An Energy Principle for Ideal MHD Equilibria with Flows
Authors: Yao Zhou and Hong Qin
Abstract:
In the standard ideal MHD energy principle for equilibria with no
flows, the stability criterion, which is the defi niteness of the perturbed potential energy, is usually
constructed from the linearized equation of motion. Equivalently while more
straightforwardly, it can also be obtained from the second variation of the Hamiltonian
calculated with proper constraints. For equilibria with flows, a stability criterion
was proposed from the linearized equation of motion, but not explained as an energy
principle1. In this paper, the second variation of the Hamiltonian is found to provide
a stability criterion equivalent to, while more straightforward than, what was constructed
from the linearized equation of motion. To calculate the variations of the
Hamiltonian, a complete set of constraints on the dynamics of the perturbations is
derived from the Euler-Poincare structure of the ideal MHD. In addition, a previous
calculation of the second variation of the Hamiltonian was claimed to give a different
stability criterion2, and in this paper we argue such a claim is incorrect.
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Submitted to: Physics of Plasmas (March 2013)
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Download PPPL-4858 (pdf 274 KB 16 pp)
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