The Transverse Nonlinear Tune Shift as Stabilizing Factor in Halo Creation in Space Charge Dominated Beam

One of the most important problems for space charge dominated beams in the low energy part of superconducting linacs is halo creation. Many authors show one of the key effects in halo creatiation is parametric resonance due to the mismatched beta-function oscillation (between core and particle). To estimate parametric resonance conditions the nonlinear tune shift for binomial distributed beam is described theoretically in this article. Simultaneously the beam dynamics simulation 3D PIC code was developed. The transverse oscillation frequencies are compared with parametric resonance criteria. As a result the recommendation for space charge shift is concluded to minimize halo creation.