A least Action principle for visco-resistive Hall Magnetohydrodynamic with metriplectic reformulation

TL;DR

This paper introduces a new variational framework for viscous and resistive Hall MHD, incorporating metriplectic reformulation to unify ideal and dissipative dynamics.

Contribution

It develops a novel variational principle for viscous and resistive Hall MHD and reformulates it using metriplectic structures, bridging ideal and dissipative plasma models.

Findings

Derived a variational principle for viscous and resistive Hall MHD.

Established a metriplectic reformulation combining Lie-Poisson and metric brackets.

Provides a unified geometric framework for dissipative plasma dynamics.

Abstract

We present a new variational formulation for Viscous and resistive Hall Magnetohydrodynamic. We first find a variational principle for ideal HMHD by applying the physical assumptions leading to HMHD at the lagrangian level, and then we add the viscous and resistive terms by the means of constrained variations. We also provide a metriplectic reformulation of our formulation, based on two canonical Lie-Poisson brackets for the ideal part and metric 4-brackets for the dissipative part.