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Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. (English) Zbl 1112.76090
Summary: We study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from Vlasov-Maxwell system, we derive a nonlinear Schrödinger-like system which takes into account the energy exchanged between plasma waves and electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting spectral discretizations for Zakharov system and a finite difference scheme for electron diffusion equation, we perform numerical simulations and show how Landau damping works quantitatively.

MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76M20 Finite difference methods applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
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