Proceedings Article | 25 October 1996

Proc. SPIE. 2858, Charged-Particle Optics II

KEYWORDS: Optical spheres, Electrodes, Computing systems, Numerical integration, 3D modeling, Particle filters, Chemical elements, Spherical lenses, Information operations, Charged particle optics

In calculating potential field for a system consisting of several conductors by means of the boundary (or surface) charge method (BCM or SCM), every conductor surface is divided into n small surface elements, and the surface (or boundary) charge density on each surface element is obtained by solving a set of n-dimensional simultaneous linear equations, where the coefficient matrix element is expressed as a double integral. In the 3D BCM, the coefficient matrix element is usually obtained by direct double numerical integration, which is a serious obstacle to a practical use of the method because of extremely long computation time. We have been developing an improved 3D BCM, where any given conductor geometry can faithfully be modeled by a suitable combination of parts and/or all of several basic surfaces such as plane surface, cylindrical surface, conical surface, discoidal surface, spherical surface and torus surface. We have found that the first integration in the double integral of the coefficient matrix element can be done analytically for the above-mentioned basic surfaces, thereby greatly improving the computation time without any loss of accuracy.