Geodesic
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 961-990

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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.

DOI : 10.1051/m2an:2007004
Classification : 35Q60, 65T50, 65M06
Keywords: Landau damping, Zakharov system 
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     title = {Theoretical and numerical study of a quasi-linear {Zakharov} system describing {Landau} damping},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Belaouar, R.; Colin, T.; Gallice, G.; Galusinski, C. Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 961-990. doi: 10.1051/m2an:2007004

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