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.
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)
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.)
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)
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)
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.
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)
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)
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)
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
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
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
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
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)
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)
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
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.
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
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
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 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)
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
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 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
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
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)
QUIL: a chemical equilibrium code
International Nuclear Information System (INIS)
Lunsford, J.L.
1977-02-01
A chemical equilibrium code QUIL is described, along with two support codes FENG and SURF. QUIL is designed to allow calculations on a wide range of chemical environments, which may include surface phases. QUIL was written specifically to calculate distributions associated with complex equilibria involving fission products in the primary coolant loop of the high-temperature gas-cooled reactor. QUIL depends upon an energy-data library called ELIB. This library is maintained by FENG and SURF. FENG enters into the library all reactions having standard free energies of reaction that are independent of concentration. SURF enters all surface reactions into ELIB. All three codes are interactive codes written to be used from a remote terminal, with paging control provided. Plotted output is also available
Axisymmetric MHD equilibrium solver with bicubic Hermite elements
International Nuclear Information System (INIS)
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
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
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)
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)
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.
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.
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)
MHD code using multi graphical processing units: SMAUG+
Gyenge, N.; Griffiths, M. K.; Erdélyi, R.
2018-01-01
This paper introduces the Sheffield Magnetohydrodynamics Algorithm Using GPUs (SMAUG+), an advanced numerical code for solving magnetohydrodynamic (MHD) problems, using multi-GPU systems. Multi-GPU systems facilitate the development of accelerated codes and enable us to investigate larger model sizes and/or more detailed computational domain resolutions. This is a significant advancement over the parent single-GPU MHD code, SMAUG (Griffiths et al., 2015). Here, we demonstrate the validity of the SMAUG + code, describe the parallelisation techniques and investigate performance benchmarks. The initial configuration of the Orszag-Tang vortex simulations are distributed among 4, 16, 64 and 100 GPUs. Furthermore, different simulation box resolutions are applied: 1000 × 1000, 2044 × 2044, 4000 × 4000 and 8000 × 8000 . We also tested the code with the Brio-Wu shock tube simulations with model size of 800 employing up to 10 GPUs. Based on the test results, we observed speed ups and slow downs, depending on the granularity and the communication overhead of certain parallel tasks. The main aim of the code development is to provide massively parallel code without the memory limitation of a single GPU. By using our code, the applied model size could be significantly increased. We demonstrate that we are able to successfully compute numerically valid and large 2D MHD problems.
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.
CAFE: A NEW RELATIVISTIC MHD CODE
Energy Technology Data Exchange (ETDEWEB)
Lora-Clavijo, F. D.; Cruz-Osorio, A. [Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal 04510, México (Mexico); Guzmán, F. S., E-mail: fdlora@astro.unam.mx, E-mail: aosorio@astro.unam.mx, E-mail: guzman@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán, México (Mexico)
2015-06-22
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
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.)
Magnus: A New Resistive MHD Code with Heat Flow Terms
Navarro, Anamaría; Lora-Clavijo, F. D.; González, Guillermo A.
2017-07-01
We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity—but not dominant—and heat transference in a uniform 3D grid. The code is based on the finite-volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error (˜ 1× {10}-12). For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere-transition-corona region, while the second one consists of a 2D simulation of a transverse velocity pulse in a coronal loop.
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)
An approach to verification and validation of MHD codes for fusion applications
Energy Technology Data Exchange (ETDEWEB)
Smolentsev, S., E-mail: sergey@fusion.ucla.edu [University of California, Los Angeles (United States); Badia, S. [Centre Internacional de Mètodes Numèrics en Enginyeria, Barcelona (Spain); Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Bhattacharyay, R. [Institute for Plasma Research, Gandhinagar, Gujarat (India); Bühler, L. [Karlsruhe Institute of Technology (Germany); Chen, L. [University of Chinese Academy of Sciences, Beijing (China); Huang, Q. [Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui (China); Jin, H.-G. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Krasnov, D. [Technische Universität Ilmenau (Germany); Lee, D.-W. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Mas de les Valls, E. [Centre Internacional de Mètodes Numèrics en Enginyeria, Barcelona (Spain); Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Mistrangelo, C. [Karlsruhe Institute of Technology (Germany); Munipalli, R. [HyPerComp, Westlake Village (United States); Ni, M.-J. [University of Chinese Academy of Sciences, Beijing (China); Pashkevich, D. [St. Petersburg State Polytechnical University (Russian Federation); Patel, A. [Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Pulugundla, G. [University of California, Los Angeles (United States); Satyamurthy, P. [Bhabha Atomic Research Center (India); Snegirev, A. [St. Petersburg State Polytechnical University (Russian Federation); Sviridov, V. [Moscow Power Engineering Institute (Russian Federation); Swain, P. [Bhabha Atomic Research Center (India); and others
2015-11-15
Highlights: • Review of status of MHD codes for fusion applications. • Selection of five benchmark problems. • Guidance for verification and validation of MHD codes for fusion applications. - Abstract: We propose a new activity on verification and validation (V&V) of MHD codes presently employed by the fusion community as a predictive capability tool for liquid metal cooling applications, such as liquid metal blankets. The important steps in the development of MHD codes starting from the 1970s are outlined first and then basic MHD codes, which are currently in use by designers of liquid breeder blankets, are reviewed. A benchmark database of five problems has been proposed to cover a wide range of MHD flows from laminar fully developed to turbulent flows, which are of interest for fusion applications: (A) 2D fully developed laminar steady MHD flow, (B) 3D laminar, steady developing MHD flow in a non-uniform magnetic field, (C) quasi-two-dimensional MHD turbulent flow, (D) 3D turbulent MHD flow, and (E) MHD flow with heat transfer (buoyant convection). Finally, we introduce important details of the proposed activities, such as basic V&V rules and schedule. The main goal of the present paper is to help in establishing an efficient V&V framework and to initiate benchmarking among interested parties. The comparison results computed by the codes against analytical solutions and trusted experimental and numerical data as well as code-to-code comparisons will be presented and analyzed in companion paper/papers.
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.
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)
GRADSPMHD: A parallel MHD code based on the SPH formalism
Vanaverbeke, S.; Keppens, R.; Poedts, S.
2014-03-01
We present GRADSPMHD, a completely Lagrangian parallel magnetohydrodynamics code based on the SPH formalism. The implementation of the equations of SPMHD in the “GRAD-h” formalism assembles known results, including the derivation of the discretized MHD equations from a variational principle, the inclusion of time-dependent artificial viscosity, resistivity and conductivity terms, as well as the inclusion of a mixed hyperbolic/parabolic correction scheme for satisfying the ∇ṡB→ constraint on the magnetic field. The code uses a tree-based formalism for neighbor finding and can optionally use the tree code for computing the self-gravity of the plasma. The structure of the code closely follows the framework of our parallel GRADSPH FORTRAN 90 code which we added previously to the CPC program library. We demonstrate the capabilities of GRADSPMHD by running 1, 2, and 3 dimensional standard benchmark tests and we find good agreement with previous work done by other researchers. The code is also applied to the problem of simulating the magnetorotational instability in 2.5D shearing box tests as well as in global simulations of magnetized accretion disks. We find good agreement with available results on this subject in the literature. Finally, we discuss the performance of the code on a parallel supercomputer with distributed memory architecture. Catalogue identifier: AERP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 620503 No. of bytes in distributed program, including test data, etc.: 19837671 Distribution format: tar.gz Programming language: FORTRAN 90/MPI. Computer: HPC cluster. Operating system: Unix. Has the code been vectorized or parallelized?: Yes, parallelized using MPI. RAM: ˜30 MB for a
TEA: A CODE CALCULATING THERMOCHEMICAL EQUILIBRIUM ABUNDANCES
Energy Technology Data Exchange (ETDEWEB)
Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver, E-mail: jasmina@physics.ucf.edu [Planetary Sciences Group, Department of Physics, University of Central Florida, Orlando, FL 32816-2385 (United States)
2016-07-01
We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature–pressure pairs. We tested the code against the method of Burrows and Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows and Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.
TEA: A CODE CALCULATING THERMOCHEMICAL EQUILIBRIUM ABUNDANCES
International Nuclear Information System (INIS)
Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver
2016-01-01
We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature–pressure pairs. We tested the code against the method of Burrows and Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows and Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.
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)
A coupled systems code-CFD MHD solver for fusion blanket design
Energy Technology Data Exchange (ETDEWEB)
Wolfendale, Michael J., E-mail: m.wolfendale11@imperial.ac.uk; Bluck, Michael J.
2015-10-15
Highlights: • A coupled systems code-CFD MHD solver for fusion blanket applications is proposed. • Development of a thermal hydraulic systems code with MHD capabilities is detailed. • A code coupling methodology based on the use of TCP socket communications is detailed. • Validation cases are briefly discussed for the systems code and coupled solver. - Abstract: The network of flow channels in a fusion blanket can be modelled using a 1D thermal hydraulic systems code. For more complex components such as junctions and manifolds, the simplifications employed in such codes can become invalid, requiring more detailed analyses. For magnetic confinement reactor blanket designs using a conducting fluid as coolant/breeder, the difficulties in flow modelling are particularly severe due to MHD effects. Blanket analysis is an ideal candidate for the application of a code coupling methodology, with a thermal hydraulic systems code modelling portions of the blanket amenable to 1D analysis, and CFD providing detail where necessary. A systems code, MHD-SYS, has been developed and validated against existing analyses. The code shows good agreement in the prediction of MHD pressure loss and the temperature profile in the fluid and wall regions of the blanket breeding zone. MHD-SYS has been coupled to an MHD solver developed in OpenFOAM and the coupled solver validated for test geometries in preparation for modelling blanket systems.
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)
International Nuclear Information System (INIS)
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
Study of MHD stability beta limit in LHD by hierarchy integrated simulation code
International Nuclear Information System (INIS)
Sato, M.; Watanabe, K.Y.; Nakamura, Y.
2008-10-01
The beta limit by the ideal MHD instabilities (so-called 'MHD stability beta limit') for helical plasmas is studied by a hierarchy integrated simulation code. A numerical model for the effect of the MHD instabilities is introduced such that the pressure profile is flattened around the rational surface due to the MHD instabilities. The width of the flattening of the pressure gradient is determined from the width of the eigenmode structure of the MHD instabilities. It is assumed that there is the upper limit of the mode number of the MHD instabilities which directly affect the pressure gradient. The upper limit of the mode number is determined using a recent high beta experiment in the Large Helical Device (LHD). The flattening of the pressure gradient is calculated by the transport module in a hierarchy integrated code. The achievable volume averaged beta value in the LHD is expected to be beyond 6%. (author)
Development of chemical equilibrium analysis code 'CHEEQ'
International Nuclear Information System (INIS)
Nagai, Shuichiro
2006-08-01
'CHEEQ' code which calculates the partial pressure and the mass of the system consisting of ideal gas and pure condensed phase compounds, was developed. Characteristics of 'CHEEQ' code are as follows. All the chemical equilibrium equations were described by the formation reactions from the mono-atomic gases in order to simplify the code structure and input preparation. Chemical equilibrium conditions, Σν i μ i =0 for the gaseous compounds and precipitated condensed phase compounds and Σν i μ i > 0 for the non-precipitated condensed phase compounds, were applied. Where, ν i and μ i are stoichiometric coefficient and chemical potential of component i. Virtual solid model was introduced to perform the calculation of constant partial pressure condition. 'CHEEQ' was consisted of following 3 parts, (1) analysis code, zc132. f. (2) thermodynamic data base, zmdb01 and (3) input data file, zindb. 'CHEEQ' code can calculate the system which consisted of elements (max.20), condensed phase compounds (max.100) and gaseous compounds. (max.200). Thermodynamic data base, zmdb01 contains about 1000 elements and compounds, and 200 of them were Actinide elements and their compounds. This report describes the basic equations, the outline of the solution procedure and instructions to prepare the input data and to evaluate the calculation results. (author)
MHD Kelvin-Helmholtz instability in non-hydrostatic equilibrium
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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)
Experimental and theoretical studies of the effects of nonuniformities in equilibrium MHD generators
International Nuclear Information System (INIS)
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
Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM
Energy Technology Data Exchange (ETDEWEB)
Feng, Jingchao; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; He, Qingyun; Ye, Minyou
2015-11-15
Highlights: • Specific correction scheme has been adopted to revise the calculating result for non-orthogonal meshes. • The developed MHD code based on OpenFOAM platform has been validated by benchmark cases under uniform and non-uniform magnetic field in round and rectangular ducts. • ALEX experimental results have been used to validate the MHD code based on OpenFOAM. - Abstract: In fusion liquid metal blankets, complex geometries involving contractions, expansions, bends, manifolds are very common. The characteristics of liquid metal flow in these geometries are significant. In order to extend the magnetohydrodynamic (MHD) solver developed on OpenFOAM platform to be applied in the complex geometry, the MHD solver based on unstructured meshes has been implemented. The adoption of non-orthogonal correction techniques in the solver makes it possible to process the non-orthogonal meshes in complex geometries. The present paper focused on the validation of the code under critical conditions. An analytical solution benchmark case and two experimental benchmark cases were conducted to validate the code. Benchmark case I is MHD flow in a circular pipe with arbitrary electric conductivity of the walls in a uniform magnetic field. Benchmark cases II and III are experimental cases of 3D laminar steady MHD flow under fringing magnetic field. In all these cases, the numerical results match well with the benchmark cases.
Further validation of liquid metal MHD code for unstructured grid based on OpenFOAM
International Nuclear Information System (INIS)
Feng, Jingchao; Chen, Hongli; He, Qingyun; Ye, Minyou
2015-01-01
Highlights: • Specific correction scheme has been adopted to revise the calculating result for non-orthogonal meshes. • The developed MHD code based on OpenFOAM platform has been validated by benchmark cases under uniform and non-uniform magnetic field in round and rectangular ducts. • ALEX experimental results have been used to validate the MHD code based on OpenFOAM. - Abstract: In fusion liquid metal blankets, complex geometries involving contractions, expansions, bends, manifolds are very common. The characteristics of liquid metal flow in these geometries are significant. In order to extend the magnetohydrodynamic (MHD) solver developed on OpenFOAM platform to be applied in the complex geometry, the MHD solver based on unstructured meshes has been implemented. The adoption of non-orthogonal correction techniques in the solver makes it possible to process the non-orthogonal meshes in complex geometries. The present paper focused on the validation of the code under critical conditions. An analytical solution benchmark case and two experimental benchmark cases were conducted to validate the code. Benchmark case I is MHD flow in a circular pipe with arbitrary electric conductivity of the walls in a uniform magnetic field. Benchmark cases II and III are experimental cases of 3D laminar steady MHD flow under fringing magnetic field. In all these cases, the numerical results match well with the benchmark cases.
A Fast MHD Code for Gravitationally Stratified Media using ...
Indian Academy of Sciences (India)
namic (MHD) algorithms are important for numerical modelling of highly .... include OpenMP-style pragma-based programming, e.g., developed by PGI, HMPP, .... Thus, the formula (10) returns the one-dimensional index for a field point. A.
Ideal MHD equilibrium of a weakly toroidal plasma column with elongated cross-section
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
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
Divergence-free MHD Simulations with the HERACLES Code
Directory of Open Access Journals (Sweden)
Vides J.
2013-12-01
Full Text Available Numerical simulations of the magnetohydrodynamics (MHD equations have played a significant role in plasma research over the years. The need of obtaining physical and stable solutions to these equations has led to the development of several schemes, all requiring to satisfy and preserve the divergence constraint of the magnetic field numerically. In this paper, we aim to show the importance of maintaining this constraint numerically. We investigate in particular the hyperbolic divergence cleaning technique applied to the ideal MHD equations on a collocated grid and compare it to the constrained transport technique that uses a staggered grid to maintain the property. The methods are implemented in the software HERACLES and several numerical tests are presented, where the robustness and accuracy of the different schemes can be directly compared.
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
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)
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)
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.
Newtonian CAFE: a new ideal MHD code to study the solar atmosphere
González-Avilés, J. J.; Cruz-Osorio, A.; Lora-Clavijo, F. D.; Guzmán, F. S.
2015-12-01
We present a new code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centres on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvénic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the Harten-Lax-van Leer-Einfeldt (HLLE) flux formula combined with Minmod, MC, and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.
A simulation of driven reconnection by a high precision MHD code
International Nuclear Information System (INIS)
Kusano, Kanya; Ouchi, Yasuo; Hayashi, Takaya; Horiuchi, Ritoku; Watanabe, Kunihiko; Sato, Tetsuya.
1988-01-01
A high precision MHD code, which has the fourth-order accuracy for both the spatial and time steps, is developed, and is applied to the simulation studies of two dimensional driven reconnection. It is confirm that the numerical dissipation of this new scheme is much less than that of two-step Lax-Wendroff scheme. The effect of the plasma compressibility on the reconnection dynamics is investigated by means of this high precision code. (author)
NOVA: a nonvariational code for solving MHD stability of axisymmetric toroidal plasmas
International Nuclear Information System (INIS)
Cheng, C.Z.; Chance, M.S.
1986-04-01
A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B-spline finite elements and Fourier expansion in a general flux coordinate (psi, theta, zeta) system. Better accuracy and faster convergence were obtained in comparison with the variational PEST and ERATO codes. The nonvariational approach can be extended to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained
A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG
Griffiths, M. K.; Fedun, V.; Erdélyi, R.
2015-03-01
Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.
Development of a potential based code for MHD analysis of LLCB TBM
International Nuclear Information System (INIS)
Bhuyan, P.J.; Goswami, K.S.
2010-01-01
A two dimensional solver is developed for MHD flows with low magnetic Reynolds' number based on the electrostatic potential formulation for the Lorentz forces and current densities which will be used to calculate the MHD pressure drop inside the channels of liquid breeder based Test Blanket Modules (TBMs). The flow geometry is assumed to be rectangular and perpendicular to the flow direction, with flow and electrostatic potential variations along the flow direction neglected. A structured, non-uniform, collocated grid is used in the calculation, where the velocity (u), pressure (p) and electrostatic potential (φ) are calculated at the cell centers, whereas the current densities are calculated at the cell faces. Special relaxation techniques are employed in calculating the electrostatic potential for ensuring the divergence-free condition for current density. The code is benchmarked over a square channel for various Hartmann numbers up to 25,000 with and without insulation coatings by (i) comparing the pressure drop with the approximate analytical results found in literature and (ii) comparing the pressure drop with the ones obtained in our previous calculations based on the induction formulation for the electromagnetic part. Finally the code is used to determine the MHD pressure drop in case of LLCB TBM. The code gives similar results as obtained by us in our previous calculations based on the induction formulation. However, the convergence is much faster in case of potential based code.
Computer codes incorporating pre-equilibrium decay
International Nuclear Information System (INIS)
Prince, A.
1980-01-01
After establishing the need to describe the high-energy particle spectrum which is evident in the experimental data, the various models used in the interpretation are presented. This includes the following: a) Cascade Model; b) Fermi-Gas Relaxation Model; c) Exciton Model; d) Hybrid and Geometry-Dependent Model. The codes description and preparation of input data for STAPRE was presented (Dr. Strohmaier). A simulated output was employed for a given input and comparison with experimental data substantiated the rather sophisticated treatment. (author)
CHMTRNS, Non-Equilibrium Chemical Transport Code
International Nuclear Information System (INIS)
Noorishad, J.; Carnahan, C.L.; Benson, L.V.
1998-01-01
1 - Description of program or function: CHMTRNS simulates solute transport for steady one-dimensional fluid flow by convection and diffusion or dispersion in a saturated porous medium based on the assumption of local chemical equilibrium. The chemical interactions included in the model are aqueous-phase complexation, solid-phase ion exchange of bare ions and complexes using the surface complexation model, and precipitation or dissolution of solids. The program can simulate the kinetic dissolution or precipitation for calcite and silica as well as irreversible dissolution of glass. Thermodynamic parameters are temperature dependent and are coupled to a companion heat transport simulator; thus, the effects of transient temperature conditions can be considered. Options for oxidation-reduction (redox) and C-13 fractionation as well as non-isothermal conditions are included. 2 - Method of solution: The governing equations for both reactive chemical and heat transport are discretized in time and space. For heat transport, the Crank-Nicolson approximation is used in conjunction with a LU decomposition and backward substitution solution procedure. To deal with the strong nonlinearity of the chemical transport equations, a generalized Newton-Raphson method is used
INCORPORATING AMBIPOLAR AND OHMIC DIFFUSION IN THE AMR MHD CODE RAMSES
International Nuclear Information System (INIS)
Masson, J.; Mulet-Marquis, C.; Chabrier, G.; Teyssier, R.; Hennebelle, P.
2012-01-01
We have implemented non-ideal magnetohydrodynamics (MHD) effects in the adaptive mesh refinement code RAMSES, namely, ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test, and the Alfvén wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.
Geochemical modelling of groundwater evolution using chemical equilibrium codes
International Nuclear Information System (INIS)
Pitkaenen, P.; Pirhonen, V.
1991-01-01
Geochemical equilibrium codes are a modern tool in studying interaction between groundwater and solid phases. The most common used programs and application subjects are shortly presented in this article. The main emphasis is laid on the approach method of using calculated results in evaluating groundwater evolution in hydrogeological system. At present in geochemical equilibrium modelling also kinetic as well as hydrologic constrains along a flow path are taken into consideration
FARGO3D: A NEW GPU-ORIENTED MHD CODE
Energy Technology Data Exchange (ETDEWEB)
Benitez-Llambay, Pablo [Instituto de Astronomía Teórica y Experimental, Observatorio Astronónomico, Universidad Nacional de Córdoba. Laprida 854, X5000BGR, Córdoba (Argentina); Masset, Frédéric S., E-mail: pbllambay@oac.unc.edu.ar, E-mail: masset@icf.unam.mx [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 48-3,62251-Cuernavaca, Morelos (Mexico)
2016-03-15
We present the FARGO3D code, recently publicly released. It is a magnetohydrodynamics code developed with special emphasis on the physics of protoplanetary disks and planet–disk interactions, and parallelized with MPI. The hydrodynamics algorithms are based on finite-difference upwind, dimensionally split methods. The magnetohydrodynamics algorithms consist of the constrained transport method to preserve the divergence-free property of the magnetic field to machine accuracy, coupled to a method of characteristics for the evaluation of electromotive forces and Lorentz forces. Orbital advection is implemented, and an N-body solver is included to simulate planets or stars interacting with the gas. We present our implementation in detail and present a number of widely known tests for comparison purposes. One strength of FARGO3D is that it can run on either graphical processing units (GPUs) or central processing units (CPUs), achieving large speed-up with respect to CPU cores. We describe our implementation choices, which allow a user with no prior knowledge of GPU programming to develop new routines for CPUs, and have them translated automatically for GPUs.
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
Energy Technology Data Exchange (ETDEWEB)
Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel [Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain); Müller, Ewald, E-mail: tomasz.rembiasz@uv.es [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)
2017-06-01
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.
Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas
Energy Technology Data Exchange (ETDEWEB)
Hamlin, Nathaniel D., E-mail: nh322@cornell.edu [438 Rhodes Hall, Cornell University, Ithaca, NY, 14853 (United States); Seyler, Charles E., E-mail: ces7@cornell.edu [Cornell University, Ithaca, NY, 14853 (United States)
2014-12-15
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.
Laser-Plasma Modeling Using PERSEUS Extended-MHD Simulation Code for HED Plasmas
Hamlin, Nathaniel; Seyler, Charles
2017-10-01
We discuss the use of the PERSEUS extended-MHD simulation code for high-energy-density (HED) plasmas in modeling the influence of Hall and electron inertial physics on laser-plasma interactions. By formulating the extended-MHD equations as a relaxation system in which the current is semi-implicitly time-advanced using the Generalized Ohm's Law, PERSEUS enables modeling of extended-MHD phenomena (Hall and electron inertial physics) without the need to resolve the smallest electron time scales, which would otherwise be computationally prohibitive in HED plasma simulations. We first consider a laser-produced plasma plume pinched by an applied magnetic field parallel to the laser axis in axisymmetric cylindrical geometry, forming a conical shock structure and a jet above the flow convergence. The Hall term produces low-density outer plasma, a helical field structure, flow rotation, and field-aligned current, rendering the shock structure dispersive. We then model a laser-foil interaction by explicitly driving the oscillating laser fields, and examine the essential physics governing the interaction. This work is supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative agreements DE-FOA-0001153 and DE-NA0001836.
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)
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)
CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
Energy Technology Data Exchange (ETDEWEB)
Anninos, Peter; Lau, Cheuk [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94550 (United States); Bryant, Colton [Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208 (United States); Fragile, P. Chris [Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, SC 29424 (United States); Holgado, A. Miguel [Department of Astronomy and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801 (United States); Nemergut, Daniel [Operations and Engineering Division, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States)
2017-08-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD
International Nuclear Information System (INIS)
Anninos, Peter; Lau, Cheuk; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Nemergut, Daniel
2017-01-01
We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.
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)
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)
Construction of a path of MHD equilibrium solutions by an iterative method
International Nuclear Information System (INIS)
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)
QUIC: a chemical kinetics code for use with the chemical equilibrium code QUIL
International Nuclear Information System (INIS)
Lunsford, J.L.
1977-10-01
A chemical rate kinetics code QUIC is described, along with a support code RATE. QUIC is designed to allow chemical kinetics calculations on a wide variety of chemical environments while operating in the overlay environment of the chemical equilibrium code QUIL. QUIC depends upon a rate-data library called LIBR. This library is maintained by RATE. RATE enters into the library all reactions in a standardized format. The code QUIC, operating in conjunction with QUIL, is interactive and written to be used from a remote terminal, with paging control provided. Plotted output is also available
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)
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].
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
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)
Tokamak equilibrium reconstruction code LIUQE and its real time implementation
International Nuclear Information System (INIS)
Moret, J.-M.; Duval, B.P.; Le, H.B.; Coda, S.; Felici, F.; Reimerdes, H.
2015-01-01
Highlights: • Algorithm vertical stabilisation using a linear parametrisation of the current density. • Experimentally derived model of the vacuum vessel to account for vessel currents. • Real-time contouring algorithm for flux surface averaged 1.5 D transport equations. • Full real time implementation coded in SIMULINK runs in less than 200 μs. • Applications: shape control, safety factor profile control, coupling with RAPTOR. - Abstract: Equilibrium reconstruction consists in identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. The LIUQE code adopts a computationally efficient method to solve this problem, based on an iterative solution of the Poisson equation coupled with a linear parametrisation of the plasma current density. This algorithm is unstable against vertical gross motion of the plasma column for elongated shapes and its application to highly shaped plasmas on TCV requires a particular treatment of this instability. TCV's continuous vacuum vessel has a low resistance designed to enhance passive stabilisation of the vertical position. The eddy currents in the vacuum vessel have a sizeable influence on the equilibrium reconstruction and must be taken into account. A real time version of LIUQE has been implemented on TCV's distributed digital control system with a cycle time shorter than 200 μs for a full spatial grid of 28 by 65, using all 133 experimental measurements and including the flux surface average of quantities necessary for the real time solution of 1.5 D transport equations. This performance was achieved through a thoughtful choice of numerical methods and code optimisation techniques at every step of the algorithm, and was coded in MATLAB and SIMULINK for the off-line and real time version respectively
Comparing DINA code simulations with TCV experimental plasma equilibrium responses
International Nuclear Information System (INIS)
Khayrutdinov, R.R.; Lister, J.B.; Lukash, V.E.; Wainwright, J.P.
2000-08-01
The DINA non-linear time dependent simulation code has been validated against an extensive set of plasma equilibrium response experiments carried out on the TCV tokamak. Limited and diverted plasmas are found to be well modelled during the plasma current flat top. In some simulations the application of the PF coil voltage stimulation pulse sufficiently changed the plasma equilibrium that the vertical position feedback control loop became unstable. This behaviour was also found in the experimental work, and cannot be reproduced using linear time-independent models. A single null diverted plasma discharge was also simulated from start-up to shut-down and the results were found to accurately reproduce their experimental equivalents. The most significant difference noted was the penetration time of the poloidal flux, leading to a delayed onset of sawtoothing in the DINA simulation. The complete set of frequency stimulation experiments used to measure the open loop tokamak plasma equilibrium response was also simulated using DINA and the results were analysed in an identical fashion to the experimental data. The frequency response of the DINA simulations agrees with the experimental results. Comparisons with linear models are also discussed to identify areas of good and only occasionally less good agreement. (author)
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.
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
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.)
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)
First experimental validation on the core equilibrium code: HARMONIE
International Nuclear Information System (INIS)
Van Dorsselaere, J.; Cozzani, M.; Gnuffi, M.
1981-08-01
The code HARMONIE calculates the mechanical equilibrium of a fast reactor. An experimental program of deformation, in air, of groups of subassemblies, was performed on a mock-up, in the Super Phenix 1- geometry. This program included three kinds of tests, all performed without and then with grease: on groups of 2 or 3 rings of subassemblies, subjected to a force acting upon flats or angles; on groups of 35 and 41 subassemblies, subjected to a force acting on the first row, then with 1 or 2 empty cells; and on groups with 1 or 2 bowed subassemblies or 1 enlarged one over flats. A preliminary test on the friction coefficient in air between two pads showed some dependance upon the pad surface condition with a scattering factor of 8. Two basic code hypotheses were validated: the rotation of the subassemblies around their axis was negligible after deformation of the group, and the choice of a mean Maxwell coefficient, between those of 1st and 2nd slope, led to very similar results to experimental. The agreement between tests and HARMONIE calculations was suitable, qualitatively for all the groups and quantitatively for regular groups of 3 rings at most. But the difference increased for larger groups of 35 or 41 subassemblies: friction between pads, neglected by HARMONIE, seems to be the main reason. Other reasons for these differences are: the influence of the loading order on the mock-up, and the initial contacts issued from the gap between foot and diagrid-insert, and from manufacture bowings
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
Large Scale Earth's Bow Shock with Northern IMF as Simulated by PIC Code in Parallel with MHD Model
Baraka, Suleiman
2016-06-01
In this paper, we propose a 3D kinetic model (particle-in-cell, PIC) for the description of the large scale Earth's bow shock. The proposed version is stable and does not require huge or extensive computer resources. Because PIC simulations work with scaled plasma and field parameters, we also propose to validate our code by comparing its results with the available MHD simulations under same scaled solar wind (SW) and (IMF) conditions. We report new results from the two models. In both codes the Earth's bow shock position is found to be ≈14.8 R E along the Sun-Earth line, and ≈29 R E on the dusk side. Those findings are consistent with past in situ observations. Both simulations reproduce the theoretical jump conditions at the shock. However, the PIC code density and temperature distributions are inflated and slightly shifted sunward when compared to the MHD results. Kinetic electron motions and reflected ions upstream may cause this sunward shift. Species distributions in the foreshock region are depicted within the transition of the shock (measured ≈2 c/ ω pi for Θ Bn = 90° and M MS = 4.7) and in the downstream. The size of the foot jump in the magnetic field at the shock is measured to be (1.7 c/ ω pi ). In the foreshocked region, the thermal velocity is found equal to 213 km s-1 at 15 R E and is equal to 63 km s -1 at 12 R E (magnetosheath region). Despite the large cell size of the current version of the PIC code, it is powerful to retain macrostructure of planets magnetospheres in very short time, thus it can be used for pedagogical test purposes. It is also likely complementary with MHD to deepen our understanding of the large scale magnetosphere.
Modeling extreme (Carrington-type) space weather events using three-dimensional MHD code simulations
Ngwira, C. M.; Pulkkinen, A. A.; Kuznetsova, M. M.; Glocer, A.
2013-12-01
There is growing concern over possible severe societal consequences related to adverse space weather impacts on man-made technological infrastructure and systems. In the last two decades, significant progress has been made towards the modeling of space weather events. Three-dimensional (3-D) global magnetohydrodynamics (MHD) models have been at the forefront of this transition, and have played a critical role in advancing our understanding of space weather. However, the modeling of extreme space weather events is still a major challenge even for existing global MHD models. In this study, we introduce a specially adapted University of Michigan 3-D global MHD model for simulating extreme space weather events that have a ground footprint comparable (or larger) to the Carrington superstorm. Results are presented for an initial simulation run with ``very extreme'' constructed/idealized solar wind boundary conditions driving the magnetosphere. In particular, we describe the reaction of the magnetosphere-ionosphere system and the associated ground induced geoelectric field to such extreme driving conditions. We also discuss the results and what they might mean for the accuracy of the simulations. The model is further tested using input data for an observed space weather event to verify the MHD model consistence and to draw guidance for future work. This extreme space weather MHD model is designed specifically for practical application to the modeling of extreme geomagnetically induced electric fields, which can drive large currents in earth conductors such as power transmission grids.
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)
Boss, Alan P.; Keiser, Sandra A.
2013-01-01
Magnetic fields are important contributors to the dynamics of collapsing molecular cloud cores, and can have a major effect on whether collapse results in a single protostar or fragmentation into a binary or multiple protostar system. New models are presented of the collapse of magnetic cloud cores using the adaptive mesh refinement code Enzo2.0. The code was used to calculate the ideal magnetohydrodynamics (MHD) of initially spherical, uniform density, and rotation clouds with density perturbations, i.e., the Boss and Bodenheimer standard isothermal test case for three-dimensional (3D) hydrodynamics codes. After first verifying that Enzo reproduces the binary fragmentation expected for the non-magnetic test case, a large set of models was computed with varied initial magnetic field strengths and directions with respect to the cloud core axis of rotation (parallel or perpendicular), density perturbation amplitudes, and equations of state. Three significantly different outcomes resulted: (1) contraction without sustained collapse, forming a denser cloud core; (2) collapse to form a single protostar with significant spiral arms; and (3) collapse and fragmentation into binary or multiple protostar systems, with multiple spiral arms. Comparisons are also made with previous MHD calculations of similar clouds with a barotropic equations of state. These results for the collapse of initially uniform density spheres illustrate the central importance of both magnetic field direction and field strength for determining the outcome of dynamic protostellar collapse.
Two-Fluid 2.5D MHD-Code for Simulations in the Solar Atmosphere
Czech Academy of Sciences Publication Activity Database
Piantschitsch, I.; Amerstorfer, U.; Thalmann, J.; Utz, D.; Hanslmeier, A.; Bárta, Miroslav; Thonhofer, S.; Lemmerer, B.
2014-01-01
Roč. 38, č. 1 (2014), s. 59-66 ISSN 1845-8319 R&D Projects: GA MŠk(CZ) 7AMB14AT022 Institutional support: RVO:67985815 Keywords : MHD simulation * chromosphere * reconnection Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics
International Nuclear Information System (INIS)
Bosak, K.; Blum, J.; Joffrin, E.
2004-01-01
Recent development of real-time equilibrium code Equinox using a fixed-point algorithm allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code providing magnetic flux values on the first wall of vacuum vessel. By means of least-square minimization of differences between magnetic field obtained from previous solution and the next measurements the code identifies the source term of the non-linear Grad-Shafranov equation. The strict use of analytical equations together with a flexible algorithm offers an opportunity to include new measurements into stable magnetic equilibrium code and compare the results directly between several tokamaks while maintaining the same physical model (i.e. no iron model is necessary inside the equilibrium code). The successful implementation of this equilibrium code for JET and Tore Supra has already been published. In this paper, we show the preliminary results of predictive runs of the Equinox code using the ITER geometry. Because the real-time control experiments of plasma profile at JET using the code has been shown unstable when using magnetic and polarimetric measurements (that could be indirectly translated into accuracy vs robustness tradeoff), we plan an outline of the algorithm that will allow us to further constrain the plasma current profile using the central value of pressure of the plasma in real-time in order to better define the poloidal beta (this constraint is not necessary with purely magnetic equilibrium). (authors)
Energy Technology Data Exchange (ETDEWEB)
Bosak, K.; Blum, J. [Universite de Nice-Sophia-Antipolis, Lab. J. A. Dieudonne, 06 - Nice (France); Joffrin, E. [Association Euratom-CEA Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
2004-07-01
Recent development of real-time equilibrium code Equinox using a fixed-point algorithm allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code providing magnetic flux values on the first wall of vacuum vessel. By means of least-square minimization of differences between magnetic field obtained from previous solution and the next measurements the code identifies the source term of the non-linear Grad-Shafranov equation. The strict use of analytical equations together with a flexible algorithm offers an opportunity to include new measurements into stable magnetic equilibrium code and compare the results directly between several tokamaks while maintaining the same physical model (i.e. no iron model is necessary inside the equilibrium code). The successful implementation of this equilibrium code for JET and Tore Supra has already been published. In this paper, we show the preliminary results of predictive runs of the Equinox code using the ITER geometry. Because the real-time control experiments of plasma profile at JET using the code has been shown unstable when using magnetic and polarimetric measurements (that could be indirectly translated into accuracy vs robustness tradeoff), we plan an outline of the algorithm that will allow us to further constrain the plasma current profile using the central value of pressure of the plasma in real-time in order to better define the poloidal beta (this constraint is not necessary with purely magnetic equilibrium). (authors)
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)
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
International Nuclear Information System (INIS)
Hernandez Caceres, Jose Luis; Hong, Rolando; Martinez Ortiz, Carlos; Sautie Castellanos, Miguel; Valdes, Kiria; Guevara Erra, Ramon
2004-10-01
Under the assumption of even point mutation pressure on the DNA strand, rates for transitions from one amino acid into another were assessed. Nearly 25% of all mutations were silent. About 48% of the mutations from a given amino acid stream either into the same amino acid or into an amino acid of the same class. These results suggest a great stability of the Standard Genetic Code respect to mutation load. Concepts from chemical equilibrium theory are applicable into this case provided that mutation rate constants are given. It was obtained that unequal synonymic codon usage may lead to changes in the equilibrium concentrations. Data from real biological species showed that several amino acids are close to the respective equilibrium concentration. However in all the cases the concentration of leucine nearly doubled its equilibrium concentration, whereas for the stop command (Term) it was about 10 times lower. The overall distance from equilibrium for a set of species suggests that eukaryotes are closer to equilibrium than prokaryotes, and the HIV virus was closest to equilibrium among 15 species. We obtained that contemporary species are closer to the equilibrium than the Last Universal Common Ancestor (LUCA) was. Similarly, nonpreserved regions in proteins are closer to equilibrium than the preserved ones. We suggest that this approach can be useful for exploring some aspects of biological evolution in the framework of Standard Genetic Code properties. (author)
The PHREEQE Geochemical equilibrium code data base and calculations
International Nuclear Information System (INIS)
Andersoon, K.
1987-01-01
Compilation of a thermodynamic data base for actinides and fission products for use with PHREEQE has begun and a preliminary set of actinide data has been tested for the PHREEQE code in a version run on an IBM XT computer. The work until now has shown that the PHREEQE code mostly gives satisfying results for specification of actinides in natural water environment. For U and Np under oxidizing conditions, however, the code has difficulties to converge with pH and Eh conserved when a solubility limit is applied. For further calculations of actinide and fission product specification and solubility in a waste repository and in the surrounding geosphere, more data are needed. It is necessary to evaluate the influence of the large uncertainties of some data. A quality assurance and a check on the consistency of the data base is also needed. Further work with data bases should include: an extension to fission products, an extension to engineering materials, an extension to other ligands than hydroxide and carbonate, inclusion of more mineral phases, inclusion of enthalpy data, a control of primary references in order to decide if values from different compilations are taken from the same primary reference and contacts and discussions with other groups, working with actinide data bases, e.g. at the OECD/NEA and at the IAEA. (author)
Kumar, A.; Graves, R. A., Jr.; Weilmuenster, K. J.
1980-01-01
A vectorized code, EQUIL, was developed for calculating the equilibrium chemistry of a reacting gas mixture on the Control Data STAR-100 computer. The code provides species mole fractions, mass fractions, and thermodynamic and transport properties of the mixture for given temperature, pressure, and elemental mass fractions. The code is set up for the electrons H, He, C, O, N system of elements. In all, 24 chemical species are included.
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)
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)
Marx, Alain; Lütjens, Hinrich
2017-03-01
A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.
Numerical verification of equilibrium chemistry software within nuclear fuel performance codes
International Nuclear Information System (INIS)
Piro, M.H.; Lewis, B.J.; Thompson, W.T.; Simunovic, S.; Besmann, T.M.
2010-01-01
A numerical tool is in an advanced state of development to compute the equilibrium compositions of phases and their proportions in multi-component systems of importance to the nuclear industry. The resulting software is being conceived for direct integration into large multi-physics fuel performance codes, particularly for providing transport source terms, material properties, and boundary conditions in heat and mass transport modules. Consequently, any numerical errors produced in equilibrium chemistry computations will be propagated in subsequent heat and mass transport calculations, thus falsely predicting nuclear fuel behaviour. The necessity for a reliable method to numerically verify chemical equilibrium computations is emphasized by the requirement to handle the very large number of elements necessary to capture the entire fission product inventory. A simple, reliable and comprehensive numerical verification method called the Gibbs Criteria is presented which can be invoked by any equilibrium chemistry solver for quality assurance purposes. (author)
GATO: an MHD stability code for axisymmetric plasmas with internal separatrices
International Nuclear Information System (INIS)
Bernard, L.C.; Helton, F.J.; Moore, R.W.
1981-07-01
The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40,000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas
GATO: An MHD stability code for axisymmetric plasmas with internal separatrices
International Nuclear Information System (INIS)
Bernard, L.C.; Helton, F.J.; Moore, R.W.
1981-01-01
The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40 000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas. (orig.)
International Nuclear Information System (INIS)
Smolentsev, Sergey; Morley, Neil; Abdou, Mohamed
2005-01-01
The paper presents details of a new numerical code for analysis of a fully developed MHD flow in a channel of a liquid metal blanket using various insulation techniques. The code has specially been designed for channels with a 'sandwich' structure of several materials with different physical properties. The code includes a finite-volume formulation, automatically generated Hartmann number sensitive meshes, and effective convergence acceleration technique. Tests performed at Ha ∼ 10 4 have showed very good accuracy. As an illustration, two blanket flows have been considered: Pb-17Li flow in a channel with a silicon carbide flow channel insert, and Li flow in a channel with insulating coating
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
International Nuclear Information System (INIS)
Nagata, A.; Ashida, H.; Okamoto, M.; Hirano, K.
1981-03-01
Two dimentional fluid simulation code ''TOPICS'' is developed for the STP-2, the shock heated screw pinch at Nagoya. It involves the effects of impurity ions and neutral atoms. In order to estimate the radiation losses, the impurity continuity equations with ionizations and recombinations are solved simultaneously with the plasma fluid equations. The results are compared with the coronal equilibrium model. It is found that the coronal equilibrium model underestimates the radiation losses from shock heated pinch plasmas in its initial dynamic phase. The present calculations including impurities and neutrals show the importance of the radiation losses from the plasma of the STP-2. Introducing the anomalous resistivity caused by the ion acoustic instability, the observed magnetic field penetration is explained fairly well. (author)
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.
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
International nuclear model and code comparison on pre-equilibrium effects
International Nuclear Information System (INIS)
Gruppelaar, H.; van der Kamp, H.A.J.; Nagel, P.
1983-01-01
This paper gives the specification of an intercomparison of statistical nuclear models and codes with emphasis on pre-equilibrium effects. It is partly based upon the conclusions of a meeting of an ad-hoc working group on this subject. The parameters studied are: masses, Q values, level scheme data, optical model parameters, X-ray competition parameters, total level-density specifications, for 86 Rb, 89 Sr, 90 Y, 92 Y, 92 Zr, 93 Zr, 89 Y, 91 Nb, 92 Nb and 93 Nb
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
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)
Energy Technology Data Exchange (ETDEWEB)
Batet, L.; Mas de les Valls, E.; Sedano, L. A.
2012-07-01
In the context of regenerating sheaths for fusion reactors, the CFD simulations of liquid metal channels (ML) are essential to know the phenomenology and obtain relevant information for design as: ML thermal gain, to know the thermal efficiency of the component, existence of hot spots, to define the materials to use, existence of flow inversion, etc. Apart from design parameters there are others, bridge parameter, required as inputs into system code. In this work shown GREENER/T4F capabilities for obtaining both parameters with a CFD tool based on open source OpenFOAM.
Experimental benchmark of non-local-thermodynamic-equilibrium plasma atomic physics codes
International Nuclear Information System (INIS)
Nagels-Silvert, V.
2004-09-01
The main purpose of this thesis is to get experimental data for the testing and validation of atomic physics codes dealing with non-local-thermodynamical-equilibrium plasmas. The first part is dedicated to the spectroscopic study of xenon and krypton plasmas that have been produced by a nanosecond laser pulse interacting with a gas jet. A Thomson scattering diagnostic has allowed us to measure independently plasma parameters such as electron temperature, electron density and the average ionisation state. We have obtained time integrated spectra in the range between 5 and 10 angstroms. We have identified about one hundred xenon rays between 8.6 and 9.6 angstroms via the use of the Relac code. We have discovered unknown rays for the krypton between 5.2 and 7.5 angstroms. In a second experiment we have extended the wavelength range to the X UV domain. The Averroes/Transpec code has been tested in the ranges from 9 to 15 angstroms and from 10 to 130 angstroms, the first range has been well reproduced while the second range requires a more complex data analysis. The second part is dedicated to the spectroscopic study of aluminium, selenium and samarium plasmas in femtosecond operating rate. We have designed an interferometry diagnostic in the frequency domain that has allowed us to measure the expanding speed of the target's backside. Via the use of an adequate isothermal model this parameter has led us to know the plasma electron temperature. Spectra and emission times of various rays from the aluminium and selenium plasmas have been computed satisfactorily with the Averroes/Transpec code coupled with Film and Multif hydrodynamical codes. (A.C.)
Energy Technology Data Exchange (ETDEWEB)
Kolb, C.E.; Yousefian, V.; Wormhoudt, J.; Haimes, R.; Martinez-Sanchez, M.; Kerrebrock, J.L.
1978-01-30
Research has included theoretical modeling of important plasma chemical effects such as: conductivity reductions due to condensed slag/electron interactions; conductivity and generator efficiency reductions due to the formation of slag-related negative ion species; and the loss of alkali seed due to chemical combination with condensed slag. A summary of the major conclusions in each of these areas is presented. A major output of the modeling effort has been the development of an MHD plasma chemistry core flow model. This model has been formulated into a computer program designated the PACKAGE code (Plasma Analysis, Chemical Kinetics, And Generator Efficiency). The PACKAGE code is designed to calculate the effect of coal rank, ash percentage, ash composition, air preheat temperatures, equivalence ratio, and various generator channel parameters on the overall efficiency of open-cycle, coal-fired MHD generators. A complete description of the PACKAGE code and a preliminary version of the PACKAGE user's manual are included. A laboratory measurements program involving direct, mass spectrometric sampling of the positive and negative ions formed in a one atmosphere coal combustion plasma was also completed during the contract's initial phase. The relative ion concentrations formed in a plasma due to the methane augmented combustion of pulverized Montana Rosebud coal with potassium carbonate seed and preheated air are summarized. Positive ions measured include K/sup +/, KO/sup +/, Na/sup +/, Rb/sup +/, Cs/sup +/, and CsO/sup +/, while negative ions identified include PO/sub 3//sup -/, PO/sub 2//sup -/, BO/sub 2//sup -/, OH/sup -/, SH/sup -/, and probably HCrO/sub 3/, HMoO/sub 4//sup -/, and HWO/sub 3//sup -/. Comparison of the measurements with PACKAGE code predictions are presented. Preliminary design considerations for a mass spectrometric sampling probe capable of characterizing coal combustion plasmas from full scale combustors and flow trains are presented
Thompson, Richard A.; Lee, Kam-Pui; Gupta, Roop N.
1991-01-01
The computer codes developed here provide self-consistent thermodynamic and transport properties for equilibrium air for temperatures from 500 to 30000 K over a temperature range of 10 (exp -4) to 10 (exp -2) atm. These properties are computed through the use of temperature dependent curve fits for discrete values of pressure. Interpolation is employed for intermediate values of pressure. The curve fits are based on mixture values calculated from an 11-species air model. Individual species properties used in the mixture relations are obtained from a recent study by the present authors. A review and discussion of the sources and accuracy of the curve fitted data used herein are given in NASA RP 1260.
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 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.
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)
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
Stability analysis by ERATO code
International Nuclear Information System (INIS)
Tsunematsu, Toshihide; Takeda, Tatsuoki; Matsuura, Toshihiko; Azumi, Masafumi; Kurita, Gen-ichi
1979-12-01
Problems in MHD stability calculations by ERATO code are described; which concern convergence property of results, equilibrium codes, and machine optimization of ERATO code. It is concluded that irregularity on a convergence curve is not due to a fault of the ERATO code itself but due to inappropriate choice of the equilibrium calculation meshes. Also described are a code to calculate an equilibrium as a quasi-inverse problem and a code to calculate an equilibrium as a result of a transport process. Optimization of the code with respect to I/O operations reduced both CPU time and I/O time considerably. With the FACOM230-75 APU/CPU multiprocessor system, the performance is about 6 times as high as with the FACOM230-75 CPU, showing the effectiveness of a vector processing computer for the kind of MHD computations. This report is a summary of the material presented at the ERATO workshop 1979(ORNL), supplemented with some details. (author)
Neutronics/Thermo-fluid Coupled Analysis of PMR-200 Equilibrium Cycle by CAPP/GAMMA+ Code System
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun Chul; Tak, Nam-il [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
The equilibrium core was obtained by performing CAPP stand-alone multi-cycle depletion calculation with critical rod position search. In this work, a code system for coupled neutronics and thermo-fluids simulation was developed using CAPP and GAMMA+ codes. A server program, INTCA, controls the two codes for coupled calculations and performs the mapping between the variables of the two codes based on the nodalization of the two codes. In order to extend the knowledge about the coupled behavior of a prismatic VHTR, the CAPP/GAMMA+ code system was applied to steady state performance analysis of PMR-200. The coupled calculation was carried out for the equilibrium core of PMR-200 from BOC to EOC. The peak fuel temperature was predicted to be 1372 .deg. C near MOC. However, the cycle-average fuel temperature was calculated as 1230 .deg. C, which is slightly below the design target of 1250 .deg. C. In addition, significant impact of the bypass flow on the central reflector temperature was found. Without bypass flow, the temperature of the active core region was slightly decreased while the temperature of the central and side reflector region was increased much. The both changes in the temperature increase the multiplication factor and the total change of the multiplication factor was more than 300 pcm. On the other hand, the effect of the bypass flow on the power density profile was not significant.
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
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.
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)
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.
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
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
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.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Bae, Seong Jun; Lee, Won Woong; Oh, Bongseong; Lee, Jeong Ik [KAIST, Daejeon (Korea, Republic of)
2016-10-15
The features of the S-CO{sub 2} Brayton cycle come from a small compressing work by designing the compressor inlet close the critical point of CO{sub 2}. This means the system condition can be operating under two-phase or sub-critical phase during transient situations such as changes of cooling system performance, load variations, etc. Since there is no operating MW scale S-CO{sub 2} Brayton cycle system in the world yet, using an analytical code is the only way to predict the system behavior and develop operating strategies of the S-CO{sub 2} Brayton cycles. Therefore, the development of a credible system code is an important part for the practical S-CO{sub 2} system research. The current status of the developed system analysis code for S-CO{sub 2} Brayton cycle transient analyses in KAIST and verification results are presented in this paper. To avoid errors related with convergences of the code during the phase changing flow calculation in GAMMA+ code, the authors have developed a system analysis code using Homogeneous Equilibrium Model (HEM) for the S-CO{sub 2} Brayton cycle transient analysis. The backbone of the in-house code is the GAMMA+1.0 code, but treating the quality of fluid by tracking system enthalpy gradient every time step. Thus, the code adopts pressure and enthalpy as the independent scalar variables to track the system enthalpy for updating the quality of the system every time step. The heat conduction solving method, heat transfer correlation and frictional losses on the pipe are referred from the GAMMA+ code.
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.)
W7-X vacuum and finite-β magnetic field structure resolved with the HINT 3D equilibrium code
International Nuclear Information System (INIS)
Hayashi, T.; Merkel, P.; Nuehrenberg, J.; Schwenn, U.
1994-01-01
The 3D equilibrium code HINT allows the direct investigation of finite-β effects on sizes and phases of islands in genuinely 3D configurations like the W7-X stellarator planned by the Max-Planck-Institut fuer Plasmaphysik in Germany. The code does not require the existence of nested flux surfaces. This, in contrast to the inverse formulation used in the VMEC code, leads to a considerably more complex computational goal. The HINT code combines some crucial features reducing the numerical problems and the computational effort to such an extent as to allow computation of 3D equilibria at finite-β with magnetic islands. The code is based on a two-step procedure: Starting from a given B and an initial pressure, the iteration technique for the pressure advancement is differencing in an artificial time with an explicit 4th order scheme, or - alternatively for resolving the island topology - field lines starting from all gridpoints are followed long enough to allow pressure equalization along these. B.∇p 0, for fixed B. In a second step, p is kept fixed and B is advanced with an artificial time for solving ∇p - jxB = 0 under the constraint of vanishing toroidal current J. The differential equations are discretized in space with 4th order difference approximations on an Eulerian grid spanned by a rectangular box whose toroidal rotation law follows the W7-X geometry. The two sub-iteration steps are repeated until the force balance is satisfied to an appropriate accuracy. The boundaries (where the boundary conditions are prescribed) are far enough away from the last closed magnetic surface, thus guaranteeing the motion of the plasma column not being constrained by the boundary conditions. Due to the stellarator symmetry in the toroidal direction only half of an equilibrium period is computed, using modified periodic boundary conditions guaranteeing the 4th order of the spatial discretization. (author) 5 refs., 4 figs
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.)
The beta equilibrium, stability, and transport codes. Applications to the design of stellarators
International Nuclear Information System (INIS)
Bauer, F.; Garabedian, P.; Betancourt, O.; Wakatani, M.
1987-01-01
This book gives a detailed exposition of the available computational methods, documents the codes, and presents many examples showing how to run them and how to interpret the results. A listing of the recently completed BETA transport code is included. Current stellarator experiments are discussed, and the book contains significant applications to the design of major new stellarator experiments that are now in the planning stage
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)
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.)
An interactive computer code for calculation of gas-phase chemical equilibrium (EQLBRM)
Pratt, B. S.; Pratt, D. T.
1984-01-01
A user friendly, menu driven, interactive computer program known as EQLBRM which calculates the adiabatic equilibrium temperature and product composition resulting from the combustion of hydrocarbon fuels with air, at specified constant pressure and enthalpy is discussed. The program is developed primarily as an instructional tool to be run on small computers to allow the user to economically and efficiency explore the effects of varying fuel type, air/fuel ratio, inlet air and/or fuel temperature, and operating pressure on the performance of continuous combustion devices such as gas turbine combustors, Stirling engine burners, and power generation furnaces.
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)
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
Energy Technology Data Exchange (ETDEWEB)
Nagels-Silvert, V
2004-09-15
The main purpose of this thesis is to get experimental data for the testing and validation of atomic physics codes dealing with non-local-thermodynamical-equilibrium plasmas. The first part is dedicated to the spectroscopic study of xenon and krypton plasmas that have been produced by a nanosecond laser pulse interacting with a gas jet. A Thomson scattering diagnostic has allowed us to measure independently plasma parameters such as electron temperature, electron density and the average ionisation state. We have obtained time integrated spectra in the range between 5 and 10 angstroms. We have identified about one hundred xenon rays between 8.6 and 9.6 angstroms via the use of the Relac code. We have discovered unknown rays for the krypton between 5.2 and 7.5 angstroms. In a second experiment we have extended the wavelength range to the X UV domain. The Averroes/Transpec code has been tested in the ranges from 9 to 15 angstroms and from 10 to 130 angstroms, the first range has been well reproduced while the second range requires a more complex data analysis. The second part is dedicated to the spectroscopic study of aluminium, selenium and samarium plasmas in femtosecond operating rate. We have designed an interferometry diagnostic in the frequency domain that has allowed us to measure the expanding speed of the target's backside. Via the use of an adequate isothermal model this parameter has led us to know the plasma electron temperature. Spectra and emission times of various rays from the aluminium and selenium plasmas have been computed satisfactorily with the Averroes/Transpec code coupled with Film and Multif hydrodynamical codes. (A.C.)
Energy Technology Data Exchange (ETDEWEB)
Nagels-Silvert, V
2004-09-15
The main purpose of this thesis is to get experimental data for the testing and validation of atomic physics codes dealing with non-local-thermodynamical-equilibrium plasmas. The first part is dedicated to the spectroscopic study of xenon and krypton plasmas that have been produced by a nanosecond laser pulse interacting with a gas jet. A Thomson scattering diagnostic has allowed us to measure independently plasma parameters such as electron temperature, electron density and the average ionisation state. We have obtained time integrated spectra in the range between 5 and 10 angstroms. We have identified about one hundred xenon rays between 8.6 and 9.6 angstroms via the use of the Relac code. We have discovered unknown rays for the krypton between 5.2 and 7.5 angstroms. In a second experiment we have extended the wavelength range to the X UV domain. The Averroes/Transpec code has been tested in the ranges from 9 to 15 angstroms and from 10 to 130 angstroms, the first range has been well reproduced while the second range requires a more complex data analysis. The second part is dedicated to the spectroscopic study of aluminium, selenium and samarium plasmas in femtosecond operating rate. We have designed an interferometry diagnostic in the frequency domain that has allowed us to measure the expanding speed of the target's backside. Via the use of an adequate isothermal model this parameter has led us to know the plasma electron temperature. Spectra and emission times of various rays from the aluminium and selenium plasmas have been computed satisfactorily with the Averroes/Transpec code coupled with Film and Multif hydrodynamical codes. (A.C.)
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
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
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
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)
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
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
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)
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)
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
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
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
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.
BALDUR: a one-dimensional plasma transport code
International Nuclear Information System (INIS)
Singer, C.E.; Post, D.E.; Mikkelsen, D.R.
1986-07-01
The purpose of BALDUR is to calculate the evolution of plasma parameters in an MHD equilibrium which can be approximated by concentric circular flux surfaces. Transport of up to six species of ionized particles, of electron and ion energy, and of poloidal magnetic flux is computed. A wide variety of source terms are calculated including those due to neutral gas, fusion, and auxiliary heating. The code is primarily designed for modeling tokamak plasmas but could be adapted to other toroidal confinement systems
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
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.
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
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
International Nuclear Information System (INIS)
Feber, R.D.; Lunsford, J.L.; Stark, W.A. Jr.
1976-05-01
An equilibrium analysis has been made of the fission-product cesium in the primary coolant loop of the high-temperature gas-cooled reactor (HTGR). The species distributions that result at equilibrium have been calculated for various conditions of reactor operation. The cesium species considered were the monomer, dimer, oxides, hydroxides, and the hydride. The effect of cesium sorption isotherms on graphite also was included in the analysis. During normal reactor operations, the abundant species of cesium were calculated to be elemental cesium, Cs, and the monomeric hydroxide, CsOH. Under most conditions of steam ingress, the abundant species was calculated to be CsOH. Cesium adsorbed onto graphite was stable under all steam-ingress conditions considered. Thermal transients above 1500 0 K were required for equilibrium transport of cesium from the core to the coolant. The analysis was carried out using the complex equilibrium code QUIL, designed and written with special emphasis on features that make it applicable to the fission-product problem
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.)
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
International Nuclear Information System (INIS)
Goulo, V.G.
1988-01-01
This document describes the content of the diskettes with nuclear data production codes SCAT2 and STAPRE and the example data set for implementing and testing of these codes for personal computers IBM/AT. They are available on two diskettes, free fo charge, upon request from the NEA Data Bank, Saclay, France. (author). 4 refs, 1 fig
International Nuclear Information System (INIS)
Anderson, D.V.; Cohen, R.H.; Ferguson, J.R.; Johnston, B.M.; Sharp, C.B.; Willmann, P.A.
1981-01-01
The single particle orbit code, TIBRO, has been modified extensively to improve the interpolation methods used and to allow use of vector potential fields in the simulation of charged particle orbits on a 3D domain. A 3D cubic B-spline algorithm is used to generate spline coefficients used in the interpolation. Smooth and accurate field representations are obtained. When vector potential fields are used, the 3D cubic spline interpolation formula analytically generates the magnetic field used to push the particles. This field has del.BETA = 0 to computer roundoff. When magnetic induction is used the interpolation allows del.BETA does not equal 0, which can lead to significant nonphysical results. Presently the code assumes quadrupole symmetry, but this is not an essential feature of the code and could be easily removed for other applications. Many details pertaining to this code are given on microfiche accompanying this report
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)
Formation and healing of n = 1 magnetic islands in LHD equilibrium
International Nuclear Information System (INIS)
Kanno, Ryutaro; Hayashi, Takaya; Okamoto, Masao
2005-01-01
Magnetic islands with the toroidal mode number n = 1, e.g. m/n = 1/1 and 2/1 islands, in a Large Helical Device (LHD) equilibrium are studied using the three-dimensional MHD equilibrium code, HINT. In order to accomplish this purpose, the HINT code has been improved. The equilibrium analysis, in particular an analysis of the LHD equilibrium with an m/n = 1/1 island, is required for the local island divertor experiment, in order to understand the magnetic structures of field lines, i.e. flux surfaces, islands and ergodic field lines. We find that the m/n = 2/1 island can be healed for a finite equilibrium beta, while the m/n = 1/1 island is not healed and is surrounded with ergodic field lines for finite-β. From the latter result, we can conjecture that the island divertor concept is effective even for finite equilibrium beta-values, but the performance of the island divertor is deteriorated for finite-β because of the existence of the ergodic zone between the closed surfaces (i.e. the core region) and the m/n = 1/1 island. We also find that the width of the m/n = 1/1 island depends on the equilibrium beta value and that the island located at the inside of the torus has the advantage of retaining its width
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
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.
International Nuclear Information System (INIS)
Takase, Haruhiko; Senda, Ikuo
1999-01-01
A Toroidally Symmetric Plasma Simulation (TSPS) code has been developed for investigating the position and shape control on tokamak plasmas. The analyses of three-dimensional eddy currents on the conducting components around the plasma and the two-dimensional magneto-hydrodynamic (MHD) equilibrium are taken into account in this code. The code can analyze the plasma position and shape control during the minor disruption in which the deformation of plasma is not negligible. Using the ITER (International Thermonuclear Experimental Reactor) parameters, some examples of calculations are shown in this paper. (author)
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)
Marchiori, G.; Grando, L.; Cavinato, M.
2007-01-01
The load assembly of RFX-mod consists of three toroidal conducting structures whose eddy currents affect the plasma equilibrium magnetic configuration. The high number of electromagnetic probes mounted on the components of the load assembly allowed to analyse the response of each structure to a variation of the magnetic field vertical component. The capability of evaluating the axisymmetric toroidal currents in the passive structures and therefore their contribution to the equilibrium configuration by a 2D FE MHD equilibrium code was validated. The design and implementation of a feedback control system of the magnetic field vertical component before the gas ionization allowed meeting the requirement of an accurate control of this quantity in view of operation at higher plasma current and independently of the magnetizing winding programming
Jetto a free boundary plasma transport code
International Nuclear Information System (INIS)
Cenacchi, G.; Taroni, A.
1988-01-01
JETTO is a one-and-a-half-dimensional transport code calculating the evolution of plasma parameters in a time dependent axisymmetric MHD equilibrium configuration. A splitting technique gives a consistent solution of coupled equilibrium and transport equations. The plasma boundary is free and defined either by its contact with a limiter (wall) or by a separatrix or by the toroidal magnetic flux. The Grad's approach to the equilibrium problem with adiabatic (or similar) constraints is adopted. This method consists of iterating by alternately solving the Grad-Schluter-Shafranov equation (PDE) and the ODE obtained by averaging the PDE over the magnetic surfaces. The bidimensional equation of the poloidal flux is solved by a finite difference scheme, whereas a Runge-Kutta method is chosen for the averaged equilibrium equation. The 1D transport equations (averaged over the magnetic surfaces) for the electron and ion densities and energies and for the rotational transform are written in terms of a coordinate (ρ) related to the toroidal flux. Impurity transport is also considered, under the hypothesis of coronal equilibrium. The transport equations are solved by an implicit scheme in time and by a finite difference scheme in space. The centering of the source terms and transport coefficients is performed using a Predictor-Corrector scheme. The basic version of the code is described here in detail; input and output parameters are also listed
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
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.
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
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
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)
Energy Technology Data Exchange (ETDEWEB)
Hedayat, Afshin, E-mail: ahedayat@aeoi.org.ir
2016-12-01
Highlights: • Introducing a high-beneficent and low-cost multipurpose research reactor. • High technical documents and standard safety issues are introduced coherently. • High effective conceptual neutronic analyses and fuel management strategy. • Gaining high score design criteria and safety margins via 3-D core modeling. • Capacity and capability to produce all medical and industrial radioisotopes. - Abstract: In this paper, neutronic and equilibrium refueling parameters of a multi-purpose cost-effective research reactor have been studied and analyzed. It has been tried to provide periodic and long-term requirements of the irradiating applications coherently. The WIMSD5B and CITVAP codes are used to calculate neutronic parameters and simulate fuel management strategy. The used nuclear data, codes, and calculating methods have been severally benchmarked and verified, successfully. Fundamental concepts, design criteria, and safety issues are introduced and discussed, coherently. Design criteria are selected to gain the most economic benefits per capital costs via minimum required reactor power. Accurate, fast and simplified models have been tried for an integrated decision making and analyses using deterministic codes. Core management, power effects, fuel consumption and burn up effects, and also a complete simulation of the fuel management strategy are presented and analyzed. Results show that the supposed reactor core design can be promisingly suitable in accordance with the commercial multi-purpose irradiating applications. It also retains Operating Limits and Conditions (OLCs) due to standard safety issues, conservatively where safety parameters are calculated using best estimate tools. Such reactor core configuration and integrated refueling task can effectively enhance the Quality Assurance (QA) of the general irradiating applications of the current MTR within their power limits and corresponding OLCs.
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
International Nuclear Information System (INIS)
Yamazaki, K.; Yamada, I.; Taniguchi, S.; Oishi, T.
2009-01-01
Full text: The high performance plasma behavior is required to realize economic and environmental-friendly fusion reactors compatible with conventional power plant systems. To improve plasma confinement, the formation of internal transport barrier (ITB) is anticipated, and its behavior is analyzed by the simulation code TOTAL (Toroidal Transport Linkage Analysis). This TOTAL code comprises a 2- or 3-dimensional equilibrium and 1-dimensional predictive transport code for both tokamak and helical systems. In the tokamak code TOTAL-T, the external current drive, bootstrap current, sawtooth oscillation, ballooning mode and neoclassical tearing mode (NTM) analyses are included. The steady-state burning plasma operation is achieved by the feedback control of pellet injection fuelling and external heating power control. The impurity dynamics of iron and tungsten is also included in this code. The NTM effects are evaluated using the modified Rutherford Model with the stabilization of the ECCD current drive. The excitation of m=2/n=1 NTM leads to the 20 % reduction in the central temperature in ITER-like reactors. Recently, the external non-resonant helical field application is analyzed and its stabilization properties are evaluated. The pellet injection effects on ITB formation is also clarified in tokamak and helical plasmas. Relationship between sawtooth oscillation and impurity ejection is recently simulated in comparison with experimental data. In this conference, we will show above-stated new results on MHD instability effects on burning plasma transport. (author)
Engineering design and development of lead lithium loop for thermo-fluid MHD studies
International Nuclear Information System (INIS)
Kumar, M.; Patel, Anita; Jaiswal, A.; Ranjan, A.; Mohanta, D.; Sahu, S.; Saraswat, A.; Rao, T.S.; Mehta, V.; Bhattacharyay, R.; Rajendra Kumar, E.
2017-01-01
In the frame of the design and development of LLCB TBM, number of R and D activities is in progress in the area of Pb-Li technology development. Molten Pb-Li is used as a tritium breeder and also as a coolant for the internals of the TBM structure. In presence of strong plasma confining toroidal magnetic field, motion of electrically conducting Pb-Li leads to Magneto Hydro Dynamic (MHD) phenomena, as a consequence of which the flow profile of Pb-Li is significantly modified inside the Pb-Li channels of TBM. This causes additional pressure drop inside TBM and affects the heat transfer from internal structure. The detail studies of these MHD effects are of prime importance for successful design of LLCB TBM and its performance evaluation. Although, various numerical MHD codes have been developed, validated in simple flow configuration and are being used to study MHD phenomena in LLCB TBM, experimental validation of these codes in TBM relevant complex flow geometry is yet to be performed. A Pb-Li MHD experimental loop is, therefore, being developed at IPR to perform thermo-fluid MHD experiments in various LLCB TBM relevant flow configuration. MHD experiments are planned with different test sections instrumented with potential pins, thermo couples, etc. under a uniform magnetic field of ∼1.4 T. The obtained experimental data will be analyzed to understand the MHD phenomena in TBM like flow configuration and also for validation of MHD codes. This paper describes the detailed process as well as engineering design of the Pb-Li MHD loop and its major components along with the plan of MHD experiments in various test mock ups. (author)
International Nuclear Information System (INIS)
Wong, C.P.C.; Merrill, B.
2014-01-01
Highlights: • With the use of a system code, tritium burn-up fraction (f burn ) can be determined. • Initial tritium inventory for steady state DT machines can be estimated. • f burn of ARIES-AT, CFETR and FNSF-AT are in the range of 1–2.8%. • Respective total tritium inventories of are 7.6 kg, 6.1 kg, and 5.2 kg. - Abstract: ITER is under construction and will begin operation in 2020. This is the first 500 MW fusion class DT device, and since it is not going to breed tritium, it will consume most of the limited supply of tritium resources in the world. Yet, in parallel, DT fusion nuclear component testing machines will be needed to provide technical data for the design of DEMO. It becomes necessary to estimate the tritium burn-up fraction and corresponding initial tritium inventory and the doubling time of these machines for the planning of future supply and utilization of tritium. With the use of a system code, tritium burn-up fraction and initial tritium inventory for steady state DT machines can be estimated. Estimated tritium burn-up fractions of FNSF-AT, CFETR-R and ARIES-AT are in the range of 1–2.8%. Corresponding total equilibrium tritium inventories of the plasma flow and tritium processing system, and with the DCLL blanket option are 7.6 kg, 6.1 kg, and 5.2 kg for ARIES-AT, CFETR-R and FNSF-AT, respectively
Energy Technology Data Exchange (ETDEWEB)
Wong, C.P.C., E-mail: wongc@fusion.gat.com [General Atomics, San Diego, CA (United States); Merrill, B. [Idaho National Laboratory, Idaho Falls, ID (United States)
2014-10-15
Highlights: • With the use of a system code, tritium burn-up fraction (f{sub burn}) can be determined. • Initial tritium inventory for steady state DT machines can be estimated. • f{sub burn} of ARIES-AT, CFETR and FNSF-AT are in the range of 1–2.8%. • Respective total tritium inventories of are 7.6 kg, 6.1 kg, and 5.2 kg. - Abstract: ITER is under construction and will begin operation in 2020. This is the first 500 MW{sub fusion} class DT device, and since it is not going to breed tritium, it will consume most of the limited supply of tritium resources in the world. Yet, in parallel, DT fusion nuclear component testing machines will be needed to provide technical data for the design of DEMO. It becomes necessary to estimate the tritium burn-up fraction and corresponding initial tritium inventory and the doubling time of these machines for the planning of future supply and utilization of tritium. With the use of a system code, tritium burn-up fraction and initial tritium inventory for steady state DT machines can be estimated. Estimated tritium burn-up fractions of FNSF-AT, CFETR-R and ARIES-AT are in the range of 1–2.8%. Corresponding total equilibrium tritium inventories of the plasma flow and tritium processing system, and with the DCLL blanket option are 7.6 kg, 6.1 kg, and 5.2 kg for ARIES-AT, CFETR-R and FNSF-AT, respectively.
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
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
International Nuclear Information System (INIS)
Yamamoto, Takaya; Kitamura, Masashi; Ohi, Tadashi; Akagi, Katsumi
1999-01-01
As advanced monitoring and controlling systems, such as the advanced main control console and the operator support system have been developed, real-time simulators' simulation accuracy must be improved and simulation limits must be extended. Therefore the authors have developed a distributed simulation system to achieve high processing performance using low cost hardware. Moreover, the authors have developed a thermal-hydraulic computer code, using drift-flux non-equilibrium model, which can realize a high precision two-phase flow analysis, which is considered to have the same prediction capability as two-fluid models, while achieving high speed and stability for real-time simulators. The distributed plant simulator for PWR plants was realized as a result. The distributed simulator consists of multi-processors connected to each other by an optical fiber network. Controlling software for synchronized scheduling and memory transfer was also developed. The simulation results of the four loop PWR simulator are compared with experimental data and real plant data; the agreement is satisfactory for a plant simulator. The simulation speed is also satisfactory being twice as fast as real-time. (author)
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.
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
Ideal MHD stability analysis of KSTAR target AT mode
International Nuclear Information System (INIS)
Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.
2009-01-01
Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)
CASTOR: Normal-mode analysis of resistive MHD plasmas
Kerner, W.; Goedbloed, J. P.; Huysmans, G. T. A.; Poedts, S.; Schwarz, E.
1998-01-01
The CASTOR (complex Alfven spectrum of toroidal plasmas) code computes the entire spectrum of normal-modes in resistive MHD for general tokamak configurations. The applied Galerkin method, in conjunction with a Fourier finite-element discretisation, leads to a large scale eigenvalue problem A (x)
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.
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
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
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
The computation of multiple MHD equilibria in axisymmetric and straight geometry
International Nuclear Information System (INIS)
Thomas, C.Ll.
1979-01-01
The details of the numerical methods used in codes for computing MHD equilibria in discrete conductor configurations are described with both code users and code writers in mind. Results produced by the codes have been successfully verified against analytic results and independent computations. The axisymmetric code has proved to be a valuable diagnostic aid for the TOSCA experiment. The user images of the codes are described in the appendices. (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
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
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....
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)
International Nuclear Information System (INIS)
Burke, B. J.; Kruger, S. E.; Hegna, C. C.; Zhu, P.; Snyder, P. B.; Sovinec, C. R.; Howell, E. C.
2010-01-01
A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10 8 and 10 3 for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10 5 , which is much larger than experimentally measured values using T e values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.
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.
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.
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
International Nuclear Information System (INIS)
Reiman, A.; Monticello, D.; Pomphrey, N.
1993-01-01
The three-dimensional MHD equilibrium equation is a mixed elliptic-hyperbolic partial differential equation. Unlike more familiar equations of this sort, the source term in the elliptic part of the equation is dependent on the time-asymptotic solution of the hyperbolic part, because the pressure and the force-free part of the current are constant along magnetic field lines. The equations for the field line trajectories can be put in the form of Hamilton's equations for a one-dimensional time-dependent system. The authors require an accurate solution for the KAM surfaces of this nonintegrable Hamiltonian. They describe a new algorithm they have developed for this purpose, and discuss its relationship to previously developed algorithms for computing KAM surfaces. They also discuss the numerical issues that arise in self-consistently coupling the output of this algorithm to the elliptic piece of the equation to calculate the magnetic field driven by the current. For nominally axisymmetric devices, they describe how the code is used to directly calculate the saturated state of nonaxisymmetric instabilities by following the equilibrium solution through a bifurcation. They argue that this should be the method of choice for evaluating stability to tearing modes in toroidal magnetic confinement devices
International Nuclear Information System (INIS)
Zhang, Xiujie; Pan, Chuanjie; Xu, Zengyu
2013-01-01
Highlights: ► 2D MHD code based on a fully developed modeling is developed and validated by Samad analytical results. ► The results of MHD effect of liquid metal through circular pipes at high Hartmann numbers are given. ► M type velocity profile is observed for MHD circular pipe flow at high wall conductance ratio condition. ► Non-uniform wall electrical conductivity leads to high jet velocity in Robert layers. -- Abstract: Magnetohydrodynamics (MHD) laminar flows through circular pipes are studied in this paper by numerical simulation under the conditions of Hartmann numbers from 18 to 10000. The code is developed based on a fully developed modeling and validated by Samad's analytical solution and Chang's asymptotic results. After the code validation, numerical simulation is extended to high Hartmann number for MHD circular pipe flows with conducting walls, and numerical results such as velocity distribution and MHD pressure gradient are obtained. Typical M-type velocity is observed but there is not such a big velocity jet as that of MHD rectangular duct flows even under the conditions of high Hartmann numbers and big wall conductance ratio. The over speed region in Robert layers becomes smaller when Hartmann numbers increase. When Hartmann number is fixed and wall conductance ratios change, the dimensionless velocity is through one point which is in agreement with Samad's results, the locus of maximum value of velocity jet is same and effects of wall conductance ratio only on the maximum value of velocity jet. In case of Robert walls are treated as insulating and Hartmann walls as conducting for circular pipe MHD flows, there is big velocity jet like as MHD rectangular duct flows of Hunt's case 2
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)
A versatile ray-tracing code for studying rf wave propagation in toroidal magnetized plasmas
International Nuclear Information System (INIS)
Peysson, Y; Decker, J; Morini, L
2012-01-01
A new ray-tracing code named C3PO has been developed to study the propagation of arbitrary electromagnetic radio-frequency (rf) waves in magnetized toroidal plasmas. Its structure is designed for maximum flexibility regarding the choice of coordinate system and dielectric model. The versatility of this code makes it particularly suitable for integrated modeling systems. Using a coordinate system that reflects the nested structure of magnetic flux surfaces in tokamaks, fast and accurate calculations inside the plasma separatrix can be performed using analytical derivatives of a spline-Fourier interpolation of the axisymmetric toroidal MHD equilibrium. Applications to reverse field pinch magnetic configuration are also included. The effects of 3D perturbations of the axisymmetric toroidal MHD equilibrium, due to the discreteness of the magnetic coil system or plasma fluctuations in an original quasi-optical approach, are also studied. Using a Runge–Kutta–Fehlberg method for solving the set of ordinary differential equations, the ray-tracing code is extensively benchmarked against analytical models and other codes for lower hybrid and electron cyclotron waves. (paper)
Ma, Xinxing; Ennis, D. A.; Hanson, J. D.; Hartwell, G. J.; Knowlton, S. F.; Maurer, D. A.
2017-10-01
Non-axisymmetric equilibrium reconstructions have been routinely performed with the V3FIT code in the Compact Toroidal Hybrid (CTH), a stellarator/tokamak hybrid. In addition to 50 external magnetic measurements, 160 SXR emissivity measurements are incorporated into V3FIT to reconstruct the magnetic flux surface geometry and infer the current distribution within the plasma. Improved reconstructions of current and q profiles provide insight into understanding the physics of density limit disruptions observed in current-carrying discharges in CTH. It is confirmed that the final scenario of the density limit of CTH plasmas is consistent with classic observations in tokamaks: current profile shrinkage leads to growing MHD instabilities (tearing modes) followed by a loss of MHD equilibrium. It is also observed that the density limit at a given current linearly increases with increasing amounts of 3D shaping fields. Consequently, plasmas with densities up to two times the Greenwald limit are attained. Equilibrium reconstructions show that addition of 3D fields effectively moves resonance surfaces towards the edge of the plasma where the current profile gradient is less, providing a stabilizing effect. This work is supported by US Department of Energy Grant No. DE-FG02-00ER54610.
Influence of Equilibrium Perpendicular Shear Flow on Peeling-ballooning Instabilities
Xi, P. W.; Xu, X. Q.
2011-10-01
The influence of perpendicular ExB shear flow on peeling-ballooning instabilities is investigated with BOUT++ code. In our simulation, a set of reduced MHD equations are solved for a very unstable equilibrium and a marginal unstable equilibrium in shifted-circular tokamak geometry. For ideal MHD cases without diamagnetic terms and resistivity, we find that flow shear shows dramatic stabilizing effect on peeling-ballooning modes and the stabilizing degree increases with mode number. When the flow shear is large enough, we find the curvature of growth rate verse mode number has the same shape like that for the case with only diamagnetic term, and this implies that diamagnetic term and the shear flow have the same mechanism acting on peeling-ballooning instabilities. The role of Kelvin-Helmholtz term is also investigated and we find it is destabilizing and the effect depends on both flow shear and mode number. For cases with both diamagnetic term and the applied shear flow, modes with intermediate mode number are strongest stabilized while high n and low n mode keep unstable. Based on these results, an ELM trigger sketch is proposed. Performed for USDoE by LLNL Contract DE-AC52-07NA27344.
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.
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
Vectorization, parallelization and porting of nuclear codes (porting). Progress report fiscal 1998
International Nuclear Information System (INIS)
Nemoto, Toshiyuki; Kawai, Wataru; Ishizuki, Shigeru; Kawasaki, Nobuo; Kume, Etsuo; Adachi, Masaaki; Ogasawara, Shinobu
2000-03-01
Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system, the AP3000 system and the Paragon system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. We dealt with 12 codes in fiscal 1998. These results are reported in 3 parts, i.e., the vectorization and parallelization on vector processors part, the parallelization on scalar processors part and the porting part. In this report, we describe the porting. In this porting part, the porting of Monte Carlo N-Particle Transport code MCNP4B2 and Reactor Safety Analysis code RELAP5 on the AP3000 are described. In the vectorization and parallelization on vector processors part, the vectorization of General Tokamak Circuit Simulation Program code GTCSP, the vectorization and parallelization of Molecular Dynamics Ntv Simulation code MSP2, Eddy Current Analysis code EDDYCAL, Thermal Analysis Code for Test of Passive Cooling System by HENDEL T2 code THANPACST2 and MHD Equilibrium code SELENEJ on the VPP500 are described. In the parallelization on scalar processors part, the parallelization of Monte Carlo N-Particle Transport code MCNP4B2, Plasma Hydrodynamics code using Cubic Interpolated propagation Method PHCIP and Vectorized Monte Carlo code (continuous energy model/multi-group model) MVP/GMVP on the Paragon are described. (author)
International Nuclear Information System (INIS)
Ishizuki, Shigeru; Kawai, Wataru; Nemoto, Toshiyuki; Ogasawara, Shinobu; Kume, Etsuo; Adachi, Masaaki; Kawasaki, Nobuo; Yatake, Yo-ichi
2000-03-01
Several computer codes in the nuclear field have been vectorized, parallelized and transported on the FUJITSU VPP500 system, the AP3000 system and the Paragon system at Center for Promotion of Computational Science and Engineering in Japan Atomic Energy Research Institute. We dealt with 12 codes in fiscal 1998. These results are reported in 3 parts, i.e., the vectorization and parallelization on vector processors part, the parallelization on scalar processors part and the porting part. In this report, we describe the vectorization and parallelization on vector processors. In this vectorization and parallelization on vector processors part, the vectorization of General Tokamak Circuit Simulation Program code GTCSP, the vectorization and parallelization of Molecular Dynamics NTV (n-particle, Temperature and Velocity) Simulation code MSP2, Eddy Current Analysis code EDDYCAL, Thermal Analysis Code for Test of Passive Cooling System by HENDEL T2 code THANPACST2 and MHD Equilibrium code SELENEJ on the VPP500 are described. In the parallelization on scalar processors part, the parallelization of Monte Carlo N-Particle Transport code MCNP4B2, Plasma Hydrodynamics code using Cubic Interpolated Propagation Method PHCIP and Vectorized Monte Carlo code (continuous energy model / multi-group model) MVP/GMVP on the Paragon are described. In the porting part, the porting of Monte Carlo N-Particle Transport code MCNP4B2 and Reactor Safety Analysis code RELAP5 on the AP3000 are described. (author)
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.
Extended MHD Effects in High Energy Density Experiments
Seyler, Charles
2016-10-01
The MHD model is the workhorse for computational modeling of HEDP experiments. Plasma models are inheritably limited in scope, but MHD is expected to be a very good model for studying plasmas at the high densities attained in HEDP experiments. There are, however, important ways in which MHD fails to adequately describe the results, most notably due to the omission of the Hall term in the Ohm's law (a form of extended MHD or XMHD). This talk will discuss these failings by directly comparing simulations of MHD and XMHD for particularly relevant cases. The methodology is to simulate HEDP experiments using a Hall-MHD (HMHD) code based on a highly accurate and robust Discontinuous Galerkin method, and by comparison of HMHD to MHD draw conclusions about the impact of the Hall term. We focus on simulating two experimental pulsed power machines under various scenarios. We examine the MagLIF experiment on the Z-machine at Sandia National Laboratories and liner experiments on the COBRA machine at Cornell. For the MagLIF experiment we find that power flow in the feed leads to low density plasma ablation into the region surrounding the liner. The inflow of this plasma compresses axial magnetic flux onto the liner. In MHD this axial flux tends to resistively decay, whereas in HMHD a force-free current layer sustains the axial flux on the liner leading to a larger ratio of axial to azimuthal flux. During the liner compression the magneto-Rayleigh-Taylor instability leads to helical perturbations due to minimization of field line bending. Simulations of a cylindrical liner using the COBRA machine parameters can under certain conditions exhibit amplification of an axial field due to a force-free low-density current layer separated by some distance from the liner. This results in a configuration in which there is predominately axial field on the liner inside the current layer and azimuthal field outside the layer. We are currently attempting to experimentally verify the simulation
MHD Advanced Power Train Phase I, Final Report, Volume 7
Energy Technology Data Exchange (ETDEWEB)
A. R. Jones
1985-08-01
This appendix provides additional data in support of the MHD/Steam Power Plant Analyses reported in report Volume 5. The data is in the form of 3PA/SUMARY computer code printouts. The order of presentation in all four cases is as follows: (1) Overall Performance; (2) Component/Subsystem Information; (3) Plant Cost Accounts Summary; and (4) Plant Costing Details and Cost of Electricity.
Two-dimensional simulation of the MHD stability, (1)
International Nuclear Information System (INIS)
Kurita, Gen-ichi; Amano, Tsuneo.
1976-03-01
The two-dimensional computer code has been prepared to study MHD stability of an axisymmetric toroidal plasma with and without the surrounding vacuum region. It also includes the effect of magnetic surfaces with non-circular cross sections. The linearized equations of motion are solved as an initial value problem. The results by computer simulation are compared with those by the theory for the cylindrical plasma; they are in good agreement. (auth.)
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
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.
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.
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
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
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.
International Nuclear Information System (INIS)
Aiba, N.; Tokuda, S.; Oyama, N.; Ozeki, T.; Furukawa, M.
2009-01-01
Effects of a sheared toroidal rotation are investigated numerically on the stability of the MHD modes in the tokamak edge pedestal, which relate to the type-I edge-localized mode. A linear MHD stability code MINERVA is newly developed for solving the Frieman-Rotenberg equation that is the linear ideal MHD equation with flow. Numerical stability analyses with this code reveal that the sheared toroidal rotation destabilizes edge localized MHD modes for rotation frequencies which are experimentally achievable, though the ballooning mode stability changes little by rotation. This rotation effect on the edge MHD stability becomes stronger as the toroidal mode number of the unstable MHD mode increases when the stability analysis was performed for MHD modes with toroidal mode numbers smaller than 40. The toroidal mode number of the unstable MHD mode depends on the stabilization of the current-driven mode and the ballooning mode by increasing the safety factor. This dependence of the toroidal mode number of the unstable mode on the safety factor is considered to be the reason that the destabilization by toroidal rotation is stronger for smaller edge safety factors.
Recent progress on MHD-induced loss of D-D fusion products in TFTR
International Nuclear Information System (INIS)
Zweben, S.J.; Darrow, D.S.; Budny, R.V.; Cheng, C.Z.; Fredrickson, E.D.; Herrmann, H.; Mynick, H.E.; Schivell, J.
1993-08-01
This paper reviews the recent progress made toward understanding the MHD-induced loss of D-D fusion products which has been seen on TFTR since 1988. These measurements have been made using the ''lost alpha'' diagnostic, which is described briefly. The largest MHD- induced loss occurs with coherent 3/2 or 2/1 MHD activity (kink/tearing modes), which can cause up to ∼3--5 times the first-orbit loss at I∼1.6--1.8 MA, roughly a ∼20--30% global los of D-D fusion products. Modeling of these MHD-induced losses has progressed to the point where the basic loss mechanism can be accounted for qualitatively, but the experimental results can not yet be understood quantitatively. Several alpha loss codes are being developed to improve the quantitative comparison between experiment and theory
Equations of state for self-excited MHD generator studies
Energy Technology Data Exchange (ETDEWEB)
Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K.
1980-02-26
We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range.
Liquid metal MHD research and development in Israel
International Nuclear Information System (INIS)
Branover, H.
1993-01-01
The study of liquid metal MHD in Israel commenced in 1973. Initially it was concentrated mainly on laminar flows influenced by external magnetic fields. In 1978 a liquid metal MHD energy conversion program was started. This program was developed at the Center for MHD Studies at Ben-Gurion University in Beer-Sheva, with the participation of specialists from the Technion, the Hebrew University of Jerusalem, Israel Atomic Energy Commission, and others. The program was sponsored initially by the Israel Ministry of Energy and Infrastructure, and later by the Ministry of Industry and Trade. Since 1980, Solmecs, a private commercial company has become a major factor in the development of liquid metal MHD in Israel. From the very beginning the program was based on broad international cooperation. A number of overseas institutions and individuals became participants in the program. Through extensive research and evaluation of a number of concepts of liquid metal MHD power generation systems, It was established that the most promising concept, demanding a relatively short period of development, is the gravitational system using heavy metals (lead, lead alloys) as the magneto-hydrodynamic fluid and steam or gases as thermodynamic fluids. This concept was chosen for further development and industrial application, and the program related to such systems was named the Etgar Program. The main directions of research and development activities have been defined as follows: investigations of physical phenomena, development of universal numerical code for parametric studies, optimization and design of the system, material studies, development of engineering components, building and testing of integrated small-scale Etgar type systems, economic evaluation of the system and comparison with conventional technologies, development of moderate scale industrial demonstration plant. At this time 6 items have been fully implemented and activities on the last item were started. (author)
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.
Flow aerodynamics modeling of an MHD swirl combustor - calculations and experimental verification
International Nuclear Information System (INIS)
Gupta, A.K.; Beer, J.M.; Louis, J.F.; Busnaina, A.A.; Lilley, D.G.
1981-01-01
This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Tue produces as output the flow field map of the non-dimensional stream function, axial and swirl velocity. 19 refs
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
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)
United States Superconducting MHD Magnet Technology Development Program
International Nuclear Information System (INIS)
Dawson, A.M.; Marston, P.G.; Thome, R.J.; Iwasa, Y.; Tarrh, J.M.
1981-01-01
A three-faceted program supported by the U.S. Dep of Energy is described. These facets include basic technology development, technology transfer and construction by industry of magnets for the national MHD program. The program includes the maintenance of a large component test facility; investigation of superconductor stability and structural behavior; measurements of materials' properties at low temperatures; structural design optimization; analytical code development; cryogenic systems and power supply design. The technology transfer program is designed to bring results of technology development and design and construction effort to the entire superconducting magnet community. The magnet procurement program is responsible for developing conceptual designs of magnets needed for the national MHD program, for issuing requests for quotation, selecting vendors and supervising design, construction, installation and test of these systems. 9 refs
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.
HPC parallel programming model for gyrokinetic MHD simulation
International Nuclear Information System (INIS)
Naitou, Hiroshi; Yamada, Yusuke; Tokuda, Shinji; Ishii, Yasutomo; Yagi, Masatoshi
2011-01-01
The 3-dimensional gyrokinetic PIC (particle-in-cell) code for MHD simulation, Gpic-MHD, was installed on SR16000 (“Plasma Simulator”), which is a scalar cluster system consisting of 8,192 logical cores. The Gpic-MHD code advances particle and field quantities in time. In order to distribute calculations over large number of logical cores, the total simulation domain in cylindrical geometry was broken up into N DD-r × N DD-z (number of radial decomposition times number of axial decomposition) small domains including approximately the same number of particles. The axial direction was uniformly decomposed, while the radial direction was non-uniformly decomposed. N RP replicas (copies) of each decomposed domain were used (“particle decomposition”). The hybrid parallelization model of multi-threads and multi-processes was employed: threads were parallelized by the auto-parallelization and N DD-r × N DD-z × N RP processes were parallelized by MPI (message-passing interface). The parallelization performance of Gpic-MHD was investigated for the medium size system of N r × N θ × N z = 1025 × 128 × 128 mesh with 4.196 or 8.192 billion particles. The highest speed for the fixed number of logical cores was obtained for two threads, the maximum number of N DD-z , and optimum combination of N DD-r and N RP . The observed optimum speeds demonstrated good scaling up to 8,192 logical cores. (author)
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
Implementation of a 3-D nonlinear MHD [magnetohydrodynamics] calculation on the Intel hypercube
International Nuclear Information System (INIS)
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
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)
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
Equilibrium studies of helical axis stellarators
International Nuclear Information System (INIS)
Hender, T.C.; Carreras, B.A.; Garcia, L.; Harris, J.H.; Rome, J.A.; Cantrell, J.L.; Lynch, V.E.
1984-01-01
The equilibrium properties of helical axis stellarators are studied with a 3-D equilibrium code and with an average method (2-D). The helical axis ATF is shown to have a toroidally dominated equilibrium shift and good equilibria up to at least 10% peak beta. Low aspect ratio heliacs, with relatively large toroidal shifts, are shown to have low equilibrium beta limits (approx. 5%). Increasing the aspect ratio and number of field periods proportionally is found to improve the equilibrium beta limit. Alternatively, increasing the number of field periods at fixed aspect ratio which raises and lowers the toroidal shift improves the equilibrium beta limit
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
FAST Plasma Scenarios and Equilibrium Configurations
International Nuclear Information System (INIS)
Calabro, G.; Crisanti, F.; Ramogida, G.; Cardinali, A.; Cucchiaro, A.; Maddaluno, G.; Pizzuto, A.; Pericoli Ridolfini, V.; Tuccillo, A.A.; Zonca, F.; Albanese, R.; Granucci, G.; Nowak, S.
2008-01-01
In this paper we present the Fusion Advanced Studies Torus (FAST) plasma scenarios and equilibrium configurations, designed to reproduce the ITER ones (with scaled plasma current) and suitable to fulfil plasma conditions for integrated studies of burning plasma physics, Plasma Wall interaction, ITER relevant operation problems and Steady State scenarios. The attention is focused on FAST flexibility in terms of both performance and physics that can be investigated: operations are foreseen at a wide range of parameters from high performance H-Mode (toroidal field, B T , up to 8.5 T; plasma current, I P , up to 8 MA) to advanced tokamak (AT) operation (I P =3 MA) as well as full non inductive current scenario (I P =2 MA). The coupled heating power is provided with 30MW delivered by an Ion Cyclotron Resonance Heating (ICRH) system (30-90MHz), 6 MW by a Lower Hybrid (LH) system (3.7 or 5 GHz) for the long pulse AT scenario, 4 MW by an Electron Cyclotron Resonant Heating (ECRH) system (170 GHz-B T =6T) for MHD and electron heating localized control and, eventually, with 10 MW by a Negative Ion Beam (NNBI), which the ports are designed to accommodate. In the reference H-mode scenario FAST preserves (with respect to ITER) fast ions induced as well as turbulence fluctuation spectra, thus, addressing the cross-scale couplings issue of micro- to meso-scale physics. The noninductive scenario at I P =2MA is obtained with 60-70 % of bootstrap and the remaining by LHCD. Predictive simulations of the H-mode scenarios described above have been performed by means of JETTO code, using a semi-empirical mixed Bohm/gyro-Bohm transport model. Plasma position and Shape Control studies are also presented for the reference scenario
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
Real-time simulation of MHD/steam power plants by digital parallel processors
International Nuclear Information System (INIS)
Johnson, R.M.; Rudberg, D.A.
1981-01-01
Attention is given to a large FORTRAN coded program which simulates the dynamic response of the MHD/steam plant on either a SEL 32/55 or VAX 11/780 computer. The code realizes a detailed first-principle model of the plant. Quite recently, in addition to the VAX 11/780, an AD-10 has been installed for usage as a real-time simulation facility. The parallel processor AD-10 is capable of simulating the MHD/steam plant at several times real-time rates. This is desirable in order to develop rapidly a large data base of varied plant operating conditions. The combined-cycle MHD/steam plant model is discussed, taking into account a number of disadvantages. The disadvantages can be overcome with the aid of an array processor used as an adjunct to the unit processor. The conversion of some computations for real-time simulation is considered
Experimental transport analysis code system in JT-60
International Nuclear Information System (INIS)
Hirayama, Toshio; Shimizu, Katsuhiro; Tani, Keiji; Shirai, Hiroshi; Kikuchi, Mitsuru
1988-03-01
Transport analysis codes have been developed in order to study confinement properties related to particle and energy balance in ohmically and neutral beam heated plasmas of JT-60. The analysis procedure is divided into three steps as follows: 1) LOOK ; The shape of the plasma boundary is identified with a fast boundary identification code of FBI by using magnetic data, and flux surfaces are calculated with a MHD equilibrium code of SELENE. The diagnostic data are mapped to flux surfaces for neutral beam heating calculation and/or for radial transport analysis. 2) OFMC ; On the basis of transformed data, an orbit following Monte Carlo code of OFMC calculates both profiles of power deposition and particle source of neutral beam injected into a plasma. 3) SCOOP ; In the last stage, a one dimensional transport code of SCOOP solves particle and energy balance for electron and ion, in order to evaluate transport coefficients as well as global parameters such as energy confinement time and the stored energy. The analysis results are provided to a data bank of DARTS that is used to find an overview of important consideration on confinement with a regression analysis code of RAC. (author)
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...
Analysis of MHD equilibria by toroidal multipolar expansions
International Nuclear Information System (INIS)
Alladio, F.; Crisanti, F.
1986-01-01
The use of fully toroidal co-ordinates permits the two-dimensional problem of the axisymmetric plasma toroidal equilibrium to be reduced to the one-dimensional problem of determining a limited number of its toroidal multipolar moments. This has allowed the creation of a fast semi-analytic predictive equilibrium code that can be used in both free and fixed boundary conditions for plasmas with circular or mildly non-circular cross-section. The concept of toroidal multipoles is also particularly suitable for the analysis of experimental data from magnetic probe measurements and clarifies the conditions under which the plasma thermal and electrical self-inductances βsub(p) and lsub(i) can be estimated separately. Finally, the interpretation of the magnetic equilibrium measurements in terms of toroidal multipoles can directly provide the boundary conditions for a fast equilibrium reconstruction code. Examples of the application of such a code to the JET magnetic measurements are reported. (author)
Non-equilibrium hydrogen ionization in 2D simulations of the solar atmosphere
Leenaarts, J.; Carlsson, M.; Hansteen, V.; Rutten, R. J.
2007-10-01
Context: The ionization of hydrogen in the solar chromosphere and transition region does not obey LTE or instantaneous statistical equilibrium because the timescale is long compared with important hydrodynamical timescales, especially of magneto-acoustic shocks. Since the pressure, temperature, and electron density depend sensitively on hydrogen ionization, numerical simulation of the solar atmosphere requires non-equilibrium treatment of all pertinent hydrogen transitions. The same holds for any diagnostic application employing hydrogen lines. Aims: To demonstrate the importance and to quantify the effects of non-equilibrium hydrogen ionization, both on the dynamical structure of the solar atmosphere and on hydrogen line formation, in particular Hα. Methods: We implement an algorithm to compute non-equilibrium hydrogen ionization and its coupling into the MHD equations within an existing radiation MHD code, and perform a two-dimensional simulation of the solar atmosphere from the convection zone to the corona. Results: Analysis of the simulation results and comparison to a companion simulation assuming LTE shows that: a) non-equilibrium computation delivers much smaller variations of the chromospheric hydrogen ionization than for LTE. The ionization is smaller within shocks but subsequently remains high in the cool intershock phases. As a result, the chromospheric temperature variations are much larger than for LTE because in non-equilibrium, hydrogen ionization is a less effective internal energy buffer. The actual shock temperatures are therefore higher and the intershock temperatures lower. b) The chromospheric populations of the hydrogen n = 2 level, which governs the opacity of Hα, are coupled to the ion populations. They are set by the high temperature in shocks and subsequently remain high in the cool intershock phases. c) The temperature structure and the hydrogen level populations differ much between the chromosphere above photospheric magnetic elements
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
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
International Nuclear Information System (INIS)
He, Qingyun; Chen, Hongli; Feng, Jingchao
2015-01-01
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
Acceleration of the OpenFOAM-based MHD solver using graphics processing units
Energy Technology Data Exchange (ETDEWEB)
He, Qingyun; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Feng, Jingchao
2015-12-15
Highlights: • A 3D PISO-MHD was implemented on Kepler-class graphics processing units (GPUs) using CUDA technology. • A consistent and conservative scheme is used in the code which was validated by three basic benchmarks in a rectangular and round ducts. • Parallelized of CPU and GPU acceleration were compared relating to single core CPU in MHD problems and non-MHD problems. • Different preconditions for solving MHD solver were compared and the results showed that AMG method is better for calculations. - Abstract: The pressure-implicit with splitting of operators (PISO) magnetohydrodynamics MHD solver of the couple of Navier–Stokes equations and Maxwell equations was implemented on Kepler-class graphics processing units (GPUs) using the CUDA technology. The solver is developed on open source code OpenFOAM based on consistent and conservative scheme which is suitable for simulating MHD flow under strong magnetic field in fusion liquid metal blanket with structured or unstructured mesh. We verified the validity of the implementation on several standard cases including the benchmark I of Shercliff and Hunt's cases, benchmark II of fully developed circular pipe MHD flow cases and benchmark III of KIT experimental case. Computational performance of the GPU implementation was examined by comparing its double precision run times with those of essentially the same algorithms and meshes. The resulted showed that a GPU (GTX 770) can outperform a server-class 4-core, 8-thread CPU (Intel Core i7-4770k) by a factor of 2 at least.
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
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...
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.)
MHD simulation of a beat frequency heated plasma
International Nuclear Information System (INIS)
Milroy, R.D.; Capjack, C.E.; James, C.R.; McMullin, J.N.
1976-01-01
The heating of a plasma in a solenoid, with a beat frequency harmonic which is excited at a frequency near to that of a Langmuir mode in a plasma, is examined. It is shown that at high temperatures the heating rate is very insensitive to changes in plasma density. The amount of energy that can be coupled to a plasma in a solenoid with this heating scheme is investigated by using a one-dimensional computer code which incorporates an exact solution of the relevant MHD equations. The absorption of energy from a high powered laser is shown to be significantly enhanced with this process. (author)
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.
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.
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.)
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
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.)
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
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)
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
Numerical Verification Of Equilibrium Chemistry
International Nuclear Information System (INIS)
Piro, Markus; Lewis, Brent; Thompson, William T.; Simunovic, Srdjan; Besmann, Theodore M.
2010-01-01
A numerical tool is in an advanced state of development to compute the equilibrium compositions of phases and their proportions in multi-component systems of importance to the nuclear industry. The resulting software is being conceived for direct integration into large multi-physics fuel performance codes, particularly for providing boundary conditions in heat and mass transport modules. However, any numerical errors produced in equilibrium chemistry computations will be propagated in subsequent heat and mass transport calculations, thus falsely predicting nuclear fuel behaviour. The necessity for a reliable method to numerically verify chemical equilibrium computations is emphasized by the requirement to handle the very large number of elements necessary to capture the entire fission product inventory. A simple, reliable and comprehensive numerical verification method is presented which can be invoked by any equilibrium chemistry solver for quality assurance purposes.
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)
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.
Directory of Open Access Journals (Sweden)
C. Nabert
2017-05-01
Full Text Available The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms magnetosheath data to estimate Earth's dipole moment.
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
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)
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
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)
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)
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.)
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
PHANTOM: Smoothed particle hydrodynamics and magnetohydrodynamics code
Price, Daniel J.; Wurster, James; Nixon, Chris; Tricco, Terrence S.; Toupin, Stéven; Pettitt, Alex; Chan, Conrad; Laibe, Guillaume; Glover, Simon; Dobbs, Clare; Nealon, Rebecca; Liptai, David; Worpel, Hauke; Bonnerot, Clément; Dipierro, Giovanni; Ragusa, Enrico; Federrath, Christoph; Iaconi, Roberto; Reichardt, Thomas; Forgan, Duncan; Hutchison, Mark; Constantino, Thomas; Ayliffe, Ben; Mentiplay, Daniel; Hirsh, Kieran; Lodato, Giuseppe
2017-09-01
Phantom is a smoothed particle hydrodynamics and magnetohydrodynamics code focused on stellar, galactic, planetary, and high energy astrophysics. It is modular, and handles sink particles, self-gravity, two fluid and one fluid dust, ISM chemistry and cooling, physical viscosity, non-ideal MHD, and more. Its modular structure makes it easy to add new physics to the code.
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 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.
Collapse and equilibrium of rotating, adiabatic clouds
International Nuclear Information System (INIS)
Boss, A.P.
1980-01-01
A numerical hydrodynamics computer code has been used to follow the collapse and establishment of equilibrium of adiabatic gas clouds restricted to axial symmetry. The clouds are initially uniform in density and rotation, with adiabatic exponents γ=5/3 and 7/5. The numerical technique allows, for the first time, a direct comparison to be made between the dynamic collapse and approach to equilibrium of unconstrained clouds on the one hand, and the results for incompressible, uniformly rotating equilibrium clouds, and the equilibrium structures of differentially rotating polytropes, on the other hand
Implementation of Premixed Equilibrium Chemistry Capability in OVERFLOW
Olsen, Mike E.; Liu, Yen; Vinokur, M.; Olsen, Tom
2004-01-01
An implementation of premixed equilibrium chemistry has been completed for the OVERFLOW code, a chimera capable, complex geometry flow code widely used to predict transonic flowfields. The implementation builds on the computational efficiency and geometric generality of the solver.
MHD Modeling of Conductors at Ultra-High Current Density
International Nuclear Information System (INIS)
ROSENTHAL, STEPHEN E.; DESJARLAIS, MICHAEL P.; SPIELMAN, RICK B.; STYGAR, WILLIAM A.; ASAY, JAMES R.; DOUGLAS, M.R.; HALL, C.A.; FRESE, M.H.; MORSE, R.L.; REISMAN, D.B.
2000-01-01
In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator, the authors have revisited a problem first described in detail by Heinz Knoepfel. Unlike the 1-Tesla MITLs of pulsed power accelerators used to produce intense particle beams, Z's disc transmission line (downstream of the current addition) is in a 100--1,200 Tesla regime, so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 they have been investigating the conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. Three purposes of this work are (1) to quantify power flow losses owing to ultra-high magnetic fields, (2) to model the response of VISAR diagnostic samples in various configurations on Z, and (3) to incorporate the most appropriate equation of state and conductivity models into the MHD computations. Certain features are strongly dependent on the details of the conductivity model
MHD Modeling of Conductors at Ultra-High Current Density
International Nuclear Information System (INIS)
Rosenthal, S.E.; Asay, J.R.; Desjarlais, M.P.; Douglas, M.R.; Frese, M.H.; Hall, C.A.; Morse, R.L.; Reisman, D.; Spielman, R.B.; Stygar, W.A.
1999-01-01
In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator we have revisited a problem first described in detail by Heinz Knoepfel. MITLs of previous pulsed power accelerators have been in the 1-Tesla regime. Z's disc transmission line (downstream of the current addition) is in a 100-1200 Tesla regime, so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 we have been investigating conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. Three purposes of this work are ( 1) to quantify power flow losses owing to ultra-high magnetic fields, (2) to model the response of VISAR diagnostic samples in various configurations on Z, and (3) to incorporate the most appropriate equation of state and conductivity models into our MHD computations. Certain features are strongly dependent on the details of the conductivity model. Comparison with measurements on Z will be discussed
Relativistic MHD simulations of stellar core collapse and magnetars
Energy Technology Data Exchange (ETDEWEB)
Font, Jose A; Gabler, Michael [Departamento de AstronomIa y Astrofisica, Universitat de Valencia, 46100 Burjassot (Valencia) (Spain); Cerda-Duran, Pablo; Mueller, Ewald [Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany); Stergioulas, Nikolaos, E-mail: j.antonio.font@uv.es [Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124 (Greece)
2011-02-01
We present results from simulations of magneto-rotational stellar core collapse along with Alfven oscillations in magnetars. These simulations are performed with the CoCoA/CoCoNuT code, which is able to handle ideal MHD flows in dynamical spacetimes in general relativity. Our core collapse simulations highlight the importance of genuine magnetic effects, like the magneto-rotational instability, for the dynamics of the flow. For the modelling of magnetars we use the anelastic approximation to general relativistic MHD, which allows for an effective suppression of fluid modes and an accurate description of Alfven waves. We further compute Alfven oscillation frequencies along individual magnetic field lines with a semi-analytic approach. Our work confirms previous results based on perturbative approaches regarding the existence of two families of quasi-periodic oscillations (QPOs), with harmonics at integer multiples of the fundamental frequency. Additional material is presented in the accompanying contribution by Gabler et al (2010b) in these proceedings.
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.
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)
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.
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts
International Nuclear Information System (INIS)
Sidorenkov, S.I.; Hua, T.Q.; Araseki, H.
1994-01-01
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction
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)
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
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)
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
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)
Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium
Hunt, J. L.; Boney, L. R.
1973-01-01
Equations and in computer code are presented for the thermodynamic and transport properties of gaseous, undissociated tetrafluoromethane (CF4) in chemical equilibrium. The computer code calculates the thermodynamic and transport properties of CF4 when given any two of five thermodynamic variables (entropy, temperature, volume, pressure, and enthalpy). Equilibrium thermodynamic and transport property data are tabulated and pressure-enthalpy diagrams are presented.
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.
Studies of MHD generator performance with oxygen enriched coal combustion
Wormhoudt, J.; Yousefian, V.; Kolb, C. E.; Martinez-Sanchez, M.
1980-07-01
This paper presents calculations made using the Aerodyne PACKAGE (Plasma Analysis, Chemical Kinetics, and Generator Efficiency) computer code which bear on two questions which arise in connection with choices between oxygen enrichment and air preheating to attain the high combustion temperatures needed for open-cycle, coal-fired MHD power generation. The first question is which method produces the highest enthalpy extraction per unit channel length. The second is, in test facilities intended to study tradeoffs between oxygen enrichment and preheated air, can good generator performance be obtained from the same physical channel for different combustor compositions. The answer to the first question is found to depend on what combustor conditions are taken to be comparable. As for the second question, it is found that operation with channel input from off-design combustor conditions can cause serious problems, which can be partially alleviated by changing the channel load factors.
International Nuclear Information System (INIS)
Pletzer, A.; Bondeson, A.; Dewar, R.L.
1993-11-01
The quest to determine accurately the stability of tearing and resistive interchange modes in two-dimensional toroidal geometry led to the development of the PEST-3 code, which is based on solving the singular, zero-frequency ideal MHD equation in the plasma bulk and determining the outer data Δ', Γ' and A' needed to match the outer region solutions to those arising in the inner layers. No assumption regarding the aspect ratio, the number of rational surfaces or the pressure are made a priori. This approach is numerically less demanding than solving the full set of resistive equations, and has the major advantage of non-MHD theories of the non-ideal layers. Good convergence is ensured by the variational Galerkin scheme used to compute the outer matching data. To validate the code, we focus on the growth rate calculations of resistive kink modes which are reproduced in good agreement with those obtained by the full resistive MHD code MARS. (author) 11 figs., 27 refs
New Developments in Modeling MHD Systems on High Performance Computing Architectures
Germaschewski, K.; Raeder, J.; Larson, D. J.; Bhattacharjee, A.
2009-04-01
Modeling the wide range of time and length scales present even in fluid models of plasmas like MHD and X-MHD (Extended MHD including two fluid effects like Hall term, electron inertia, electron pressure gradient) is challenging even on state-of-the-art supercomputers. In the last years, HPC capacity has continued to grow exponentially, but at the expense of making the computer systems more and more difficult to program in order to get maximum performance. In this paper, we will present a new approach to managing the complexity caused by the need to write efficient codes: Separating the numerical description of the problem, in our case a discretized right hand side (r.h.s.), from the actual implementation of efficiently evaluating it. An automatic code generator is used to describe the r.h.s. in a quasi-symbolic form while leaving the translation into efficient and parallelized code to a computer program itself. We implemented this approach for OpenGGCM (Open General Geospace Circulation Model), a model of the Earth's magnetosphere, which was accelerated by a factor of three on regular x86 architecture and a factor of 25 on the Cell BE architecture (commonly known for its deployment in Sony's PlayStation 3).
Ohdachi, Satoshi; Watanabe, Kiyomasa; Sakakibara, Satoru; Suzuki, Yasuhiro; Tsuchiya, Hayato; Ming, Tingfeng; Du, Xiaodi; LHD Expriment Group Team
2014-10-01
In the Large Helical Device (LHD), the plasma is surrounded by the so-called magnetic stochastic region, where the Kolmogorov length of the magnetic field lines is very short, from several tens of meters and to thousands meters. Finite pressure gradient are formed in this region and MHD instabilities localized in this region is observed since the edge region of the LHD is always unstable against the pressure driven mode. Therefore, the saturation level of the instabilities is the key issue in order to evaluate the risk of this kind of MHD instabilities. The saturation level depends on the pressure gradient and on the magnetic Reynolds number; there results are similar to the MHD mode in the closed magnetic surface region. The saturation level in the stochastic region is affected also by the stocasticity itself. Parameter dependence of the saturation level of the MHD activities in the region is discussed in detail. It is supported by NIFS budget code ULPP021, 028 and is also partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research 26249144, by the JSPS-NRF-NSFC A3 Foresight Program NSFC: No. 11261140328.
Jackson, B. V.; Yu, H. S.; Hick, P. P.; Buffington, A.; Odstrcil, D.; Kim, T. K.; Pogorelov, N. V.; Tokumaru, M.; Bisi, M. M.; Kim, J.; Yun, J.
2017-12-01
The University of California, San Diego has developed an iterative remote-sensing time-dependent three-dimensional (3-D) reconstruction technique which provides volumetric maps of density, velocity, and magnetic field. We have applied this technique in near real time for over 15 years with a kinematic model approximation to fit data from ground-based interplanetary scintillation (IPS) observations. Our modeling concept extends volumetric data from an inner boundary placed above the Alfvén surface out to the inner heliosphere. We now use this technique to drive 3-D MHD models at their inner boundary and generate output 3-D data files that are fit to remotely-sensed observations (in this case IPS observations), and iterated. These analyses are also iteratively fit to in-situ spacecraft measurements near Earth. To facilitate this process, we have developed a traceback from input 3-D MHD volumes to yield an updated boundary in density, temperature, and velocity, which also includes magnetic-field components. Here we will show examples of this analysis using the ENLIL 3D-MHD and the University of Alabama Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) heliospheric codes. These examples help refine poorly-known 3-D MHD variables (i.e., density, temperature), and parameters (gamma) by fitting heliospheric remotely-sensed data between the region near the solar surface and in-situ measurements near Earth.
A data parallel pseudo-spectral semi-implicit magnetohydrodynamics code
Keppens, R.; Poedts, S.; Meijer, P. M.; Goedbloed, J. P.; Hertzberger, B.; Sloot, P.
1997-01-01
The set of eight nonlinear partial differential equations of magnetohydrodynamics (MHD) is used for time dependent simulations of three-dimensional (3D) fluid flow in a magnetic field. A data parallel code is presented, which integrates the MHD equations in cylindrical geometry, combining a
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
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.
Equilibrium reconstruction in stellarators: V3FIT
Energy Technology Data Exchange (ETDEWEB)
Hanson, J.D.; Knowlton, S.F. [Physics Department, Auburn University, Auburn, AL (United States); Hirshman, S.P.; Lazarus, E.A. [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Lao, L.L. [General Atomics, San Diego, CA (United States)
2003-07-01
The first section describes a general response function formalism for computing stellarator magnetic diagnostic signals, which is the first step in developing a reconstruction capability. The approach parallels that used in the EFIT two-dimensional (2-D) equilibrium reconstruction code. The second section describes the two codes we have written, V3RFUN and V3POST. V3RFUN computes the response functions for a specified magnetic diagnostic coil, and V3POST uses the response functions calculated by V3RFUN, along with the plasma current information supplied by the equilibrium code VMEC, to compute the expected magnetic diagnostic signals. These two codes are currently being used to design magnetic diagnostic for the NCSX stellarator (at PPPL) and the CTH toroidal hybrid stellarator (at Auburn University). The last section of the paper describes plans for the V3FIT code. (orig.)
Energy Technology Data Exchange (ETDEWEB)
S.S. Medley; N.N. Gorelenkov; R. Andre; R.E. Bell; D.S. Darrow; E.D. Fredrickson; S.M. Kaye; B.P. LeBlanc; A.L. Roquemore; and the NSTX Team
2004-03-15
MHD-induced energetic ion loss in neutral-beam-heated H-mode [high-confinement mode] discharges in NSTX [National Spherical Torus Experiment] is discussed. A rich variety of energetic ion behavior resulting from magnetohydrodynamic (MHD) activity is observed in the NSTX using a horizontally scanning Neutral Particle Analyzer (NPA) whose sightline views across the three co-injected neutral beams. For example, onset of an n = 2 mode leads to relatively slow decay of the energetic ion population (E {approx} 10-100 keV) and consequently the neutron yield. The effect of reconnection events, sawteeth, and bounce fishbones differs from that observed for low-n, low-frequency, tearing-type MHD modes. In this case, prompt loss of the energetic ion population occurs on a time scale of less than or equal to 1 ms and a precipitous drop in the neutron yield occurs. This paper focuses on MHD-induced ion loss during H-mode operation in NSTX. After H-mode onset, the NPA charge-exchange spectrum usually exhibits a significant loss of energetic ions only for E > E(sub)b/2 where E(sub)b is the beam injection energy. The magnitude of the energetic ion loss was observed to decrease with increasing tangency radius, R(sub)tan, of the NPA sightline, increasing toroidal field, B(sub)T, and increasing neutral-beam injection energy, E(sub)b. TRANSP modeling suggests that MHD-induced ion loss is enhanced during H-mode operation due to an evolution of the q and beam deposition profiles that feeds both passing and trapped ions into the region of low-n MHD activity. ORBIT code analysis of particle interaction with a model magnetic perturbation supported the energy selectivity of the MHD-induced loss observed in the NPA measurements. Transport analysis with the TRANSP code using a fast-ion diffusion tool to emulate the observed MHD-induced energetic ion loss showed significant modifications of the neutral- beam heating as well as the power balance, thermal diffusivities, energy confinement times
International Nuclear Information System (INIS)
Medley, S.S.; Gorelenkov, N.N.; Andre, R.; Bell, R.E.; Darrow, D.S.; Fredrickson, E.D.; Kaye, S.M.; LeBlanc, B.P.; Roquemore, A.L.
2004-01-01
MHD-induced energetic ion loss in neutral-beam-heated H-mode [high-confinement mode] discharges in NSTX [National Spherical Torus Experiment] is discussed. A rich variety of energetic ion behavior resulting from magnetohydrodynamic (MHD) activity is observed in the NSTX using a horizontally scanning Neutral Particle Analyzer (NPA) whose sightline views across the three co-injected neutral beams. For example, onset of an n = 2 mode leads to relatively slow decay of the energetic ion population (E ∼ 10-100 keV) and consequently the neutron yield. The effect of reconnection events, sawteeth, and bounce fishbones differs from that observed for low-n, low-frequency, tearing-type MHD modes. In this case, prompt loss of the energetic ion population occurs on a time scale of less than or equal to 1 ms and a precipitous drop in the neutron yield occurs. This paper focuses on MHD-induced ion loss during H-mode operation in NSTX. After H-mode onset, the NPA charge-exchange spectrum usually exhibits a significant loss of energetic ions only for E > E(sub)b/2 where E(sub)b is the beam injection energy. The magnitude of the energetic ion loss was observed to decrease with increasing tangency radius, R(sub)tan, of the NPA sightline, increasing toroidal field, B(sub)T, and increasing neutral-beam injection energy, E(sub)b. TRANSP modeling suggests that MHD-induced ion loss is enhanced during H-mode operation due to an evolution of the q and beam deposition profiles that feeds both passing and trapped ions into the region of low-n MHD activity. ORBIT code analysis of particle interaction with a model magnetic perturbation supported the energy selectivity of the MHD-induced loss observed in the NPA measurements. Transport analysis with the TRANSP code using a fast-ion diffusion tool to emulate the observed MHD-induced energetic ion loss showed significant modifications of the neutral- beam heating as well as the power balance, thermal diffusivities, energy confinement times, and
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)
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
Theoretical modeling of the feedback stabilization of external MHD modes of toroidal geometry
International Nuclear Information System (INIS)
Chance, M.S.; Chu, M.S.; Okabayashi, M.
2001-01-01
A theoretical framework for understanding the feedback mechanism against external MHD modes has been formulated. Efficient computational tools - the GATO stability code coupled with a substantially modified VACUUM code - have been developed to effectively design viable feedback systems against these modes. The analysis assumed a thin resistive shell and a feedback coil structure accurately modeled in θ, with only a single harmonic variation in φ. An optimized configuration and placement of the feedback and sensor coils as well as the time constants and induced currents in the enclosing resistive shell have been computed for the DIII-D device. Up to 90% of the effectiveness of an ideal wall can be achieved. (author)
THEORETICAL MODELING OF THE FEEDBACK STABILIZATION OF EXTERNAL MHD MODES IN TOROIDAL GEOMETRY
International Nuclear Information System (INIS)
CHANCE, M.S.; CHU, M.S.; OKABAYASHI, M.; TURNBULL, A.D.
2001-02-01
OAK-B135 A theoretical framework for understanding the feedback mechanism against external MHD modes has been formulated. Efficient computational tools--the GATO stability code coupled with a substantially modified VACUUM code--have been developed to effectively design viable feedback systems against these modes. The analysis assumed a thin resistive shell and a feedback coil structure accurately modeled in θ, with only a single harmonic variation in φ. Time constants and induced currents in the enclosing resistive shell are calculated. An optimized configuration based on an idealized model have been computed for the DIII-D device. Up to 90% of the effectiveness of an ideal wall can be achieved
New method for computing ideal MHD normal modes in axisymmetric toroidal geometry
International Nuclear Information System (INIS)
Wysocki, F.; Grimm, R.C.
1984-11-01
Analytic elimination of the two magnetic surface components of the displacement vector permits the normal mode ideal MHD equations to be reduced to a scalar form. A Galerkin procedure, similar to that used in the PEST codes, is implemented to determine the normal modes computationally. The method retains the efficient stability capabilities of the PEST 2 energy principle code, while allowing computation of the normal mode frequencies and eigenfunctions, if desired. The procedure is illustrated by comparison with earlier various of PEST and by application to tilting modes in spheromaks, and to stable discrete Alfven waves in tokamak geometry
Creating Synthetic Coronal Observational Data From MHD Models: The Forward Technique
Rachmeler, Laurel A.; Gibson, Sarah E.; Dove, James; Kucera, Therese Ann
2010-01-01
We present a generalized forward code for creating simulated corona) observables off the limb from numerical and analytical MHD models. This generalized forward model is capable of creating emission maps in various wavelengths for instruments such as SXT, EIT, EIS, and coronagraphs, as well as spectropolari metric images and line profiles. The inputs to our code can be analytic models (of which four come with the code) or 2.5D and 3D numerical datacubes. We present some examples of the observable data created with our code as well as its functional capabilities. This code is currently available for beta-testing (contact authors), with the ultimate goal of release as a SolarSoft package
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
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
Energy Technology Data Exchange (ETDEWEB)
Ramakanth Munipalli; P.-Y.Huang; C.Chandler; C.Rowell; M.-J.Ni; N.Morley; S.Smolentsev; M.Abdou
2008-06-05
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as “canonical”,) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
International Nuclear Information System (INIS)
Munipalli, Ramakanth; Huang, P.-Y.; Chandler, C.; Rowell, C.; Ni, M.-J.; Morley, N.; Smolentsev, S.; Abdou, M.
2008-01-01
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as 'canonical',) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
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)
Students’ misconceptions on solubility equilibrium
Setiowati, H.; Utomo, S. B.; Ashadi
2018-05-01
This study investigated the students’ misconceptions of the solubility equilibrium. The participants of the study consisted of 164 students who were in the science class of second year high school. Instrument used is two-tier diagnostic test consisting of 15 items. Responses were marked and coded into four categories: understanding, misconception, understand little without misconception, and not understanding. Semi-structured interviews were carried out with 45 students according to their written responses which reflected different perspectives, to obtain a more elaborated source of data. Data collected from multiple methods were analyzed qualitatively and quantitatively. Based on the data analysis showed that the students misconceptions in all areas in solubility equilibrium. They had more misconceptions such as in the relation of solubility and solubility product, common-ion effect and pH in solubility, and precipitation concept.
Influence of MHD effects and edge conditions on ITER helium ash accumulation and sustained ignition
International Nuclear Information System (INIS)
Redi, M.H.; Cohen, S.A.
1990-06-01
Dilution of reacting species by build-up of helium ash and its effect on ignition in the ITER tokamak have been studies in a series of simulations with the one-dimensional BALDUR transport code. Thermal diffusivities, obtained from ITER scaling laws and with radial variations observed in JET, gave τ E ∼ 2--4 sec. Refueling of deuterium and tritium maintained constant electron density, while carbon recycling was 100% and the helium ash recycling was varied from 1.0 to 0.5. Including MHD effects, specifically sawteeth and beta limits, we find that ignition can be sustained for 200 seconds with R helium = 0.95. These simulations, the only non-zero-dimensional, time-dependent simulations thus far made for ITER plasmas, emphasize that edge plasma conditions, MHD behavior, and helium particle transport are critical synergistic issues for sustained ignition. 27 refs., 2 figs., 1 tab
Gas Core Reactor Numerical Simulation Using a Coupled MHD-MCNP Model
Kazeminezhad, F.; Anghaie, S.
2008-01-01
Analysis is provided in this report of using two head-on magnetohydrodynamic (MHD) shocks to achieve supercritical nuclear fission in an axially elongated cylinder filled with UF4 gas as an energy source for deep space missions. The motivation for each aspect of the design is explained and supported by theory and numerical simulations. A subsequent report will provide detail on relevant experimental work to validate the concept. Here the focus is on the theory of and simulations for the proposed gas core reactor conceptual design from the onset of shock generations to the supercritical state achieved when the shocks collide. The MHD model is coupled to a standard nuclear code (MCNP) to observe the neutron flux and fission power attributed to the supercritical state brought about by the shock collisions. Throughout the modeling, realistic parameters are used for the initial ambient gaseous state and currents to ensure a resulting supercritical state upon shock collisions.
Comparison of MHD-induced rotation damping with NTV predictions on MAST
International Nuclear Information System (INIS)
Hua, M-D; Chapman, I T; Field, A R; Hastie, R J; Pinches, S D
2010-01-01
Plasma rotation in tokamaks is of special interest for its potential stabilizing effect on micro- and macro-instabilities, leading to increased confinement. In MAST, the torque from neutral beam injection can spin the plasma to a core velocity ∼300 km s -1 (Alfven Mach number ∼0.3). Low density plasmas often exhibit a weakly non-monotonic safety factor profile just above unity. Theory predicts that such equilibria are prone to magneto-hydro-dynamic (MHD) instabilities, which was confirmed by recent observations. The appearance of the mode is accompanied by strong damping of core rotation on a timescale much faster than the momentum confinement time. The mode's saturated structure is estimated using the CASTOR code together with soft x-ray measurements, enabling the calculation of the plasma braking by the MHD mode according to neoclassical toroidal viscosity (NTV) theory. The latter exhibits strong similarities with the torque measured experimentally.
Gasdynamic performance in relation to the power extraction of an MHD generator
International Nuclear Information System (INIS)
Massee, P.
1983-01-01
A study of the gasdynamical processes in MHD generators has been made both theoretically and experimentally. A core flow and boundary layer model has been developed. In order to obtain a fast computer code which can be used for engineering purposes the quasi-one-dimensional approximation is used. It is shown in this thesis that the boundary layers have to be calculated from integral equations describing momentum, kinetic energy and stagnation enthalpy respectively, when the MHD effects in the boundary layers are properly taken into account. Calculations with the developed core flow and boundary layer model have shown that the electrical power output is limited by the design of the existing facility and have indicated possibilities to circumvent this limitation. (Auth.)
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...
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.
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)
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
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.
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
ZORNOC: a 1 1/2-D tokamak data analysis code for studying noncircular high beta plasmas
International Nuclear Information System (INIS)
Zurro, B.; Wieland, R.M.; Murakami, M.; Swain, D.W.
1980-03-01
A new tokamak data analysis code, ZORNOC, was developed to study noncircular, high beta plasmas in the Impurity Study Experiment (ISX-B). These plasmas exhibit significant flux surface shifts and elongation in both ohmically heated and beam-heated discharges. The MHD equilibrium flux surface geometry is determined by solving the Grad-Shafranov equation based on: (1) the shape of the outermost flux surface, deduced from the magnetic loop probes; (2) a pressure profile, deduced by means of Thomson scattering data (electrons), charge exchange data (ions), and a Fokker-Planck model (fast ions); and (3) a safety factor profile, determined from the experimental data using a simple model (Z/sub eff/ = const) that is self-consistently altered while the plasma equilibrium is iterated. For beam-heated discharches the beam deposition profile is determined by means of a Monte Carlo scheme and the slowing down of the fast ions by means of an analytical solution of the Fokker-Planck equation. The code also carries out an electron power balance and calculates various confinement parameters. The code is described and examples of its operation are given
Pedestal characteristics and MHD stability of H-mode plasmas in TCV
International Nuclear Information System (INIS)
Pitzschke, A.
2011-01-01
temperature profile during the ELM cycle, the low repetition rate of the lasers used for Thomson scattering is a limiting. Although the system on TCV comprises 3 laser units that may be triggered in sequence with time separations down to 1 ms, time evolution over longer periods can only be reconstructed from repetitive events. In this context, an adjustment of the laser trigger to improve the synchronization with the ELM event is an advantage. A method was developed and implemented to generate a synchronizing trigger sequence, by a real-time monitoring of the D-alpha emission, which provides a marker for the ELM event. Recently, a ‘snowflake’ (SF) divertor configuration, proposed as a possible solution to reduce the plasma-wall interaction by changing the divertor’s poloidal magnetic field topology, was generated, for the first time, in TCV. A numerical code (KINX), based on a magnetohydrodynamic model (ideal MHD), was used to investigate the stability limits of this configuration under H-mode conditions and compare them with a similar standard single-null equilibrium. In a series of experiments, improved energy confinement was found and explained by improved stability of the edge region in the SF configuration. The influence of the pedestal structure in ELMy H-mode plasmas on the energy confinement and on ELM energy losses was investigated. The different ELM regimes found in TCV were analyzed, in particular the transition between type-III to type-I ELMs. The operational boundary of each ELM regime was characterized and verified by ideal MHD stability simulations for the ETB region. Recent studies on the scaling of the pedestal width with normalized poloidal pressure were confirmed. Using the capabilities of TCV, the influence of plasma shaping on pedestal parameters and MHD stability limits was investigated. In the past, models were developed to describe the onset of type-I ELMs, which are associated with modes in the ETB region arising from a coupling of pressure- and
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.)
Modelling of diamagnetic stabilization of ideal MHD eigenmodes associated with the transport barrier
International Nuclear Information System (INIS)
Huysmans, G.; Sharapov, S.; Mikhailovskii, A.; Kerner, W.
2001-01-01
A new code, MISHKA-D (Drift MHD), has been developed as an extension of the ideal MHD code MISHKA-1 in order to investigate the finite gyroradius stabilizing effect of ion diamagnetic drift frequency, ω *i , on linear ideal MHD eigenmodes in tokamaks with shaped plasma cross-section. The MISHKA-D code gives a self-consistent computation of both stable and unstable eigenmodes with eigenvalues [γ] ≅ ω *i in plasmas with strong radial variation in the ion diamagnetic frequency. Test results of the MISHKA-D code show good agreement with the analytically obtained ω *i -spectrum and stability limits of the internal kink mode, n/m=1/1, used as a benchmark case. Finite-n ballooning and low-n kink (peeling) modes in the edge transport barrier just inside the separatrix are studied for H-mode plasma with the ω *i -effect included. The ion diamagnetic stabilization of the ballooning modes is found to be most effective for narrow edge pedestals. For low enough plasma density the ω *i - stabilization can lead to a second zone of ballooning stability, in which all the ballooning modes are stable for any value of the pressure gradient. For internal transport barriers typical of JET optimised shear discharges, the stabilizing influence of ion diamagnetic frequency on the n=1 global pressure driven disruptive mode is studied. A strong radial variation of ω *i is found to significantly decrease the stabilizing ω *i - effect on the n=1 mode, in comparison with the case of constant ω *i estimated at the foot of the internal transport barrier. (author)
Peterson, Ethan; Anderson, Jay; Clark, Mike; Egedal, Jan; Endrizzi, Douglass; Flanagan, Ken; Harvey, Robert; Lynn, Jacob; Milhone, Jason; Wallace, John; Waleffe, Roger; Mirnov, Vladimir; Forest, Cary
2017-10-01
Equilibrium reconstructions of rotating magnetospheres in the lab are computed using a user-friendly extended Grad-Shafranov solver written in Python and various magnetic and kinetic measurements. The stability of these equilibria are investigated using the NIMROD code with two goals: understand the onset of the classic ``wobble'' in the heliospheric current sheet and demonstrating proof-of-principle for a laboratory source of high- β turbulence. Using the same extended Grad-Shafranov solver, equilibria for an axisymmetric, non-paraxial magnetic mirror are used as a design foundation for a high-field magnetic mirror neutron source. These equilibria are numerically shown to be stable to the m=1 flute instability, with higher modes likely stabilized by FLR effects; this provides stability to gross MHD modes in an axisymmetric configuration. Numerical results of RF heating and neutral beam injection (NBI) from the GENRAY/CQL3D code suite show neutron fluxes promising for medical radioisotope production as well as materials testing. Synergistic effects between NBI and high-harmonic fast wave heating show large increases in neutron yield for a modest increase in RF power. work funded by DOE, NSF, NASA.
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
Calculating Shocks In Flows At Chemical Equilibrium
Eberhardt, Scott; Palmer, Grant
1988-01-01
Boundary conditions prove critical. Conference paper describes algorithm for calculation of shocks in hypersonic flows of gases at chemical equilibrium. Although algorithm represents intermediate stage in development of reliable, accurate computer code for two-dimensional flow, research leading up to it contributes to understanding of what is needed to complete task.
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
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
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.
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)
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.
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).
Modeling of flow-dominated MHD instabilities at WiPPAL using NIMROD
Flanagan, K.; McCollam, K. J.; Milhone, J.; Mirnov, V. V.; Nornberg, M. D.; Peterson, E. E.; Siller, R.; Forest, C. B.
2017-10-01
Using the NIMROD (non-ideal MHD with rotation - open discussion) code developed at UW-Madison, we model two different flow scenarios to study the onset of MHD instabilities in flow-dominated plasmas in the Big Red Ball (BRB) and the Plasma Couette Experiment (PCX). Both flows rely on volumetric current drive, where a large current is drawn through the plasma across a weak magnetic field, injecting J × B torque across the whole volume. The first scenario uses a vertical applied magnetic field and a mostly radial injected current to create Couette-like flows which may excite the magnetorotational instability (MRI). In the other scenario, a quadrupolar field is applied to create counter-rotating von Karman-like flow that demonstrates a dynamo-like instability. For both scenarios, the differences between Hall and MHD Ohm's laws are explored. The implementation of BRB geometry in NIMROD, details of the observed flows, and instability results are shown. This work was funded by DoE and NSF.
Kinetic-MHD simulations of gyroresonance instability driven by CR pressure anisotropy
Lebiga, O.; Santos-Lima, R.; Yan, H.
2018-05-01
The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs (≲100 GeV) in the interstellar and intracluster medium of galaxies has been shown in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this, we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient Dμμ produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasi-linear theory (QLT). Our results support the applicability of the QLT for modelling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.
PROPERTIES OF UMBRAL DOTS AS MEASURED FROM THE NEW SOLAR TELESCOPE DATA AND MHD SIMULATIONS
International Nuclear Information System (INIS)
Kilcik, A.; Yurchyshyn, V. B.; Abramenko, V.; Goode, P. R.; Cao, W.; Rempel, M.; Kitai, R.; Watanabe, H.
2012-01-01
We studied bright umbral dots (UDs) detected in a moderate size sunspot and compared their statistical properties to recent MHD models. The study is based on high-resolution data recorded by the New Solar Telescope at the Big Bear Solar Observatory and three-dimensional (3D) MHD simulations of sunspots. Observed UDs, living longer than 150 s, were detected and tracked in a 46 minute long data set, using an automatic detection code. A total of 1553 (620) UDs were detected in the photospheric (low chromospheric) data. Our main findings are (1) none of the analyzed UDs is precisely circular, (2) the diameter-intensity relationship only holds in bright umbral areas, and (3) UD velocities are inversely related to their lifetime. While nearly all photospheric UDs can be identified in the low chromospheric images, some small closely spaced UDs appear in the low chromosphere as a single cluster. Slow-moving and long-living UDs seem to exist in both the low chromosphere and photosphere, while fast-moving and short-living UDs are mainly detected in the photospheric images. Comparison to the 3D MHD simulations showed that both types of UDs display, on average, very similar statistical characteristics. However, (1) the average number of observed UDs per unit area is smaller than that of the model UDs, and (2) on average, the diameter of model UDs is slightly larger than that of observed ones.
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
Geochemical computer codes. A review
International Nuclear Information System (INIS)
Andersson, K.
1987-01-01
In this report a review of available codes is performed and some code intercomparisons are also discussed. The number of codes treating natural waters (groundwater, lake water, sea water) is large. Most geochemical computer codes treat equilibrium conditions, although some codes with kinetic capability are available. A geochemical equilibrium model consists of a computer code, solving a set of equations by some numerical method and a data base, consisting of thermodynamic data required for the calculations. There are some codes which treat coupled geochemical and transport modeling. Some of these codes solve the equilibrium and transport equations simultaneously while other solve the equations separately from each other. The coupled codes require a large computer capacity and have thus as yet limited use. Three code intercomparisons have been found in literature. It may be concluded that there are many codes available for geochemical calculations but most of them require a user that us quite familiar with the code. The user also has to know the geochemical system in order to judge the reliability of the results. A high quality data base is necessary to obtain a reliable result. The best results may be expected for the major species of natural waters. For more complicated problems, including trace elements, precipitation/dissolution, adsorption, etc., the results seem to be less reliable. (With 44 refs.) (author)
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
Improved core-edge tokamak transport simulations with the CORSICA 2 code
International Nuclear Information System (INIS)
Tarditi, A.; Cohen, R.H.; Crotinger, J.A.
1996-01-01
The CORSICA 2 code models the nonlinear transport between the core and the edge of a tokamak plasma. The code couples a 2D axisymmetric edge/SOL model (UEDGE) to a 1D model for the radial core transport in toroidal flux coordinates (the transport module from the CORSICA 1 code). The core density and temperature profiles are joined to the flux-surface average profiles from the 2D code sufficiently inside the magnetic separatrix, at a flux surface on which the edge profiles are approximately constant. In the present version of the code, the deuterium density and electron and ion temperatures are coupled. The electron density is determined by imposing quasi-neutrality, both in the core and in the edge. The model allows the core-edge coupling of multiple ion densities while retaining a single temperature (corresponding to the equilibration value) for the all ion species. Applications of CORSICA 2 to modeling the DIII-D tokamak are discussed. This work will focus on the simulation of the L-H transition, coupling a single ion species (deuterium) and the two (electron and ion) temperatures. These simulations will employ a new self-consistent model for the L-H transition that is being implemented in the UEDGE code. Applications to the modeling of ITER ignition scenarios are also discussed. This will involve coupling a second density species (the thermal alphas), bringing the total number of coupled variables up to four. Finally, the progress in evolving the magnetic geometry is discussed. Currently, this geometry is calculated by CORSICA's MHD equilibrium module (TEQ) at the beginning of the run and fixed thereafter. However, CORSICA 1 can evolve this geometry quasistatically, and this quasistatic treatment is being extended to include the edge/SOL geometry. Recent improvements for code speed-up are also presented
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
Review of the equilibrium fitting for non-circular tokamak
International Nuclear Information System (INIS)
Luo Jiarong
2002-01-01
As the equilibrium fitting code (EFIT) is developing to perform the magnetic and the kinetic-magnetic analysis for tokamak device operation, it can be not only run in either the fitting mode or the equilibrium mode but also control operation of modern experimental fusion device. The history of EFIT code and its capabilities are described in section 2. A brief description of the off-line EFIT code and the development of the real-time EFIT (RTEFIT) code is shown in section 3 and 4 respectively. In the last section the summary is given
Flow predictions for MHD channels with an approximation for three-dimensional effects
International Nuclear Information System (INIS)
Blottner, F.G.
1978-01-01
A finite-difference procedure has been formulated for predicting the flow properties across channels. A quasi-two-dimensional approach has been developed which allows the three-dimensional channel effects to be taken into account. Comparison of the numerical solutions with experimental results show that this approach is a reasonable approximation for MHD flow conditions if there is not significant merging of the wall boundary layers. The resulting code provides a technique to obtain the flow details in the symmetry plane of the channel and requires only a small amount of computer time
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)
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)
Numerical MHD study for plasmoid instability in uniform resistivity
Shimizu, Tohru; Kondoh, Koji; Zenitani, Seiji
2017-11-01
The plasmoid instability (PI) caused in uniform resistivity is numerically studied with a MHD numerical code of HLLD scheme. It is shown that the PI observed in numerical studies may often include numerical (non-physical) tearing instability caused by the numerical dissipations. By increasing the numerical resolutions, the numerical tearing instability gradually disappears and the physical tearing instability remains. Hence, the convergence of the numerical results is observed. Note that the reconnection rate observed in the numerical tearing instability can be higher than that of the physical tearing instability. On the other hand, regardless of the numerical and physical tearing instabilities, the tearing instability can be classified into symmetric and asymmetric tearing instability. The symmetric tearing instability tends to occur when the thinning of current sheet is stopped by the physical or numerical dissipations, often resulting in the drastic changes in plasmoid chain's structure and its activity. In this paper, by eliminating the numerical tearing instability, we could not specify the critical Lundquist number Sc beyond which PI is fully developed. It suggests that Sc does not exist, at least around S = 105.
Hayek, W.; Asplund, M.; Carlsson, M.; Trampedach, R.; Collet, R.; Gudiksen, B.V.; Hansteen, V.H.; Leenaarts, J.|info:eu-repo/dai/nl/304837946
2010-01-01
Aims. We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes
International Nuclear Information System (INIS)
Liu Yueqiang; Albanese, R.; Rubinacci, G.; Portone, A.; Villone, F.
2008-01-01
In order to model a magnetohydrodynamic (MHD) instability that strongly couples to external conducting structures (walls and/or coils) in a fusion device, it is often necessary to combine a MHD code solving for the plasma response, with an eddy current code computing the fields and currents of conductors. We present a rigorous proof of the coupling schemes between these two types of codes. One of the coupling schemes has been introduced and implemented in the CARMA code [R. Albanese, Y. Q. Liu, A. Portone, G. Rubinacci, and F. Villone, IEEE Trans. Magn. 44, 1654 (2008); A. Portone, F. Villone, Y. Q. Liu, R. Albanese, and G. Rubinacci, Plasma Phys. Controlled Fusion 50, 085004 (2008)] that couples the MHD code MARS-F[Y. Q. Liu, A. Bondeson, C. M. Fransson, B. Lennartson, and C. Breitholtz, Phys. Plasmas 7, 3681 (2000)] and the eddy current code CARIDDI[R. Albanese and G. Rubinacci, Adv. Imaging Electron Phys. 102, 1 (1998)]. While the coupling schemes are described for a general toroidal geometry, we give the analytical proof for a cylindrical plasma.
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.
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)
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
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.
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.
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)
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.
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
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
Neoclassical equilibrium in gyrokinetic simulations
International Nuclear Information System (INIS)
Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.
2009-01-01
This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.
Energy Technology Data Exchange (ETDEWEB)
Fajeau, M; Nguyen, L T; Saunier, J [Commissariat a l' Energie Atomique, Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France)
1966-09-01
This code handles the following problems: -1) Analysis of thermal experiments on a water loop at high or low pressure; steady state or transient behavior; -2) Analysis of thermal and hydrodynamic behavior of water-cooled and moderated reactors, at either high or low pressure, with boiling permitted; fuel elements are assumed to be flat plates: - Flowrate in parallel channels coupled or not by conduction across plates, with conditions of pressure drops or flowrate, variable or not with respect to time is given; the power can be coupled to reactor kinetics calculation or supplied by the code user. The code, containing a schematic representation of safety rod behavior, is a one dimensional, multi-channel code, and has as its complement (FLID), a one-channel, two-dimensional code. (authors) [French] Ce code permet de traiter les problemes ci-dessous: 1. Depouillement d'essais thermiques sur boucle a eau, haute ou basse pression, en regime permanent ou transitoire; 2. Etudes thermiques et hydrauliques de reacteurs a eau, a plaques, a haute ou basse pression, ebullition permise: - repartition entre canaux paralleles, couples on non par conduction a travers plaques, pour des conditions de debit ou de pertes de charge imposees, variables ou non dans le temps; - la puissance peut etre couplee a la neutronique et une representation schematique des actions de securite est prevue. Ce code (Cactus) a une dimension d'espace et plusieurs canaux, a pour complement Flid qui traite l'etude d'un seul canal a deux dimensions. (auteurs)
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
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)
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
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.
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)
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.
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
Unsteady MHD free convective flow past a vertical porous plate ...
African Journals Online (AJOL)
user
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.
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.
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....
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.)
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
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
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)
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
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
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.
MHD natural convection in open inclined square cavity with a heated circular cylinder
Hosain, Sheikh Anwar; Alim, M. A.; Saha, Satrajit Kumar
2017-06-01
MHD natural convection in open cavity becomes very important in many scientific and engineering problems, because of it's application in the design of electronic devices, solar thermal receivers, uncovered flat plate solar collectors having rows of vertical strips, geothermal reservoirs, etc. Several experiments and numerical investigations have been presented for describing the phenomenon of natural convection in open cavity for two decades. MHD natural convection and fluid flow in a two-dimensional open inclined square cavity with a heated circular cylinder was considered. The opposite wall to the opening side of the cavity was first kept to constant heat flux q, at the same time the surrounding fluid interacting with the aperture was maintained to an ambient temperature T∞. The top and bottom wall was kept to low and high temperature respectively. The fluid with different Prandtl numbers. The properties of the fluid are assumed to be constant. As a result a buoyancy force is created inside the cavity due to temperature difference and natural convection is formed inside the cavity. The Computational Fluid Dynamics (CFD) code are used to discretize the solution domain and represent the numerical result to graphical form.. Triangular meshes are used to obtain the solution of the problem. The streamlines and isotherms are produced, heat transfer parameter Nu are obtained. The results are presented in graphical as well as tabular form. The results show that heat flux decreases for increasing inclination of the cavity and the heat flux is a increasing function of Prandtl number Pr and decreasing function of Hartmann number Ha. It is observed that fluid moves counterclockwise around the cylinder in the cavity. Various recirculations are formed around the cylinder. The almost all isotherm lines are concentrated at the right lower corner of the cavity. The object of this work is to develop a Mathematical model regarding the effect of MHD natural convection flow around
Integration of Extended MHD and Kinetic Effects in Global Magnetosphere Models
Germaschewski, K.; Wang, L.; Maynard, K. R. M.; Raeder, J.; Bhattacharjee, A.
2015-12-01
Computational models of Earth's geospace environment are an important tool to investigate the science of the coupled solar-wind -- magnetosphere -- ionosphere system, complementing satellite and ground observations with a global perspective. They are also crucial in understanding and predicting space weather, in particular under extreme conditions. Traditionally, global models have employed the one-fluid MHD approximation, which captures large-scale dynamics quite well. However, in Earth's nearly collisionless plasma environment it breaks down on small scales, where ion and electron dynamics and kinetic effects become important, and greatly change the reconnection dynamics. A number of approaches have recently been taken to advance global modeling, e.g., including multiple ion species, adding Hall physics in a Generalized Ohm's Law, embedding local PIC simulations into a larger fluid domain and also some work on simulating the entire system with hybrid or fully kinetic models, the latter however being to computationally expensive to be run at realistic parameters. We will present an alternate approach, ie., a multi-fluid moment model that is derived rigorously from the Vlasov-Maxwell system. The advantage is that the computational cost remains managable, as we are still solving fluid equations. While the evolution equation for each moment is exact, it depends on the next higher-order moment, so that truncating the hiearchy and closing the system to capture the essential kinetic physics is crucial. We implement 5-moment (density, momentum, scalar pressure) and 10-moment (includes pressure tensor) versions of the model, and use local approximations for the heat flux to close the system. We test these closures by local simulations where we can compare directly to PIC / hybrid codes, and employ them in global simulations using the next-generation OpenGGCM to contrast them to MHD / Hall-MHD results and compare with observations.
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.
Ideal MHD stability of high poloidal beta equilibria in TFTR
International Nuclear Information System (INIS)
Sabbagh, S.A.; Mauel, M.E.; Navratil, G.A.; Bell, M.G.; Budny, R.V.; Chance, M.S.; Fredrickson, E.D.; Jardin, S.C.; Manickam, J.; McCune, D.C.; McGuire, K.M.; Wieland, R.M.; Zarnstorff, M.C.; Phillips, M.W.; Hughes, M.H.; Kesner, J.
1991-01-01
Recent experiments in TFTR have expanded the operating space of the device to include plasmas with values of var-epsilon β p dia ≡ 2μ 0 var-epsilon perpendicular >/ p >> 2 as large as 1.6, and Troyon normalized diamagnetic beta β N dia ≡ β t perpendicular aB t /10 -8 I p as large as 4.7. At values of var-epsilon β p dia ≥ 1.3, a separatrix was observed to enter the vacuum vessel, producing a naturally diverted discharge. Plasmas with large values of var-epsilon β p dia were created with both the plasma current, I p , held constant and with I p decreased, or ramped down, before the start of neutral beam injection. A convenient characterization of the change in I p using experimental parameters can be defined by the ratio of I p before the ramp down, to I p during the neutral beam heating phase, F I p . The ideal MHD stability of these equilibria is investigated to determine their location in stability space, and to study the role of plasma current and pressure profile modification in the creation of these high var-epsilon β p and β N plasmas. The evolution of these plasmas is modelled from experimental data using the TRANSP code. Two-dimensional equilibria are computed from the TRANSP results and used as input to both high and low-n stability codes including PEST. The high var-epsilon β p equilibria, which generally have an oblate cross-sectional shape, are in the first stability region to high-n ballooning modes. At constant I p , these equilibria generally have maximum pressure gradients near the magnetic axis and are stable to n=1 modes without a stabilizing conducting wall. The effect of the current profile shape on the stability of low-n kink/ballooning modes and the requirements for these plasmas to access the second stability region are examined. 6 refs
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.)
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Equilibrium statistical mechanics
Jackson, E Atlee
2000-01-01
Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t
DEFF Research Database (Denmark)
Bollerslev, Tim; Sizova, Natalia; Tauchen, George
Stock market volatility clusters in time, carries a risk premium, is fractionally inte- grated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast i......, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes....
Molecular equilibrium with condensation
International Nuclear Information System (INIS)
Sharp, C.M.; Huebner, W.F.
1990-01-01
Minimization of the Gibbs energy of formation for species of chemical elements and compounds in their gas and condensed phases determines their relative abundances in a mixture in chemical equilibrium. The procedure is more general and more powerful than previous abundance determinations in multiphase astrophysical mixtures. Some results for astrophysical equations of state are presented, and the effects of condensation on opacity are briefly indicated. 18 refs
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)
Equilibrium calculations, ch. 6
International Nuclear Information System (INIS)
Deursen, A.P.J. van
1976-01-01
A calculation is presented of dimer intensities obtained in supersonic expansions. There are two possible limiting considerations; the dimers observed are already present in the source, in thermodynamic equilibrium, and are accelerated in the expansion. Destruction during acceleration is neglected, as are processes leading to newly formed dimers. On the other hand one can apply a kinetic approach, where formation and destruction processes are followed throughout the expansion. The difficulty of this approach stems from the fact that the density, temperature and rate constants have to be known at all distances from the nozzle. The simple point of view has been adopted and the measured dimer intensities are compared with the equilibrium concentration in the source. The comparison is performed under the assumption that the detection efficiency for dimers is twice the detection efficiency for monomers. The experimental evidence against the simple point of view that the dimers of the onset region are formed in the source already, under equilibrium conditions, is discussed. (Auth.)
A MHD channel study for the ETF conceptual design
Wang, S. Y.; Staiger, P. J.; Smith, J. M.
1981-01-01
The procedures and computations used to identify an MHD channel for a 540 mW(I) EFT-scale plant are presented. Under the assumed constraints of maximum E(x), E(y), J(y) and Beta; results show the best plant performance is obtained for active length, L is approximately 12 M, whereas in the initial ETF studies, L is approximately 16 M. As MHD channel length is reduced from 16 M, the channel enthalpy extraction falls off, slowly. This tends to reduce the MHD power output; however, the shorter channels result in lower heat losses to the MHD channel cooling water which allows for the incorporation of more low pressure boiler feedwater heaters into the system and an increase in steam plant efficiency. The net result of these changes is a net increase in the over all MHD/steam plant efficiency. In addition to the sensitivity of various channel parameters, the trade-offs between the level of oxygen enrichment and the electrical stress on the channel are also discussed.
Further analysis of MHD acceleration for a hypersonic wind tunnel
International Nuclear Information System (INIS)
Christiansen, M.J.; Schmidt, H.J.; Chapman, J.N.
1995-01-01
A previously completed MHD study of the use of an MHD accelerator with seeded air from a state-of-the-art arc heater, was generally hailed as showing that the system studied has some promise of meeting the most critical hypersonic testing requirements. However, some concerns existed about certain aspects of the results. This paper discusses some of these problems and presents analysis of potential solutions. Specifically the problems addressed are; reducing the amount of seed in the flow, reducing test chamber temperatures, and reducing the oxygen dissociation. Modeling techniques are used to study three design variables of the MHD accelerator. The accelerator channel inlet Mach number, the accelerator channel divergence angle, and the magnetic field strength are all studied. These variables are all optimized to meet the goals for seed, temperature, and dissociated oxygen reduction. The results of this paper are encouraging, showing that all three goals can be met. General relationships are observed as to how the design variables affect the performance of the MHD accelerator facility. This paper expands on the results presented in the UTSI report and further supports the feasibility of MHD acceleration as a means to provide hypersonic flight simulation
Resistive MHD Stability Analysis in Near Real-time
Glasser, Alexander; Kolemen, Egemen
2017-10-01
We discuss the feasibility of a near real-time calculation of the tokamak Δ' matrix, which summarizes MHD stability to resistive modes, such as tearing and interchange modes. As the operational phase of ITER approaches, solutions for active feedback tokamak stability control are needed. It has been previously demonstrated that an ideal MHD stability analysis is achievable on a sub- O (1 s) timescale, as is required to control phenomena comparable with the MHD-evolution timescale of ITER. In the present work, we broaden this result to incorporate the effects of resistive MHD modes. Such modes satisfy ideal MHD equations in regions outside narrow resistive layers that form at singular surfaces. We demonstrate that the use of asymptotic expansions at the singular surfaces, as well as the application of state transition matrices, enable a fast, parallelized solution to the singular outer layer boundary value problem, and thereby rapidly compute Δ'. Sponsored by US DOE under DE-SC0015878 and DE-FC02-04ER54698.