Diffusion limit of the Vlasov equation in the weak turbulent regime
| Autor: | Claude Bardos, Nicolas Besse |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Hamiltonian mechanics Diffusion equation Weak topology Mathematical analysis Vlasov equation FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) symbols.namesake Mathematics - Analysis of PDEs Distribution function Compact space Electric field FOS: Mathematics symbols Landau damping Mathematical Physics Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Mathematical Physics. 62:101505 |
| ISSN: | 1089-7658 0022-2488 |
| Popis: | In this paper we study the Hamiltonian dynamics of charged particles subject to a non-self-consistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov equation is a diffusion equation in the velocity space, but homogeneous in the physical space. We obtain a diffusion matrix, quadratic with respect to the electric field, which can be related to the diffusion matrix of the resonance broadening theory and of the quasilinear theory, depending on whether the typical autocorrelation time of particles is finite or not. In the self-consistent deterministic case, we show that the asymptotic distribution function is homogenized in the space variables, while the electric field converges weakly to zero. We also show that the lack of compactness in time for the electric field is necessary to obtain a genuine diffusion limit. By contrast, the time compactness property leads to a "cheap" version of the Landau damping: the electric field converges strongly to zero, implying the vanishing of the diffusion matrix, while the distribution function relaxes, in a weak topology, towards a spatially homogeneous stationary solution of the Vlasov-Poisson system. |
| Databáze: | OpenAIRE |
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