An investigation into the use of iteration methods for the analysis of axially symmetric and sheet beam electrode shapes with an emitting surface

The techniques for analyzing an axially symmetric or two-dimensional electrode system with an emitting surface have been studied with a computer program. The program is very easy to use and performs in one pass the steps which have usually previously been followed on analog and digital devices separately. The program alternately solves Poisson´s equation by a relaxation technique, traces trajectories, recomputes the space-charge distribution and again performs a relaxation process. This procedure continues until satisfactory convergence has been achieved. The ease of use of the computer program has allowed the investigation of different methods of speeding up the convergence. The results are illustrated with two specific examples.