Dependence of trapped-flux-induced surface resistance of a large-grain Nb superconducting radio-frequency cavity on spatial temperature gradient during cooldown through $T_c$

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 $80\mathrm{K}/\mathrm{m}$ are studied under various applied magnetic fields from 5 to $20\mu \mathrm{T}$. 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.

Figure 1

Experimental setup: A 1.5 GHz single cell cavity located on test stand (a), its front view (b), and top view (c). Red filled circles and black rectangular symbols represent temperature sensors and magnetometers, respectively.

Figure 2

Examples of measured temperatures and magnetic flux densities as functions of time during a cooldown process, where the applied magnetic field is $\sim 5\mu \mathrm{T}$. The horizontal dashed line indicates the critical temperature of Nb, $T_c=9.25\mathrm{K}$.

Figure 3

Model of the temperature gradients at the phase transition front along the curved cavity wall.

Figure 4

The flux expulsion ratio ${\epsilon }_{\mathrm{eq}}$ as a function of the cooling rate (a), the inverse of the propagation speed of the phase transition front (b) and the temperature gradient (c) when the NC-SC phase transition front arrives at the equator under various applied magnetic fields. The definition of ${\epsilon }_{\mathrm{eq}}$ is given by Eq. (2).

Figure 5

The $R_{\mathrm{fl}}$ normalized by an applied field $B_a$ as a function of $dT/ds$. The red solid curve represents the fitting curve given by Eq. (7).

Figure 6

The sensitivity $r_{\mathrm{fl}}$ of cavities made of fine-gain and large-grain niobium with different surface treatments.

Figure 7

The magnetic flux trapping ratio ${\tau }_{\mathrm{eq}}(=1-{\epsilon }_{\mathrm{eq}})$ and $R_{\mathrm{fl}}$ normalized by an applied field as functions of the reciprocal of $dT/ds$ for all the data shown in Table 1.