High-power proton linacs for nuclear materials transmutation and production, and new accelerator-driven neutron spallation sources must be designed to control beam-halo formation, which leads to beam loss. The study of particle-core models is leading to a better understanding of the causes and characteristics of beam halo produced by space-charge forces in rms mismatched beams. Detailed studies of the models have resulted in predictions of the dependence of the maximum amplitude of halo particles on a mismatch parameter and on the space-charge tune-depression ratio. Scaling formulas have been derived which will provide guidance for choosing the aperture radius to contain the halo without loss.