  The radiation emitted by a charged particle moving along a helical orbit
inside a dielectric cylinder immersed into a homogeneous medium is
investigated. Expressions are derived for the electromagnetic potentials,
electric and magnetic fields, and for the spectral-angular distribution of
radiation in the exterior medium. It is shown that under the Cherenkov
condition for dielectric permittivity of the cylinder and the velocity of the
particle image on the cylinder surface, strong narrow peaks are present in the
angular distribution for the number of radiated quanta. At these peaks the
radiated energy exceeds the corresponding quantity for a homogeneous medium by
some orders of magnitude. The results of numerical calculations for the angular
distribution of radiated quanta are presented and they are compared with the
corresponding quantities for radiation in a homogeneous medium. The special
case of relativistic charged particle motion along the direction of the
cylinder axis with non-relativistic transverse velocity (helical undulator) is
considered in detail. Various regimes for the undulator parameter are
discussed. It is shown that the presence of the cylinder can increase
essentially the radiation intensity.
