Error analysis for intrinsic quality factor measurement in superconducting radio frequency resonators

In this paper, we discuss error analysis for intrinsic quality factor (Q0) and accelerating gradient (Eacc) measurements in superconducting radio frequency (SRF) resonators. The analysis is applicable for cavity performance tests that are routinely performed at SRF facilities worldwide. We review the sources of uncertainties along with the assumptions on their correlations and present uncertainty calculations with a more complete procedure for treatment of correlations than in previous publications [T. Powers, in Proceedings of the 12th Workshop on RF Superconductivity, SuP02 (Elsevier, 2005), pp. 24-27]. Applying this approach to cavity data collected at Vertical Test Stand facility at Fermilab, we estimated total uncertainty for both Q0 and Eacc to be at the level of approximately 4% for input coupler coupling parameter β1 in the [0.5, 2.5] range. Above 2.5 (below 0.5) Q0 uncertainty increases (decreases) with β1 whereas Eacc uncertainty, in contrast with results in Powers [in Proceedings of the 12th Workshop on RF Superconductivity, SuP02 (Elsevier, 2005), pp. 24-27], is independent of β1. Overall, our estimated Q0 uncertainty is approximately half as large as that in Powers [in Proceedings of the 12th Workshop on RF Superconductivity, SuP02 (Elsevier, 2005), pp. 24-27].