Current-Conserving Relativistic Linear Response for Collisional Plasmas

TL;DR

This paper develops a current-conserving relativistic linear response theory for collisional plasmas, providing explicit solutions and analyzing plasma wave damping in different regimes of collision frequency.

Contribution

It introduces a covariant, gauge invariant, and current conserving polarization tensor framework for relativistic plasmas with collisions, including explicit solutions and damping analysis.

Findings

Explicit solution for linearized distribution perturbation.

Dependence of susceptibility on relaxation rate κ.

Dispersion relation analysis showing overdamping for κ > 2ω_p.

Abstract

We investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi-Dirac equilibrium distribution in terms of the average relaxation rate $\kappa$. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on $\kappa$. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for $\kappa> 2\omega_p$, where $\omega_p$ is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, $\kappa \ll \omega_p$, the propagating plasma modes are weakly damped.