Foundations of magnetohydrodynamics

LeVan, Jarett; Baalrud, Scott D.

doi:10.1063/5.0274784

Foundations of magnetohydrodynamics

Journal Article · Wed Jul 02 00:00:00 EDT 2025 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0274784· OSTI ID:2572008

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University of Michigan, Ann Arbor, MI (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0002789; NA0004148

OSTI ID:: 2572008

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 32; ISSN 1070-664X; ISSN 1089-7674

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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