Beam–Wave Interaction in the Passbands and Stopbands of Periodic Slow-Wave Systems

A method of analysis of beam–wave interaction in passbands and stopbands of periodic slow-wave systems (SWSs), based on the use of the finite-difference equation of excitation of such systems by an electron beam, is presented. In contrast to equations of a well-known beam–wave interaction theory, it includes the local coupling impedance that characterizes the interaction of electrons with the total field of two waves (forward and counter propagating) of the SWS and does not tend to infinity at cutoff frequencies. It allowed to develop a general theory of interaction of electron beams and waves in passbands and stopbands of SWSs without using their equivalent circuits. A study of beam–wave interaction in the folded waveguide-type SWSs has been performed. An elementary analytical calculation of electrodynamic characteristics of such SWSs necessary to study the interaction is given. Specifies of interaction in passbands and near the cutoff frequencies of periodic SWSs are considered. Amplification conditions in stopbands of such SWSs are discovered. Properties of the beam–wave interaction at the cutoff frequency where the folded waveguide is an analog of multigap open resonators used in such electron devices, as an orotron, are examined.