Existence and calculation of sharp boundary magnetohydrodynamic equilibrium in three-dimensional toroidal geometry

Journal Article · Wed Oct 01 00:00:00 EDT 1986 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.865845· OSTI ID:5209821

Berk, H L; Freidberg, J P; Llobet, X; Morrison, P J; Tataronis, J A

The problem of sharp boundary, ideal magnetohydrodynamic equilibria in three-dimensional toroidal geometry is addressed. The sharp boundary, which separates a uniform pressure, current-free plasma from a vacuum, is determined by a magnetic surface of a given vacuum magnetic field. The pressure balance equation has the form of a Hamilton-Jacobi equation with a Hamiltonian that is quadratic in the momentum variables, which are the two covariant components of the magnetic field on the outer surface of the plasma. The condition of finding a unique solution on the outer surface is identical with finding phase-space tori in nonlinear dynamics problems, and the Kolmogorov-Arnold-Moser (KAM) theorem guarantees that such solutions exist for a wide band of parameters. Perturbation theory is used to calculate the properties of the magnetic field just outside the plasma. Special perturbation theory is needed to treat resonances and it is explicitly shown that there are bands of pressure where there are no solutions.

• Research Organization: Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1081
• OSTI ID: 5209821
• Journal Information: Phys. Fluids; (United States), Vol. 29:10
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
PLASMA
EQUILIBRIUM
MAGNETOHYDRODYNAMICS
BOUNDARY LAYERS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
MAGNETIC SURFACES
NONLINEAR PROBLEMS
PERTURBATION THEORY
PHASE SPACE
RENORMALIZATION
THREE-DIMENSIONAL CALCULATIONS
TORI
TOROIDAL CONFIGURATION
VACUUM SYSTEMS
ANNULAR SPACE
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
LAYERS
MAGNETIC FIELD CONFIGURATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE
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