Abstract: Based on Boltzmann distribution law which is the derived distribution characteristic of electrons by potential energy in a conservative field from Boltzmann integrally differential equation in equilibrium state, the distribution functions of volume charge density and the velocity of electron pulse system in the externally supported unequal-potential space are achieved from the perspective of statistical physics by solving Poisson’s equation. And the qualitative analysis of the dynamic variation characteristics of the two parametric distributions indicates that a higher external potential will restrain the unwelcome space charge effects which cause electron pulse broadening and energy spread. The physical mechanism of the optimization effect of higher electric field in the vicinity of the