New approach to nonrelativistic ideal magnetohydrodynamics

TL;DR

This paper introduces a new action principle for nonrelativistic ideal magnetohydrodynamics using a Clebsch parametrisation, exploring both Lagrangian and Hamiltonian formulations with novel constraint analyses.

Contribution

It presents a novel action principle and dual Hamiltonian formulations for nonrelativistic ideal magnetohydrodynamics, including incompressible cases, with detailed constraint analysis.

Findings

Developed a new Eulerian action principle for magnetohydrodynamics.

Analyzed Hamiltonian structures with Dirac's constraints.

Explored conservation properties of the stress tensor.

Abstract

We provide a novel action principle for nonrelativistic ideal magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type parametrisation. Both Lagrangian and Hamiltonian formulations have been considered. Within the Hamiltonian framework, two complementary approaches have been discussed using Dirac's constraint analysis. In one case the Hamiltonian is canonical involving only physical variables but the brackets have a noncanonical structure, while the other retains the canonical structure of brackets by enlarging the phase space. The special case of incompressible magnetohydrodynamics is also considered where, again, both the approaches are discussed in the Hamiltonian framework. The conservation of the stress tensor reveals interesting aspects of the theory.