Resonant excitation of electrostatic modes with electromagnetic waves

Two electromagnetic waves, propagating in opposite directions, can resonantly excite electron or ion waves, if the difference frequency Δω and wave number Δk satisfy the linear dispersion relation of such modes. This process damps the higher-frequency electromagnetic wave and amplifies the lower-frequency one (nonlinear Landau damping). The amplitude of the electrostatic mode may be limited by Landau damping, trapping, or by loss of resonance due to the frequency shift of the electromagnetic modes.