Asymptotic evolution of nonlinear landau damping.

The long-time evolution of nonlinear Landau damping in collisionless plasmas is analyzed by solving the Vlasov-Poisson system numerically. The value of the parameter marking the transition between Landau's and O'Neil's regimes is determined and compared with analytical results. The long-time evolution of a finite-amplitude electric field with wavelength lambda equal to the length of the simulation box L is given by a superposition of two counterpropagating "averaged" Bernstein-Greene-Kruskal (BGK) waves. When L>lambda and longer wavelength modes can be excited, the BGK waves correspond to an intermediate regime that is eventually modified by the excitation of the sideband instability. Ions dynamics is found not to affect these behaviors significantly.