Scattered and guided radiation emitted by an electron moving near a dielectric rod

The scattered and guided radiation excited by a point charge moving in the vicinity of an infinite, dielectric cylinder is considered. It is shown that guided waves constitute the dominant contribution to the emitted radiation for short distances between the particle and the cylinder, low yet relativistic particle energies (roughly 10-1<γ-1<101, where γ is the Lorentz factor), and large cylinder permittivity. In all the complementary cases, radiation by scattered waves dominates the spectrum. Analytic, approximate expressions for the spectrum of the scattered radiation are presented, with the spectrum for high energies resembling that of plane-wave scattering. The relative contribution of the various cylinder eigenmodes to the guided radiation is also investigated. The effect of a finite-size bunch on the emitted radiation is considered. Finally, the number of emitted photons via both scattered and guided radiation is examined, with the scattered photon number observed to scale for high energies as ln(bγ).