Wave-particle interaction and nonlinear Landau damping in collisionless electron plasmas

Nonlinear wave-particle interaction in the propagation of electrostatic waves in unmagnetized collisionless plasma is investigated using a Lagrangian approach. The self-consistent electric field evaluated by solving numerically the Vlasov-Poisson system of equations is used to advance the equations of motion of a large number of test particles. A statistical study of the phase space trajectories of resonant particles shows that the dynamics near the border of the resonant region becomes ergodic and chaotic and the particles can escape from the potential well and perform more or less long flights in the phase space. Our numerical results show that these phase space flights, able in principle to dissipate the electric energy, are of limited extent; in fact, after a characteristic time, the escaped particles are almost all retrapped in the potential well. Therefore the phase space flights are not sufficiently long to allow dissipation to go on, but their characteristic length determines the undamped, oscillating, long time behavior of solutions.