| Issue |
ESAIM: M2AN
Volume 45, Number 1, January-February 2011
|
|
|---|---|---|
| Page(s) | 1 - 22 | |
| DOI | https://doi.org/10.1051/m2an/2010037 | |
| Published online | 24 June 2010 | |
A multi-D model for Raman amplification
Université de Bordeaux, IMB, INRIA Bordeaux Sud Ouest, Team MC2,
351 cours de la libération, 33405 Talence Cedex, France. mcolin@math.u-bordeaux1.fr; colin@math.u-bordeaux1.fr
Received:
15
January
2009
Revised:
18
July
2009
Revised:
25
November
2009
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.
Mathematics Subject Classification: 35Q55 / 35Q60 / 78A60 / 74S20
Key words: Raman amplification / Zakharov system / weakly nonlinear theory
© EDP Sciences, SMAI, 2010
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