Asymptotic evolution of nonlinear Landau damping

The long-time evolution of nonlinear Landau damping in collisionless plasma s is analyzed by solving the Vlasov-Poisson system numerically. The value o f the parameter marking the transition between Landau's and O'Neil's regime s is determined and compared with analytical results. The long-time evoluti on 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 counterp ropagating ''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 s ideband instability. Ions dynamics is found not to affect these behaviors s ignificantly.