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

Abstract

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.

submitted to Physics of Plasmas, 16 pages

References in corpus (2)

• A sufficient condition for the linear stability of magnetohydrodynamic equilibria with field aligned incompressible flows
• Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows

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