Mechanism of instability development during the stimulated coherent scattering of an electromagnetic wave by a relativistic beam of oscillators

The instability increment under the stimulated coherent scattering of an electromagnetic wave by a relativistic beam of oscillators is calculated with reference to processes in free-electron lasers. The calculation is based on the explicit determination of the strength of the electric field scattered by a single electron undergoing forced oscillations in the electric field of the incident pump wave; the composition of the scattered electric fields of a modulated ensemble of such electron oscillators; and the analysis of the inverse effect of high-frequency pressure forces arising from the incident and scattered waves on the motion of the oscillators.