Intense radiation from a relativistic electron rotating about a   dielectric ball
  The radiation from a relativistic electron uniformly rotating along an orbit in the equatorial plane of a dielectric ball was calculated taking into account the dielectric losses of energy and dispersion of electromagnetic oscillations inside the substance of ball. It was shown that due to the presence of ball the radiation from the particle at some harmonics may be several dozens of times more intense than that from the particle rotating in an infinite homogeneous (and transparent) dielectric. The generation of such a high power radiation is possible only at some particular values of the ratio of ball radius to that of electron orbit and when the Cherenkov condition for the ball material and the velocity of particle "image" on the ball surface is met. 
M.L. Grigoryan