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

Published online by Cambridge University Press:  15 February 2007

R. Belaouar ,
T. Colin ,
G. Gallice  and
C. Galusinski
R. Belaouar
Affiliation:
SIS, CEA CESTA, BP 2, 33114 Le Barp, France. Mathématiques Appliquées de Bordeaux, UMR CNRS 5466 et CEA LRC M03, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France. [email protected].
T. Colin
Affiliation:
Mathématiques Appliquées de Bordeaux, UMR CNRS 5466 et CEA LRC M03, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France. [email protected]. INRIA Futurs, project MC2.
G. Gallice
Affiliation:
SIS, CEA CESTA, BP 2, 33114 Le Barp, France.
C. Galusinski
Affiliation:
Mathématiques Appliquées de Bordeaux, UMR CNRS 5466 et CEA LRC M03, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France. [email protected]. INRIA Futurs, project MC2.
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Abstract

In this paper, we study a Zakharov system coupled to an electrondiffusion equation in order to describe laser-plasma interactions. Starting fromthe 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.

Keywords

Landau dampingZakharov system.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 6 , November 2006 , pp. 961 - 990
Copyright
© EDP Sciences, SMAI, 2007

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