Three kinds of models are used for beam instability analyses: those based on a solid beam, an infinitesimally thin annular beam, and a finitely thick annular beam. In high-power experiments, the electron beam is an annulus of finite thickness. In this paper, a numerical code for a sinusoidally corrugated waveguide with a finitely thick annular beam is presented and compared with other models. Our analysis is based on a new version of the selfconsistent linear theory that takes into account three-dimensional beam perturbations. Slow-wave instabilities in a K-band oversized sinusoidally corrugated waveguide are analyzed. The dependence of the Cherenkov and slow cyclotron instabilities on the annular thickness and guiding magnetic field are examined.

The dispersion characteristics and slow-wave instabilities of a sinusoidally corrugated waveguide with coaxial slow-wave structure (SWS) are analyzed. In SWS, a central cylindrical conductor is surrounded by an outer cylindrical conductor. Sinusoidal corrugation is formed on either conductor or both conductors. The corrugation parameters are those used for an X-band SWS. The relative phase between the sinusoidal corrugations on the inner and outer conductors affects the dispersion characteristics. Instabilities due to beam interactions with the slow-waves are examined by considering three-dimensional beam perturbations. The slow cyclotron instability occurs in addition to the Cherenkov instability, since transverse as well as longitudinal perturbations are included.