Structure and computation of two-dimensional incompressible extended MHD

• Published in: arXiv.org
• Main Authors: Grasso, D, Tassi, E, Abdelhamid, H M, Morrison, P J
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 03.11.2016
• Subjects: Computational fluid dynamics; Computer simulation; Energy conservation; Equations of motion; Fluid flow; Incompressible flow; Invariants; Magnetohydrodynamics; Mathematical models; Physics - Plasma Physics; Three dimensional models; Two dimensional models
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1611.00955

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.