Working point and resonance studies at the CERN Proton Synchrotron

The Proton Synchrotron (PS) is the oldest yet the most versatile particle accelerator operating at CERN. Having accelerated a multitude of different particle species within the last five decades, it is today used to define the longitudinal structure of the proton beams going into collision in the Large Hadron Collider (LHC), and thus constitutes an integral part of the LHC injector chain. Around 2020 the LHC will be subject to an upgrade to significantly increase the number of collisions at the interaction points. The beam parameters demanded by the High Luminosity LHC (HL-LHC) will, as a result, require substantial improvements of the pre-accelerators, which are currently being studied within the LHC Injectors Upgrade (LIU) project. The increase of luminosity will be accompanied by an increase of beam intensity, which might result in instabilities appearing on the injection flat bottom of the PS. Transverse Head-Tail instabilities have already been observed on operational LHC beams and an alternative stabilizing mechanism for this type of instability is currently being studied. It consists of reducing the mode number of the transverse oscillation by changing linear chromaticity and in succession completely damping the instability by a damper system with appropriate bandwidth. However, nowadays at the PS there is no chromaticity correction scheme implemented at low energy. Special circuits mounted on top of the main magnet poles - the Pole Face Windings (PFW) - could account for that, but so far they are only used to control the betatron tunes and linear chromaticities at high energy. The first part of this thesis is therefore dedicated to extensive studies concerning the correction of betatron tunes, linear and higher order chromaticities by exploitation of the intrinsic opportunities these special circuits offer at low energy. An additional limitation of the PS for high-brightness and high-intensity beams is the presence of beam destructive betatron resonances, which restrict the choice of the injection working point and the maximum acceptable tune spread. This is especially the case for the double batch injection for LHC beams: four bunches are kept at injection energy for 1.2 seconds, leaving enough time for degradation of the transverse beam characteristics in case the space charge induced tune spread causes the beam to touch stop bands of different resonances. Detailed knowledge of the working point plane is thus necessary in order to choose both transverse tunes in an area sufficiently free of resonances. To improve the current working point control scheme, the influence of the PFW on the machine resonances is examined in the second part of this thesis, leading to a deeper understanding of the limits of the PS.