Differential algebraic method for aberration analysis of typical electrostatic lenses

In this paper up to fifth-order geometric and third-order chromatic aberration coefficients of typical electrostatic lenses are calculated by means of the charged particle optics code, COSY INFINITY, based on the differential algebraic (DA) method. A two-tube immersion lens and a symmetric einzel lens have been chosen as two examples, whose axial potential distributions are numerically calculated by a FORTRAN program using the finite difference method. The DA results are in good agreement with those evaluated by the aberration integrals in electron optics. The DA method presented here can easily be extended to aberration analysis of other numerically computed electron lenses, including magnetic lenses.