Thermal effects in the ultrarelativistic two-stream instability

The dispersion relation for longitudinal waves in a one-dimensional ultrarelativistic plasma is calculated. Analytical and numerical results for the growth rate and frequency of the two-stream instability are presented as a function of the energy spread in the denser stream when the dilute stream is cold. The case of energy spreads in both beams is investigated numerically: it is found that relatively small energy spreads in both streams can lead to suppression of the instability.