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

Interplay of Space Charge and Intra-Beam Scattering in the LHC ion injector chain

The ion injectors of the CERN accelerator chain, in particular the Super Proton Synchrotron (SPS) and the Low Energy Ion Ring (LEIR), operate in a strong Space Charge (SC) and Intra-Beam Scattering (IBS) regime, which can degrade beam quality. Optimizing the ion beam performance requires thus to study the interplay of these two effects in tracking simulations by incorporating both SC and IBS effects interleaved with lattice non-linearities. In this respect, the kinetic theory approach of treating IBS effects has been deployed. A new, modified approach has been introduced using the formalism of the Bjorken and Mtingwa model and the complete integrals of the second kind for faster numerical evaluation. This IBS kick is implemented in PyORBIT and extensive benchmarking cases against analytical models are shown. Results of combined space charge and intra-beam scattering simulations for the SPS and LEIR are presented and compared with observations from beam measurements.Comment: 13 pages, 13 figures, to be submitted to Physical Review Accelerators and Beam

Space charge and lattice driven resonances at the CERN injectors

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 Qy=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. Simulation studies reveal the incoherent nature of the resonance observed at Qy=6.25 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

Resonance Driving Terms From Space Charge Potential

This note presents the calculation of the Resonance Driving Terms (RDTs) and the tune spread coming from the space charge potential of a Gaussian beam. These can be obtained by including this potential in the linear Hamiltonian of the accelerator. Through the RDTs, incoherent resonances excited by the space charge potential can be identified. The analytical method has been implemented in a self contained Python module, PySCRDT, in order to generalise the derivation and apply it to various rings and beams. The analytical approach as well as numerical examples and applications of PySCRDT are presented

Space Charge Resonance Analysis at the Integer Tune for the CERN PS

In the context of the LHC Injectors Upgrade (LIU) project, a series of studies have been performed in order to better understand the beam brightness limitations imposed by resonances and space charge effects. Space charge simulations using the adaptive space charge solver as implemented in the MAD-X code conducted for the CERN Proton Synchrotron (PS) show that a particle approaching the integer tune of Qx = 6 demonstrates a resonant behavior. The analysis of the single particle transverse motion reveals the excitation of a second order resonance. The interplay of the space charge effect and the optics perturbation in the regime of the integer tune on this excitation was further investigated. The simulations were complemented with the analysis of the resonance driving terms coming from the space charge potential derived in a classical perturbative approach