New approach to Hamiltonian formulation of Hall magnetohydrodynamics

TL;DR

This paper introduces a novel Hamiltonian formulation for barotropic Hall magnetohydrodynamics, utilizing Dirac's constraint analysis to develop two complementary approaches with different Hamiltonian and bracket structures.

Contribution

It provides the first Hamiltonian formulations of Hall MHD using Dirac's method, offering both canonical and noncanonical bracket structures for the theory.

Findings

Developed a canonical Hamiltonian with physical variables only.

Established a phase space enlargement approach with canonical brackets.

Facilitated future analytical and numerical studies of Hall MHD.

Abstract

We present a new Hamiltonian formulation of barotropic Hall magnetohydrodynamics in two complementary approaches based on Dirac's constraint analysis. In one case the Hamiltonian is canonical involving physical variables only but the brackets are noncanonical, while in the other case the phase space is enlarged to retain the canonical structure of brackets.