Single Bunch Longitudinal Instability in the CERN SPS

The longitudinal single bunch instability observed in the SPS leads to uncontrolled emittance blow-up and limits the quality of high intensity beams required for the High Luminosity LHC and AWAKE projects at CERN. The present SPS impedance model developed from a thorough survey of machine elements was used in macro-particle simulations (with the code BLonD) of the bunch behavior through the acceleration cycle. Comparison of simulations with measurements of the synchrotron frequency shift, performed on the SPS flat bottom to probe the impedance, show a reasonable agreement. During extensive experimental studies various beam and machine parameters (bunch intensity, longitudinal emittance, RF voltage, with single and double RF systems) were scanned in order to further benchmark the SPS impedance model with measurements and to better understand the mechanism behind the instability. It was found that the dependence of instability threshold on longitudinal emittance and beam energy has an unexpected non-monotonic behavior, leading to islands of (in)stability. The results of this study are presented and can be used to define possible parameter settings for the future CERN projects.