  The radiation from a charge moving along a helical trajectory inside a
cylindrical hole in homogeneous dielectric medium is investigated. Prompted by
availability of materials with large dielectric permittivity $\epsilon $ and
small absorption, we discuss the features of this type of radiation for media
with $\epsilon \gg 1$. It is shown that there are high peaks in the angular
distribution of radiation intensity at well-defined harmonics. The conditions
are specified for the cavity-to-helix radii ratio, $\rho_{1}/\rho_{0}$, under
which the angle-integrated radiation intensity on some harmonics exceeds that
in the empty space. Though the amplification of radiation intensity increases
with increasing $\epsilon $, the corresponding "resonant" values of $\rho
_{1}/\rho_{0}$ ratio are practically independent of the dielectric permittivity
of surrounding medium. It is shown that an analogous amplification of radiation
takes place essentially for the same values of $\rho_{1}/\rho_{0}$ also for the
radiation in a cylindrical waveguide with conducting walls. An explanation of
this phenomenon is given.
