The transverse motion of beam halo particles is described by a particle-core model which uses the space-charge field of a continuous cylindrical oscillating beam core in a uniform linear focusing channel to provide the force that drives particles to large amplitudes. The model predicts a maximum amplitude for the resonantly-driven particles as a function of the initial mismatch. We have calculated these amplitude limits and have estimated the growth times for extended-halo formation as a function of both the space-charge tune-depression ratio and a mismatch parameter. We also present formulas for the scaling of the maximum amplitudes as a function of the beam parameters. The model results are compared with multiparticle simulations and we find very good agreement for a variety of initial particle distributions.
