Nonresistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation

Abstract

We derive the equations of motion of relativistic, nonresistive, 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 nonresistive, 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, nonresistive, 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.