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Inductance is a key parameter when optimizing the performance ofsuperconducting quantum interference device (SQUID) magnetometers made from thehigh temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) because lowerSQUID inductance $L$ leads to lower flux noise, but also weaker coupling to thepickup loop. In order to optimize the SQUID design, we combine inductancesimulations and measurements to extract the different inductance contributions,and measure the dependence of the transfer function $V_{\Phi}$ and flux noise$S_\Phi^{1/2}$ on $L$. A comparison between two samples shows that the kineticinductance contribution varies strongly with film quality, hence makinginductance measurements a crucial part of the SQUID characterization. Thanks tothe improved estimation of the kinetic inductance contribution, previouslyfound discrepancies between theoretical estimates and measured values of$V_{\Phi}$ and $S_\Phi^{1/2}$ could to a large extent be avoided. We then usethe measurements and improved theoretical estimations to optimize the SQUIDgeometry and reach a noise level of $S_B^{1/2}$ = 44 fT/$\sqrt{\textrm{Hz}}$for the best SQUID magnetometer with a 8.6 mm $\times$ 9.2 mm directly coupledpickup loop. Lastly, we demonstrate a method for reliable one-time sensorcalibration that is constant in a temperature range of several kelvin despitethe presence of temperature dependent coupling contributions, such as thekinetic inductance. The found variability of the kinetic inductancecontribution has implications not only for the design of YBCO SQUIDmagnetometers, but for all narrow linewidth SQUID-based devices operated closeto their critical temperature.

The role of kinetic inductance on the performance of YBCO SQUID magnetometers