High field $Q$ slope and the baking effect: Review of recent experimental results and new data on Nb heat treatments

The performance of superconducting radio-frequency (SRF) cavities made of bulk Nb at high fields (peak surface magnetic field greater than about 90 mT) is characterized by exponentially increasing rf losses (high-field $Q$ slope), in the absence of field emission, which are often mitigated by low-temperature ($100–140°\mathrm{C}$, 12–48 h) baking. In this contribution, recent experimental results and phenomenological models to explain this effect will be briefly reviewed. New experimental results on the high-field $Q$ slope will be presented for cavities that had been heat treated in a vacuum furnace at high temperature without subsequent chemical etching. These studies are aimed at understanding the role of hydrogen on the high-field $Q$ slope and at the passivation of the Nb surface during heat treatment. Improvement of the cavity performances, particularly of the cavities’ quality factor, have been obtained following the high-temperature heat treatments, while secondary ion mass spectroscopy surface analysis measurements on Nb samples treated with the cavities revealed significantly lower hydrogen concentration than for samples that followed standard cavity treatments.

Figure 1

Typical $Q_0(B_p)$ curve of a bulk Nb cavity limited by the $Q$ drop fitted with Gurevich and Weingarten models. The data are from a CEBAF single-cell cavity (1.47 GHz) measured at 1.4 K [10].

Figure 2

Atomic oxygen concentration profile as a function of depth into Nb below the oxide layer, measured using x-ray diffuse scattering on a single-crystal Nb sample before and after baking. The figure is taken from Ref. 17.

Figure 3

Vortex pinned by a chain of defects near the surface. The solid line shows the equilibrium vortex shape due to competition of pinning and image attraction forces. The dashed lines show instantaneous vortex profiles for $B(t)=B_p$ and $B(t)=-B_p$, between which the vortex line oscillates. The figure is taken from Ref. 18.

Figure 4

Trajectory $u(t)$ of a vortex entering the surface at $B_p=B_v$ during one rf period. The dashed line shows the trajectory of an antivortex entering the surface at $-B_p=-B_v$. The figure is taken from Ref. 18.

Figure 5

In black, average conductance curves of EP (top) and vacuum baked (bottom) Nb samples, shifted for greater clarity. In red are fits with Shiba theory. Inset: Corresponding Shiba density of states. The figure is taken from Ref. 24.

Figure 6

Hydrogen outgassing vs temperature measured on Nb samples ($\mathrm{RRR}\sim 590$) after various treatments. The black curve refers to the “as received” sample, the blue curve is after $200\mu \mathrm{m}$ removal by BCP, the magenta curve is after additional vacuum heat treatment at $600°\mathrm{C}$ for 10 h, and the green curve is after additional $20\mu \mathrm{m}$ removal by BCP. The figure is taken from Ref. 31.

Figure 7

Hydrogen concentration as a function of depth from the surface of Nb samples prepared by BCP, before and after low-temperature baking in UHV, as measured by NRA. The figure is taken from Ref. 10.

Figure 8

$Q_0$ vs $B_p$ measured at 1.7 K after the baseline test (empty squares), after storing the cavity in air for four months and filling with ${\mathrm{H}}_2$ at 1 atm for 11 h (red triangles), after baking twice in ${\mathrm{H}}_2$ at 1 atm at $120°\mathrm{C}$ for 12 h (blue squares), after heat treatment at $600°\mathrm{C}$ for 10 h in UHV (green diamonds), and after baking at $120°\mathrm{C}$ for 12 h in UHV (empty diamonds). The arrows indicate the quench fields in the various tests. There was no field emission in any of the tests.

Figure 9

“Unfolded” temperature maps at 1.7 K at the highest field achieved in the high-power rf tests of a large-grain CEBAF single-cell cavity ($Q_0$ vs $B_p$ data shown in Fig. 8) after storing in air for four months and filling with ${\mathrm{H}}_2$ at 1 atm for 11 h (a), after baking twice in ${\mathrm{H}}_2$ at 1 atm at $120°\mathrm{C}$ for 12 h (b), after heat treatment at $600°\mathrm{C}$ for 10 h in UHV (c), and after baking at $120°\mathrm{C}$ for 12 h in UHV (d). Note the different $\Delta T$ scales. Strong hot spots causing the $Q$ drop are visible in (c). Sensors No. 1 and 16 are located at the top and bottom iris of the cavity, respectively, while the equator weld is between sensors No. 8 and No. 9.

Figure 10

Partial pressure of the residual gases and temperature profile during the $600°\mathrm{C}/10\mathrm{h}$ heat treatment.

Figure 11

Nitridization cart holding a semiconductor grade nitrogen gas bottle, pressure regulator, and needle valve connected to the high-temperature vacuum furnace used for the cavity heat treatments.

Figure 12

Partial pressure of the residual gases and temperature profile during the cavity heat treatment. Nitrogen was injected into the furnace at $400°\mathrm{C}$ for 15 min.

Figure 13

$Q_0$ vs $B_p$ measured at 1.7 K on a large-grain CEBAF single-cell cavity after the baseline test (squares) and after the $800°\mathrm{C}/3\mathrm{h}$, $400°\mathrm{C}/20\min$ with $1\times {10}^{-5}\mathrm{mbar}$ ${\mathrm{N}}_2$ injection heat treatment (triangles). The round symbols are the data after additional in situ baking at $120°\mathrm{C}$ for 12 h.

Figure 14

$Q_0$ vs $B_p$ measured at 2.0 K on a large-grain CEBAF single-cell cavity after two cycles of tests consisting of a baseline, established with BCP, and a heat treatment. “Heat treatment 2” consisted of the same process shown in Fig. 12 with the addition of holding the furnace at $120°\mathrm{C}/6\mathrm{h}$ before final cooldown to room temperature. “Heat treatment 3” consisted of the same process shown in Fig. 12 but without ${\mathrm{N}}_2$ injection.

Figure 15

Unfolded temperature maps at 2.0 K at the highest field achieved in the high-power rf tests of a large-grain CEBAF single-cell cavity after baseline tests 2 (a) and 3 (c) and after heat treatments 2 (b) and 3 (d). Note the different $\Delta T$ scales. Large hot spots present in the baseline tests are greatly reduced after heat treatments. Sensors No. 1 and 16 are located at the top and bottom iris of the cavity, respectively, while the equator weld is between sensors No. 8 and No. 9.

Figure 16

$Q_0$ vs $B_p$ measured at 2.0 K on a “rolled” single-crystal ILC single-cell cavity after the baseline test (squares) and after the heat treatment (triangles) at $800°\mathrm{C}/3\mathrm{h}$, $400°\mathrm{C}/20\min$ with $1\times {10}^{-5}\mathrm{mbar}$ ${\mathrm{N}}_2$ injection, $120°\mathrm{C}/6\mathrm{h}$. The round symbols are the data after additional in situ baking at $120°\mathrm{C}$ for 48 h.

Figure 17

$Q_0$ vs $B_p$ measured at 2.0 K on the fine-grain ILC single-cell cavity “AES001” after the baseline test (squares) and after the heat treatment (triangles) at $800°\mathrm{C}/3\mathrm{h}$, $400°\mathrm{C}/20\min$. The round symbols are the data after additional in situ baking at $120°\mathrm{C}$ for 24 h.

Figure 18

$Q_0$ vs $B_p$ measured at 2.0 K on a large-grain ILC single-cell cavity after the baseline test (squares) and after the heat treatment (circles) at $800°\mathrm{C}/3\mathrm{h}$, $120°\mathrm{C}/12\mathrm{h}$.

Figure 19

SIMS reduced data depth profile for the heat treated sample L16. The heat-treatment parameters are $800°\mathrm{C}/3\mathrm{h}$, $400°\mathrm{C}/20\min$ with ${\mathrm{N}}_2$, $120°\mathrm{C}/6\mathrm{h}$ (see Table ).

Figure 20

SIMS reduced data depth profile for control sample L14.

Figure 21

SIMS reduced data depth profile for the heat treated sample L10. The heat-treatment parameters are $800°\mathrm{C}/3\mathrm{h}$, $400°\mathrm{C}/20\min$ (see Table ).

Figure 22

SIMS mass spectrum of heat treated sample L10.

Figure 23

SIMS mass spectrum of control sample L14.

Figure 24

SIMS reduced data depth profile for sample L8 ($800°\mathrm{C}/3\mathrm{h}$, $120°\mathrm{C}/12\mathrm{h}$).

Figure 25

SIMS reduced data depth profile for the fine-grain heat treated sample F3. The heat-treatment parameters are $800°\mathrm{C}$ $3\mathrm{h}/400°\mathrm{C}$ 20 min (see Table ).

Figure 26

SIMS reduced data depth profile for the heat treated sample L5. The heat-treatment parameters are listed in Table .

Figure 27

SIMS reduced data depth profile for sample L7 (identical to L5) after additional $120°\mathrm{C}/48\mathrm{h}$ baking.

Figure 28

SIMS reduced data depth profile for electropolished sample EP1.