Equidistant optimization of elliptical superconducting rf standing wave cavities

A record accelerating rate was achieved earlier in standing wave (SW) SRF cavities when their shape was optimized for a lower peak surface magnetic field sacrificing the peak surface electric field. In view of new materials with higher limiting magnetic fields, expected for SRF cavities, in the first line of the Nb3Sn, the approach to optimization of cavity shape should be revised. A method of equidistant optimization, offered earlier for traveling wave (TW) cavities is applied to SW cavities. It is shown here that without limitation by magnetic field, the maximal accelerating rate is defined not only by limitations of the electric field but to a significant degree by the cavity shape. For example, for a cavity with the aperture radius of Ra = 35 mm, the minimal ratio of the peak surface electric field to the accelerating rate is about Epk/Eacc = 1.54. So, with the maximal surface field experimentally achieved Epk similar to 125 MV/m, the maximal achievable accelerating rate is about 80 MeV/m even if there are no restrictions by the magnetic field. Optimized cavity shapes with and without limitations by a magnetic field are presented. Another opportunity-optimization for a low magnetic field, is opening for the same material, Nb3Sn, with the purpose of having a high quality factor and increased accelerating rate that can be used for industrial linacs with cryocooler-based cooling scheme.