Convergence and accuracy criteria of iteration methods for the analysis of axially symmetric and sheet beam electrode shapes with an emitting surface

Convergence and accuracy criteria have been determined for computer techniques analyzing an axially symmetric or two-dimensional electrode system with an emitting surface. The convergence criterion has been drawn from analytical studies of the one-dimensional model and verified numerically by the computer program for an analytically designed, axially symmetric Pierce-type electrode system. The accuracy of the computer program is illustrated with two electron gun configurations of known analytical solutions, and comparison of cathode current emission, beam minimum radius, and its location is made with experimental data of a high perveance Pierce-type gun.