Impedance model of the CERN SPS and aspects of LHC single-bunch stability

Upgrades of the CERN particle accelerators complex are planned to increase the potential of physics discovery in the LHC. In this respect, the beam coupling impedances of the SPS and LHC are expected to be among the limitations to the intensity upgrade scheme. In this thesis work, we present a general framework to better understand the impedance of a particle accelerator. In a first step, the impedance of single components are gathered into an impedance model accounting for the whole machine. In order to assess the relevance of this impedance model, its impact on beam dynamics is simulated and can be compared to impedance observables measured with beam. This general framework was applied to compute a more accurate transverse impedance model of the SPS from theoretical models for the 20 kickers and the 6.9 km long beam pipe, as well as time domain electromagnetic simulations of the 106 horizontal and 96 vertical SPS beam position monitors. Comparing HEADTAIL macroparticle simulations to beam-based measurements in the SPS, this transverse impedance model turned out to account for 65% of the vertical impedance measured in the machine and showed in addition that the large negative quadrupolar horizontal impedance of the kickers can be held responsible for the measured positive coherent horizontal tune shift with increasing beam intensity. In the course of implementing this framework, new contributions were brought to the understanding of impedances and wake fields. A more general formula was derived for the longitudinal impedance of a multilayer cylindrical beam pipe. New formulae for the transverse quadrupolar impedances of simple models of kickers were also derived and successfully benchmarked to electromagnetic simulations. In addition, MOSES mode coupling analytical calculations were successfully benchmarked against HEADTAIL macroparticle simulations in predicting a Transverse Mode Coupling Instability at injection in the SPS between azimuthal modes -2 and -3. Finally, new RF bench measurements validated the theory proposed by B. Zotter and E. Métral, thereby confirming that the low frequency transverse impedance of the LHC collimators –, which largely dominates the LHC transverse impedance – is less critical than initially expected.

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