Halo formation from mismatched axisymmetric beams in a periodic focusing channel

In a recent paper [H. Okamoto and M. Ikegami: Phys. Rev. E 55 (1997) 4694], we investigated halo formation from mismatched axisymmetric beams in a uniform focusing channel, developing a 1D space-charge code dedicated to breathing-mode study. We proceed now to a periodic focusing situation, generalizing the work. Several realistic beam distributions are used to self-consistently explore the halo properties of breathing beams. It is found that the fundamental quantities, such as maximum halo extent, halo intensity, etc., exhibit the features analogous to those obtained in the previous study unless the resonant instability driven by the periodicity of the external restoring force takes place. A large-stop band of the second-order structure-driven resonance is encountered in the region sigma(0) > 90 degrees while higher-order resonances are usually much weaker. We further demonstrate that a halo may be removed by means of a multiple collimator system provided that the wake fields generated by the collimators are negligible.