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

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.
Authors:
 [1] ;  [2] ;  [3]
  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)
Publication Date:
OSTI Identifier:
22220571
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 20; Journal Issue: 9; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CASIMIR EFFECT; HAMILTONIANS; LAGRANGIAN FUNCTION; MAGNETOHYDRODYNAMICS; PERTURBATION THEORY; PLASMA; PLASMA INSTABILITY; STABILITY; SYMMETRY; VARIATIONAL METHODS; VARIATIONS