Interaction of Premodulated Electron Streams with Propagating Circuits†

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Abstract
Previously all analyses of linear stream devices assumed that the electron stream was unbundled before interacting with an r.f. wave on a propagating circuit. Linear and non-linear analyses are presented for prebunched beams interacting with a travelling r.f. wave in both growing-wave and beating-wave devices. In the linear case the modulation is sinusoidal and is described in terms of space-charge waves. The increase in gain achieved is calculated and conditions for optimizing the increase with respect to predrift angle for the stream and initial phase of the r.f. wave are developed analytically. Calculations are presented and analysed for both the TWA and the Crestatron. The non -linear analysis utilizes the non -linear TWA equations and a nearly ideal bunch of width equal to 1 /20 of an r.f. cycle and arbitrary entrance phase. The increase in efficiency and gain and the decrease in length for optimally bunched beams are calculated and the process of phase focusing a nearly ideal bunch in the presence of a circuit field and space-charge forces is analysed.

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