Evaluation of transition radiation with wake field theory

Transition radiation and diffraction radiation are produced when there is optical inhomogeneity in space, the presence of which would induce changing currents that give rise to radiation. On the other hand, these phenomena can also be considered as wake fields generated by a charged particle electromagnetically interacting with its surroundings. However, one problem is unsolved that whether the transition radiation or diffraction radiation field is part of the wake fields generated when electron passes through a target or it is just the total wake field. In this paper, we generalized the Condon method to deal with the case in which particle's velocity is smaller than that of light. As a first step, we report here the evaluation of transition radiation generated by an infinitely large ideally conducting plate with the generalized Condon method. Our results show that transition radiation field is just the total wake field. This method could be further extended to study diffraction radiation and the finite size target effect on the spectral angular distribution of transition radiation.