Numerical calculation of the Lorentz force detuning and the pressure sensitivity for the HL-LHC crab cavity

Crab cavities are fundamental components of the HL-LHC upgrade project. These Radio Frequency cavities, operated at the appropriate frequency, ‘tilt’ the proton bunches to increase the luminosity at the collision points IP1 (ATLAS) and IP5 (CMS). Two different superconducting crab cavities were developed: RF Dipole (RFD) for horizontal deflection and Double Quarter Wave (DQW) for vertical deflection. During operation, the cavity walls are deformed due to the loading conditions. This deformation changes the electro-magnetic field inside the cavity and consequently its RF frequency. In the present study, the numerical evaluation of the Lorentz Force Detuning (LFD) and the Pressure Sensitivity (PS) of the DQW cavity, using COMSOL Multiphysics, is presented. The LFD is the fundamental frequency change of the cavity due to the electro-magnetic forces acting on its walls, while the PS is the frequency shift when the cavity is subjected to pressure fluctuations of the helium bath. Finally, a comparison with the results measured during the cold test of the manufactured cavities, and with the previous simulations results obtained for the RFD cavity is done.