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

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 stabil...

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Bibliographic Details
Published in:Physics of plasmas 2020-01, Vol.27 (1)
Main Authors: Kaltsas, D. A., Throumoulopoulos, G. N., Morrison, P. J.
Format: Article
Language:English
Subjects:
Accessibility
Computational fluid dynamics
Dynamic stability
Electron mass
Equations of motion
Equilibrium
Fluid flow
Magnetohydrodynamics
Plasma physics
Stability analysis
Stability criteria
Two fluid models
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Summary: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.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.5125573