General Physics Institute RAS, Moscow, Russia

Research Institute for Electron and Ion Optics, Moscow, Russia

In the paper, numerical algorithms and software intended for electron guns computation in the near-cathode region with taking into account space charge effects are developed. These algorithms ensure stable iterative solution of the self-consistent problem for various cathode geometry types (flat, convex, concave, etc.), and for various operation modes. Close correlation between numerical results and the well-known analytical solution for one-dimensional flat diode is achieved. Some peculiarities of electron beam forming at the edges of emitter area are studied.