Nonlinear stability in anisotropic magnetohydrodynamics
Formal stability, i.e., positive energy linear stability, and nonlinear stability are defined. The generic way in which a system with infinite degrees of freedom may be nonlinearly unstable in spite of formal stability is illustrated. The “energy-Casimir” method of proof of nonlinear stability is applied to “relaxed states” of anisotropic magnetohydrodynamics (MHD). Such states are consistent with ergodic magnetic field lines and are formally stable under mild restrictions. Specifically, there is no free energy to drive interchange modes. Nonlinear stability is guaranteed under somewhat more restrictive conditions than is formal stability.
KeywordsPoisson Bracket General Entropy Formal Stability Nonlinear Stability Magnetic Helicity
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