Microwave excitation by a constrained large-orbit electron Beam-a unified dispersion relation for slow- and fast-wave devices

A unified linear dispersion relation that describes both slow- and fast-wave devices excited by a constrained large gyration orbit (LO) monoenergetic electron beam of infinitely small thickness has been derived and studied numerically. Beam electrons in a sufficiently long sinusoidally corrugated metal slow-wave structure are assumed completely neutralized by the background ions in equilibrium state. An exact dispersion relation of an LO backward-wave oscillator that can reasonably describe instabilities in the slow-wave device region has been obtained. A parameter a, defined as a ratio of the transverse to the longitudinal component of the electron velocity, is found to have a critical value above which the excitation of a nonaxisymmetric quasi-TE₁₁ mode caused by the fast cyclotron instability dominates the conventional Cherenkov instability. However, for an SWS having infinitely small amplitude of corrugation, radiation with wW is altogether suppressed; instead, an alternate mechanism, namely, Cherenkov instability in the azimuthal direction with w\n\n\t\t