High power Cherenkov radiation from a relativistic particle rotating   around a dielectric ball
  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. 
L.Sh. Grigoryan, H.F. Khachatryan, S.R. Arzumanyan, M.L. Grigoryan