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

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

2012-02-02

arxiv.org/abs/1202.0468v1

Physics

Plasma Physics

submitted to Physics of Plasmas, 16 pages

Scientific paper

The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for 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.

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