| Issue |
ESAIM: M2AN
Volume 40, Number 6, November-December 2006
|
|
|---|---|---|
| Page(s) | 961 - 990 | |
| DOI | https://doi.org/10.1051/m2an:2007004 | |
| Published online | 15 February 2007 | |
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
1
SIS, CEA CESTA,
BP 2, 33114 Le Barp, France.
2
Mathématiques Appliquées de Bordeaux, UMR CNRS 5466 et CEA LRC
M03, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France. Thierry.Colin@math.u-bordeaux1.fr.
3
INRIA Futurs, project MC2.
Received:
24
May
2006
Revised:
31
July
2006
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.
Mathematics Subject Classification: 35Q60 / 65T50 / 65M06
Key words: Landau damping / Zakharov system.
© EDP Sciences, SMAI, 2007
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