Luminosity Reduction Caused by the Full-Detuning LLRF Scheme on the HL-LHC Crab Cavities

The High-Luminosity LHC (HL-LHC) crab cavities (CCs) will be installed on both sides of IP1 (ATLAS) and IP5 (CMS) to compensate for the geometric luminosity reduction due to the crossing angle. To cope with the increased beam current (0.55 A DC for LHC, 1.1 A for HL-LHC), the operation of the LLRF system has been changed: rather than fully compensating the transient beam loading, we allow the phase to vary along the turn (100 ps peak-peak with 1.1 A DC). This has been implemented at LHC since July 2017. The CCs have high loaded Q (5e5) and the available RF power is insufficient to follow the bunch phase modulation. The crabbing voltage is not modulated, causing a phase error w.r.t. the individual bunch centroids, leading to transverse kicks of the centroids and an asymmetric crabbing of the bunch cores. We present an analytical model for the resulting luminosity reduction and validate with particle tracking simulations. Due to the symmetry of the bunch filling patterns for the counter-rotating beams, the peak luminosity is reduced by only 2% for nominal HL-LHC parameters at IPs 1 and 5, which is within tolerable limits.