  The regularities of narrow-band resonance in a two-layer circular waveguide
due to the radiation of the bunch, moving along its axis are investigated. Its
connection with the synchronous component of a two-layer TM01 mode of the
waveguide is established. Also performed numerical and analytical calculations
of wake functions (particle radiation fields) and are investigated its
properties. The possibility of using a two-layer waveguide as a powerful source
of quasi-monochromatic terahertz radiation and as an efficient device for the
two-beam acceleration is shown. Preliminary experimental scheme is proposed.
