Modelling and Control of Longitudinal Vibrations in a Radio Frequency Cavity

Radio frequency (RF) cavities hold a crucial role in Electron Linear Accelerators, serving to provide precisely controlled accelerating fields. However, the susceptibility of these cavities to microphonic interference necessitates the development of effective controllers to mitigate vibration due to interference and disturbances. This paper undertakes an investigation into the modeling of RF cavities, treating them as cylindrical beams. To this end, a pseudo-rigid body model is employed to represent the translational vibration of the beam under various boundary conditions. The model is systematically analyzed using ANSYS software (from Ansys, Inc., Canonsburg, PA, USA, 2022). The study further delves into the controllability and observability of the proposed model, laying the foundation for the subsequent design of an observer-based controller geared towards suppressing longitudinal vibrations. The paper presents the design considerations and methodology for the controller. The performance of the proposed controller is evaluated via comprehensive simulations, providing valuable insights into its effectiveness in mitigating microphonic interference and enhancing the stability of RF cavities in Electron Linear Accelerators.