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

R. Belaouar; T. Colin; G. Gallice; C. Galusinski

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

  • Volume: 40, Issue: 6, page 961-990
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Belaouar, R., et al. "Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 40.6 (2006): 961-990. <http://eudml.org/doc/244648>.

@article{Belaouar2006,
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.},
author = {Belaouar, R., Colin, T., Gallice, G., Galusinski, C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Landau damping; Zakharov system; electron diffusion equation; existence theorems; finite difference scheme},
language = {eng},
number = {6},
pages = {961-990},
publisher = {EDP-Sciences},
title = {Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping},
url = {http://eudml.org/doc/244648},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Belaouar, R.
AU - Colin, T.
AU - Gallice, G.
AU - Galusinski, C.
TI - Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2006
PB - EDP-Sciences
VL - 40
IS - 6
SP - 961
EP - 990
AB - 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.
LA - eng
KW - Landau damping; Zakharov system; electron diffusion equation; existence theorems; finite difference scheme
UR - http://eudml.org/doc/244648
ER -

References

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