Transition radiation at an annular lattice under grazing incidence of charge

The possibility of transition radiation occurring at an annular grating when electric and magnetic charges pass through its center, where vx/vz≪1, vy=0, is examined in this paper. The grating, which lies in the plane z=0, consists of concentric, ideally conducting rings and can be considered in the one-sided conductivity (cylindrical) approximation for the long-wavelength part of the radiation. It is demonstrated that to within terms of the order of (vx/vz)2 this radiation can be ignored for an electric charge. A magnetic charge gives the same radiation as on a continuous, ideally conducting plane.