In this paper, we continue the study of the Raman amplification in plasmas that we initiated in [Colin and Colin, Diff. Int. Eqs. 17 (2004) 297-330; Colin and Colin, J. Comput. Appl. Math. 193 (2006) 535-562]. We point out that the Raman instability gives rise to three components. The first one is collinear to the incident laser pulse and counter propagates. In 2-D, the two other ones make a non-zero angle with the initial pulse and propagate forward. Furthermore they are symmetric with respect to the direction of propagation of the incident pulse. We construct a non-linear system taking into account all these components and perform some 2-D numerical simulations.
Keywords: Raman amplification, Zakharov system, weakly nonlinear theory
@article{M2AN_2011__45_1_1_0,
author = {Colin, Mathieu and Colin, Thierry},
title = {A {multi-D} model for {Raman} amplification},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1--22},
year = {2011},
publisher = {EDP Sciences},
volume = {45},
number = {1},
doi = {10.1051/m2an/2010037},
mrnumber = {2781129},
zbl = {06183193},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2010037/}
}
TY - JOUR AU - Colin, Mathieu AU - Colin, Thierry TI - A multi-D model for Raman amplification JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 1 EP - 22 VL - 45 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2010037/ DO - 10.1051/m2an/2010037 LA - en ID - M2AN_2011__45_1_1_0 ER -
%0 Journal Article %A Colin, Mathieu %A Colin, Thierry %T A multi-D model for Raman amplification %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 1-22 %V 45 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2010037/ %R 10.1051/m2an/2010037 %G en %F M2AN_2011__45_1_1_0
Colin, Mathieu; Colin, Thierry. A multi-D model for Raman amplification. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 1, pp. 1-22. doi: 10.1051/m2an/2010037
[1] and , A general framework for diffractive optics and its applications to lasers with large spectrums and short pulses. SIAM J. Math. Anal. 34 (2002) 636-674. | Zbl | MR
[2] , , and , Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. ESAIM: M2AN 40 (2006) 961-990. | Zbl | MR | Numdam
[3] , , and , On the dominant and subdominant behaviour of stimulated Raman and Brillouin scattering driven by nonuniform laser beams. Phys. Plasma 5 (1998) 4337-4356.
[4] , Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson. C. R. Acad. Sci. Paris. Sér. I Math. 326 (1998) 1427-1432. | Zbl | MR
[5] , Geometrics optics and instability for semi-linear Schrödinger equations. Arch. Ration. Mech. Anal. 183 (2007) 525-553. | Zbl | MR
[6] and , On a quasi-linear Zakharov system describing laser-plasma interactions. Diff. Int. Eqs. 17 (2004) 297-330. | Zbl | MR
[7] and , A numerical model for the Raman amplification for laser-plasma interactions. J. Comput. Appl. Math. 193 (2006) 535-562. | Zbl | MR
[8] , , and , Spatial temporal theory of Raman forward scattering. Phys. Plasma 3 (1996) 1360-1372.
[9] , , and , Simulation of laser beam propagation with a paraxial model in a tilted frame. J. Comput. Phys. 228 (2009) 861-880. | Zbl | MR
[10] , Convergence of an energy-preserving scheme for the Zakharov equation in one space dimension. Math. Comput. 58 (1992) 83-102. | Zbl | MR
[11] , and , Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete Contin. Dyn. Syst. 5 (1999) 685-695. | Zbl | MR
[12] , The physics of laser plama interactions. Addison-Wesley, New York (1988)
[13] , Mathematical models for laser-plasma interaction. ESAIM: M2AN 39 (2005) 275-318. | Zbl | MR | Numdam
[14] , Derivation of the Zakharov equations. Arch. Ration. Mech. Anal. 184 (2007) 121-183. | MR
[15] , and , Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Reports 129 (1985) 285-366. | MR
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