Simulation Studies of Longitudinal Stability for High-Intensity LHC-Type Beams in the CERN SPS

Beams in the SPS for the High Luminosity LHC (HL-LHC) must be stabilized in the longitudinal plane up to an intensity of 2.4·10¹¹ protons per bunch. The fourth harmonic RF system increases Landau damping, and controlled longitudinal emittance blow-up is applied to cope with coupled-bunch instabilities along the ramp and at flat-top. Longitudinal multi-bunch beam dynamics simulations of the SPS cycle were performed starting from realistic bunch distributions, as injected from the PS. The full SPS impedance model was included, as well as the effect of low-level RF (LLRF) feedback for beam-loading compensation. A realistic model of the beam-based LLRF loops was used for the particle tracking studies. Controlled longitudinal emittance blow-up was included by generating bandwidth-limited RF phase noise and by injecting it into the beam phase-loop input, exactly as in hardware. Due to the stringent constraints on particle losses and extracted bunch lengths, particular attention was paid to monitoring these parameters in the simulations, and to determining the best configuration for a stable acceleration of the beam.