A new method to measure the unloaded quality factor of superconducting cavities

We describe an method that measures the unloaded quality factor $Q_0$, the external quality factor $Q_E$, and the cavity detuning $\mathrm{\Delta }\omega$ with a recursive least-squares algorithm. It combines a large number of consecutive measurements to successively improve an estimate of fit parameters that asymptotically converges to the ``real’’ values. Exploiting the large amount of data acquired by a digital low-level RF system permits us to reach this asymptotic regime in a moderate time frame of seconds to minutes. Simulations show that the method works both for critically coupled and over-coupled cavities. A new calibration method adresses very tight tolerances of the method on system parameters.