The theory of Cutler and Hines is extended in this paper to permit an analysis of beam-spreading in electron guns of high convergence. A lens correction for the finite size of the anode aperture is also included. The Culter and Hines theory was not applicable to cases where the effects of thermal velocities are large compared with those of space charge and it did not include a lens correction. Gun design charts are presented which include all of these effects. These charts may be conveniently used in choosing design parameters to produce a prescribed beam.
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Danielson et al. (1956) studied this question.
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