Multi-region relaxed Hall magnetohydrodynamics with flow

TL;DR

This paper extends multi-region relaxed magnetohydrodynamics to include Hall effects, revealing new equilibrium states and analyzing the impact of Hall physics on plasma relaxation and stability.

Contribution

It introduces a generalized MRxMHD framework with Hall effects, deriving new equilibrium states and analyzing the physical implications of Hall terms.

Findings

Derivation of partially relaxed states with Hall effects

Identification of double Beltrami states as special cases

Comparison with existing variational principles

Abstract

The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of "ideal barriers" that prevent global relaxation, and flow. In this paper, we generalize MRxMHD with flow to include Hall effects (MRxHMHD), and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.