance rapide des champs de fuite. Lorsque quelques inducteurs sont en panne, le propulseur reste toujours opérationnel, mais les champs de fuite sont importants aux environs des modules hors service. Étant donné un matériau supraconducteur, il est possible de déterminer la forme des inducteurs dans le but de réduire à la fois les forces électromagnétiques et le surchamp supporté par le bobinage. Pour un propulseur annulaire constitué de 24 modules inducteurs, et un champ actif de 10 T au centre de la partie active du canal (r = 6 m) on obtient avec du Nb3Sn un champ maximun sur le conducteur de 15,5 T et la structure supporte une force de 10^8 N/m. De plus, la nécessité de placer des écrans magnétique ou supraconducteur en régime dégradé (mise
Global and kinetic MHD simulation by the Gpic-MHD code
International Nuclear Information System (INIS)
Naitou, Hiroshi; Yamada, Yusuke; Kajiwara, Kenji; Lee, Wei-li; Tokuda, Shinji; Yagi, Masatoshi
2011-01-01
In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC (particle-in-cell) code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic (MHD) simulation]. In the new algorithm, the vortex equation and the generalized ohm's law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential A z . Particle information is mainly used to estimate second order moments in the generalized ohm's law. Because the lower order moments of the charge density and the longitudinal current density are not used explicitly to determine φ and A z , the numerical noise induced by the discreteness of particle quantities reduces drastically. Another advantage of the algorithm is that the longitudinal induced electric field, E Tz =-∂A z /∂t, is explicitly estimated by the generalized ohm's law and used in the equations of motion. The particle velocities along the magnetic field are used (v z -formulation) instead of generalized momentums (p z -formulation), hence there is no problem of 'cancellation', which appear when estimating A z from the Ampere's law in the p z -formulation. The successful simulation of the collisionless internal kink mode by new Gpic-MHD with the realistic values of the large-scale and high-beta, revealed the usefulness of the new algorithm. (author)
EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION
Energy Technology Data Exchange (ETDEWEB)
Lawson, Nicolas; Strugarek, Antoine; Charbonneau, Paul, E-mail: nicolas.laws@gmail.ca, E-mail: strugarek@astro.umontreal.ca, E-mail: paulchar@astro.umontreal.ca [Département de Physique, Université de Montréal, C.P. 6128 Succ. Centre-ville, Montréal, Qc H3C 3J7 (Canada)
2015-11-10
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD “millennium simulation” of Passos and Charbonneau. This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally oriented bands of strong magnetic fields accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly sub-adiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities that are otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of sub-adiabaticity in the stable fluid layers underlying the convection zone.
17th Workshop on MHD Stability Control: addressing the disruption challenge for ITER
Buttery, Richard
2013-08-01
This annual workshop on magnetohydrodynamic stability control was held on 5-7 November 2012 at Columbia University in the city of New York, in the aftermath of a violent hydrodynamic instability event termed 'Hurricane Sandy'. Despite these challenging circumstances, Columbia University managed an excellent meeting, enabling the full participation of the community. This Workshop has been held since 1996 to help in the development of understanding and control of magnetohydrodynamic (MHD) instabilities for future fusion reactors. It covers a wide range of stability topics—from disruptions, to tearing modes, error fields, edge-localized modes (ELMs), resistive wall modes (RWMs) and ideal MHD—spanning many device types (tokamaks, stellarators and reversed field pinches) to identify commonalities in the physics and a means of control. The theme for 2012 was 'addressing the disruption challenge for ITER', and thus the first day had a heavy focus on both the avoidance and mitigation of disruptions in ITER. Key elements included understanding how to apply 3D fields to maintain stability, as well as managing the disruption process itself through mitigating loads in the thermal quench and handling so called 'runaway electrons'. This culminated in a panel discussion on the disruption mitigation strategy for ITER, which noted that heat load asymmetries during the thermal quench appear to be an artifact of MHD processes, and that runaway electron generation may be inevitable, suggesting research should focus on control and dissipation of the runaway beam. The workshop was combined this year with the annual US-Japan MHD Workshop, with a special section looking more deeply at 'Fundamentals of 3D Perturbed Equilibrium Control', with interesting sessions on 3D equilibrium reconstruction, RWM physics, novel control concepts such as non-magnetic sensing, adaptive control, q operation, and the effects of flow. The final day turned to tearing mode interactions, exploring the state
Microeconomics : Equilibrium and Efficiency
Ten Raa, T.
2013-01-01
Microeconomics: Equilibrium and Efficiency teaches how to apply microeconomic theory in an innovative, intuitive and concise way. Using real-world, empirical examples, this book not only covers the building blocks of the subject, but helps gain a broad understanding of microeconomic theory and
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Comments on equilibrium, transient equilibrium, and secular equilibrium in serial radioactive decay
International Nuclear Information System (INIS)
Prince, J.R.
1979-01-01
Equations describing serial radioactive decay are reviewed along with published descriptions or transient and secular equilibrium. It is shown that terms describing equilibrium are not used in the same way by various authors. Specific definitions are proposed; they suggest that secular equilibrium is a subset of transient equilibrium
Energy Technology Data Exchange (ETDEWEB)
NONE
1981-03-01
'Research on MHD generation system' was implemented by its expert committee in the electric joint study group, with the results of fiscal 1980 reported. This year, a detailed conceptual design was carried out on a coal fired MHD generation system, with points for the technological development concretely examined. In addition, investigation was conducted on the progress of MHD generation technology, development situation of other generation systems, state of energy resources, etc., in various foreign countries. In the conceptual design of the coal fired MHD generation plant, the system structure of a 2,000 MWt class commercial MHD generation plant was explained, as were the conceptual design of the structural elements and proposals for a 500 MWt class demonstration plant and an 100 MWt class experimental plant, for example. In the overseas trend of R and D on MHD generation, investigations were made concerning the U.S., Soviet Union, and China, with details compiled for such items as generation plants, combustors, generation channels, heat resisting materials, superconducting magnets, heat exchangers, seed slags, inverters, boilers and environments, and commercial plants. (NEDO)
Recent progress of nonlinear simulation on the toroidal Alfven eigenmode
International Nuclear Information System (INIS)
Todo, Yasushi; Sato, Tetsuya
1998-01-01
Linear and nonlinear particle-magnetohydrodynamic (MHD) simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with a slowing-down distribution are considered and the behavior of n=2 toroidal Alfven eigenmodes (TAE modes) is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation two n=2 TAE modes are destabilized and alpha particle losses induced by these TAE modes take place. Counter-passing particles are lost when they cross the passing-trapped boundary as a result of the interaction with the TAE modes. They are the major part of lost particles, but trapped particles are also lost appreciably. (author)
Pricing decisions in an experimental dynamic stochastic general equilibrium economy
Noussair, C.N.; Pfajfar, D.; Zsiros, J.
We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian dynamic stochastic general equilibrium (DSGE) model. We analyze the behavior of firms’ pricing decisions in four different experimental economies. We consider how
Mapping Isobaric Aging onto the Equilibrium Phase Diagram
DEFF Research Database (Denmark)
Niss, Kristine
2017-01-01
The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of p...
Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder
Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.
2018-06-01
An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.
New insights into MHD dynamics of magnetically confined plasmas from experiments in RFX
International Nuclear Information System (INIS)
Martin, P.; Martini, S.; Antoni, V.
2001-01-01
The experimental and theoretical activity performed in the RFX experiment has allowed a deeper insight into the MHD properties of the RFP configuration. A set of successful experiments has demonstrated the possibility of influencing both the amplitude and the spectrum of the magnetic fluctuations which characterise the RFP configuration. A new regime (QSH states) where the dynamo mechanism works in a nearly laminar way and a helical core plasma is produced has been investigated. With these studies a reduction of the magnetic chaos has been obtained. The continuos rotation of wall locked resistive tearing modes has been obtained by an m=0 rotating perturbation. This perturbation induces rotation of m=1 non-linearly coupled modes. (author)
Directory of Open Access Journals (Sweden)
Muhammad Mubashir Bhatti
2016-05-01
Full Text Available In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.
MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects
Institute of Scientific and Technical Information of China (English)
M Ramzan; M Farooq; T Hayat; A Alsaedi; J Cao
2015-01-01
Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
Non-disruptive MHD dynamics in inward-shifted LHD configurations
International Nuclear Information System (INIS)
Miura, H.; Ichiguchi, K.; Nakajima, N.; Hayashi, T.; Carreras, B.A.
2005-01-01
Two kinds of nonlinear simulations are conducted to study behaviors of the pressure-driven modes in the Large Helical Device (LHD) plasma with the vacuum magnetic axis located at R ax =3.6 m (so called inward-shifted configuration). One is the three-field reduced magnetohydrodynamic (RMHD) simulations. The other is the direct numerical simulations (DNS) of fully three-dimensional (3D) compressible MHD equations. The RMHD results suggest that the plasma behavior depends on the strength of the interaction between the unstable modes with different helicity. Similar plasma behaviors are also obtained in the DNS. In addition to some basic coincidence between RMHD and DNS, substantial toroidal flow generation is observed in the DNS. It is shown that toroidal flow can become stronger than the poloidal flow. (author)
Non-disruptive MHD dynamics in inward-shifted LHD configurations
International Nuclear Information System (INIS)
Miura, H.; Ichiguchi, K.; Nakajima, N.; Hayashi, T.; Carreras, B.A.
2005-01-01
Two kinds of nonlinear simulations are conducted to study behaviors of the pressure-driven modes in the Large Helical Device (LHD) plasma with the vacuum magnetic axis located at R ax = 3.6m (so called inward-shifted configuration). One is the three-field reduced magnetohydrodynamic (RMHD) simulations. The other is the direct numerical simulations (DNS) of fully three-dimensional (3D) compressible MHD equations. The RMHD results suggest that the plasma behavior depends on the strength of the interaction between the unstable modes with different helicity. Similar plasma behaviors are also obtained in the DNS. In addition to some basic coincidence between RMHD and DNS, substantial toroidal flow generation is observed in the DNS. It is shown that toroidal flow can become stronger than the poloidal flow. (author)
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Analysis of Linear MHD Power Generators
Energy Technology Data Exchange (ETDEWEB)
Witalis, E A
1965-02-15
The finite electrode size effects on the performance of an infinitely long MHD power generation duct are calculated by means of conformal mapping. The general conformal transformation is deduced and applied in a graphic way. The analysis includes variations in the segmentation degree, the Hall parameter of the gas and the electrode/insulator length ratio as well as the influence of the external circuitry and loading. A general criterion for a minimum of the generator internal resistance is given. The same criterion gives the conditions for the occurrence of internal current leakage between adjacent electrodes. It is also shown that the highest power output at a prescribed efficiency is always obtained when the current is made to flow between exactly opposed electrodes. Curves are presented showing the power-efficiency relations and other generator properties as depending on the segmentation degree and the Hall parameter in the cases of axial and transverse power extraction. The implications of limiting the current to flow between a finite number of identical electrodes are introduced and combined with the condition for current flow between opposed electrodes. The characteristics of generators with one or a few external loads can then be determined completely and examples are given in a table. It is shown that the performance of such generators must not necessarily be inferior to that of segmented generators with many independent loads. However, the problems of channel end losses and off-design loading have not been taken into consideration.
Alpha particle effects on MHD ballooning
International Nuclear Information System (INIS)
1991-01-01
During the period, as the first step towards the goal of detail understanding of the effects of alpha particle on MHD Ballooning Modes, a new numerical approach to investigate the stability of low-frequency fluctuations in high temperature tokamaks was developed by solving the gyrokinetic equations for the ion and electron directly as an initial value problem. The advantage of this approach is the inclusion of many important kinetic features of the problem without approximations and computationally more economical than particle-pushing simulation. The ion-temperature-gradient-mode was investigated to benchmark this new simulation technique. Previous results in literature were recovered. Both the adiabatic electron model and the full drift-kinetic electron model are studied. Numerical result shows that the full drift-kinetic electron model is more unstable. The development of subcycling technique to handle the fast electron bounce time is particularly significant to apply this new approach to the alpha particle problem since alpha particle bounce frequency is also significantly higher than the mode frequency. This new numerical technique will be the basis of future study of the microstability in high temperature tokamaks with alpha particles (or any energetic species). 15 refs., 13 figs
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
International Nuclear Information System (INIS)
Ito, A.; Nakajima, N.
2010-11-01
Effects of flow, finite ion temperature and pressure anisotropy on equilibrium and stability of a high-beta toroidal plasma are studied in the framework of reduced magnetohydrodynamics (MHD). A set of reduced equilibrium equations for high-beta tokamaks with toroidal and poloidal flow comparable to the poloidal sound velocity is derived in a unified form of single-fluid and Hall MHD models and a two-fluid MHD model with ion finite Larmor radius (FLR) terms. Pressure anisotropy is introduced with equations for the parallel heat flux which are closed by a fluid closure model. It is solved analytically for the single-fluid model and the solutions shows complicated characteristics in the region around the poloidal sound velocity due to pressure anisotropy and the parallel heat flux. Numerical solutions are found by using the finite element method for the two-fluid model with FLR effects in the case of isotropic, adiabatic pressure and indicate the following features of two-fluid equilibria: the isosurfaces of the magnetic flux, the pressure and the ion stream function do not coincide with each other, and the solutions depend on the sign of the radial electric field. Reduced single-fluid MHD equations with time evolution that are consistent with the above equilibria are also derived in order to study their stability. They conserve the energy up to the order required by the equilibria. (author)
Study on closed cycle MHD generation systems; Closed cycle MHD hatsuden system no kento
Energy Technology Data Exchange (ETDEWEB)
NONE
1988-03-01
The closed cycle noble gas MHD generation systems are surveyed and studied. The concept of closed cycle noble gas MHD generation is confirmed to extract high enthalpy, and now going into the engineering demonstration stage from the basic research stage. These systems have various characteristics. The highest working temperature is around 1,700 degrees C, which is close to that associated with the existing techniques. Use of helium or argon gas as the working fluid makes the system relatively free of various problems, e.g., corrosion. It can attain a much higher efficiency than the combined cycle involving gas turbine. It suffers less heat loss in the passages, is suitable for small- to medium-capacity power generation systems, and copes with varying load. The compact power generation passages decrease required size of the superconducting magnet. The technical problems to be solved include optimization of power generation conditions, demonstration of durability of the power generation passages, injection/recovery of the seed material, treatment of the working gas to remove molecular impurities, and development of heat exchangers serviceable at high temperature produced by direct combustion of coal. The conceptual designs of the triple combined system are completed. (NEDO)
Report on studies on closed cycle MHD power generation; Closed cycle MHD hatsuden kento hokokusho
Energy Technology Data Exchange (ETDEWEB)
NONE
1991-04-01
Summarized herein are results of the studies on closed cycle MHD (CCMHD) power generation by the study committee. The studied system is based on the MHD gas turbine combined Brayton cycle of about 500,000 kW in output power, firing natural gas as the fuel, and the conceptual design works therefor are completed. The major findings are: the overall plant efficiency: 54.2% at the power transmission side, plot area required per unit power output: 0.04 m{sup 2}/KW, unit construction cost: 251,000 yen/KW, and unit power generation cost: 10.2 yen/KWh. This system will be more operable than the gas turbine combined cycle with steam system, because start-up time, output change rate, optimum load and so on are constrained not on the power generator side but on the gas turbine side. The expected environmental effects include the exhaust gas NOX concentration being equivalent with that associated with the conventional power generator of 2-stage combustion system, quantity of combustion gases to be treated being approximately 40% of that associated with the gas turbine combined cycle, and reduced CO2 gas emissions, resulting from enhanced power generation efficiency. It is expected that the CCMHD system can exhibit higher efficiency than the high-temperature gas turbine combined cycle system. (NEDO)
Equilibrium and pre-equilibrium emissions in proton-induced ...
Indian Academy of Sciences (India)
necessary for the domain of fission-reactor technology for the calculation of nuclear transmutation ... tions occur in three stages: INC, pre-equilibrium and equilibrium (or compound. 344. Pramana ... In the evaporation phase of the reaction, the.
Gated equilibrium bloodpool scintigraphy
International Nuclear Information System (INIS)
Reinders Folmer, S.C.C.
1981-01-01
This thesis deals with the clinical applications of gated equilibrium bloodpool scintigraphy, performed with either a gamma camera or a portable detector system, the nuclear stethoscope. The main goal has been to define the value and limitations of noninvasive measurements of left ventricular ejection fraction as a parameter of cardiac performance in various disease states, both for diagnostic purposes as well as during follow-up after medical or surgical intervention. Secondly, it was attempted to extend the use of the equilibrium bloodpool techniques beyond the calculation of ejection fraction alone by considering the feasibility to determine ventricular volumes and by including the possibility of quantifying valvular regurgitation. In both cases, it has been tried to broaden the perspective of the observations by comparing them with results of other, invasive and non-invasive, procedures, in particular cardiac catheterization, M-mode echocardiography and myocardial perfusion scintigraphy. (Auth.)