Extended Pierce Method for Sheet-Beam Injector Design
There has been renewed interest in the design of injectors for intense electron beams with non-circular cross sections. The motivating application is the generation of narrow sheet beams to drive novel high-frequency, high-power microwave sources. This paper discusses a simple paradigm for designing high-current, sheet-beam guns based on the work of J.R. Pierce1 determined electrode shapes to generate an ideal, space-charge-limited beam with the following limitations, The result applies to a planar beam of infinite length. In other words, end effects are not addressed. The anode is a fixed-potential surface (i.e., a Grid), so the effect of an extraction aperture is not included. The output beam is non-relativistic i.e., electron kinetic energy less than 100 keV.