  Radiation of charged particles moving in the presence of dielectric targets
is of significant interest for various applications in the accelerator and beam
physics. The size of these targets is typically much larger than the
wavelengths under consideration. This fact gives us an obvious small parameter
of the problem and allows developing approximate methods for analysis. We
develop two methods, which are called the "ray optics method" and the "aperture
method". In the present paper, we apply these methods to analysis of Cherenkov
radiation from a charge moving through a vacuum channel in a solid dielectric
sphere. We present the main analytical results and describe the physical
effects. In particular, it is shown that the radiation field possesses an
expressed maximum at a certain distance from the sphere at the Cherenkov angle.
Additionally, we perform simulations in COMSOL Multiphysics and show a good
agreement between numerical and analytical results.
