Numerical Solution to Laplace's Equation in Spherical Coordinates with Axial Symmetry
- 1 April 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 41 (5) , 1879-1882
- https://doi.org/10.1063/1.1659137
Abstract
A numerical method for solving Laplace's equation in spherical coordinates for an axially symmetric geometry has been developed. Dirichlet boundary conditions on a closed surface yield a set of difference equations. The method of successive overrelaxation has been employed to find solutions to those equations. Application of the method is illustrated by finding the field configuration in a new type of electron gun used in a spherical electron monochromator.This publication has 7 references indexed in Scilit:
- Computer experiments on electron gunsIEEE Transactions on Electron Devices, 1966
- Computation of Electrostatic and Rapidly Pulsed Magnetic FieldsJournal of Applied Physics, 1966
- An investigation into the use of iteration methods for the analysis of axially symmetric and sheet beam electrode shapes with an emitting surfaceIEEE Transactions on Electron Devices, 1964
- Electrode Design for Axially Symmetric Electron GunsJournal of Applied Physics, 1962
- Determination of Electrode Shapes for Axially Symmetric Electron GunsJournal of Applied Physics, 1960
- Note on the Determination of Electrode Shapes for a Pierce-Type Electron GunJournal of Applied Physics, 1957
- The Focusing of Charged Particles by a Spherical CondenserPhysical Review B, 1938