Breaking of Large Amplitude Relativistically Intense Electron Plasma Waves in a Warm Plasma

In this paper, the effect of finite electron temperature on the space-time evolution and breaking of a large amplitude relativistically intense electron plasma wave has been studied, using a 1-D relativistic Particle-in-Cell (PIC) code. We have found that for phase velocities for which $\gamma _\phi \ll 1 + \frac{k_BT_e}{mc^2}$, the wave damps within a few plasma period and essentially follows the relativistic Landau Damping rate predicted by Buti. In the opposite regime (i.e. for $\gamma _\phi \gg 1 + \frac{k_BT_e}{mc^2}$) we have observed that waves propagate through the system for a long period of time and in small amplitude limit follow the relativistic warm plasma dispersion relation. Further we have demonstrated that in the same regime (i.e. for $\gamma _\phi \gg 1 + \frac{k_BT_e}{mc^2}$), for the phase velocities less than the velocity of light $c$, like the cold plasma Akhiezer - Polovin wave, in a warm plasma also, relativistically intense waves break via phase mixing when perturbed by an arbitrarily small amplitude longitudinal perturbation. Using the simulation results, we have also shown that the phase mixing time scale in a warm plasma can be interpreted using Dawson's formula for phase mixing time for a non-relativistic cold inhomogeneous plasma, which is based on out of phase motion of neighbouring oscillators constituting the wave.