  We study the angular distribution of the radiation from a relativistic
charged particle uniformly rotating along an equatorial orbit around a
dielectric ball. Earlier it was shown that for some values of the problem
parameters and in the case of weak absorption in the ball material, the
radiation intensity on a given harmonic can be essentially larger than that for
the same charge rotating in the vacuum or in a homogeneous transparent medium
having the same real part of dielectric permittivity as the ball material. The
generation of such high power radiation is a consequence of the constructive
superposition of electromagnetic oscillations of Cherenkov radiation induced
near the trajectory of the particle and partially locked inside the ball. The
angular distribution of the number of the emitted quanta is investigated for
such high power radiation. It is shown that the radiation is mainly located in
the angular range near the rotation plane determined by the Cherenkov condition
for the velocity of the charge image on the ball surface. The numerical
analysis is given for balls made of strontium titanate, melted quartz and
teflon in the gigahertz and terahertz frequency ranges.
