Measurement of the high-ﬁeld Q drop in the TM 010 and TE 011 modes in a niobium cavity

In the last few years superconducting radio-frequency (rf) cavities made of high-purity (residual resistivity ratio > 200 ) niobium achieved accelerating gradients close to the theoretical limits. An obstacle towards achieving reproducibly higher ﬁelds is represented by ‘‘anomalous’’ losses causing a sharp degradation of the cavity quality factor when the peak surface magnetic ﬁeld ( B p ) is above about 90 mT, in the absence of ﬁeld emission. This effect, called ‘‘ Q drop’’ has been measured in many laboratories with single- and multicell cavities mainly in the gigahertz range. In addition, a low-temperature (100–140 (cid:1) C) ‘‘ in situ ’’ baking of the cavity was found to be beneﬁcial in reducing the Q drop. In order to gain some understanding of the nature of these losses, a single-cell cavity has been tested in the TM 010 and TE 011 modes at 2 K. The feature of the TE 011 mode is to have zero electric ﬁeld on the cavity surface, so that electric ﬁeld effects can be excluded as a source for the Q drop. This article will present some of the experimental results for different cavity treatments and will compare them with existing models.


I. INTRODUCTION
A useful technique to investigate the dependence of the surface resistance as a function of the peak surface magnetic field is to excite a single-cell cavity in various resonant modes characterized by different surface field distributions. This provides some insight about the nature and location of the rf losses.
Field emission free superconducting cavities made of bulk niobium show a severe degradation of the quality factor Q 0 at peak magnetic surface fields above about 90 mT. An empirical method that is effective in reducing the Q drop is a low-temperature (100 -140 C) ''in situ'' baking of the cavity in ultrahigh vacuum. The majority of the models that try to describe the Q-drop phenomenon involve a magnetic field effect [1] while a model proposed by Halbritter [2,3] involves an electric field effect. The validity of these models can be tested by measuring a single-cell cavity in the usual TM 010 mode, used for particle acceleration, and in the TE 011 mode which has no electric field on the surface. Using properly designed input and output loop couplers it is possible to excite both modes of the cavity at 2 K under ultrahigh vacuum and therefore allows testing both TE and TM mode under the same conditions of the niobium surface. The results presented in this article include different treatments of the niobium cavity, besides the low-temperature baking, which further test the hypothesis of various Q-drop models. In particular, a thick oxide layer can be formed on the niobium surface by anodization and this should lower the onset field for the Q drop, according to the model of Refs. [2,3]. Postpurification of the niobium cavity improves the thermal conductivity of the material, which should reduce the Q drop if it would be caused by the limited heat transfer from the rf surface to the helium bath, as proposed by the so-called thermal feedback model described in Ref. [4].

A. Experimental setup
The cavity used for this experimental study has the same shape as the one used in the CEBAF accelerator [5]. The main electromagnetic parameters of the TM 010 and TE 011 mode are shown in Table I as calculated with SUPERFISH [6]. The cavity effective area, A eff , represents the surface area where most of the heat due to rf losses is dissipated. It is defined as [7] A eff (1) Figure 1 shows the fields distribution on the cavity surface. The TM 010 mode has high magnetic field in the equator area while the TE 011 mode has high magnetic field on the 0.0586 0.0320 side wall and iris region, where the electric field is high in the TM 010 mode. The input and output loop couplers couple to the magnetic field of the cavity mode. They are inserted in cylindrical side ports close to the cavity irises (Fig. 2). Their size has been determined experimentally by ''trial and error'' and the orientation is such that the plane of the loop is parallel to the cavity equatorial plane. The Q ext of the input coupler is about 2 10 10 for the TM 010 mode and 1 10 10 for the TE 011 mode while the Q ext of the output coupler is about 7 10 10 for the TM 010 mode and 4 10 10 for the TE 011 mode.
The standard cavity preparation for rf test at 2 K consists of the following: (i) ultrasonic degreasing for 20 min; (ii) buffered chemical polishing (BCP) with HNO 3 , HF, H 3 PO 4 (1:1:1) at 25 C removing about 20 m of niobium from the inner cavity surface, after initial removal of about 130 m after the cavity fabrication; (iii) high-pressure rinsing (HPR) with ultrapure water at a pressure of 80 bar for 1 h; (iv) drying overnight in class 10 clean room; (v) assembly of beam pipe niobium flanges with indium wire 1.52 mm thick as gasket and input and output loop couplers in class 10 clean room; (vi) the cavity is attached to a test stand and evacuated to about 10 ÿ8 mbar prior to cool-down to 2 K. Figure 2 shows a picture of the cavity assembled on the test stand. The cavity side ports have Nb55Ti 2 3 4 00 Conflat flanges while the loop couplers have stainless steel Conflat flanges and a copper gasket is used for seal. This design showed to be very reliable, since no leaks were detected in superfluid helium after about 20 thermal cycles from room temperature to 2 K. nitrogen on the cavity outer surface. The TM 010 mode shows a sharp decrease of the quality factor starting at B p 90 mT without field emission while the TE 011 mode shows a smoother drop up to B p 125 mT where the cavity quenched. The quality factor at low field improved in both modes after baking and in the TM 010 mode the maximum field increased up to 124 mT in the absence of field emission but the Q drop is still present. A brief multipacting activity was found at about B p 100 mT in the TM mode. The quality factor at high field in the TE mode improved by baking, most probably due to the reduction of the BCS surface resistance, as will be discussed in Sec. III. The cavity was subsequently baked at higher temperature (120 C, 48 h) but no improvement was obtained in either mode.

B. Measurements with BCP-treated cavity
The low-field (B p 10 mT) surface resistance as a function of the He bath temperature was measured in both modes, before and after baking, and the data were fitted [8] with the sum of the T-independent residual resistance, R res , and the Bardeen-Cooper-Schrieffer (BCS) surface resistance [9]. The fitting parameters were the normal electrons' mean free path, l, the energy gap at 0 K divided by the critical temperature, =kT c , and R res . The critical temperature (T c 9:25 K), coherence length ( 39 nm) and the penetration depth at 0 K ( 32 nm) are considered material constants for niobium. A plot of R s as a function of 1=T for both modes before and after baking at 100 C for about 40 h is shown in Fig. 4. The BCS surface resistance decreased by about 30% in both modes while the residual resistance increased by about 5 n by baking, consistent with previous studies [10 -12].
After the rf tests, the inner surface of the cavity was visually inspected and two ''black spots'' of a millimeter size were seen on the walls, in the area of high magnetic field for the TE mode. Since they were suspected to be the cause of the quenches, they were mechanically ground away with a carbide tool.

Anodization
After a new chemical etching of about 50 m with BCP 1:1:1, the cavity was anodized by filling it with ammonium hydroxide (NH 4 OH) 30% diluted and applying a constant voltage between the cavity (anode) and a niobium rod (cathode) inserted in the cavity. This process grows a niobium pentoxide layer on the cavity surface at a rate of about 2 nm=V [13]. The cavity was processed at 45 V, 1 A (current density of about 1 mA=cm 2 ) until the current dropped to about 100 mA, growing a Nb 2 O 5 layer about 90 nm thick (about 50 times thicker than the natural oxide grown without anodization).
The rf test at 2 K did not show a significant difference from the previous ones: the Q drop starts at about B p 95 mT in both modes. The cavity was baked in the cryostat with hot helium up to 115 C for about 40 h. The maximum field in the TM 010 mode improved by about 16% with some residual Q drop while the TE 011 mode quenched at B p 102 mT. The BCS surface resistance decreased by about 42% in both modes while the residual resistance increased by about 2 n. Figure 5 shows a plot of Q 0 vs B p for both modes before and after baking. The low-field quality factor is lower than usually measured due to higher residual resistance. It was found that the reason for it was a current drift in the power supply of the compensation coil which shields the Earth's magnetic field. The residual field was measured to be about 20 mG, corresponding to about 6 n of additional residual resistance.

Postpurification
One way to increase the quench field of a cavity is to improve the thermal conductivity of the niobium. This can be accomplished by heat treating the cavity in a vacuum furnace at 1250 C in the presence of titanium as a solid state getter material. The treatment followed the recipe developed in Ref. [14]: the temperature is raised to 1250 C in about 4 h and is held for 12 h, allowing the titanium to sublimate and deposit on the niobium cavity. The temperature is then lowered to 1000 C at a rate of ÿ0:2 C= min and the purification of the niobium occurs. After reaching 1000 C, the cool-down to room temperature began and took about 9 h. The maximum pressure was about 10 ÿ4 mbar at 1250 C, decreasing to about 10 ÿ7 mbar before cool-down. The main gas species detected by the residual gas analyzer were hydrogen, nitrogen and water. As an indication of the effectiveness of the process, the residual resistivity ratio (RRR) of a niobium sample was measured before and after the postpurification: it improved from 390 to 720. During the postpurification process, the niobium homogenizes and recrystallizes to large (millimeter-size) grains.
Following postpurification, about 95 m were removed from the inner cavity surface by BCP 1:1:1 and the results of the rf test at 2 K showed about 20% increase in the onset of the Q drop in both modes (110 mT in the TM 010 mode, 120 mT in the TE 011 mode). The cavity was in situ baked with hot helium in the cryostat at 120 C for about 30 h. The test results after baking showed a recovery from the Q drop in both modes but the TE 011 quenched at the same field as before baking (B p 145 mT) while the maximum field in the TM 010 increased by 13% (up to 135 mT). The residual resistance increased 7 n in the TM 010 mode while it did not change in the TE 011 mode. Figure 6 shows the Q 0 vs B p curves at 2 K before and after baking. The cavity was tested again after a new surface preparation and baked afterwards at 115 C for 22 h and the results confirmed the ones shown in Fig. 6.
In a study of the effect of the low-temperature baking [12] it was found that the baking temperature which allows the largest reduction in the BCS surface resistance and a recovery from the Q drop is 120 C. The baking time was kept fixed at 48 h. In this series of tests we reduced the baking time down to 12 h, keeping the temperature at 115-120 C and we found similar reductions of the Q drop for baking time between 12 and 48 h, as shown in Fig. 7. 1 Visentin recently showed that baking at 100 C for only 3 h gives only a marginal improvement of the Q drop [15]. The effect of baking time on the BCS surface resistance is shown in Fig. 8, with larger reduction occurring for baking time up to 48 h and consistent with a previous study by Kneisel at 145 C [10].

III. COMPARISON OF MODELS
The average values of the material parameters, in a 40 nm depth from the niobium surface, before and after baking are shown in Table II. Those values are consistent with the ones reported in Ref. [12] and the strong reduction of the mean free path by baking suggests a diffusion of impurities from the surface towards the bulk as the main process occurring during bakeout. The reduction of the BCS surface resistance is accomplished by the reduction of the mean free path and the slight increase (about 6%) of =kT c . The causes for the increases of =kT c and of R res are not yet clear. A possible explanation for the higher R res could be the enhancement of the metal/oxide interface losses, as proposed by Halbritter [16], or an increase of magnetic impurities as indicated in Ref. [17]. The reduction of the mean free path by baking indicates that the surface resistance changes from clean (l > ) to dirty (l < ) limit and therefore the development of a theoretical treatment of the BCS surface resistance at low temperature (T=T c < 0:23) and high rf field (B rf =B c > 0:5) as a function of the mean free path could be very useful, as already pointed out in Ref. [4].
Regarding the high-field losses, the most important experimental evidence shown here is given by the presence of the Q drop and its elimination by baking in the TE 011 mode, where only magnetic field is present on the cavity surface. In the following, the experimental results are compared with different Q-drop models.

A. Thermal feedback model
A possible explanation for the Q drop is the so-called thermal feedback model (TFBM), outlined in detail in Ref. [4]. According to this model, the Joule heating generated at the cavity inner surface due to the rf field cannot be completely dissipated in the He bath, due to the limited thermal conductivity of the niobium and of the Kapitza resistance at the Nb=He interface. Consequently, the BCS surface resistance increases, due to its exponential dependence on temperature, causing even higher dissipated power and such positive feedback lowers the quality factor and ultimately causes a thermal breakdown of the cavity. As part of the model, an intrinsic increase of the BCS surface resistance at higher field due to pair-breaking effects is introduced. Figure 9 shows a plot of Q 0 vs B p for both TE 011 and TM 010 data before postpurification and baking, compared with the prediction of the TFBM model   with and without the nonlinear pair-breaking correction to the BCS surface resistance. The thermal conductivity and Kapitza resistance of RRR 300 niobium were taken from Refs. [4,18], respectively. Figure 9 shows that the TFBM model does not predict the Q drop in the TM mode, while it describes it well in the TE mode, without the nonlinear contribution. Therefore, the Q drop in the TE mode before postpurification is due most likely to ''global heating'' because of the higher frequency than in the TM mode (R s / f 2 ) and its reduction by baking (Fig. 3) could be due to the lower BCS surface resistance. On the other hand, the Q drop cannot be described by the TFBM with higher thermal conductivity after postpurification as shown in Fig. 10. The thermal conductivity and Kapitza resistance of RRR 700 niobium were taken from Refs. [4,19], respectively. The fact that the nonlinear BCS does not describe well the experimental data for the TE mode indicates that the frequency dependence of the pair-breaking term might be overestimated, as suggested also by data on cavities at 3.9 GHz [4].

B. Magnetic field enhancement model
Another model which tries to explain the cause of the Q drop is the so-called magnetic field enhancement model (MFE), described in detail in Ref. [7]. The model considers the geometric magnetic field enhancement caused by sharp corners, especially at grain boundaries, on the cavity surface. The edge of a grain boundary can become normal conducting because the local magnetic field, enhanced by a factor m , exceeds the thermodynamic critical field. This causes a progressive reduction of the quality factor as more boundaries become normal conducting at higher fields.
The grain boundary size (taken to be 50 m and 1 mm before and after postpurification, respectively), the center of the distribution of field enhancement factors, 0 , and the width of the distribution, , are parameters of the model. The values of 0 and obtained from a fit of the model with the TM and TE mode data are shown in Table III and they are consistent with the ones reported in Ref. [7]. Although the model describes well the data before baking, as shown in Fig. 11, the reduction of Q drop by baking would be explained by a decrease of the geometric field enhancement factor, which could be hardly justified since the baking temperature is low enough to cause any change of the surface topography.  trons between conduction levels in the metal and localized states for sufficiently high electric fields. This additional contribution to the surface resistance at high fields, R E s , has an exponential dependence to the peak surface electric field:

C. Interface tunnel exchange model
where b is proportional to the oxide thickness and the density of localized states, c depends on tunneling distance, energy gap, dielectric constant and a field enhancement factor. E 0 is the onset field for the Q drop. The average values of b, E 0 , and c obtained from a fit of the data for the TM 010 mode before and after baking for different cavity treatments are shown in Table IV. The values of c and E 0 are consistent with those reported in Ref. [12] and the exponential dependence well describes the data, as shown in Fig. 12.

IV. DISCUSSION
The data presented in this contribution show that the Q drop is present in the TE 011 mode, which has zero electric field on the surface, as well as in the TM 010 mode and that the presence of an oxide layer much thicker than the one formed naturally by the oxidation of niobium in air does not change significantly the onset of the Q drop. These results are in contradiction with the predictions of the ITE model. Furthermore, recent experimental data show that the Q drop does not reappear in a baked cavity after the oxide layer is stripped by HF treatments and a new one is formed [15]. Therefore there is sufficient experimental evidence to indicate that the Q drop is not caused by the niobium oxide layer.
The TFBM does not provide a good description of the experimental data at high field, as shown also in Ref. [4]. The MFE model is in good agreement with the data but does not provide a physical explanation for the reduction of the Q drop by baking or the presence of the Q drop on cavity with much smoother surfaces, such as those treated by electropolishing [20] or made of single crystal [21].
The dependence of the material parameters on the baking time and temperature suggest an impurity diffusion process occurring during bakeout. The only impurity present in noticeable quantities in niobium which has a diffusion length comparable to the rf penetration depth for the usual baking parameters is oxygen. New models [22,23] link the presence of interstitial oxygen near the metal/oxide interface to a reduction of the surface barrier, allowing fluxons to penetrate at a reduced lower critical field, B c1 . Baking would allow a redistribution of oxygen, creating a more uniform ''contaminated'' layer with higher B c1 . Rabinowitz [24] was able to estimate the power loss due to a single isolated fluxoid trapped near the surface of a superconductor in the presence of rf field. He predicts an exponential dependence of the surface resistance on the peak magnetic field, above the onset of flux penetration, which well describes the experimental data. The data also show that the onset of the Q drop in the TE mode is higher than in the TM mode and this is compatible with the hypothesis of delayed flux penetration by the higher frequency of the rf field [25].

V. CONCLUSIONS
The experimental results presented in Sec. II show that high-field losses characterized by a sudden exponential increase of the surface resistance as a function of the peak surface magnetic field, in absence of field emission, are present both in the TM 010 mode as well as in the TE 011 mode, under the same surface conditions. This suggests that the magnetic, rather than the electric field is responsible for the additional losses. The data cannot be described by a ''global'' uniform heating of the surface (TFBM model). This became clear for the TE 011 mode also once the thermal conductivity of the niobium was improved by postpurification. Other models (ITE and MFE) provide good numerical description of the data but lack a good physical explanation for some of the results such as the drastic reduction of the Q drop by baking and the presence of the Q drop in the TE 011 mode. Models based on reduced surface barrier by oxygen contamination seem promising to explain the Q drop and the baking effect but need further experimental and theoretical investigation.