Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles

Journal Article · Tue May 15 04:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4714761· OSTI ID:22072320

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, University of Texas at Austin, Austin, Texas 78712-1060 (United States)
3. Dipartimento di Fisica E. Fermi, Pisa 56127 (Italy)

The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for continuously symmetric equilibrium configurations of magnetized plasma, including flow. In particular, helical symmetry is considered, and results on axial and translational symmetries are retrieved as special cases of the helical configurations. The symmetry condition, which allows the description in terms of a magnetic flux function, is exploited to deduce a symmetric form of the noncanonical Poisson bracket of MHD. Casimir invariants are then obtained directly from the Poisson bracket. Equilibria are obtained from an energy-Casimir principle and reduced forms of this variational principle are obtained by the elimination of algebraic constraints.

• OSTI ID: 22072320
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 19; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CASIMIR EFFECT
HAMILTONIANS
HELICAL CONFIGURATION
MAGNETIC FLUX
MAGNETOHYDRODYNAMICS
PLASMA
SYMMETRY
VARIATIONAL METHODS