Simulations of a fast feedback system for the High Luminosity LHC

The High-Luminosity LHC upgrade, expected to be finished by 2025, will generate a tenfold increase in the number of recorded collisions. Part of this improvement~will come from the implementation of crab cavities, which exert transverse momentum kicks on the bunches of particles just before they collide, in order to have head-on collisions. The crab cavity field will include amplitude and phase noise, leading to undesirable consequences, such as the increase of the particle cloud size~(emittance). Simulations were performed to evaluate the performance improvement with a proposed fast feedback system acting through the crab cavities.