Collective Effects for the LHC Injectors: Non-ultrarelativistic Approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the performances of the Large Hadron Collider (LHC) in exploring high-energy frontiers. One of the main limitations to the intensity upgrade scheme is represented by collective instabilities. They are caused by the interaction of travelling charged particles, via electromagnetic fields, with the geometry and the conductivity of the beam environment and they are proportional to the beam intensity. These electromagnetic interactions are expressed in terms of wake fields (time domain) or impedances (frequency domain). High intensity beams might be driven unstable by collective phenomena and beam coupling impedances are expected to be among the main limitations to the intensity upgrade. Impedances are usually studied assuming ultrarelativistic bunches while low and medium energy regimes have been less explored. In this thesis work we present a detailed analysis of the impedance structure for low and medium energy particle accelerators. The models developed in this thesis have been applied to the Proton Synchrotron Booster (PSB) which accelerates the proton bunch from a kinetic energy of 50 MeV up to 1.4 GeV. In this energy range high intensity phenomena need to be studied with a different formalism than in high energy (ultrarelativistic) machines. The impedance of the PSB has been analysed through dedicated measurements, numerical simulations and analytical modelling, in a non-ultrarelativistic approach. Through these analysis we quantified the impedance structure of the PSB and pointed to some main candidates as sources of intensity-dependent instabilities