Minimizing the RF Fields on the Surface of an SRF Cavity by Optimizing its Shape

Accelerating gradients in SRF cavities have consistently been increasing in recent years, largely due to better surface preparation techniques. This makes the critical magnetic eld, at which the cavity loses its superconductivity, a very important limit to address. We worked to minimize the peak magnetic eld Hpk on the surface of the cavity with respect to the acceleration rate Eacc. Allowing the peak electric eld Epk to increase slightly with respect to Eacc was acceptable because the critical magnetic eld is a hard limit that cannot be exceeded, whereas the limiting electric eld at which eld emission starts depends heavily on the surface treatment of the cavity. Previous work used two conjugated elliptical arcs to describe the pro le of a reentrant half-cell of a cavity and to minimize the Hpk/ (42 · Eacc) ratio for Epk/ (2 · Eacc) = 1.2. These two ratios are used to allow for easier comparison with the TESLA cavity, which has values of one for both Hpk/(42 ·Eacc) and Epk/(2 ·Eacc). The optimal shape had an Hpk/ (42 · Eacc) value of 0.9000. We allowed for more intricately shaped cells by using six conjugated elliptical arcs to construct half-cell pro les, and we tried the optimization for Epk/ (2 · Eacc) = 1.2 again with this model. Our best result was a reentrant cavity that had Hpk/ (42 · Eacc) = 0.8950, which showed that using six arcs instead of two causes some improvement to the optimization, but the two arc geometry remains a good approach.