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

Gabriel S. Denicol, Xu-Guang Huang, Etele Molnár, Gustavo M. Monteiro, Harri Niemi, Jorge Noronha, Dirk H. Rischke, Qun Wang

Published 2018-04-14Version 1

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. We also 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 new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.