Multiconstrained variational problems in magnetohydrodynamics: Equilibrium and slow evolution

A computational method is proposed for solving magnetohydrodynamical equilibrium problems with prescribed flux and mass within the magnetic surfaces that foliate the plasma. Such problems arise in tokamak modeling, for instance, where they determine either equilibria with given adiabatic profiles or...

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Bibliographic Details
Published inJournal of computational physics Vol. 106; no. 2; pp. 269 - 285
Main Authors Turkington, Bruce, Lifschitz, Alexander, Eydeland, Alexander, Spruck, Joel
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 01.06.1993
Subjects
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
990200 > Mathematics & Computers
ALGORITHMS
CLOSED PLASMA DEVICES
COMPUTERIZED SIMULATION
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
HEATING
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MATHEMATICAL LOGIC
MECHANICS
NUCLEAR REACTIONS
NUCLEOSYNTHESIS
NUMERICAL SOLUTION
OPTIMIZATION
PLASMA HEATING
PLASMA WAVES
SIMULATION
SYNTHESIS
THERMONUCLEAR DEVICES 700340 > Plasma Waves, Oscillations, & Instabilities > (1992-)
THERMONUCLEAR REACTIONS
TOKAMAK DEVICES
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ISSN0021-9991
1090-2716
DOI10.1016/S0021-9991(83)71107-1

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Summary:A computational method is proposed for solving magnetohydrodynamical equilibrium problems with prescribed flux and mass within the magnetic surfaces that foliate the plasma. Such problems arise in tokamak modeling, for instance, where they determine either equilibria with given adiabatic profiles or slowly evolving quasi-equilibria governed by the Grad-Hogan equations. The classical variational principles of Kruskal and Kulsrud and Woltjer, which express these problems in terms of energy minimization subject to infinite families of nonlinear, nonlocal constraints, are taken as the basis for a direct method of solution. A natural discretization of the classical constraint families is devised, and an iterative algorithm is developed to solve the resulting optimization problems. A convergence theory for the algorithm is established, and an effective numerical implementation of the method is presented for flux-conserving tokamak equilibria. Some computed examples involving plasma heating and adiabatic compression are described.
Bibliography:None
ISSN:0021-9991
1090-2716
DOI:10.1016/S0021-9991(83)71107-1