A study on fundamental theory for spread launch model of electrons

This paper presents a study on the mechanism of electronic emission by constructing electronic spread launching model and solving Poisson equation analytically between two planar plane. The results show that electron beam introduces periodic and non-periodic perturbation to primary vacuum potential. The overall effect of periodic perturbation can be ignored because of symmetry but non-periodic perturbation is dependent on initial condition intensively, especially emitting velocity´s direction. When the launch angle varies from 0 degree to 90 degree, 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.