New method to measure the unloaded quality factor of superconducting cavities

We describe a method that measures the unloaded quality factor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>Q</a:mi><a:mn>0</a:mn></a:msub></a:math>, the external quality factor <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>Q</c:mi><c:mi>E</c:mi></c:msub></c:math>, and the cavity detuning <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Δ</e:mi><e:mi>ω</e:mi></e:math> 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 radio frequency 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 overcoupled cavities. A new calibration method addresses very tight tolerances of the method on system parameters.