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Abstract
In this paper, as part of a three-dimensional ribbon beam gun design, Laplace equation is solved in 3D for the case of boundaries which can be represented as simple surfaces which are subjected to specified voltages. Curve fitting by the least squares method is used to characterize the accelerator electrode shape as an extension of the 1D laminar electron flow in a Pierce type electron gun. The method involves solution of governing equations by an iterative finite difference technique. Modification of the standard Leibmann procedure is used to greatly increase the rapidity of convergence. The technique of handling irregular boundary points is considered in detail.
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