Impact of Broadband Impedance on Longitudinal Coupled-Bunch Instability Threshold

Coupled-bunch instabilities (CBI) and the loss of Landau damping (LLD) in the longitudinal plane can affect the performance of high-current synchrotrons. The former is driven by the narrowband impedance of resonant structures, while the latter is mainly determined by the broadband impedance of the entire accelerator and is a single-bunch effect. Therefore, the CBI and LLD thresholds are usually evaluated separately in order to define the corresponding critical impedance budget for given beam parameters. In this paper, we show that the CBI threshold in the presence of broadband impedance can be significantly lower than the one defined by only the narrowband impedance, especially if the LLD threshold is below the CBI threshold. In some cases, the beam becomes unstable even below the LLD threshold. This explains the low CBI threshold observed for the LHC-type beams in the CERN SPS. For HL-LHC, the broadband impedance may also significantly reduce the CBI threshold driven by higher-order modes of the crab cavities.