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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 ε and small absorption, we discuss the features of this type of radiation for media with ε ≫ 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, ρ 1 /ρ 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 ε, the corresponding "resonant" values of ρ 1 /ρ 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 ρ 1 /ρ 0 also for the radiation in a cylindrical waveguide with conducting walls. An explanation of this phenomenon is given. PACS number(s): 41.60. Ap, 41.60.Bq

A relativistic electron uniformly rotating along an equatorial orbit around a dielectric ball may generate Cherenkov radiation tens of times more intense as that in case of revolution of a particle in a continuous, infinite and transparent medium. The root-mean-square values of electric and magnetic field strengths of particle are practically not localized in the central part of the equatorial plane of ball and close to the poles of ball.