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A numerical model for the Raman amplification for laser-plasma interaction. (English) Zbl 1092.35101
Summary: We continue the study of the Raman amplification initiated in [Differ. Integral Equations 17, 297–330 (2004)]. 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 1D and 2D simulations.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
78A60 Lasers, masers, optical bistability, nonlinear optics
35Q60 PDEs in connection with optics and electromagnetic theory
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
82D10 Statistical mechanical studies of plasmas
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[1] Besse, C., Schéma de relaxation pour l’équation de Schrödinger non linéaire et LES systémes de Davey et Stewartson, C.R. acad. sci. Paris. Sér. I math., 326, 1427-1432, (1998) · Zbl 0911.65072
[2] Chemin, J.-Y., Fluides parfaits incompréssibles, Astérisque, 230, (1995) · Zbl 0829.76003
[3] Colin, M.; Colin, T., On a quasi-linear Zakharov system describing laser-plasma interactions, Differential integral equations, 17, 3-4, 297-330, (2004) · Zbl 1174.35528
[4] Galusinski, C., A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence, M2AN math. model. numer. anal., 34, 1, 109-125, (2000) · Zbl 0961.76096
[5] Glassey, R.T., Convergence of an energy-preserving scheme for the Zakharov equation in one space dimension, Math. comput., 58, 197, 83-102, (1992) · Zbl 0746.65066
[6] Joly, J.L.; Métivier, G.; Rauch, J., Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke math. J., 70, 2, 373-404, (1993) · Zbl 0815.35066
[7] Russel, D.A.; Dubois, D.F.; Rose, H.A., Nonlinear saturation of simulated Raman scattering in laser hot spots, Phys. plasmas, 6, 4, 1294-1317, (1999)
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