On nonlinear theory of electromagnetic wave scattering by the density-modulated nonrelativistic electron beam in the anomalous Doppler mode

The nonlinear dynamics of electromagnetic wave scattering by a dense monoenergetic electron beam, premodulated in density, is studied. Analytical formulas for the amplitudes of interacting waves and the characteristic evolution time of the processes are obtained. It is found that increasing the beam modulation depth greatly reduces the instability decay time. The wave saturation amplitudes are almost independent of the modulation depth.