Theory of electron waves in periodic structures

With the help of the difference theory of excitation of periodic waveguides obtained by the characteristic equation of the electron waves formed by the interaction of an electron beam with the forward and backward electromagnetic waves periodic waveguides. The resulting characteristic equation describes the electron-wave interaction in the passband and stopband of periodic waveguides and includes as special cases of well-known equation for the "smooth" slow-wave systems and resonator slow-wave systems near the cutoff frequency. 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 waveguides.