An Extended SPS Longitudinal Impedance Model

Longitudinal multi-bunch instability in the CERN SPS with a very low intensity threshold is a serious limitation for the future doubling of bunch intensity required by Hi-Lumi LHC project. A complete and accurate impedance model is essential to understand the nature of this instability and to plan possible cures. This contribution describes in detail the current longitudinal impedance model of the SPS. Recently, the model was updated with new findings and includes now the impedance of accelerating cavities, kicker and septum magnets, beam position monitors, vacuum Flanges, shielded and unshielded pumping ports, electrostatic septa and resistive wall. Electromagnetic simulations and bench measurements were used to build the model. The contribution from each element is described and compared to the total machine impedance. Together with relevant beam measurements and simulations, the analysis of the different sources of impedance is used to identify the source of the longitudinal instability limiting the SPS performance so that the responsible elements can be acted upon.