Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action

Publication Year
2020
Abstract

A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamilton's Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross helicity and entropy, as the only constraints on variations of density, pressure, fluid velocity, and magnetic vector potential over a relaxation domain. A novel phase-space version of the MHD Lagrangian is derived, which gives Euler--Lagrange equations consistent with previous work on exact ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether E⃗+u⃗×B⃗=0 should be a constraint is discussed.

Journal
Physics of Plasmas
Volume
27
Issue
6/2020
Date Published
06/2020
ISSN Number
1089-7674
Other Numbers
https://arxiv.org/abs/2002.04892
Category