Current-conserving relativistic linear response for collisional plasmas

Highlights: • Fully covariant solution of the linearized Boltzmann equation. • Collision term conserving current explicitly. • Arbitrary four–velocity of the medium. • Ultra-relativistic limit of the polarization tensor in medium rest frame. • Non-relativistic limit of the polarization tensor in medium rest frame. • Frequency dependent plasma response to external EM fields. • Plasma susceptibility and conductivity. 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.