Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
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.
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