Relativistic effects in the traveling-wave amplifier

A relativistically correct large-signal theory is developed for the analysis of high-power, axially symmetric traveling-wave amplifiers in order to investigate the physical phenomena involved in the interaction process. The nonlinear integro-differential system equations are developed from the Lorentz force equation, the one-dimensional equivalent circuit equation, the wave equation, and the continuity of charge relation. These equations are applied to two electron stream models: a ring model which permits the effects of nonlaminar flow and space-charge forces to be evaluated, and a disk-electron model in which these effects are ignored. The ring model space-charge fields are obtained from the appropriate Green\´s function for Poisson\´s equation in a moving frame of reference. Numerical solutions are presented and discussed with major emphasis on the disk-model solutions. The principal results are that the gain per unit length decreases with increasing beam velocity, the circuit phase velocity for optimum power output approaches the dc beam velocity u0, as approaches unity, and the conversion efficiency is almost independent of u0for the synchronous case. The linearized one-dimensional theory of the traveling-wave tube is also discussed. Several of the large-signal results are predicted from the small-signal theory.