Studies of longitudinal coupled-bunch instabilities in the LHC injectors chain

Colliders are the privileged instruments to explore the high energy frontier in particle physics. They require high quality particle beams with high intensity, low transverse emittances, and low energy spread to achieve high luminosity. These requirements present a number of challenges, including the suppression of beam instabilities driven by collective e ects that lead to intensity limitations and have a considerable detrimental impact on the performance of high intensity machines. Collective e ects are caused by the interactions between charged particles and their surroundings and become more significant, and therefore more disrupting, at a high beam intensity. The electromagnetic fields produced by the interaction between protons and their surroundings, the so-called wakefields, can lead to longitudinal and transverse instabilities, which limit the ultimate achievable beam current because, typically, they produces beam losses. Among these instabilities, the coupled bunch (CB) instabilities are a serious issue in accelerators operated with multiple bunches at a high beam current. This research focuses on the study of longitudinal CB instabilities in the CERN Proton Synchrotron (PS) in the framework of the LHC Injectors Upgrade (LIU) project. One of LIU goal is to double the beam intensity in the PS in order to achieve the integrated luminosity target of the High-Luminosity LHC. The CB oscillations induce longitudinal blow up and large bunch-to-bunch intensity and longitudinal variation, not compatible with the specifications of the future LHC-type beams. Up to present intensities (2014) they could be suppressed by a dedicated feedback system which used the 10 MHz cavities as longitudinal kicker, in addition to their function for acceleration. In the framework of the LIU project a new wide-band Finemet cavity has been installed in the PS in 2014 as a longitudinal kicker for a new digital coupled-bunch feedback system. In Chapter 1 I will provide the theoretical background introducing the concepts of impedance, spectrum, wakefields and I will report in detail on the theory of longitudinal multi-particle beam dynamics. In Chapter 2 I will present the PS Complex explaining its features, the operation of the cycle that leads to the production of the nominal beam for the LHC and I will describe the RF system involved in the preparation of the LHC nominal beam longitudinal structure. I will focus in particular on two RF systems: the 10 MHz accelerating system which is the main impedance source of CB instabilities andata the Finemet cavity, a part of the new coupled-bunch feedback (FB) system. For all these cavities, starting from machine measurements, I derived a simplified model used in simulations. In Chapter 3 I will introduce the tools used for this research work: the simulation code MuSiC, the data acquisition techniques, and the analysis algorithm that I developed, based on the circulant matrix theory. I will also show simulations and measurements results to clarify the source of instability and to predict the beam performance after the upgrade implemented by the LIU project. In Chapter 4 I will analyze in detail the new digital feedback system with all its com- ponents and the measurements carried out during its commissioning to confirm that the system interacts with the beam as expected. Finally I will present recent mea- surements results we obtained during 2016 machine run with the feedback contribute. In the Conclusions I will give an overview of my research activity and draw conclusions on the current state of the art for CB instabilities in the CERN PS.