A Method for High-Precision Characterization of the ${Q}$ -Slope of Superconducting RF Cavities

We propose a novel method for high-precision determination of a quality factor Q
₀
of a superconducting radio-frequency cavity as a function of the strength of the field excited in the cavity, the so-called Q-slope. Usually, the cavity parameters are measured only at resonance for different cavity field strengths, but such a single data point measurement for a given field strength results in a 10%-15% uncertainty in Q
₀
. In contrast, we propose a method that improves the accuracy of Q
₀
determination by an order of magnitude. We vary the phase of an excited stabilized field in the cavity and measure the reflection coefficient of the cavity as a function of the phase. The procedure is repeated for different strengths of the excited field. Given the fact that the complex reflection coefficient of a cavity describes a perfect circle in polar coordinates as a function of the field phase for a constant field strength, we find the coupling coefficient much more accurately by fitting the overdetermined set of measured data to the circle for each value of the cavity field. From the time-decay measurement, which allows least-squares minimization, we accurately find the total (loaded) quality factor and deduce Q
₀
with an uncertainty of around 1%.