Vlasov-Poisson numerical simulations of wave-particle interactions in the relativistic regime

The Landau damping of an electrostatic wave is analyzed in relativistic plasmas by solving the Vlasov-Poisson system numerically The Juttner-Synge distribution function is perturbed in order to obtain the numerical dispersion relation for short wavelenghts and for nu(ph) less than or similar to c, upsilon(ph) being the phase velocity of the wave. This is compared with the analytical results available in the literature. The ordering of the time-scales characterizing the system and the corresponding formation of vortices in phase space, as a function of the initial temperature, are investigated.