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The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC). Multi-bunch instabilities limit the intensity of the beam that can be accelerated to 450 GeV in the SPS and transferred to the LHC. Without mitigation measures, the threshold of bunch intensity of the longitudinal instability is three times below the nominal bunch intensity of the LHC beam. The High Luminosity LHC project (HL-LHC), which requires a doubling of the nominal bunch intensity, relies on improvement of beam stability in the SPS. A fourth harmonic RF system allows, presently, to stabilize the beam up to nominal LHC intensity. It increases the synchrotron frequency spread inside the bunch, providing more efficient Landau damping of beam instability. However, nonlinearities of the synchrotron frequency distribution inside the bunch pose a limitation on bunch length. This paper explores possible intensity increase in the SPS by studying the effect on beam stability of the voltage ratio between two RF systems. The results are substantiated by beam measurements and particle-tracking simulations. An optimized voltage program of the second RF system during the cycle has been tested in operation and beam stability and the quality have been successfully improved.

The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC), the world's largest particle collider. The High-Luminosity LHC (HL-LHC) project is a major step forward in the improvement of the LHC performances and it requires a doubling of the nominal bunch intensity of the current LHC beam. In the SPS, multi-bunch instabilities and particle losses limit the beam intensity that can be accelerated to 450 GeV/c and transferred to the LHC. Without mitigation measures, the bunch intensity threshold for longitudinal instabilities is three times below the nominal intensity of the LHC beam. Moreover, the present limited RF power is not sufficient to accelerate beams with intensities well above nominal without substantial particle losses and a reduction of the RF voltage available for the beam at the flat top energy. The SPS will undergo significant upgrades but they may not be sufficient to ensure the stability of the HL-LHC beam. The objectives of this doctoral research are to study the longitudinal intensity limitations of the LHC proton beam in the SPS and to find possible mitigation measures to ensure the beam stability and quality at HL-LHC intensity. Beam measurements and particle simulations are used in conjunction with analytical estimations to study the multi-bunch instabilities during the cycle in the SPS. This work attempts to identify the main sources of instabilities and beam quality degradation. Possible scenarios of mitigation measures are investigated to explore the future beam parameters achievable after upgrades. The effects on beam stability of the foreseen RF upgrade, the double RF operation and the reduction of various longitudinal beam-coupling impedances are analysed in detail. The scenario of a lower-harmonic RF system in the SPS, for particle losses reduction, is also studied.