FIELD-EVALUATION FROM POTENTIALS CALCULATED BY THE FINITE-ELEMENT METHOD FOR RAY TRACING - THE SLICE METHOD

In order to do ray tracing in a charged particle optics system it is necessary to be able to evaluate the fields at an arbitrary point along the path. The finite element method (FEM), using a variable-length quadratic mesh, can yield accurate values for the potentials at mesh points. If the ray paths are in a restricted region about the axis, then this region can be divided into cylindrical slices, within which the potential can be well represented by a local fifth-order polynomial solution to Laplace's equation. The coefficients are found by fitting to the FEM values at the slice boundaries. The potential is continuous across the boundaries and sufficiently smooth to allow accurate ray tracing. The method has been successfully applied in the calculation of secondary electron paths in a rotationally symmetric magnetic field in a design problem which placed high requirements on the accuracy of ray traces. © 1990.