Propagation of the 50 Hz Perturbations in the Large Hadron Collider Sector Dipoles and Equivalent Model Circuit.

Observations of harmonics of the mains power frequency in the beam spectrum have been observed in the past in several accelerators. Indeed, since 1986 this phenomenon was already known in the SPS at CERN. In particular, it was observed that these excitations can lead to emittance blow-up and shortening of the beam lifetime. For these reasons, in the Summary of the $220^{th}$ LMC Meeting held on 3rd June 2015, it was decided to invest more energy to study the origin of this excitation and to understand the tolerance that we would have for the next upgrade of the LHC, that is the High Luminosity LHC (HL-LHC) that will enter service after 2025. Several observations were made during the 2018 proton run in order to understand the origin of this issue; in particular, all the observations suggest that the harmonics are the result of a real beam excitation, rather than an instrumental feature. Based on these considerations, potential sources have been found leading to plausible correlation to the magnets power converters. In this context, this work of thesis aims to provide the bases of analysis for a particle accelerator under the effect of perturbations and how their propagation occurs in the Large Hadron Collider sector dipoles at CERN. In particular, after an analytical approach at the issue, an equivalent circuit model of the LHC dipoles chain will be used in order to give a first estimation of excitation given by the ripple, at the mains frequency, due to the power converters of the main bending magnets.