Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

TL;DR

This paper explores the geometric and topological structures of extended magnetohydrodynamics (MHD), revealing universal Hamiltonian features and topological invariants like helicities, which deepen understanding of plasma physics models.

Contribution

It demonstrates how ideal MHD geometric properties extend to models with two-fluid effects, highlighting their Hamiltonian structure and topological invariants.

Findings

Generalized Kelvin circulation theorems derived

Existence of two Lie-dragged 2-forms identified

Two helicities studied via Jones polynomial in Chern-Simons theory

Abstract

The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, which is widely utilized in Chern-Simons theory. The ensuing commonality is traced to the existence of an underlying Hamiltonian structure for all the extended MHD models, exemplified by the presence of a unique noncanonical Poisson bracket, and its associated energy.