Algebraic damping in the one-dimensional Vlasov equation

Julien Barré (1) , Alain Olivetti (1) , Yoshiyuki Y. Yamaguchi (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Applied Mathematics and Physics [Kyoto]

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Julien Barré, Alain Olivetti, Yoshiyuki Y. Yamaguchi. Algebraic damping in the one-dimensional Vlasov equation. Journal of Physics A: Mathematical and Theoretical, 2011, 44, pp.405502. ⟨hal-00753669⟩