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.cavities with resonant frequencies of 70 MHz power the cyclotron of the PROSCAN facility for cancer treatment. In the storage ring of the Swiss Synchrotron Light Source (SLS), four 500 MHz ELETTRA-type [5] cavities compensate for the energy loss due to synchrotron radiation and focus the electron bunches in longitudinal direction. A pair of passive superconducting cavities with operation frequency at the third harmonic provide bunch lengthening and Landau damping [6]. The newest accelerator at PSI is the SwissFEL facility [7], with pulsed RF cavities at operation frequencies of 3, 5.7 and 12 GHz. Compared to other PSI facilities, where standing wave cavities are used, most of the cavities of the SwissFEL LINAC are of the traveling wave cavity type. Other than for beam acceleration, RF cavities are also used for beam diagnostics, like beam current and position monitors [8,9], for bunch rotation in deflecting cavities [10], or in power amplifiers of accelerators, like klystrons, or filters.PSI is currently elaborating an upgrade proposal for SLS, called SLS-2 [11], for dramatically improved synchrotron light quality. This process is triggered by the development of distributed vacuum pumping, which allowed a reduction of the vacuum chamber dimensions, larger number and more compact magnets, and advancements in high precision machining. It is foreseen to reuse the existing main cavities, extended by a new type of absorber for the most troubling beam excited higher order modes (HOMs).In order to efficiently accelerate the beam, the RF cavity has to be optimized and engineered to satis...

Algorithm 1028: VTMOP: Solver for Blackbox Multiobjective Optimization Problems

“…Design optimizations were performed using an evolutionary MOA [57] and genetic algorithms, especially those of [29]. Genetic algorithms are the most widely methods in the field of particle accelerator design [11,12,35,36,38,43,62,66] and are commonly used at SLAC. In targeting commissioning goals for LCLS-II, ongoing optimizations have been performed in a piecewise fashion to reduce the number of free parameters.…”

Constrained multiobjective shape optimization of superconducting rf cavities considering robustness against geometric perturbations

“…The implementation of the optimization algorithm from the previous section is based on a combination of a massively parallel implementation of an EA [31,32], written in C++ and parallelized using MPI, with the axisymmetric Maxwell eigensolver [43]. For a point d, a mesh of half of the cross section of the corresponding cavity is created using the Gmsh [44] C++ API, and the resulting GEVPs are solved using the symmetric Jacobi-Davidson algorithm [45].…”

RF design of APEX2 two-cell continuous-wave normal conducting photoelectron gun cavity based on multi-objective genetic algorithm

“…The idea of implementing GA into RF cavity geometry design was first proposed in 90s [16] but without much follow-up for almost two decades. In recent years, with the advance of both GA algorithms and computation capability, as well as the ever-increasing demand on the cavity performance, more efforts have been invested into this approach [17,18,19]. In the conventional design method, the designer starts with an overall cavity shape and defines the geometric variables.…”