Noniterative Synthesis of Convergent Pierce Electron Guns by the Conformal Mapping of Electrode Shapes Using Logarithmic Transformation

Abstract

In this brief, a noniterative synthesis method has been proposed to generate the electrode shapes of a convergent Pierce electron gun. The method combines the known results of the parallel-flow gun of the planar geometry with those of Langmuir and Blodgett’s solution for 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 has been shown. The electrode shapes for typical practical electron guns using this method have also been presented. © 1988 IEEE