Recent Developments in Numerical Electron Optics

The familiar methods for the numerical calculation of fields in electron optical devices are outlined briefly. for the solution of self- adjoint elliptic differential equations in orthogonal curvilinear coordinate systems a favourable ninepoint discretization is worked out which can be applied favourably e.g. to spherical mesh grids. The field calculation in magnetic deflection systems by means of an integral equation method is also highly advantageous. The methods for the field calculation can be still more improved by means of suitable hybrid procedures. A second and shorter contribution is concerned with ray tracing and aberrations. Some favourable numerically stable new forms of the ray equation are derived and thereafter a new simple method for the determination of aberrations is outlined