Effect of amplification of Cherenkov radiation in an active medium with two resonant frequencies

Some results of analytical and numerical studies of Cherenkov radiation (CR) in an active medium with two resonant frequencies are presented. It is shown that an unbounded bi-resonant medium amplifies CR even in the case of a purely real refractive index if the lower resonance is active, the higher one is passive and some restrictions on charge velocity are met. It is also demonstrated that amplification of CR from an ultra- relativistic beam is possible if the medium is located in a waveguide.