Transition radiation from an extended bunch of charged particles

The spatial distribution of the transition radiation generated by an extended system of charges is studied. The charges sequentially cross the interface at equispaced points. Also, the transition from a spherical bunch with the uniform charge distribution is considered. The radiation patterns produced by the point charge and by the bunch of the charges are shown to differ significantly at certain sizes of the bunch expressed in terms of the wavelength. Charge distributions such that the transition radiation exhibits the properties typical of the Doppler effect or of Vavilov-Cherenkov radiation are found to be possible.