The Relationship Between the Emitter Position and the Wehnelt Cylinder Aperture Radius of the Thermionic Electron Gun

This paper includes finding a mathematical relationship between the distance from the emitter to the width of the Wehnelt cylinder bore and the diameter of that bore, by studying the effect and correlation of these two parameters on the quality of the electron beam. A group of electron guns with identical and variable geometric parameters were designed for the values of the Wehnelt cylinder aperture radius for each case from the emitter site, which represents the distance from the emitter head to the Wehnelt cylinder aperture. As well as the calculation of the electron beam diameter and the brightness and emittance, as the mathematical relationship between these two parameters was found to be linear.