A stable and causal model of magnetohydrodynamics

TL;DR

This paper develops a stable, causal first-order magnetohydrodynamics framework that avoids extra degrees of freedom, providing a simpler alternative for modeling dissipative effects in astrophysics and heavy-ion collisions.

Contribution

It formulates a new first-order dissipative MHD theory that ensures stability and causality without additional dynamical fields, applicable across various physical contexts.

Findings

Identifies constraints on transport coefficients for stability and causality.

Shows existence of multiple hydrodynamic frames satisfying these constraints.

Provides a detailed analysis of transport properties and entropy production.

Abstract

We formulate the theory of first-order dissipative magnetohydrodynamics in an arbitrary hydrodynamic frame under the assumption of parity-invariance and discrete charge symmetry. We study the mode spectrum of Alfv\'en and magnetosonic waves as well as the spectrum of gapped excitations and derive constraints on the transport coefficients such that generic equilibrium states with constant magnetic fields are stable and causal under linearised perturbations. We solve these constraints for a specific equation of state and show that there exists a large family of hydrodynamic frames that renders the linear fluctuations stable and causal. This theory does not require introducing new dynamical degrees of freedom and therefore is a promising and simpler alternative to M\"{u}ller-Israel-Stewart-type theories. Together with a detailed analysis of transport, entropy production and Kubo formulae, the theory presented here is well suited for studying dissipative effects in various contexts ranging from heavy-ion collisions to astrophysics.