Simulation of beam–beam interaction with crab cavities for LHC upgrade

The crab cavities are a critical component in the high luminosity LHC upgrade project to compensate the luminosity loss from large crossing angle collision. However, these crab cavities will not be perfect in the real accelerator. In this paper, we studied the effects of crab cavity imperfections on colliding beam luminosity lifetime degradation for the LHC upgrade through detailed numerical simulations. Our simulation results suggest that the white noise jitter in the crab cavity RF phase and voltage rms amplitudes should be kept below a few $10^{−5}$ for a good luminosity lifetime, while with frequency-dependent jitter, the amplitudes should be kept below a few $10^{−4}$ for a good lifetime. The RF multipole errors in the current crab cavity designs are small enough and would not cause extra luminosity degradation.