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

A semi-Lagrangian two-dimensional fully relativistic Vlasov code for multic omputer environments is developed to study trapped-particle dynamics in pha se space induced by relativistic modulational and Raman instabilities. Atte ntion is focused on the efficiency properties of the numerical scheme, whic h allows a very fine description of particle dynamics in phase space. Vlaso v simulations show the appearance of coherent vortex structures as a result of the nonlinear saturation mechanism of the relativistic modulational ins tability. 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, 280 7-2814 (1995)]. In the case of coupling between the relativistic modulation al instability and two-plasmon decay, stochastic behaviour can be observed due to the competition between different plasmas waves.