Verification and use of Herrmann's optical theory of thermal velocity effects in electron beams in the low perveance regime

A comparison between Herrmann's optical theory and a pinhole probe study of a highly converged, perveance 0.015 × 10 -6 A/V 3/2 , electron beam in a confining magnetic field is presented. This comparison shows the theory to be obeyed with a good degree of accuracy. The application of the theory to the problem of optimizing the transmission of such thermal beams through long drift tubes is shown to lead to criteria which differ radically from those prescribed by the laminar theory.