We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the coupling with the ion acoustic waves which has to be taken into account to model the so called Brillouin instability. Here, besides the macroscopic density and the velocity of the plasma, one has to handle the space-time envelope of the main laser wave, the space-time envelope of the stimulated Brillouin backscattered laser wave and the space envelope of the Brillouin ion acoustic waves. Numerical methods are also described to deal with the paraxial model and the three-wave coupling system related to the Brillouin instability.
Mots-clés : Euler-Maxwell system, numerical plasma simulation, geometrical optics, paraxial approximation, Schrödinger equation, three-wave coupling system, Brillouin instability
@article{M2AN_2005__39_2_275_0,
author = {Sentis, R\'emi},
title = {Mathematical models for laser-plasma interaction},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {275--318},
publisher = {EDP-Sciences},
volume = {39},
number = {2},
year = {2005},
doi = {10.1051/m2an:2005014},
mrnumber = {2143950},
zbl = {1080.35157},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005014/}
}
TY - JOUR AU - Sentis, Rémi TI - Mathematical models for laser-plasma interaction JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 275 EP - 318 VL - 39 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005014/ DO - 10.1051/m2an:2005014 LA - en ID - M2AN_2005__39_2_275_0 ER -
%0 Journal Article %A Sentis, Rémi %T Mathematical models for laser-plasma interaction %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 275-318 %V 39 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005014/ %R 10.1051/m2an:2005014 %G en %F M2AN_2005__39_2_275_0
Sentis, Rémi. Mathematical models for laser-plasma interaction. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 275-318. doi : 10.1051/m2an:2005014. http://www.numdam.org/articles/10.1051/m2an:2005014/
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