The features of synchrotron radiation from a relativistic particle rotating inside a spherical cavity

We have studied the radiation from a relativistic charged particle in a uniform rotation along the equatorial orbit inside a spherical cavity immersed in continuous loss-free dielectric, the permittivity of which in the frequency range under consideration is ε > 1. A formula for calculation of radiation intensity at large distances from the cavity is derived. It is shown that with a special (resonant) choice of a non-dimensional parameter ξ   the intensity of synchrotron radiation in the presence of a cavity may be either amplified or reduced almost by ε times compared with particle rotation in empty space. The resonance value of ξ is determined by the number of harmonics and is independent of other parameters. A visual explanation of this phenomenon is given and its possible application is discussed.