Nonlinear Landau Damping and Beat Wave Trapping

Abstract
The nonlinear interaction of two coherent waves with particles of velocity near (ω1−ω2) / (k1−k2) is investigated. For times short compared with the trapping time in the beat wave we recover the usual nonlinear Landau damping result, previously derived for the incoherent (turbulent) case. For two coherent waves, however, trapping severely limits the validity of this result.