Active vibration modeling and control in radio frequency (RF) cavities

Microphonic interference, created primarily by environmental and mechanical vibrations, has the potential to impact the performance of superconducting radio frequency (RF) cavities of electron linear accelerators (e-LINACs), such as the accelerator of the Advanced Rare IsotopE Laboratory (ARIEL) currently under construction at TRIUMF, Canada's particle accelerator center. In the e- LINAC, electrons are accelerated up to 50MeV along a linear beamline via an oscillating electric field generated by multi-cell RF cavity resonators. Delivering a high-quality beam requires that the amplitude and phase of the accelerated particles be precisely controlled so that bunched particles receive the same amount of energy from the multi-cell RF cavities. There should be no unwanted variation in the desired resonance frequency. However, microphonic interference can cause deformations in the shape of the cavity that creates a shift in resonance frequency. To design a controller that can reduce or suppress microphonic interference, one must first have an appropriate model of such a cavity. Yet, creating an analytical model of mechanical vibrations in a multi-cell cavity has historically proven to be an extremely complex task. Further challenges in controlling TRIUMF's nine-cell niobium RF cavity arise from its boundary conditions. Access to the cavity is restricted to either end because the cavity is suspended within a Helium bath, limiting the application of forces only to the cavity ends. This thesis outlines the development of an active vibration control to cancel out specific mechanical modes of e-LINAC multi-cell RF cavity. This work involved several steps: First, the development of a control system is presented for active noise cancellation of a conventional multi-cell cavity. To this end, an analytical RF model for a multi-cell structure was developed when the cavity is under acceleration mode. Next, two different approaches were employed for mechanical vibration analysis. In the first approach, the cavity is modeled as a pseudo-rigid cylindrical beam system that accounts for the bending and stretching of the cavity's flexible structure. From there, an observer-based controller was designed to suppress the longitudinal vibrations of the flexible structure system. Proof of its controllability, demonstrated via simulations, is presented herein. In the second step, the multi-cell cavity's dynamic equations were modeled by utilizing a cylindrical shell structure. It is verified through comparison with ANSYS software that the latter dynamics is close to the dynamics of a nine-cell cavity. This resulted in a unified solution for cylindrical shell systems with generic boundary conditions. From this model, an observer-based LQG controller—a combined Kalman filter and LQR controller—was developed, and its performance was tested through simulation analysis.