Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

TL;DR

This paper introduces a variational framework for relaxed and multi-region relaxed magnetohydrodynamics, enabling dynamic modeling of plasma states with relaxed constraints and flow, including the formation of multiple relaxation regions separated by current sheets.

Contribution

It develops a new variational principle for relaxed MHD that includes flow and extends to multiple relaxation regions separated by current sheets.

Findings

Derives a fully dynamical relaxed MHD model consistent with Taylor states.

Introduces multi-region relaxation allowing for complex plasma structures.

Provides a theoretical foundation for modeling plasma equilibria with barriers.

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.