Phase space analysis of incoherent space-charge-driven structural resonances in high-intensity hadron synchrotrons

For high-intensity and low-energy hadron synchrotrons, the resonance driven by the incoherent space charge is one of the main factors of emittance growth. For the recent upgrade project of Xi’an 200 MeV Proton Application Facility (XiPAF) hadron synchrotron, the incoherent space-charge-driven resonances are very significant, especially in the beam injection stage. In this paper, we represent a novel analytical method to identify the exact order of space-charge-driven structural resonances. The analytical method can be employed to calculate the resonance phase space structure driven by the incoherent space charge. The feasibility of this method has been verified by taking the XiPAF-Upgrading synchrotron as the example synchrotron. It is shown that during the resonance crossing, the phase space structure can be obtained and analyzed via the proposed analytical method. The analytical results are compared to particle-in-cell simulations and show good agreement. In addition, we discuss beam loss induced by multiple factors including space charge, magnet errors, power supply ripple, and chromatic effects.