  We investigate the electromagnetic radiation from a chain of relativistic
charged particles uniformly rotating along equatorial orbit around a dielectric
ball. For weak absorption of radiation in the ball material, at certain
rotation frequency the radiation intensity becomes significantly higher than
the corresponding value for a chain of charges rotating in free space or in a
transparent medium with the same dielectric constant as that for the ball
material. In the case of an equidistant distribution of charged particles along
the orbit we determine the values of parameters of the problem for which the
charges in the chain emit coherently. It is shown that the radiation intensity
on a given harmonic increases in proportion to the square of the number of
emitting charges. We also show that the relative shifts in the particles
locations up to 10\% do not destroy the coherence properties of the radiation.
It is demonstrated that the coherence effects may also dominate in the
radiation intensity for chains with non-equidistant distributions of particles.
The numerical results obtained for different dielectric balls have revealed the
emitted radiation to be in the GHz/THz frequency ranges. The high-power
radiation of the chain propagates in the angular range with respect to the
rotation plane determined by the Cherenkov condition for the velocity of the
chain projection onto the ball surface.
