Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-01T04:51:12.884Z Has data issue: false hasContentIssue false
  • English
  • Français

A multi-D model for Raman amplification

Published online by Cambridge University Press:  24 June 2010

Mathieu Colin  and
Thierry Colin
Mathieu Colin
Affiliation:
Université de Bordeaux, IMB, INRIA Bordeaux Sud Ouest, Team MC2, 351 cours de la libération, 33405 Talence Cedex, France. [email protected]; [email protected]
Thierry Colin
Affiliation:
Université de Bordeaux, IMB, INRIA Bordeaux Sud Ouest, Team MC2, 351 cours de la libération, 33405 Talence Cedex, France. [email protected]; [email protected]
Get access

Abstract

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 amplificationZakharov systemweakly nonlinear theory
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 1 , January 2011 , pp. 1 - 22
Copyright
© EDP Sciences, SMAI, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barrailh, K. and Lannes, D., 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. CrossRef
Belaouar, R., Colin, T., Gallice, G. and Galusinski, C., Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. ESAIM: M2AN 40 (2006) 961–990. CrossRef
Berger, R.L., Still, C.H., Williams, A. and Langdon, A.B., On the dominant and subdominant behaviour of stimulated Raman and Brillouin scattering driven by nonuniform laser beams. Phys. Plasma 5 (1998) 4337–4356. CrossRef
Besse, C., 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. CrossRef
Carles, R., Geometrics optics and instability for semi-linear Schrödinger equations. Arch. Ration. Mech. Anal. 183 (2007) 525–553. CrossRef
Colin, M. and Colin, T., On a quasi-linear Zakharov system describing laser-plasma interactions. Diff. Int. Eqs. 17 (2004) 297–330.
Colin, M. and Colin, T., A numerical model for the Raman amplification for laser-plasma interactions. J. Comput. Appl. Math. 193 (2006) 535–562. CrossRef
Decker, C.D., Mori, W.B., Katsouleas, T. and Hinkel, D.E., Spatial temporal theory of Raman forward scattering. Phys. Plasma 3 (1996) 1360–1372. CrossRef
Doumica, M., Duboc, F., Golse, F. and Sentis, R., Simulation of laser beam propagation with a paraxial model in a tilted frame. J. Comput. Phys. 228 (2009) 861–880. CrossRef
Glassey, R.T., Convergence of an energy-preserving scheme for the Zakharov equation in one space dimension. Math. Comput. 58 (1992) 83–102. CrossRef
Hayashi, N., Naumkin, P.I. and Pipolo, P.-N., Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete Contin. Dyn. Syst. 5 (1999) 685–695.
W.L. Kruer, The physics of laser plama interactions. Addison-Wesley, New York (1988)
Sentis, R., Mathematical models for laser-plasma interaction. ESAIM: M2AN 39 (2005) 275–318. CrossRef
Texier, B., Derivation of the Zakharov equations. Arch. Ration. Mech. Anal. 184 (2007) 121–183. CrossRef
Zakharov, V.E., Musher, S.L. and Rubenchik, A.M., Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Reports 129 (1985) 285–366. CrossRef