Improved Methods for the Measurement and Simulation of the CERN SPS Non-linear Optics

Good knowledge of the non-linear properties of the SPS lattice is crucial for modelling and optimising the machine performance in the presence of collective effects leading to incoherent tune spreads such as space charge, e-cloud and beam coupling impedance. In view of the LHC injectors upgrade (LIU) project and the future SPS operation in a regime dominated by such collective effects, detailed measurements of the SPS non-linear chromaticity and detuning with amplitude have been performed for the two optics configurations presently available for LHC type beams. The measurement results are used to fit systematic multipole components to the main magnets of the SPS MADX model as a basis for the non-linear machine model that can be used for beam dynamics simulations. The implications for the operation of the SPS with the LIU beam parameters are discussed.