New Results for Collisionless Damping in Relativistic Plasmas

New theoretical and computational results for Landau damping are presented. The plasma dispersion function is solved to machine precision using direct line integration in the complex plane, in combination with an analytic evaluation of the residue to account for the deformation along the Landau contour. The approach is generic in that it applies to arbitrary distribution functions, and here we focus on Langmuir waves. As is well-known, we confirm that the Landau root becomes increasingly undamped as the plasma becomes hotter, and furthermore show that the Landau root ceases to exist for sufficiently relativistic plasmas. We also confirm past findings of undamped modes with superluminal phase velocities, unique to a relativistic treatment of the dispersion function, and offer new insights into their properties.