Multi-turn extraction and injection by means of adiabatic capture in stable islands of phase space

Recently a novel approach has been proposed aimed at performing multi-turn extraction from a circular machine. Such a technique consists of splitting the beam by means of stable islands created in transverse phase space by magnetic elements creating nonlinear fields, such as sextupoles and octupoles. Provided a slow time-variation of the linear tune is applied, adiabatic with respect to the betatron motion, the islands can be moved in phase space and eventually charged particles may be trapped inside the stable structures. This generates a certain number of well-separated beamlets. Originally, this principle was successfully tested using a fourth-order resonance. In this paper the approach is generalised by considering other type of resonances as well as the possibility of performing multiple multi-turn extractions. The results of numerical simulations are presented and described in detail. Of course, by time-reversal, the proposed approach could be used also for multi-turn injection.