Quantum theory of stimulated Cerenkov radiation of transverse electromagnetic waves by a low-density electron beam in a medium

The quantum theory of stimulated Cerenkov radiation of transverse electromagnetic waves by an electron beam in an anisotropic medium is presented. Relativistic quantum nonlinear equations of the Cerenkov beam instability are obtained. In the linear approximation, the quantum dispersion equation is derived and the instability growth increments are determined. The nonlinear problem of the saturation of the quantum Cerenkov beam instability is solved.