Theoretical study on Vavilov-Cherenkov radiation in Hermitian media

It is very rare that in the history of science and technology that a research topic may last more than 70 years and is still attractive till recent. The Vavilov-Cherenkov radiation (VCR) is one of them. The VCR was discovered by Vavilov and Cherenkov in 1934, and the theory on VCR was worked out by Frank and Tamm in 1937. The great contributions of the research work on VCR was awarded the Nobel prize in 1958. The Vavilov-Cherenkov radiation (VCR) in Hermitian media has been studied since 1953 (Sitenko and Kolomenskii, 1953). However, it seems that there are still a lot of problems remain to be investigated. The theoretical study on the VCR in a Hermitian media is given in the paper. By means of the alternate mathematic procedure, rather than the Hankel transformation, the exact analytical solutions of the fields of the non-uniform coupled differential equations governing the VCR in the Hermitian media have been obtained. The phase velocity, the group velocity of the radiation and the effective refraction index of the Hermitian media are examined, and the radiation energy is studied as well. It indicates that in general case there are two modes, one of them is radiation mode, another one is a local field moving with the charged particle. Only in a special case it might be that both of them are radiation modes. As one of the most important example of the Hermitian media, the VCR in the magnetized plasma has been studied in details. The computer calculations have been carried out.