This paper describes a theoretical treatment for the current neutralization of intense ion beams propagating radially inward through the drift region of a cylindrical Applied‐Bdiode. The drift region is bounded by conducting walls, and the beams are taken to have a current density profile that is constant across the surface transverse to the direction of propagation. The current neutralization calculation involves breaking the return current density into spatial harmonics in the transverse coordinate in such a way that the return current density vanishes at the walls. Each spatial harmonic is then shown to approximately obey a magnetic decay equation with a time constant proportional to the electrical conductivity of the gas. This conductivity is time dependent and is calculated locally from the degree of ionization and plasma heating created by the beam and the return current. Beams composed of protons and carbon ions are considered, and time‐of‐flight effects on the beam current and energy spectra are taken into account. The effects of drift region parameter variations on the time development of the conductivity and current neutralization are evaluated. Comparisons are made with experimental measurements taken at Sandia National Laboratories on the Proto‐I accelerator, and strengths and weaknesses of the present model are discussed.