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Analysis of Slow-Wave Instability in Rectangularly Corrugated Cylindrical Waveguide

Slow-wave instability in a rectangularly corrugated cylindrical waveguide is analyzed. Fields inside corrugation is expressed by a sum of space harmonics satisfying the boundary conditions at the corrugation wall. The corrugation fields are matched to periodic fields outside the corrugation at the boundary of the two regions. Infimtesimally thin annular electron beam is considered including the three-dimensional perturbations. Effects of space harmonics in the corrugation along with the corrugation depth are examined. Slow cyclotron instability in addition to Cherenkov instability occurs when perturbed motions and modulations of infinitely thin surface are included.