Year: 2025
Type: preprint
Abstract: In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When coupled with Maxwell's equations, this provides closed fluid equations in terms of material properties of the plasma, described by the equation of state and transport coefficients. These properties are connected to microscopic dynamics using the Irving-Kirkwood procedure and Green-Kubo relations. Symmetry arguments and the Onsager-Casimir relations allow one to vastly simplify the number of independent coefficients. Importantly, expressions for current density, heat flux, and stress (conventionally Ohm's law, Fourier's law, and Newton's law) take different forms in systems with a non-ideal equation of state. The traditional form of the MHD equations, which is usually obtained from a Chapman-Enskog solution of the Boltzmann equation, corresponds to the ideal gas limit of the general equations.
Source: arXiv (Cornell University)
Authors: LeVan, Jarett, Baalrud, Scott
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979327467
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