A particle-core study of halo formation for a mismatched beam in a periodic-focusing system

This work is an attempt to explore possible techniques to graphically display the dynamics of halo particles for a mismatched beam in a periodic-focusing lattice. It is found that by using the particle-core model and a suitable change of the phase-space variables, stroboscopic plots similar to those made for the uniform-focusing channel can be created by strobing at the frequency of the core oscillation. This method does not require any smooth approximation to reduce the flutter due to the periodic focusing, and it is not limited by the constraint that the core-oscillation frequency has to be a subharmonic of the focusing frequency. The discussion will cover the applications to both the axisymmetric and the quadrupole-focusing channels. It is also found that, similar to the continuous-focusing system, the motion of halo particles, although focused by the externally applied periodic field, is strongly influenced by a parametric resonance