Interaction of a moving charged particle with a spatially dispersive medium. II. Čerenkov and transition radiation

In the preceding paper, we obtained expressions for the electromagnetic field generated by the interaction of a uniformly moving electron with a spatially dispersive half-space. One part of the field was identified with Čerenkov radiation and the other part with transition radiation. In this paper it is shown that the integrals involved in the Čerenkov part can be evaluated in closed form in terms of elementary functions, and we obtain three distinct threshold conditions for Čerenkov radiation instead of the usual one, as is the case in a spatially nondispersive medium. Furthermore, we obtain for each frequency component the asymptotic expansion of the transition radiation part of the field, valid at points that are far enough away from the path of the electron and from the boundary.