Structure and computation of two-dimensional incompressible extended MHD

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.

arXiv comment31 pages, 8 figures

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• Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles
• Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework
• Yet Another Modification of Relativistic Magnetohydrodynamic Waves: Electron Thermal Inertia
• Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia