S. V. Andreev, M. A. Monastyrski, V. A. Tarasov
General Physics Institute, Russian Academy of Sciences, Moscow, Russia

A. G. Muravjеv
State Enterprise, Research Institute for Electron and Ion Optics, Moscow, Russia

A new approach to solve the seft-consistent problem in electron gun with arbirary-shaped cathode is suggested. The main feature of the approach proposed is that the most effective numerical techniques of charged particle optics, namely finite-difference and integral equation methods on the one hand and direct ray-tracing and aberration analysis on the other, are successfully integrated. Some testing problems are considered and analyzed in details.