Abstract
The combined effect of space charge and nonlinear resonance on beam loss and emittance was measured in a benchmarking experiment over a 1.2 s long flat bottom at 1.4 GeV kinetic energy in the presence of a single controllable octupole. By lowering the working point towards the resonance, a gradual transition from a loss-free core emittance blowup to a regime dominated by continuous loss was found. We compare the observation with 3D simulations based on a new analytical space charge model and obtain good agreement in the emittance blowup regime. Our explanation is in terms of the synchrotron oscillation, which causes a periodic tune modulation due to space charge, and leads to trapping and detrapping on the resonance islands. For working points very close to the resonance this induces a beam halo with large radius. The underlying dynamics is studied in detail, and it is claimed that the predicted halo in conjunction with a reduced dynamic aperture for the real machine lattice is the source of the loss observed in the experiment.
Highlights
A detailed theoretical understanding as well as confidence in simulation modeling of the long-term (105 –106 turns) effects of high intensity or high phase space density is crucial for the SIS100 of the GSI future project
A major focus of such studies is the combined effect of space charge and nonlinear resonances and its impact on halo formation and/or beam loss
In the realm of long-term behavior, instead, where self-consistent 3D simulation is beyond current computer capabilities, the question of adequate approximations in space charge calculation is a challenging issue
Summary
A detailed theoretical understanding as well as confidence in simulation modeling of the long-term (105 –106 turns) effects of high intensity or high phase space density is crucial for the SIS100 of the GSI future project [1,2], where it is necessary to hold the high-intensity bunches between injections over typically 1 s at a loss level not exceeding 1%, likewise for the optimum performance of the CERN Proton Synchrotron (PS) for high-intensity beams. [5] it was recently suggested that the single-particle tune modulation caused by space charge and synchrotron motion may lead to trapping and detrapping on the resonance islands, which are moving in and out This process is related to the trapping during a single passage through a higher order nonlinear resonance as a result of a changing tune (i) the tune of an individual particle is strongly modulated, by an amount comparable with the incoherent tune shift, depending on two parameters, the synchrotron phase as well as the betatron amplitude; (ii) the latter is itself evolving in time, depending on the preceding trapping and detrapping events; and (iii) there is a selfconsistent time evolution due to the global changes of space charge These circumstances do not allow experimental verification of single-particle behavior. We use 3D computer simulation with space charge to demonstrate the long-term balance of trapping and detrapping as competing mechanisms and to compare the global predictions on the rms emittance and halo growth with the measurements
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