Theory of the cherenkov instability of an electron beam in the corrugated waveguide

It is shown that in waveguides with slightly corrugated metallic walls even the zero spatial harmonic can be slow. The slowdown degree can be higher, when the corrugation is deeper. During interaction between an electron beam and a slow zero spatial harmonic the instability increment, when as a result of the instability electromagnetic waves are excited by a beam, as well as the efficiency of the beam kinetic energy conversion into the electromagnetic wave energy do no depend on the corrugation depth. The group velocity of the excited waves is directed along the beam motion. It is known that the wave group velocity during beam interaction with the first spatial harmonic is opposite to the beam direction. The given peculiarity of wave excitation provides for easy distinction between these two cases in the experiment