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.