Multi-objective shape optimization of radio frequency cavities using an evolutionary algorithm

Abstract

Radio frequency (RF) cavities are commonly used 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 requirements for a stable and efficient acceleration of the beam. For example, the accelerating frequency has to match a given target frequency, the shunt impedance usually has to be maximized, and the interaction of higher order modes with the beam minimized. In this paper we formulate such problems as constrained multi-objective shape optimization problems, use a massively parallel implementation of an evolutionary algorithm to find an approximation of the Pareto front, and employ a penalty method to deal with the constraint on the accelerating frequency. Considering vacuated axisymmetric RF cavities, we parameterize and mesh their cross section and then solve time-harmonic Maxwell’s equations with perfectly electrically conducting boundary conditions using a fast 2D Maxwell eigensolver. The specific problem we focus on is the hypothetical problem of optimizing the shape of the main RF cavity of the planned upgrade of the Swiss Synchrotron Light Source (SLS), called SLS-2. We consider different objectives and geometry types and show the obtained results, i.e., the computed Pareto front approximations and the RF cavity shapes with desired properties. Finally, we compare these newfound cavity shapes with the current cavity of SLS.