Order-by-order Anisotropic Transport Coefficients of a Magnetised Fluid: a Chapman-Enskog Approach

TL;DR

This paper derives detailed anisotropic transport coefficients for a relativistic boson gas in a magnetic field using Chapman-Enskog kinetic theory, revealing magnetic field effects and order-dependent differences.

Contribution

It provides the first and second-order expressions for transport coefficients in a magnetized relativistic fluid, highlighting anisotropic effects and magnetic field dependencies.

Findings

Shear viscosity splits into five coefficients with magnetic dependence.

Bulk viscosity remains independent of magnetic field.

Thermal conductivity shows magnetic field dependence and order-dependent differences.

Abstract

We derive the first and second-order expressions for the shear, the bulk viscosity, and the thermal conductivity of a relativistic hot boson gas in a magnetic field using the relativistic kinetic theory within the Chapman-Enskog method. The order-by-order off-equilibrium distribution function is obtained in terms of the associate Laguerre polynomial with magnetic field-dependent coefficients using the relativistic Boltzmann-Uehling-Uhlenbeck transport equation. The order-by-order anisotropic transport coefficients are evaluated in powers of the dimensionless ratio of kinetic energy to the fluid temperature for finite magnetic fields. In a magnetic field, the shear viscosity (in all order) splits into five different coefficients. Four of them show a magnetic field dependence as seen in a previous study \cite{Ashutosh1} using the relaxation time approximation for the collision kernel. On the other hand, bulk viscosity, which splits into three components (in all order), is independent of the magnetic field. The thermal conductivity shows a similar splitting but is field-dependent. The difference in the first and second-order results are prominent for the thermal conductivities than the shear viscosity; moreover, the difference in the two results is most evident at low temperatures. The first and second-order results seem to converge rapidly for high temperatures.