Linear Wave-Propagation in Mildly Relativistic Thermal Pair Plasmas

Abstract We present dispersion relations and eigenmodes for linear waves propagating in fluid-like mildly relativistic thermal pair plasmas For any given wavevector, four modes are possible: two with sound wave-like properties, and two that are isobaric and essentially non-propagating. One of the isobaric modes strongly perturbs the pair balance, while the other does so much more weakly. Short-wavelength sound waves propagate non-dispersively with a speed which is not a monotonic function of temperature. All sound waves are damped in a time short compared to a wave crossing time; the isobaric modes are generally damped in a time short compared to a light crossing time. At low temperatures (corresponding to high pair content), long-wavelength sound waves are so strongly damped that they do not propagate. On this basis we predict that pressure perturbations should be very weak in thermal pair plasmas, and that even subsonic projectile motion should create pressure jumps.