This paper reports on an approach to investigate the dynamics of halo particles in mismatched charged-particle beams propagating through periodic-focusing channels using the particle-core model. The proposed method employs canonical transformations to minimize, in new phase-space variables, the flutter due to the periodic focusing to allow making stroboscopic plots. Applying this method, we find that in periodic-focusing systems, certain particles initially not in the halo region can be brought into resonance with the core oscillation to become halo particles.
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Tai-Sen F. Wang (2000) studied this question.