Non-resistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation

TL;DR

This paper derives second-order dissipative magnetohydrodynamics equations from the Boltzmann equation, incorporating magnetic field effects and providing new transport coefficients, within a 14-moment approximation.

Contribution

It introduces a novel derivation of relativistic non-resistive dissipative MHD equations from kinetic theory using the 14-moment approximation.

Findings

Reproduces first-order transport coefficients in the Navier-Stokes limit.

Derives second-order equations including magnetic field coupling effects.

Provides explicit expressions for new transport coefficients.

Abstract

We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.