Noniterative synthesis of convergent Pierce electron guns by the conformal mapping of electrode shapes using logarithmic transformation

A noninteractive synthesis method is proposed to generate the electrode shapes of a convergent Pierce electron gun. The method combines the known results for the parallel-flow gun of planar geometry with those of Langmuir and Blodgett´s solution for the potential function, inside the beam, for a convergent electron gun using the logarithmic conformal transformation. The dependence of the electrode shapes on the input beam parameters, namely, the beam voltage, current and diameter, and on the operating cathode current density is shown. Electrode shapes for typical practical electron guns using this method are presented