Radio frequency (RF) cavities are commonly used in particle accelerators to accelerate charged particle beams. The shape of the RF cavity determines the resonant electromagnetic fields and frequencies, which need to satisfy a variety of often-conflicting requirements in order to stably and efficiently accelerate the beam. We formulate such problems as constrained multi-objective shape optimization problems and search for the Pareto front using a massively parallel implementation of a multi-objective evolutionary algorithm. We focus on axisymmetric RF cavity shapes, and use a fast axisymmetric Maxwell eigensolver for computing the necessary properties of both the fundamental mode and the higher order modes (HOMs). In particular, we solve two real-world RF cavity shape optimization problems. The first problem is the hypothetical optimization of the main RF cavity of the planned Swiss Synchrotron Light Source upgrade, SLS 2.0. We provide insight into the problem by computing the Pareto front approximation, and find a few good RF cavity shapes for which the beam interaction with the HOMs is already minimized. The second problem we consider is the optimization of the superconducting RF cavity for the Z-pole operating mode of the lepton collider at the Future Circular Collider (FCC). In addition to optimizing the RF properties, we focus on finding a cavity shape that is robust with respect to geometric perturbations, which could arise, for example, from manufacturing inaccuracies or harsh operating conditions at cryogenic temperatures. We use the results of a global sensitivity analysis to reduce the search space, reformulate the problem, and devise an optimization strategy. In the end, we show a good cavity, which for example, has a robust fundamental frequency, and the frequencies of the trapped dipole modes extremely close to each other which would simplify their damping with coaxial HOM couplers. In both cases, in addition to the widely considered elliptical cavity shapes, we also explore the possibility of using a different type of geometry. The proposed approach could easily be applied to other types of geometries and other RF cavity shape optimization problems, with the underlying software used for computing the properties of arbitrary HOMs.
Dr. Andreas Adelmann