Abstract
Recent studies by Romanenko et al. revealed that cooling down a superconducting cavity under a large spatial temperature gradient decreases the amount of trapped flux and leads to reduction of the residual surface resistance. In the present paper, the flux expulsion ratio and the trapped-flux-induced surface resistance of a large-grain cavity cooled down under a spatial temperature gradient up to $80\text{ }\text{ }\mathrm{K}/\mathrm{m}$ are studied under various applied magnetic fields from 5 to $20\text{ }\text{ }\ensuremath{\mu}\mathrm{T}$. We show the flux expulsion ratio improves as the spatial temperature gradient increases, independent of the applied magnetic field: our results support and enforce the previous studies. We then analyze all rf measurement results obtained under different applied magnetic fields together by plotting the trapped-flux-induced surface resistance normalized by the applied magnetic field as a function of the spatial temperature gradient. All the data can be fitted by a single curve, which defines an empirical formula for the trapped-flux-induced surface resistance as a function of the spatial temperature gradient and applied magnetic field. The formula can fit not only the present results but also those obtained by Romanenko et al. previously. The sensitivity ${r}_{\mathrm{fl}}$ of surface resistance from trapped magnetic flux of fine-grain and large-grain niobium cavities and the origin of $dT/ds$ dependence of ${R}_{\mathrm{fl}}/{B}_{a}$ are also discussed.
Highlights
The superconducting radio-frequency (SRF) cavity is one of the core components of the present and the future particle accelerators [1]
Recent studies by Romanenko et al revealed that cooling down a superconducting cavity under a large spatial temperature gradient decreases the amount of trapped flux and leads to reduction of the residual surface resistance
We show the flux expulsion ratio improves as the spatial temperature gradient increases, independent of the applied magnetic field: our results support and enforce the previous studies
Summary
The superconducting radio-frequency (SRF) cavity is one of the core components of the present and the future particle accelerators [1]. One of the parameters that describe the performance of an SRF cavity is the unloaded quality factor, Q0, which is defined by the ratio of the stored energy to dissipation per rf cycle. The definition of Q0 is reduced to the simple relation, Q0 1⁄4 G=Rs, where G ∼ Oð102Þ Ω is the so-called geometrical factor, determined by the cavity geometry, and Rs is the microwave surface resistance of the inner surface of the cavity. The surface resistance Rs consists of two parts: the Bardeen-Cooper-Schrieffer (BCS) resistance RBCS and the residual surface resistance Rres [1,2]. The former comes from microwave absorption by the excited quasiparticles.
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