Impulse Formulations of Hall Magnetohydrodynamic Equations

TL;DR

This paper develops impulse formulations for Hall MHD equations, establishes a Lagrange invariance of a generalized ion magnetic helicity, and discusses its physical implications, including in compressible Hall MHD.

Contribution

It introduces impulse formulations for Hall MHD and demonstrates a new Lagrange invariance of ion magnetic helicity, extending understanding of invariants in plasma physics.

Findings

Lagrange invariance of generalized ion magnetic helicity established

Implications of the invariant discussed for Hall MHD physics

Compressibility does not alter the invariant's implications

Abstract

Impulse formulations of Hall magnetohydrodynamic (MHD) equations are developed. The Lagrange invariance of a generalized ion magnetic helicity is established for Hall MHD. The physical implications of this Lagrange invariant are discussed. The discussion is then extended to compressible Hall MHD. Compressibility effects are shown not to affect, as to be expected, the physical implications of the generalized ion magnetic helicity Lagrange invariant.