The Use of Graded Nets in Computer Modeling of Corotron Fields

The use of computer modeling with finite-difference techniques to solve for electrostatic fields by successive overrelaxation in regions where no exact analytic solution exists is well documented. However, for irregular Dirchlet boundary curves in two dimensions, which do not contain the nodes of a regular net, various interpolation schemes must be used. It is shown in this paper that these interpolation schemes introduce appreciable error into the solution for a boundary curve with a small radius of curvature, such as is found in the center of a corotron. An alternate technique is described which uses successive graded nets in the immediate region of the boundary. The validity of the method is confirmed in the case of a small wire with an applied voltage concentric with a grounded conducting cylinder, where an analytical solution is then possible. The method is then used for the solution of the Laplacian fields for a corotron having typical dimensions.