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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. Thierry.Colin@math.u-bordeaux1.fr.
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. Thierry.Colin@math.u-bordeaux1.fr. 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. Thierry.Colin@math.u-bordeaux1.fr. INRIA Futurs, project MC2.
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Abstract

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.

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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