Electrode Design for Axially Symmetric Electron Guns

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Abstract
In a previous article, a method for obtaining electrode shapes for axially symmetric electron guns was presented. In essence, this method depended upon reformulating the problem according to a method of Garabedian so that the solution can be obtained by finite‐difference methods. This is accomplished by an analytic continuation which transforms the Laplace equation into a form which is hyperbolic. The purpose of this paper is to present improvements in the original formulation. By introducing time as the independent variable, the derivatives in the space‐charge flow equations are made well‐behaved at the cathode. A different set of dependent variables is introduced so that the matrix of the coefficients associated with the system of partial differential equations possesses simple elementary divisors. Finally, the difference equations have been modified to a form more suitable for numerical computation.

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