ABSTRACT
This chapter studies problems where some of these assumptions are relaxed. While linear Landau damping describes the interaction between a wave and particles which are close to the phase velocity, the nonlinear counterpart of this process affects particles with velocities in the vicinity of the wave group velocity. This can be a quite general phenomenon, but we consider one basic problem, namely, the one where ions are interacting with a modulated Langmuir wave. The analysis considered a Langmuir wave, modulated by a given wave-number K. The nonlinear Landau damping effect was due to the interaction of resonant particles and the ambipolar electric field set up by the ponderomotive forces from the wave envelope which moves with the group velocity. The chapter considers electrostatic waves, but the basic features of the problem, the filamentation instability in particular, are also found for other wave types such as electromagnetic waves propagating in plasmas.
