Space Charge Modeling at the Integer Resonance for the CERN PS and SPS

In long-term tracking simulations of high-intensity beams which are typical in the CERN accelerators, the electromagnetic interaction between the individual particles can not be neglected. Simulations are required to optimize the performance of the accelerators, and to better understand the involved coherent and incoherent dynamics. The impact due to the unavoidable simplifications when modeling the complex dynamics must therefore be studied. We approach this task by examining six different tracking models, applied to the CERN Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS), both of which were dynamically operated near horizontal integer resonances. The six models, which are overall implemented in the well-known program packages MAD-X and PyOrbit, are compared to beam-based measurements on both machines, with the PS as the main emphasis.