A theory of radial beam uniformity in extraction ion diodes is presented. The theory is based on a locally one-dimensional analysis of the diamagnetic compression of magnetic streamlines and the self-consistent determination of the virtual cathode location. The radial dependence of the applied magnetic field is used to determine the critical parameters of this locally one-dimensional treatment. The theory has been incorporated into the ATHETA magnetic field code to allow the rapid evaluation of realistic magnetic field configurations. Comparisons between the theoretical results, simulations with the QUICKSILVER code, and experiments on the PBFA-X accelerator establish the usefulness of this tool for tuning magnetic fields to improve ion beam uniformity. The consequences of poor beam uniformity on the evolution of ion diode instabilities are discussed with supporting evidence from simulations, theory, and experiments. (author). 8 figs., 15 refs.