Effect of HOM Frequency Shift on Bunch Train Stability

Future operation of the Large Hadron Collider (LHC) at CERN foresees an increase of the nominal luminosity by a factor of ten. The High-Luminosity LHC (HL-LHC) project necessitates increased intensities, good quality beam delivered by the injector chain. An important quality of the beam is its stability. In the LHC injector, the Super Proton Synchrotron (SPS), the longitudinal Coupled-Bunch Instability (CBI) during the acceleration ramp is a limiting factor in the production of high intensity beam. The main source of CBI is the 630 MHz Higher-Order Mode (HOM) in the 200 MHz travelling wave RF cavities. This HOM is already heavily damped by a series of longitudinal RF couplers. To achieve greater levels of damping, additional methods are under investigation using electromagnetic simulations. It has been shown in particle simulations that shifting the resonant frequency of the HOM can significantly improve the beam stability by up to 50%. The dependence of the instability threshold with the resonant frequency of the 630 MHz HOM is studied for an SPS bunch train of 72 bunches. The results of the macro-particle simulations are substantiated with an analytical model.