Quantum theory of stimulated Cherenkov emission and stimulated compton scattering of electromagnetic waves by a low-density relativistic electron beam

A quantum theory of instabilities of a relativistic electron beam due to the stimulated Cherenkov effect in a dielectric and the stimulated Compton effect in vacuum is presented. The instability growth rates are found in a linear approximation and are shown to go over to the familiar growth rates in the classical approximation. A nonlinear theory of instabilities in the quantum case is developed. Analytic solutions are obtained that describe the nonlinear saturation of the amplitudes of the electromagnetic waves emitted by the beam.