Flat-bottom instabilities in the CERN SPS

At intensities of $2.6 \times 10^{11}$ protons per bunch (ppb), required at SPS injection for the High Luminosity LHC beam, longitudinal instabilities can degrade the beam quality delivered by the SPS, the LHC injector at CERN. In this paper, we concentrate on beam instability at flat bottom. The dependence of the instability threshold on longitudinal emittance and LLRF system settings was measured, to help identify the impedance driving this instability. While reducing the longitudinal emittance reduces the losses at injection, it can drive the beam unstable. The LLRF system of the SPS (partially) compensates beam loading, but also affects the instability. The effect of the different LLRF systems (feedback, feedforward, phase loop and longitudinal damper) and the fourth harmonic RF system on the instability was investigated. The measurements are compared to particle simulations performed with the longitudinal tracking code BLonD.