Linear stability of equilibrium states with flow is studied by means of the variational principle in Hall magnetohydrodynamics (MHD). The Lagrangian representation of the linearized Hall MHD equation is performed by considering special perturbations that preserves some constants of motion (the Casimir invariants). The resultant equation has a Hamiltonian structure which enables the variational principle. There is however some difficulties in showing the positive definiteness of the quadratic form in the presence of flow. The dynamically accessible variation is a more restricted class of perturbations which, by definition, preserves all the Casimir invariants. For such variations, the quadratic form (the second variation of Hamiltonian) can be positive definite. Some conditions for stability are derived by applying this variational principle to the double Beltrami equilibrium.
ASJC Scopus subject areas
- Condensed Matter Physics