Impact of cool-down conditions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>on the superconducting rf cavity quality factor

Many next-generation, high-gradient accelerator applications, from energy-recovery linacs to accelerator-driven systems (ADS) rely on continuous wave (CW) operation for which superconducting radio-frequency (SRF) systems are the enabling technology. However, while SRF cavities dissipate little power, they must be cooled by liquid helium and for many CW accelerators the complexity as well as the investment and operating costs of the cryoplant can prove to be prohibitive. We investigated ways to reduce the dynamic losses by improving the residual resistance (${R}_{\mathrm{res}}$) of niobium cavities. Both the material treatment and the magnetic shielding are known to have an impact. In addition, we found that ${R}_{\mathrm{res}}$ can be reduced significantly when the cool-down conditions during the superconducting phase transition of the niobium are optimized. We believe that not only do the cool-down conditions impact the level to which external magnetic flux is trapped in the cavity but also that thermoelectric currents are generated which in turn create additional flux that can be trapped. Therefore, we investigated the generation of flux and the dynamics of flux trapping and release in a simple model niobium-titanium system that mimics an SRF cavity in its helium tank. We indeed found that thermal gradients along the system during the superconducting transition can generate a thermoelectric current and magnetic flux, which subsequently can be trapped. These effects may explain the observed variation of the cavity's ${R}_{\mathrm{res}}$ with cool-down conditions.