Abstract: After electron beam passing through the anode hole, a new half convergent angle γ₀ will be formed under divergent effect of ihc anode hole. The angle γ₀ will influence the performance of image formation of electron optical system and the electron beam penetration ability directly.In this paper, an accurate expression of γ₀ has been derived, which has been taken into account of the effect of thermo-electronic velocity. An experimental method for measuring the angle γ₀ with a rectangular plate edge crossing the beam is described. Using 1 he numerical solution by the computer, the influence of the cathode shrunk distance to Ihe Wehncll hole on the angle γ₀ and other beam parameters bave been studied. An equivalent treating method of the gun has been given. Besides, we also provide ihc advanced gun design concept based on the angle γ₀. Satisfying experimental results have been achieved.