Stability theory of a toroidal plasma with viscosity, resistivity, and Hall effect
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
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
PLASMA
STABILITY
TOROIDAL PINCH DEVICES
BOUNDARY CONDITIONS
CAUCHY PROBLEM
HALL EFFECT
MAGNETOHYDRODYNAMICS
NONLINEAR PROBLEMS
STEADY-STATE CONDITIONS
CLOSED PLASMA DEVICES
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
PINCH DEVICES
THERMONUCLEAR DEVICES
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