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The particle-core model for a continuous cylindrical beam is used to describe the motion of single particles oscillating in a uniform linear focusing channel. Using a random variation of the focusing forces, the model is deployed as proof of principle for the occurrence of large single particle radii without the presence of initial mismatch of the beam core. Multiparticle simulations of a periodic 3D transport channel are then used to qualify and quantify the effects in a realistic accelerator lattice

Beam halo in high-intensity hadron accelerators caused by statistical gradient errors