Two-dimensional semi-Lagrangian Vlasov simulations of laser-plasma interaction in the relativistic regime

A semi-Lagrangian two-dimensional fully relativistic Vlasov code for multicomputer environments is developed to study trapped-particle dynamics in phase space induced by relativistic modulational and Raman instabilities. Attention is focused on the efficiency properties of the numerical scheme, which allows a very fine description of particle dynamics in phase space. Vlasov simulations show the appearance of coherent vortex structures as a result of the nonlinear saturation mechanism of the relativistic modulational instability. Growth rates are computed and found to be in good agreement with theoretical values obtained from the dispersion relation by Quesnol et al, [Phys. Plasmas 4, 3358-3368 (1997)] and Guerin et al. [Phys. Plasmas 2, 2807-2814 (1995)]. In the case of coupling between the relativistic modulational instability and two-plasmon decay, stochastic behaviour can be observed due to the competition between different plasmas waves.