Fundamental theory for spread launch model of electrons

A study is presented on the potential profile between planar plane capacitors by constructing electronic spread launch model and analytically solving Poisson equation. The results show that electron beam introduces periodic and non-periodic perturbation to vacuum potential without electron beam. Non-periodic perturbation prevails because the overall effect of periodic perturbation is zero. When the launch angle varies from 0° to 90°, four perturbation peaks take on and beside them electron beam has no impact on vacuum potential, which provide a theoretical explanation for MICHELLE’s nine-particle launch model and a guide for mesh refinement choice when a code is developed.