Self-acceleration of a charge traveling into a waveguide

The interaction of a charge with its own electromagnetic field in the case of traveling into a circular semi-infinite waveguide is considered. The total work performed by the field on the charge is calculated analytically and presented as an integral over frequency. The typical spectral density of the work performed by the field is demonstrated. The total work depending on the velocity of the charge is computed. It is shown that the kinetic energy gain of the charge is positive if the velocity is less than a certain limiting value, which is independent of the waveguide radius.