  Some characteristic features in the radiation from a relativistic electron
uniformly rotating along an equatorial orbit around a dielectric ball have been
studied. It was shown that at some harmonics, in case of weak absorption of
radiation in the ball material, the electron may generate radiation field
quanta exceeding in several dozens of times those generated by electron
rotating in a continuous, infinite and transparent medium having the same real
part of permittivity as the ball material. The rise of high power radiation is
due to the fact that electromagnetic oscillations of Cherenkov radiation
induced along the trajectory of particle are partially locked inside the ball
and superimposed in nondestructive way.
