A numerical model for the Raman amplification for laser-plasma interaction

In this paper, we continue the study of the Raman amplification initiated in [M. Colin, T. Colin, On a quasi-linear Zakharov system describing laser-plasma interactions, Differential Integral Equations 17(3–4) (2004) 297–330]. We use a dispersive, quasi-linear system. The quasi-linear part is not hyperbolic and this difficulty is overcome using the dispersion. We give an asymptotic result on a reduced system. We then introduce a simple, robust and efficient numerical scheme on the whole system that takes into account the non-hyperbolicity of the quasi-linear part as well as the nonlinear saturation of the Raman growth. The scheme is validated thanks to the asymptotic result. Finally, we present 1-D and 2-D simulations.