# Quality Factor Enhancement of 650 MHz Superconducting Radio-Frequency Cavity for CEPC
## 3 Vertical Test after Mid-T Furnace Baking  
Following mid-T furnace baking, the 650 MHz cavity was subjected to HPR and assembled with flanges. Then, it received a vertical test immediately, while the usual low-temperature baking was cancelled. The cavity demonstrated significantly high \(Q_{0}\) at all fields during the vertical test, which is shown in Figure 1. Extremely high \(Q_{0}\) was achieved at low fields, which exceeded 1.0 \(\times\) 10\({}^{11}\). The cavity also exceeded the CEPC vertical test spec of 4.0 \(\times\) 10\({}^{10}\) at 22 MV/m. The \(Q_{0}\) reached 6.3 \(\times\) 10\({}^{10}\) at 31 MV/m, which was much higher than 2.1 \(\times\) 10\({}^{10}\) of EP baseline. There was no field emission during the test, and the cavity quenched at 31.2 MV/m (\(B_{\text{peak}}\) = 131 mT) finally. Furthermore, there was no anti-\(Q\)-slope behavior, which is usual for 1.3 GHz cavities after mid-T baking [1; 2; 3].  
The surface resistance after mid-T furnace baking is depicted in Figure 2, which was remarkably lower than EP baseline. It was about 2.5 n\(\Omega\) at low fields and 4.5 n\(\Omega\) at high fields, which was significantly low and increased slowly as a function of gradient.  
The 650 MHz cavity also received vertical tests at lower temperatures (1.5-2.0 K) to investigate the composition of \(R_{\text{S}}\), which consists of BCS resistance (\(R_{\text{BCS}}\)) and residual resistance (\(R_{\text{res}}\)). The value of \(R_{\text{BCS}}\) increases exponentially as a function of temperature. However, \(R_{\text{res}}\) remains consistent when the temperature increase from 1.5 to 2.0 K [14].  
\[R_{\text{S}}=R_{\text{BCS}}+R_{\text{res}} \tag{1}\]  
\[R_{\text{BCS}}=A\frac{f^{2}}{T}\exp\biggl{(}-\frac{\Delta(T)}{kT}\biggr{)} \tag{2}\]  
Here, \(k\) is the Boltzmann constant, \(T\) is the temperature,\(f\) is the frequency of SRF cavity, 2\(\Delta\) is the energy gap of niobium. \(A\) is the coefficient that depends on the superconducting parameters of niobium, such as mean free path, coherence length and London penetration.  
\(R_{\text{BCS}}\) at 2.0 K (Figure 5) and \(R_{\text{res}}\) (Figure 6) of 650 MHz cavity were calculated according to Equations (1) and (2), and compared with 1.3 GHz cavity, which adopted the same recipe of mid-T furnace baking. \(R_{\text{res}}\) remained <2 n\(\Omega\) at both low and high fields in Figure 6, which is rather low at this frequency. It was less than 1 n\(\Omega\) at low fields. \(R_{\text{BCS}}\) was 2 n\(\Omega\) constantly at low fields, and slightly increased as a function of accelerating gradient above 20 MV/m in Figure 5. The decrease in \(R_{\text{BCS}}\) as a function of accelerating gradient for 1.3 GHz cavity [1; 2; 3] did not appear for 650 MHz cavity. It confirms that mid-T furnace baking could not reverse \(R_{\text{BCS}}\) at the frequency of 650 MHz. Therefore, the anti-\(Q\)-slope behavior cannot be observed at 650 MHz cavity mid-T furnace baked. Similarly, nitrogen doping could not reverse \(R_{\text{BCS}}\) of 650 MHz cavity, either [7; 15].  
Figure 4: Temperature and vacuum curves during mid-T furnace baking.