Structure and computation of two-dimensional incompressible extended MHD

TL;DR

This paper develops a Hamiltonian-based two-dimensional incompressible extended MHD model from two-fluid theory, analyzing its structure, invariants, and linear and nonlinear behaviors, including collisionless reconnection.

Contribution

It introduces a novel Hamiltonian four-field model for extended MHD, capturing key invariants and limits, and provides insights into collisionless tearing through simulations.

Findings

Energy conservation and Casimir invariants are derived.

Linear growth rate for collisionless reconnection is obtained.

Nonlinear simulations elucidate collisionless tearing dynamics.

Abstract

A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.