4.4 Article

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

Journal

PHYSICS OF PLASMAS
Volume 27, Issue 1, Pages -

Publisher

AIP Publishing
DOI: 10.1063/1.5125573

Keywords

-

Funding

  1. Euratom Research and Training Programme 2014-2018 [633053]
  2. Euratom Research and Training Programme 2019-2020 [633053]
  3. National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic
  4. General Secretariat for Research and Technology (GSRT)
  5. Hellenic Foundation for Research and Innovation (HFRI)
  6. U.S. Department of Energy [DEFG05-80ET-53088]

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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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