Improved low energy optics control at the CERN Proton Synchrotron

The CERN Proton Synchrotron (PS) is a versatile and reliable accelerator that has produced a multitude of beams for fixed target experiments and higher-energy accelerators such as the Large Hadron Collider (LHC). During the current Long Shutdown 2 (LS2) the PS is being upgraded in the framework of the LHC Injectors Upgrade (LIU) project with the aim of producing LHC-type beams of even higher-brightness. In this thesis the research performed to investigate and mitigate emittance blow-up observed at injection energy of high-brightness beams is presented. The investigation of beam blow-up is essential to reach the desired properties for LIU beams. The first part of the thesis focuses on optimising the lattice optics to reduce $\beta$- and dispersion-beating by re-positioning the Low Energy Quadrupoles (LEQs). The optics beatings are quantified and quadrupole configurations are obtained that can reduce the emittance blow-up by $\approx$ 35 $\%$ at the working point (6.10, 6.24) in the horizontal plane or by $\approx$ 65 $\%$ at the working point (6.21, 6.10) in the vertical plane. One of the new quadrupole configurations is easily testable as it requires to only remove a single quadrupole from the current lattice. For the second part, the dispersive contributions are deconvoluted from horizontal beam profile measurements through achieving zero-dispersion optics at the measurement location using the LEQs. The number of LEQs and the LEQ strengths are optimised for each beam measurement location to reduce optics beating through numerical optimisation. The dispersion moves faster to zero with the inclusion of space charge effects, thus the experimental optics beatings will be less than the simulated ones. The final investigation presented in this thesis looks at the accuracy of measuring the betatronic contributions of the beam emittance. The $\beta$-function is measured through K-modulation at an LEQ during a magnetic plateau of a measurement cycle. The characteristics of the modulation and the number of required cycles to achieve an accuracy of 1$\%$ on the reconstructed $\beta$-function were studied. Additionally, the impact of a transfer factor error on the final $\beta$-function was investigated.