Transition radiation emitted by a particle moving along the axis of a perfectly conducting conical surface

The spatial field distribution is determined for the transition radiation emitted by a relativistic particle moving along the axis of a perfectly conducting circular conical surface with a fixed apex. Emission from particles moving away from and towards the apex is examined. Expressions are obtained that can be used to calculate the angular distribution of radiation intensity for various apex angles between 0 and π. Significant differences are demonstrated between the spatial distributions of radiation generated by outgoing and incoming particles.