Synchrotron Radiation in a Circular Metallic Waveguide

We study theoretically the influence of a circular metallic waveguide with a longitudinal magnetic field on the synchrotron radiation of a point electric charge moving along a helical trajectory coaxial with the waveguide axis. The main attention is focused on the analysis of the energy characteristics of radiation of electromagnetic E and H waves. We derive the formulas for the radiation powers of E and H waves. It is shown that, under certain conditions, slowly moving electric charges do not radiate any of these electromagnetic waves in the circular waveguide.