Abstract
Selfconsistent laminar flow models, which enable to predict the optimal cathode and anode geometry in simple diodes, must be modified to account for the anode aperture and the effect of other electrodes. An equation for charge coupled to arbitrary laminar flows is here first presented and its numerical solutions are obtained with a new method, based on mesh transformations. It is found that a close match to theoretical flows requires an increase of the simple diode voltage v0 by an amount vδ, which, for a typical case designed for zero exit angle condition, are v0 = 0.7465 and vδ = 0.0294 in adimensional units. States "in" and "out" for the anode lens are also shown, where "out" is a new and nonlinear solution for the beam expansion in a drift tube.
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