Fine structure of the Vavilov-Cherenkov radiation

The aim of this paper is to study the fine structure of the Cherenkov rings. We analyze the experiments performed by one of authors (Zrelov) in which no special focusing devices were used. The broad Cherenkov ring was observed in the plane perpendicular to the motion axis. Using the exact and approximate formulas we investigate how a charge moving uniformly in a medium radiates in a finite space interval (the Tamm problem). The formulas obtained describe the radiation intensity in the whole space, inside and outside the Cherenkov ring. In the plane perpendicular to the motion axis, the radiation fills mainly the finite ring. Its width (proportional to the motion interval) and the energy released in this ring do not depend on the position of the observation plane. Outside the Cherenkov ring, the radiation intensity suddenly drops. Inside it, the radiation intensity exhibits small oscillations which are due to the interference of the Vavilov-Cherenkov radiation and bremsstrahlung. The bursts of the radiation intensity at the ends of the Cherenkov ring are associated with the shock waves arising at the instant when the charge velocity coincides with the light velocity in a medium. For the chosen motion interval, the well-known Tamm formula does not describe the radiation intensity inside the Cherenkov ring for any position of the observation plane. Outside the Cherenkov ring, the Tamm formula is valid only at very large distances. Theoretical calculations are in satisfactory agreement with experimental data. Thus, the combined experimental and theoretical study of the unfocused Cherenkov rings allows one to obtain information on the physical processes accompanying the Cherenkov radiation in the finite spatial interval (bremsstrahlung, transition of the light velocity barrier, etc.).