Phase space dynamics after the breaking of a relativistic Langmuir wave in a thermal plasma

Grassi, A.*; Fedeli, L.*; Macchi, A.*; Bulanov, S. V.; Pegoraro, F.*

The relativistic Vlasov equation is integrated numerically in order to investigate the phase space development of the wave break of a relativistic Langmuir wave in a thermal plasma. Relativistic effects lead to a differential retardation in the time required by the electrons to evolve in phase space, the largest momentum electron staking the longest time. This leads to the formation of long lasting spikes in momentum space at the wave break position that propagates with a velocity close to the speed of light and to extremely steep density jumps in coordinate space.