The grid lens effect in convergent Pierce guns

In a conventional Pierce-type gun, the anode aperture causes a potential reduction in the cathode-anode region from the ideal Langmuir potential distribution. For low-voltage gating of the electron beam, a mesh grid of spherical shape (conforming to an equipotential surface) is used in front of the cathode. When this grid is operated at the Langmuir potential depicted by its relative position, there is a difference in the potential gradients on its two sides. This difference causes a lens action at each mesh element which results in a displacement of the actual electron trajectory from the ideal laminar trajectory in the region beyond the anode. A means for calculating these displacements as a function of distance along the axis is developed. As the grid lenses are divergent, the images of the mesh elements in any plane beyond the anode are larger than those for ideal laminar flow, resulting in a current density distribution which differs from that of the ideal beam. A means of calculating the current density profile by summing the effects of the grid lenses is devised, and the method is applied to a sample gun design to illustrate the effect on the current density distribution.