Synchrotron radiation in the presence of a cylindrical mirror. Note on the interference of the direct radiation and the high-order whispering-gallery modes

TL;DR

This paper provides exact solutions for electromagnetic fields generated by a relativistic electron inside a cylindrical mirror, revealing resonant conditions where field amplitudes diverge due to constructive interference of direct and reflected radiation.

Contribution

It introduces exact solutions to Maxwell's equations in this setup and identifies resonance conditions caused by interference effects, advancing understanding of synchrotron radiation in cylindrical geometries.

Findings

Resonance occurs at specific radius ratios leading to diverging field amplitudes.

Constructive interference between direct and reflected radiation causes these divergences.

Exact solutions clarify the behavior of synchrotron radiation in cylindrical mirrors.

Abstract

Exact solutions are given for the Maxwell equations driven by a gyrating ultrarelativistic electron inside a reflecting cylindrical boundary. The axis of the electrons's trajectory and the axis of the surrounding cylinder are supposed to coincide. It is found that, at certain values of the ratio of the cylinder's and of the trajectory's radii, the field amplitudes diverge as functions of time. The physical reason for this resonance is the constructive interference between the radiation emitted earlier and fed back by reflection to the actual position of the radiating electron.