Prediction of the Lorentz Force Detuning and pressure sensitivity for a Pillbox cavity

The Lorentz Force Detuning (LFD) and the pressure sensitivity are two critical concerns during the design of a Superconducting Radio Frequency (SRF) cavity resonator. The mechanical deformation of the bare Niobium cavity walls, due to the electromagnetic fields and fluctuation of the external pressure in the Helium bath, can dynamically and statically detune the frequency of the cavity and can cause beam phase errors. The frequency shift can be compensated by additional RF power, that is required to maintain the accelerating gradient, or by sophisticated tuning mechanisms and control-compensation algorithms. Passive stiffening is one of the simplest and most effective tools that can be used during the early design phase, capable of satisfying the Radio Frequency (RF) requisites. This approach requires several multiphysics simulations as well as a deep mechanical and RF knowledge of the phenomena involved. In this paper, is presented a new numerical model for a pillbox cavity that can predict the frequency shifts caused by the LFD and external pressure. This method allows to greatly reduce the computational effort, which is necessary to meet the RF requirements and to keep track of the frequency shifts without using the time consuming multiphysics simulations.