Progresses in the Studies of Adiabatic Splitting of Charged Particles Beams by Crossing Nonlinear Resonances

The multi-turn extraction from a circular particle accelerator is performed by trapping the beam inside stable islands of the horizontal phase space. In general, by crossing a resonance of order n, n+1 beamlets are created whenever the resonance is stable, whereas if the resonance is unstable the beam is split in n parts. Islands are generated by non-linear magnetic fields, whereas the trapping is realized by means of a given tune variation so to cross adiabatically a resonance. Experiments at the CERN Proton Synchrotron carried out in 2007 gave the evidence of protons trapped in stable islands while crossing the one-third and one-fifth resonances. Dedicated experiments were also carried out to study the trapping process and its reversibility properties. The results of these measurement campaigns are presented and discussed in this paper.