A multi-D model for Raman amplification
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 1, pp. 1-22.

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.

DOI : 10.1051/m2an/2010037
Classification : 35Q55, 35Q60, 78A60, 74S20
Mots-clés : 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},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {1},
     year = {2011},
     doi = {10.1051/m2an/2010037},
     mrnumber = {2781129},
     zbl = {06183193},
     language = {en},
     url = {http://archive.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  - http://archive.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 http://archive.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. http://archive.numdam.org/articles/10.1051/m2an/2010037/

[1] K. Barrailh and D. Lannes, 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. | MR | Zbl

[2] R. Belaouar, T. Colin, G. Gallice and C. Galusinski, Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. ESAIM: M2AN 40 (2006) 961-990. | Numdam | MR | Zbl

[3] R.L. Berger, C.H. Still, A. Williams and A.B. Langdon, On the dominant and subdominant behaviour of stimulated Raman and Brillouin scattering driven by nonuniform laser beams. Phys. Plasma 5 (1998) 4337-4356.

[4] C. Besse, 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. | MR | Zbl

[5] R. Carles, Geometrics optics and instability for semi-linear Schrödinger equations. Arch. Ration. Mech. Anal. 183 (2007) 525-553. | MR | Zbl

[6] M. Colin and T. Colin, On a quasi-linear Zakharov system describing laser-plasma interactions. Diff. Int. Eqs. 17 (2004) 297-330. | MR | Zbl

[7] M. Colin and T. Colin, A numerical model for the Raman amplification for laser-plasma interactions. J. Comput. Appl. Math. 193 (2006) 535-562. | MR | Zbl

[8] C.D. Decker, W.B. Mori, T. Katsouleas and D.E. Hinkel, Spatial temporal theory of Raman forward scattering. Phys. Plasma 3 (1996) 1360-1372.

[9] M. Doumica, F. Duboc, F. Golse and R. Sentis, Simulation of laser beam propagation with a paraxial model in a tilted frame. J. Comput. Phys. 228 (2009) 861-880. | MR | Zbl

[10] R.T. Glassey, Convergence of an energy-preserving scheme for the Zakharov equation in one space dimension. Math. Comput. 58 (1992) 83-102. | MR | Zbl

[11] N. Hayashi, P.I. Naumkin and P.-N. Pipolo, Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete Contin. Dyn. Syst. 5 (1999) 685-695. | MR | Zbl

[12] W.L. Kruer, The physics of laser plama interactions. Addison-Wesley, New York (1988)

[13] R. Sentis, Mathematical models for laser-plasma interaction. ESAIM: M2AN 39 (2005) 275-318. | Numdam | MR | Zbl

[14] B. Texier, Derivation of the Zakharov equations. Arch. Ration. Mech. Anal. 184 (2007) 121-183. | MR

[15] V.E. Zakharov, S.L. Musher and A.M. Rubenchik, Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Reports 129 (1985) 285-366. | MR

Cité par Sources :