Vavilov–Cherenkov and transition radiations on the dielectric and metallic spheres

Closed expressions are obtained for angular and frequency radiation intensities produced by a charge moving inside the dielectric sphere S, with observations made outside S (in fact, this is a typical experimental situation when a charge moves in one medium while measurements are made in the other one). It is shown that the difference in media properties inside and outside S drastically affects angular and frequency distributions. Also, a charge motion is considered which begins and terminates in medium 2 and which passes either through the dielectric sphere filled with medium 1 or through the metallic one. The energy flux in medium 2 involves the Vavilov–Cherenkov, transition radiation and the one arising from the charge instantaneous beginning and termination of motion. The evaluated angular and frequency distributions for various charge velocities and medium properties inside and outside S show that the standard identification of the charge velocity by its radiation on the part of the charge trajectory where βn>1 is not always valid. We analyze also the frequently used interpretation of the transition radiation in terms of instantaneous charge deceleration in one medium and its sudden acceleration in another one, and find them as to be insufficient. On the other hand, attempts to interpret the transition radiation in terms of semi-infinite motions terminating in one medium and beginning in the other one turn out to be correct if one takes into account the terms corresponding to the Vavilov–Cherenkov radiation.