In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the electron diffusion equation, we perform numerical simulations and show how Landau damping works quantitatively.
Mots clés : Landau damping, Zakharov system
@article{M2AN_2006__40_6_961_0,
author = {Belaouar, R. and Colin, T. and Gallice, G. and Galusinski, C.},
title = {Theoretical and numerical study of a quasi-linear {Zakharov} system describing {Landau} damping},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {961--990},
publisher = {EDP-Sciences},
volume = {40},
number = {6},
year = {2006},
doi = {10.1051/m2an:2007004},
mrnumber = {2297101},
zbl = {1112.76090},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2007004/}
}
TY - JOUR AU - Belaouar, R. AU - Colin, T. AU - Gallice, G. AU - Galusinski, C. TI - Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 961 EP - 990 VL - 40 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007004/ DO - 10.1051/m2an:2007004 LA - en ID - M2AN_2006__40_6_961_0 ER -
%0 Journal Article %A Belaouar, R. %A Colin, T. %A Gallice, G. %A Galusinski, C. %T Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 961-990 %V 40 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007004/ %R 10.1051/m2an:2007004 %G en %F M2AN_2006__40_6_961_0
Belaouar, R.; Colin, T.; Gallice, G.; Galusinski, C. Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 961-990. doi : 10.1051/m2an:2007004. http://www.numdam.org/articles/10.1051/m2an:2007004/
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