In order to do ray tracing in a charge particle optics system it is necessary to be able to evaluate the field at an arbitrary point along the path. The finite element method (FEM) can yield the most accurate values for the potential at the mesh points when a variable quadrilateral mesh is used. The nonrectangular mesh, which is advantageous in simulating real geometries with a reasonable number of mesh points, is however, a disadvantage in field evaluation for direct ray tracing. A new method of interpolation is based on special polynomials of two variables which fulfill the Laplace equation. The polynomial representation of the potential is local to each quadrilateral in which field evaluation is done. Coefficients for these local polynomials are found by fitting to the quadrilateral corner points and their neighbors. The mesh geometry can be whichever is most suited to the FEM solution of the potential. The new method was tested on a two cylindrical electrode system used as an electron mirror, a system for which the analytical solution for the potential is known. The results indicate that for typical mesh geometries and with 20 X 20 mesh lines in the gap between the electrodes the error of the interpolation is about ten times smaller than the error of the linear finite element method.

Date Published: 3 September 1993
PDF: 11 pages
Proc. SPIE 2014, Charged-Particle Optics, (3 September 1993); doi: 10.1117/12.155693

Published in SPIE Proceedings Vol. 2014:
Charged-Particle Optics
William B. Thompson; Mitsugu Sato; Albert V. Crewe, Editor(s)