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 (SWS), 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 slow- wave system 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 slow-wave systems 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 electro-dynamic characteristics of such SWSs necessary to study the interaction is given. Particularities of interaction in passbands and near cutoff frequencies of periodic SWSs are considered. Amplification conditions in stopbands of such slow-wave systems are discovered. Properties of beam-wave interaction at the cutoff frequency where the folded waveguide is an analog of multi-gap open resonators used in such electron devices, as an orotron, are examined.