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arXiv · 1104.1890

Algebraic damping in the one-dimensional Vlasov equation

Julien Barré·Alain Olivetti·Yoshiyuki Y. Yamaguchi
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Abstract

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.

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Julien Barré, Alain Olivetti, Yoshiyuki Y. Yamaguchi. 2011-04-11. Algebraic damping in the one-dimensional Vlasov equation. https://doi.org/10.1088/1751-8113/44/40/405502

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