Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) no. 6, pp. 961-990.

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.

DOI : https://doi.org/10.1051/m2an:2007004
Classification : 35Q60,  65T50,  65M06
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: Mathematical Modelling and Numerical Analysis - 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},
zbl = {1112.76090},
mrnumber = {2297101},
language = {en},
url = {http://archive.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) no. 6, pp. 961-990. doi : 10.1051/m2an:2007004. http://archive.numdam.org/item/M2AN_2006__40_6_961_0/

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