Simulations of RF beam manipulations including intensity effects for CERN PSB and SPS upgrades

During Long Shutdown 2 (LS2, 2019-2021) all the injectors of the CERN LHC will undergo several upgrades to fulfill the requests of the LHC Injectors Upgrade (LIU) Project. Among them, an increase in luminosity of the LHC beam by a factor of ten and two respectively for proton and ion beams is expected. The upgrades of the CERN PSB, the first synchrotron in the LHC proton injection chain, will be significant. The injection and extraction beam energies will be increased respectively from 50 MeV to 160 MeV kinetic energy (via the new Linac4) and from 1.4 GeV to 2 GeV (using new magnet power supplies). The required beam intensities will be a factor of two higher for High-Luminosity LHC (HL-LHC) beams, and the currently used narrow-band ferrite RF systems will be replaced by broad-band Finemet® cavities. For ion beams instead, a fundamental upgrade will concern the CERN SPS, the LHC injector, where the Low Lever RF functionalities will be considerably enhanced to allow the interleaving of two batches in longitudinal phase space through momentum slip-stacking, aiming at halving the bunch spacing. In order to predict future longitudinal beam stability and optimize complex RF manipulations both for PSB and SPS, longitudinal macro-particle simulations have been performed. Concerning the PSB, an accurate impedance model and a careful estimation of the space charge effects were included in simulations. Beam and cavity-based feedbacks were also taken into account. Controlled longitudinal emittance blow-up, currently obtained through phase modulation with a dedicated higher harmonic RF system, was achieved in measurements and simulations for the first time injecting RF phase noise in the main harmonic cavity, showing some advantages in using this new method. As for the SPS, the slip-stacking dynamics with collective effects has been studied in details aiming at optimizing the numerous parameters present and satisfying the stringent constraints on losses and bunch length at extraction. Beam quality issues were analyzed together with possible remedies. All simulations have been performed with the macro-particle longitudinal beam dynamics CERN BLonD code, after particular efforts have been spent to implement several algorithms for non ultra-relativistic energy machines (like the PSB) and for slip-stacking dynamics in order to easily optimize the large parameter space available. Benchmarks between BLonD, other codes and analytical formulas have been performed to study different approaches for induced voltage calculation and give some guidelines on the pros and cons of each of them.