Systematical study on superconducting radio frequency elliptic cavity shapes applicable to future high energy accelerators and energy recovery linacs

Elliptic cavities at medium- and high-beta range are receiving broader use in the particle accelerator applications. Optimizing the shape of these cavities is a complex and demanding process. In this paper we propose an optimization approach to minimize the ratio of peak magnetic field to the acceleration field H-pk/E-acc while keeping the ratio of peak surface electric field to the accelerating field E-pk/E-acc, aperture radius and wall slope angle a at some permitted values. We show that it is possible to substantially vary the cavity geometry without violating the constraints or deteriorating the objective of the optimization. This gives us freedom in designing the geometry to overcome problems such as multipactor while maintaining the minimal H-pk/E-acc. The optimization is then performed to find a set of optimized geometries with minimum H-pk/E-acc for different beta's ranging from 0.4 to 1, different peak surface electric fields, wall slope angles and aperture radii. These data could be generally used as a suitable starting point in designing elliptic cavities.