Cerenkov Photon Emission near a Conducting Medium

Abstract

The average number of Cerenkov photons emitted by a charged particle, in an isotropic permeable medium, moving parallel to a perfectly conducting neutral plate is obtained at arbitmry temperature. It is shown that an explicit enhancement (a maximum) of 40 % of this number is possible due to the presence of the plate by choosing specific windows, obtained from one general universal formula, with the windows centered about any point of the frequency spectrum at any temperature and for any index of refraction. The conditions for this universality property of 40 % enhancement applicable to any point of the spectrum are given, and explicit computations are done for a microwave frequency and for blue light. The analysis is carried out from a quantum field theory viewpoint. §1. IntroductionThe Cerenkov radiation l ) emitted by a charged particle moving in a medium with a speed greater than the speed of light in the medium has fascinated physicists2)~17) for years since its discoveryl) and its early theoretical analysis. IS) In the present paper, a study of the average number density of Cerenkov photons of different frequencies emitted by a charged particle, in an isotropic permeable medium of index of refraction n = # moving parallel to a perfectly conducting neutral plate, first considered in Ref. 2), is given at arbitrary temperature T, and hence, it necessarily involves the Planck constant h. In particular, it is shown that an explicit enhancement, as a maximum, of 40 % of this number is possible in the presence of the conducting plate for photons emitted through "selective windows" , obtained from a general universal formula (Eqs. (25) and (26)), centered about any point of the frequency spectrum at any temperature and for any index of refraction. This remarkable universal property of 40 % enhancement, independent of frequency, of temperature, and of the value of the index of refraction, holds for specific values of the combination of the distance a at which the particle moves from the plate and the "distance" of the value of the speed v of the particle from its threshold value of cln, where c is the speed of light. By gradually controlling the magnitudes of a and v as the latter moves away from its threshold value, the 40 % enhancement of the photon number will be met as the selective windows, determined· from the theory, slide along the frequency spectrum. Explicit applications are made to blue light and a microwave frequency. As in most analyses, the recoil of the charged particle is not considered and is beyond the scope of the present work. The treatment is given from a quantum field theory viewpoint 2 ) via the vacuum-to-vacuum transition amplitude.