Exact Electrodes for the Formation of a Curved Space-charge Beam. II†

Abstract

The analytical method of determining Pierce-electrodes shapes for carved space-charge beams which was given in an earlier paper is extended by removing the requirement that explicit expressions are needed for the potential and field distributions along the edge of the beam. The Walker-Ivey solution for flow between inclined plane electrodes is used to demonstrate the technique when the potential and field are given only by differential equations which cannot be solved in closed form.