An electron emission apparatus, an electron gun, and a method of fabrication of the electron gun are provided. The electron gun includes a cathode, a Wehnelt, and an anode. The cathode is configured to provide an electron beam. The Wehnelt has a bore. The bore is configured to pass the electron beam. The anode is disposed proximate to the cathode. The diameter of the bore of the Wehnelt and the offset between the Wehnelt and the cathode satisfy a predetermined dimensional relationship. The predetermined dimensional relationship is at least a function of a diameter of the bore of the anode and a distance between the Wehnelt and the anode.