A space charge compensation model for positive DC ion beams

In this paper, we revisit and extend a formula to predict the compensation of space charge in positive DC ion beams of non-relativistic energy, as they are for example found in the injector beam lines of heavy ion accelerator facilities. The original formula was presented in 1975 by Igor Gabovich et al. and takes into account the de-compensation through Coulomb collisions of the primary beam ions and the compensating electrons. We extend its usability to arbitrary (positive) charge states of the ions and non-quasineutral beams. The resulting formula compares well with measurements using a retarding field analyzer and a multi-species generalization of it was incorporated into beam transport simulations using the particle-in-cell code WARP.