On the theory of nonlinear Cherenkov effect in the beams moving through the channel in dielectric

A study was made of the Cherenkov effect in a beam moving through a channel in a dielectric. A system of two equations was derived describing the non-linear self-consistent Cherenkov effect. The initial linear stage of the process was considered in detail for the case where fields and currents in the system are determined exclusively by the initial conditions at the entrance to the interaction space. Radiation conditions, the power flux of Cherenkov radiation in the region containing the dielectric and the angle of emergence of the Cherenkov radiation were defined. Limit transitions to cases studied earlier are specified