Space Charge and Lattice Driven Resonances at the CERN Injectors

Abstract

The present dissertation focuses on the space charge phenomena in the presence of betatron resonances in the CERN Injectors and in particular the Proton Synchrotron (PS) and the Proton Synchrotron Booster (PSB). Space charge dominates the dynamics in high brightness and low energy machines as the injectors and it is typically one of the main performance limitations for operation. In the PS, losses are observed for vertical tunes above , 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. Simulation studies reveal the incoherent nature of the resonance observed at while the analytical 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. Similarly, Frequency Map Analysis (FMA) studies demonstrate the excitation of resonances in simulations while revealing that the mechanism that leads to the observed losses is the periodic crossing of resonances. Experimental and simulation studies showcase the response of the operational high brightness beam in the PS in terms of losses and emittance growth. With the use of lower brightness beams lattice driven resonances excited by machine errors are identified and compensated. 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. The last part of the thesis concerns studies in the PSB, where the resonance under study is the coupling resonance excited by space charge, referred to as Montague resonance. The analytical approach of the (RDT) calculations reveals that the machine could be operated in a different tune regime, namely the Q4Q3, where the resonance is suppressed. Measurements and simulations with various crossing speeds of the resonance, show the emittance exchange that it causes in the operational tune regime (Q4Q4) while the suppression in the regime Q4Q3 is demonstrated with the preservation of the emittance in both planes during the crossing. The interplay of the Montague with the excitation of the coupling in 2nd order through skew quadrupole-like errors is also studied in both measurements and simulations.