Space-charge and secondary emission effects in a computer simulation of crossed-field distributed-emission amplifiers

A generalized steady-state nonlinear electron-wave interaction theory is developed for the crossed-field distributed-emission or emitting-sole amplifier. The system equations are non-linear integro-differential equations, developed from the one-dimensional equivalent transmission-line equation, the Lorentz force equation, the continuity equation, and Poisson's equation. The effects of dc, RF and space-charge forces are taken into account, and secondary emission from the sole electrode is included in the theory. Digital computer solutions indicate a gain threshold with RF drive, and that the inclusion of space-charge forces and secondary emission enhances the gain. A linearly decreasing magnetic field near the output also increases the gain. Approximate solutions based on a hard-kernel-bunch (HKB) model are shown to give excellent agreement with the computer solutions.