Identification and characterization of high order incoherent space charge driven structure resonances in the CERN Proton Synchrotron

Space charge is typically one of the performance limitations for the operation of high intensity and high brightness beams in circular accelerators. In the Proton Synchrotron (PS) at CERN, losses are observed for vertical tunes above $Q_y=6.25$, especially for beams with large space charge tune shift. The work presented here shows that this behaviour is associated to structure resonances excited by space charge due to the highly symmetric accelerator lattice of the PS, typical for first generation alternating gradient synchrotrons. Experimental studies demonstrate the dependency of the losses on the beam brightness and the harmonic of the resonance, and simulation studies reveal the incoherent nature of the resonance. Furthermore, the calculation of the Resonance Driving Terms (RDT) generated by the space charge potential shows that the operational working point of the PS is surrounded by multiple space charge driven incoherent resonances. Finally, measurements and simulations on both lattice driven and space charge driven resonances illustrate the different behaviour of the beam loss depending on the source of the resonance excitation and on the beam brightness.