Design optimization, commissioning, and uncertainty analysis of the quadrupole resonator system at Jefferson Lab for SRF material characterization
A quadrupole resonator (QPR) provides a sample-based platform for characterizing materials for superconducting radio-frequency (SRF) applications under controlled field, frequency, and temperature conditions. This paper presents the design optimization, commissioning, and validation of the Jefferson Lab QPR system, including a quantitative assessment of measurement uncertainty. The resonator geometry was re-optimized from the CERN version-II design to improve quadrupole-mode separation and enable four usable modes at 400, 806, 1221, and 1640 MHz. The measurement system combines self-excited-loop RF operation, cable-loss-corrected power calibration, decay-based external-Q calibration, and RF-DC thermal-substitution calorimetry to determine the peak surface magnetic field Bpk and sample surface resistance Rs. Commissioning measurements on bulk Nb and Nb3Sn-Ta-Cu samples validated the system response over a broad range of frequency, temperature, and RF field. The extracted superconducting energy-gap parameters are consistent with the reported values for Nb and Nb3Sn, as well as with those obtained from single-cell cavity measurements. The commissioned system operates from 1.8 K to near the superconducting transition temperature of the sample, with accessible Bpk values from approximately 5 mT to a sample- and temperature-dependent heater-power-budget limit; a maximum field of 60 mT was demonstrated for bulk Nb at 400 MHz and 4 K. The combined relative standard uncertainties are 8.3% for Bpk and below 18% for Rs when r = PDC2/PDC1 is less than 0.9. The worst-case Bpk resolution at the 95% confidence level is approximately 1.35 mT, while the Rs resolution is below 1 nOhm at 10 mT and 2 K. These results establish the JLab QPR as a calibrated, multi-frequency platform with quantified measurement uncertainty for SRF material characterization.