Influence of Space Charge on the Bunching of Electron Beams

Abstract

A rigorous computation of electron trajectories within plane structures may be made, with the inclusion of space-charge effects, by use of the Llewellyn method of integration. These computations can be used for a discussion of conditions leading to intercrossing trajectories, i.e., bunching. The discussion has been carried out for a conventional plane diode, for a diode wherein electrons are injected with a given initial velocity, for a velocity-modulated beam, for a plane magnetron, and for a plane magnetron with velocity modulation. In the last case it can be proved that trajectories intercross not once but many times thus disentangling themselves after a while, then crossing again and soon.