Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

Journal Article · Sun Sep 15 04:00:00 EDT 2013 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4819779· OSTI ID:22220571

Andreussi, T. ^[1]; Morrison, P. J. ^[2]; Pegoraro, F. ^[3]

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1. Alta S.p.A., Pisa 56121 (Italy)
2. Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)
3. Università di Pisa, Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

• OSTI ID: 22220571
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 20; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CASIMIR EFFECT
HAMILTONIANS
LAGRANGIAN FUNCTION
MAGNETOHYDRODYNAMICS
PERTURBATION THEORY
PLASMA
PLASMA INSTABILITY
STABILITY
SYMMETRY
VARIATIONAL METHODS
VARIATIONS