Exact Electrode Systems for the Formation of a Curved Space-Charge Beam †

Abstract

An analytical method of determining the shape of the (Pierce) electrodes required to maintain a two-dimensional space-charge beam is given, which is valid when the edge of the beam is curved. The method is applied to a solution of the space-charge equations given recently by Meltzer, in which the flow pattern is a family of arcs of concentric circles. It is found that a completely enclosed electrode system results, making it unnecessary to adopt the usual approximation of terminating the electrodes at some arbitrary distance from the beam in order to make them finite.