Stability theory of a toroidal plasma with viscosity, resistivity, and Hall effect
Thesis/Dissertation
·
OSTI ID:5410171
Some stability properties are established for solutions to the equations of viscous, resistive, incompressible magnetohydrodynamics governing a toroidal diffuse pinch and including the Hall current effect in Ohm's Law. The principal difficulties in the analysis are due to the Hall term, which causes nonlinearities to be present in the boundary conditions and in the highest order derivatives of the equations of motion. In order to formulate the linear stability problem, the governing equations are linearized about a steady-state solution and expressed as an abstract Cauchy problem. The stability or instability of the steady state is then determined by a spectral analysis of an unbounded linear operator. It is shown that the operator has a discrete spectrum and a complete set of generalized eigenfunctions with finitely many unstable eigenvalues and infinitely many stable eigenvalues confined to a triangular sector of the complex plane. A sufficient criterion for stability is established and the existence of a class of stable equilibria is proved. In the nonlinear stability analysis, it is shown that the stability or instability result obtained by the linear analysis remains valid for the full nonlinear problem as well.
- Research Organization:
- Wisconsin Univ., Madison (USA)
- OSTI ID:
- 5410171
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
640430 -- Fluid Physics-- Magnetohydrodynamics
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
700107* -- Fusion Energy-- Plasma Research-- Instabilities
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CAUCHY PROBLEM
CLOSED PLASMA DEVICES
FLUID MECHANICS
HALL EFFECT
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MECHANICS
NONLINEAR PROBLEMS
PINCH DEVICES
PLASMA
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STEADY-STATE CONDITIONS
THERMONUCLEAR DEVICES
TOROIDAL PINCH DEVICES
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
700107* -- Fusion Energy-- Plasma Research-- Instabilities
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CAUCHY PROBLEM
CLOSED PLASMA DEVICES
FLUID MECHANICS
HALL EFFECT
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MECHANICS
NONLINEAR PROBLEMS
PINCH DEVICES
PLASMA
STABILITY
STEADY-STATE CONDITIONS
THERMONUCLEAR DEVICES
TOROIDAL PINCH DEVICES