Transition from linear Landau damping to nonlinear Bernstein-Greene-Kruskal modes via phase synchronization

Dynamics of the transition from a linear plasma wave to a nonlinear state characterized by the Bernstein-Greene-Kruskal mode is studied within the framework of the Vlasov-Poisson system. In the linear stage, the plasma distribution function (f) develops finer and finer structures in velocity space through a series of "mixing"processes leading to the Landau damping of the plasma wave. These mixing processes inevitably result in strong phase irregularities in velocity space. Using numerical simulations, it was observed that starting from the wave-particle resonance region, this irregular phase pattern gets "smoothed out"through a process of spreading of phase synchronization, which tends to reduce Landau damping, facilitating the formation of the nonlinear plasma wave as a fully synchronized final state. It is also found that there exists a residual damping for the quasisteady nonlinear wave when the phases of the particles are not fully synchronized.