Long term stability studies in the presence of crab cavities and high order multipoles in the CERN super proton synchrotron and high luminosity large hadron collider

In 2018 the world's first Crab Cavity (CC) experiments with protons were successfully performed, aiming to study the CC effect on a proton beam and evaluate the engineering challenges. Before the commencement of these experiments, the impact of the CCs and their multipoles on the long term particle stability of the SPS was studied using dynamic aperture simulations. Furthermore, in order to ensure the long term stability and luminosity performance of the LHC upgrade, the High Luminosity LHC (HL-LHC), the limits of stable motion were also examined in the presence of CC multipole errors, CC voltage errors and additional non-linearities such as the beam-beam effects. This paper presents the comprehensive dynamic aperture results for the SPS and HL-LHC for different CC, accelerator and beam configurations in view of guiding the engineering specifications of the tolerances of the crab cavity multipole errors.