  It has been noted in the past, in the study of the wall-roughness impedance,
that a metallic pipe with corrugated walls supports propagation of a
high-frequency mode that is in resonance with a relativistic beam. This mode
can be excited by a beam whose length is a fraction of the wavelength. In this
paper, we study another option of excitation of the resonant mode in a metallic
pipe with corrugated walls---via the mechanism of the free electron laser
instability. This mechanism works if the bunch length is much longer than the
wavelength of the radiation.
