On transition radiation

Summary A treatment of transition radiation between two dielectric media is presented which is based on the exact expressions for the fields of the particle in the two media. Expressions for the spectral distribution of the energy emitted forward and for that emitted backward are derived. The results are in accord with experimental findings for ultra-relativistic particles. In the asymptotic region the energy spectrum becomes discrete. It is indicated how the treatment can be extended to the case of a plate and to that of a wave guide, as well as to emission by a monopole. The case of the simultaneous emission of transition radiation and Čerenkov radiation is considered and the relationship between them is clarified. In particular, it is shown that, when the particle can emit Čerenkov radiation in the forward medium, it will also emit an interference signal. This is several orders of magnitude smaller than the usual transition radiation and is concentrated in the forward direction. It is also found that the Čerenkov wave emitted by the particle in the backward medium will be partially reflected and partially refracted into the forward medium, after the particle crosses the boundary between the two media. The linear energy density for the refracted wave is calculated and it is shown that under certain feasible conditions this is amenable to experimental verification. This work was done while the author was a summer visitor at Stanford Linear Accelerator Center, Stanford University. It was supported by the U.S. Department of Energy, contract DE-AC03-76SF00515.