Studies of Longitudinal Coupled-Bunch Instabilities in the LHC Injectors Chain

Among several challenging objectives of the LHC Injectors Upgrade project, one aim is to double the beam intensity of the CERN Proton Synchrotron (PS) in order to achieve the integrated luminosity target of the High-Luminosity LHC project. A known limitation to reach the required high intensity is caused by the longitudinal coupled-bunch (CB) oscillations developing above the PS transition energy. The unwanted oscillations induce large bunch-to-bunch intensity variations not compatible with the specifications of the future LHC-type beams. In 2014 a new longitudinal kicker cavity has been installed, the Finemet cavity, as a part of the new digital coupled-bunch feedback (FB) system. The Finemet cavity allows with its large frequency bandwidth, to damp all the expected oscillation modes simultaneously. In the framework of this PhD study the impedance contribution of this equipment has been analyzed starting from the present knowledge of the machine impedance. A model of both the 10 MHz and the Finemet has been developed as a sum of resonant modes. From simulations it has been possible to show that the 10 MHz system is the main source of instabilities and to confirm that the contribution of the Finemet cavity to the couple-bunch instability is negligible compared to the stronger effect of the 10 MHz cavities. The complete prototype feedback chain of pick-up, digital processing and Finemet kicker has been installed and commissioned in 2014 and 2015. A dedicated measurement campaign was performed to qualify both the wide-band damper cavity as well as the new digital coupled-bunch low-level RF feedback system. Excitation measurements with FB in open loop showed that the Finemet cavity interacts with the different beam trains as expected and that the coupled-bunch oscillation modes can be individually excited. An original algorithm has been developed and proposed to analyze the bunch train and to perform the mode analysis of the system in order to study its stability. This approach allows sub-nanosecond detection of the bunch oscillation. Due to the symmetry of the system, for equidistant bunches covering the full azimuthal length of the PS, the eigenmodes of the CB oscillations do not depend upon the machine impedance. In practice this conditions is not verified. In this work we show a numerical approach to define the eigenmodes of the system for a generic impedance and bunch pattern. Tests during 2016 showed that coupled-bunch oscillations can be damped by the new feedback system up to an intensity of 2e11 protons per bunch at extraction.