Coupled-mode description of space-charge waves on nonuniform beams

Coupled-mode theory is employed to describe space-charge wave propagation on an electron beam drifting in a non-uniform region. The nonuniformity may arise in several ways. These include a potential variation, a beam-radius variation, or a drift-region-radius variation. To demonstrate the utility of this method of description, closed-form solutions are obtained for several particular variations of beam impedance and explicit expressions for the RF velocity and current modulations on the beam are obtained. The closed-form solutions are useful in the design of space-charge wave transformers for low-noise gun design, phototube demodulators and space-charge-wave amplification schemes.