Synchrotron radiation from a charge moving along a helix around a dielectric cylinder

In this paper we investigate the radiation emitted by a charged particle moving along a helical orbit around a dielectric cylinder immersed into a homogeneous medium. Formulae are derived for the electromagnetic potentials, electric and magnetic fields, and for the spectral-angular distribution of the radiation in the exterior medium. It is shown that under the Cherenkov condition for dielectric permittivity of the cylinder and the velocity of the particle image on the cylinder surface, strong narrow peaks appear in the angular distribution for the number of quanta radiated on a given harmonic. At these peaks the radiated energy exceeds the corresponding quantity for a homogeneous medium by several dozens of times. Simple analytic estimates are given for the heights and widths of these peaks. The results of numerical calculations for the angular distribution of the radiated quanta are presented and they are compared with the corresponding quantities for the radiation from a charge moving along a helical trajectory inside a dielectric cylinder.