The detailed understanding of particle motion in the outer region (halo) of a bunched beam is of utmost importance for all existing and future high intensity hadron accelerators in view of minimizing particle losses and machine activation. Particle-core models separate the motion of halo particles from the core and treat them as test-particles. Therefore these reduced-order models are computationally inexpensive compared to full particle-in-cell simulations and can, to some extent, be derived analytically, thus giving insights into the non-linear mechanism of halo formation.