Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

Abstract

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

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Cited by in corpus (5)

• Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Hamiltonian formulations for perturbed dissipationless plasma equations
• Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework