Some characteristic features in the radiation from a relativistic electronuniformly rotating along an equatorial orbit around a dielectric ball have beenstudied. It was shown that at some harmonics, in case of weak absorption ofradiation in the ball material, the electron may generate radiation fieldquanta exceeding in several dozens of times those generated by electronrotating in a continuous, infinite and transparent medium having the same realpart of permittivity as the ball material. The rise of high power radiation isdue to the fact that electromagnetic oscillations of Cherenkov radiationinduced along the trajectory of particle are partially locked inside the balland superimposed in nondestructive way.
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