Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

Abstract

Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, \emph{relaxed magnetohydrodynamics} (RxMHD), such that all static solutions are Taylor states but also allows flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is developed.

21 pages, 2 figures

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• Spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry
• Multi-region relaxed Hall magnetohydrodynamics with flow
• Multi-region relaxed magnetohydrodynamics in plasmas with slowly changing boundaries --- resonant response of a plasma slab
• Relaxed Magnetohydrodynamics with Ideal Ohm's Law Constraint
• The Kadomtsev pinch revisited for sheared-flow-stabilized Z-pinch modeling
• Quasisymmetric magnetic fields in asymmetric toroidal domains
• Gauge freedom in magnetostatics and the effect on helicity in toroidal volumes
• Steady Compressible 3D Euler Flows in Toroidal Volumes without Continuous Euclidean Isometries
• Near-ideal relaxed MHD in slab geometry