Computer technique for solving 3-dimensional electron-optics and capacitance problems

Electron-optics problems involving planar and axial symmetry are frequently analysed by using iterative procedures to solve Laplace´s equation within a specified boundary. The computation time and storage requirement for these procedures may be prohibitive when it is necessary to extend the analysis to three dimensions for problems involving asymmetric fields. An alternative approach is described, known as the method of moments, which does not use an iterative method, but calculates the field directly from the charges induced on the electrodes by the excitation potentials. This technique provides a further facility, which permits the capacitances between arbitrary 3-dimensional electrodes to be obtained. The basic theory and operation of a computer program which employs this method are described. As a practical application, the program has been used to investigate the electron-optical properties of a mesh with rectangular apertures.