Accurate Potential Calculations For The Two Tube Electrostatic Lens Using A Multiregion FDM Method

The multiregion FDM method is applied to the two tube electrostatic lens providing accurate and precise potential calculations for this geometry. It is shown that the multi region structure necessary for these calculations can be adaptively established in software and that the limitations of a cumulative or round off error can be overcome by the use of high precision arithmetic. Finally a comparison both with the results of other workers and the zero gap two tube exact solution shows that the technique provides a valid, accurate and precise solution for the geometry considered having a maximum on axis error of -2*10-15 for the zero gap geometry.