Analytical Technique in the Boundary Element Method for 3D Self-Consistent Problems of Electron Optics

The comparative analysis of modern mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the boundary element method (BEM) for the field evaluation, and 3-rd order aberration expansion for the trajectory analysis. The first version of such computer code "OPTICS-3", and some results of numerical simulations with this code were presented.