Hamiltonian and action formalisms for two-dimensional gyroviscous MHD

TL;DR

This paper develops a systematic method to derive action principles for gyroviscous MHD models, clarifying their Hamiltonian structure and invariants, and connecting them to existing fluid equations.

Contribution

It introduces a general procedure for constructing action principles for continuum models, specifically applied to gyroviscous MHD, revealing the origin of the gyromap and providing reduction techniques.

Findings

Constructed an action principle for gyroviscous MHD.

Connected the model to Braginskii's fluid equations.

Derived Casimir invariants and variational principles for equilibria.

Abstract

A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.