IMPROVED METHOD FOR NUMERICAL ANALYSIS OF POINT ELECTRON AND ION SOURCE OPTICS.

Abstract

Numerical calculation of the potential for point source geometries such as a field emitter diode, has long proved to be a difficult problem due to the extreme difference in the magnitude of the sizes of the cathode and anode. The authors' approach makes use of a spherical coordinate system in which the radial mesh size increases with radius according to a geometrical series with a term ratio (1 minus h// theta )** minus **1, where h// theta is the angular mesh size, in radians. With this method the truncation error in the finite difference formulas is small, the accuracy of the calculated potential is everywhere uniform and the form of the difference formulas is quite simple. As a result, one can achieve high accuracy with a comparatively small number of mesh points.