A Critical Assessment of the Finite Element Method for Calculating Magnetic Fields in Electron Optics

Abstract

The present investigation is concerned with the determination of the magnetic field distribution in magnetic electron lenses by means of the finite element method. A critical comparison is made of the available finite element computer programs. Necessary modifications have been made in certain programs, useful comments and general data format were written for two recently developed programs. Special attention has been paid to those factors that affect the efficiency of the finite element method in camputer aided design of magnetic electron lenses. These include the correct choice of boundary conditions. Another important factor investigated is the influence of mesh layout for the subsequent finite element calculations. By recomputing several examples of lenses found in the literature, discrepancies of up to 30% were reduced, resulting in excellent agreement with the associated experimental results, simply by rearranging the mesh layout in a more convenient way. Through a more systematic application of the finite element method, several misleading conclusions to be found in the literature were detected. Some of these conclusions arose from the finite element method itself,as previously mentioned. Other misleading conclusions were also discovered that were not due to the finite element method but to design errors in the lens itself. A study has been made of the errors in lens design including the inadequate thickness of iron shrouds etc.