Abstract
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.
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