Electron waves in the passbands and stopbands of periodic slow-wave systems

With the help of the finite-difference equation of excitation of periodic waveguides obtained the characteristic equation of the electron waves formed by the interaction of an electron beam with the forward and backward electromagnetic waves periodic slow-wave systems (SWS). The resulting characteristic equation describes the electron-wave interaction in the passband and stopband of periodic SWS. Found a number of analytical solutions of the characteristic equation, which allowed to compare the properties of the amplification and propagation of electron waves inside and on the border of passband and stopband of periodic slow-wave systems.