Necessary and Sufficient Conditions for Cerenkov Radiation

It is shown that in the case of charged beams of finite dimensions and/or finite electromagnetic wave-guiding structures, the condition v&c/n is a necessary but not a sufficient condition for generation of Cerenkov radiation. Depending upon the modulation, size and geometry of the beams, and dimensions of the wave-guiding structures, selected lines can be eliminated from the radiation spectrum. Since the lines in the spectrum are size and geometry dependent it is suggested that the analysis of the Cerenkov radiation spectrum may be utilized in the determination of sizes and shapes of charged particles.