Abstract
The finite-difference theory of excitation of periodic waveguides is used to derive the characteristic equation for electron waves formed during interaction of an electron beam with forward and counter-propagating electromagnetic waves of periodic waveguides (slow-wave structures). The derived characteristic equation describes interaction of electrons and waves in passbands and stopbands of periodic waveguides and contains known solutions for “smooth” slow-wave structures and resonator slow-wave structures near cutoff frequencies as particular cases. Several analytical solutions allowing comparison of amplification and propagation properties of electron waves inside and at the edges of passbands and stopbands of periodic waveguides are found.
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