Electron Reflectors with a Quadratic Axial Potential Distribution

Trajectory equations are developed for accelerated electrons which enter a retarding, axially symmetric electrostatic field with a quadratic axial potential distribution. Neglecting space-charge effects of the electrons, such a field can be produced between two charged electrodes consisting of a cone and a hyperboloid. A focus criterion is established, and under these conditions the permissible angles of divergence and convergence which an incident electron may have and still be focused back through the entering aperture are determined. An equation for the transit time of the axial electrons in the reflector is derived. By proper adjustment of dimensions and voltages, various simple electrode shapes may be made to give an axial potential distribution which is nearly quadratic, and thus give comparable performances as electron reflectors.