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 u
0
, as
u_{0}/c
approaches unity, and the conversion efficiency is almost independent of u
0
for 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.