  The radiation from a relativistic electron uniformly moving along the axis of
cylindrical waveguide filled with laminated material of finite length is
investigated. Expressions for the spectral distribution of radiation passing
throw the transverse section of waveguide at large distances from the laminated
material are derived with no limitations on the amplitude and variation profile
of the layered medium permittivity and permeability. Numerical results for
layered material consisting of dielectric plates alternated with vacuum gaps
are given. It is shown that at a special choice of problem parameters,
Cherenkov radiation generated by the relativistic electron inside the plates is
self-amplified. The visual explanation of this effect is given and a possible
application is discussed.
