Geng, R

Padamsee, H

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ON THE LOW-FIELD Q-SLOPE OF RF SUPERCONDUCTING NIOBIUMCAVITIES COOLED BY HELIUM-IR. L. Gengy , H. PadamseeLaboratory of Nuclear Studies, Cornell University, Ithaca, NY 14850, USASRF011212-10AbstractExperimental measurements have consistently shownthat RF superconducting Niobium cavities cooled by He-I exhibit a mild Q-slope starting at very low gradients.This Q-slope has been attributed to a BCS resistance in-crease resulted from the Kapitza impedance across the in-terface between the exterior surface of Niobium cavitiesand liquid Helium. Thermal modeling of Niobium cavi-ties is performed in this paper, detailing the role of Kapitzaimpedance. Our results show that Kapitza impedance playsan insignificant role in this low-field Q-slope. Experimen-tal results are also presented, showing the surface treatmenthas a strong effect on the low-field Q-slope. We concludethat this low-field Q-slope is intrinsic to the material prop-erties of the RF surface of Niobium.1 INTRODUCTIONVertical tests of 500 MHz and 508 MHz Niobium cavi-ties at 4.2 K cooled by He-I at Cornell and KEK have con-sistently shown that these cavities exhibit a mild Q-slope(Q is referred to as the unloaded quality factor), starting atvery low gradients. An example of such a Q-slope is shownin Fig. 1 which depicts the vertical test results of four Nio-bium cavities manufactured for KEK-B factory [1].10810910100 5 10 15 20Cavity#5 (LA)Cavity#6 (LB)Cavity#8 (LD)Cavity#7 (LC)Q0Eacc [MV/m]Figure 1: Test results of KEK-B 508 MHz Niobium cavi-ties at 4.2 K in a vertical cryotstat. Q0starts dropping atvery low gradients, where x-ray is not detected.Work supported by the National Science Foundationy rg58@cornell.eduApparently, this mild Q-slope is not attributable to load-ing by field emission electrons, which arise only above athreshold gradient and usually result in a much steeper Q-drop. The field emission onset gradient for Cornell cavitieswas in the range of 6 - 10 MV/m. Above this thresholdgradient, significant x-rays are detected and Q0quickly de-viates from the low-field Q-slope.In case the loading by field emission electrons is not aconcern, the unloaded quality factor Q0is directly relatedto the surface resistance RsthroughQ0=GRs; (1)where G, the geometry factor of the cavity, is dependentonly on the geometry of the resonator. It has been wellestablished that RF surface resistance is composed of twoparts, namely the BCS resistance RBCSand residual resis-tance Rres[2].Rs= RBCS+Rres: (2)As will be seen in Section 2, the surface surface resis-tance of Niobium at 4.2 K and 500 MHz is dominated bythe BCS component. From Eq. 1 and 2, it is evident thatany Q drop is readily to be interpreted as an increase inRBCS.However, our current understanding indicates that theBCS resistance of Niobium is not explicitly dependent onthe strength of the RF field. Therefore it has long beenbelieved [3] that the observed Q-slope in Niobium cavi-ties is a secondary thermal effect due to RF heating of theNiobium surface. One hypothesis correlates the Q-slope tothe Kapitza impedance across the Niobium and liquid He-lium interface: When the field gradient is increased, the in-creased heat flux across the Niobium-Helium interface re-sults in an elevated temperature on the RF surface of Nio-bium and lead to a decreasing Q. This hypothesis seemsto be reasonable but has not been seriously checked in thepast.In Section 4 and 5, a 500 MHz Cornell type Niobiumcavity is numerically modeled with special attention paidon the role of the Kapitza impedance. Our results do notsupport the above hypothesis and show that the effect ofthe Kapitza impedance alone can not account for the lowfield Q-slope of 500 MHz range Niobium cavities.In Section 6, experimental results are presented for cav-ities with different surface treatment. These results showthat the low-field Q-slope of Niobium cavities is intrinsi-cally coupled to the material properties of the RF surfaceof Niobium.In conclusion, we demonstrate that a field-dependentBCS resistance seems to be unavoidable to fully accountthe low-field Q-slope of 500MHz range Niobium cavitiescooled by He-I.2 SURFACE RESISTANCEIn the frame work of the BCS theory, the BCS resis-tance of RF superconductors depends on material prop-erties, temperature and frequency of RF fields. For thetemperature range of < 4.6 K and frequency range of< 1000 GHz, BCS resistance of Niobium can be formu-lated asRBCS= Af2Te kT; (3)where  is the energy gap, k is Boltzmann constant, T istemperature, and f is RF frequency. The constant A de-pends on material properties, such as the Fermi velocity,the London penetration depth, the coherence length, andthe mean free path of electrons. Computer programs, suchas SRIMP [4], are available for computing the BCS resis-tance of materials at known temperatures and RF frequen-cies.Common sources of the residual resistance Rres, whichis temperature independent, include trapped magnetic flux,material impurities, and surface contaminants. Measure-ments of 500 MHz cavities at lower temperatures haveplaced the residual resistance of RRR250 Niobium in theneighborhood of 10 n for a residual earth magnetic fieldlevel of about 5 Tesla (50 mGauss).Measurements at 4.2 K show that the unloaded qualityfactor ranges from 2 - 4109 at low gradients, which trans-lates into a BCS resistance in the range of 60 - 120 n. Asa result, the surface resistance of Niobium at 500 MHz isdominated by the BCS component at 4.2 K. Hence the ob-served mild Q-slope for 500 MHz range Niobium cavitiesat 4.2 K is relevant to the BCS resistance only. This isfurther justified by the fact that Q0virtually does not dropwhen the same cavity is tested at lower temperatures, wherethe residual resistance dominates over the BCS resistance.3 KAPITZA IMPEDANCE FOR HE-IBecause of the f2 dependence of the BCS resistance,500 MHz range Niobium cavities have been chosen to op-erate at 4.2 K. At this temperature, liquid Helium is in astate called He-I at saturated vapor pressure.For a heat flux of 50 - 104 W/m2 across the solid andHe-I interface, cooling process is characterized as the socalled nucleate boiling regime [5]. Across the interface be-tween the Niobium and liquid Helium, there exists a tem-perature jump, which correlates to the heat flux q throughthe Kapitza conductanceHk,q = Hk(T   Tb): (4)The inverse of the Kapitza conductance is called Kapitzaimpedance. A conservative empirical fit for Kapitza con-ductance of He-I exists [6],Hk= 104(T   TB)1:5: (5)4 THERMAL MODELINGIn this paper, the thermal behavior of a 500MHz Cornelltype cavity is modeled with the aid of the commercial codeANSYS [7] and home developed code HEAT [9].In the ANSYS model, the full cavity is accounted in atwo dimensional cylindrical coordinate system as depictedin Fig. 2.Figure 2: The two dimensional ANSYS model of the500MHz Niobium cavity.The heating effect on the RF surface of the cavity is real-ized through a convective boundary condition, which takesinto account the temperature dependence of the BCS resis-tance. A detailed description of this scheme can be foundin Ref. [8]. The cooling provided by He-I is also mod-eled as a convective boundary condition, with the Kapitzaconductance directly plugged into the code.In the HEAT model, only the most critical section of thecavity, namely the equator region, is considered. This re-sults in a slab of Niobium with circular geometry. For ther-mal calculations of Niobium free of defects, lateral heattranspotation is disabled. Detailed description of the HEATmodel can be found in Ref. [9].1010010001 10Thermal Conductivity [W/m/K]T[K]Figure 3: Thermal conductivity used in modeling forRRR250 Niobium [10].The thermal conductivity of Niobium as a function oftemperature is formulated in Eq. 6 after curve fitting theexperiment data obtained from [10] for RRR250 material(see Fig. 3).kNb(T ) = 261:92  183:72T + 39:9T2  1:794T3: (6)5 EFFECT OF KAPITZA IMPEDANCEModeling results are shown in Fig. 4, together with theexperiment results of the corresponding Niobium cavity.10810910100 2 4 6 8 10 12 14Q0Eacc[MV/m]ExperimentANSYSHEATFigure 4: The quality factor of a 500 MHz Niobium cavityas calculated by ANSYS and HEAT models, together withthe measurement results. There exists a large discrepancybetween calculation and measurement results .Both the ANSYS and HEAT results show that the qual-ity factor of the cavity drops with increasing field gradients.But the amount of Q-drop is much less than the experimen-tally observed one. The HEAT model somehow gives amore pronounced Q-drop compared to the ANSYS results.This is attributable to the fact that lateral heat transfer indisabled in the HEAT model.It is well known that the Kapitza conductance may varyby a factor of as much as 10 depending on factors like,among others, surface roughness and surface orientationwith respect to the gravitational force. Further ANSYSmodeling is therefore conducted to check the modeling tol-erance to the Kapitza conductance.Fig. 5 shows modeling results with various Kapitza con-ductance, from which one can see that the observed Q-slope is reproduced only when modeling with a Kapitzaconductance 50-100 times lower than the canonical values(which is already a conservative fitting of the low end ofexperimental data).It is evident that even with the factors such as surfaceroughness or orientation is taken into account, the low-fieldQ-slope can not be solely explained by the effect of theKapitza impedance.10810910100 2 4 6 8 10 12 14 16Q 0Eacc[MV/m]ANSYS, Hk=10000(Ts-Tb)^1.5ANSYS, Hk=200(Ts-Tb)^1.5ANSYS, Hk=100(Ts-Tb)^1.5Experiment BB1-4 after bakeFigure 5: Modeling results with various Kapitzaimpedance. The measured mild Q-slope is reproduced onlywhen modeling with a Kapitza conductance 50-100 timeslower than the canonical values.6 EFFECT OF SURFACE TREATMENTAs shown in Section 5, the effect of the Kapitzaimpedance attributes only a part to the low-field Q-slope.We will show in this section that the major contributionto the Q-slope arises from the material property of the RFlayer of Niobium.Fig. 6 depicts experimental results of Cornell and KEKtype cavities, which are subjected to different surface treat-ments. Here the unloaded quality factor is drawn againstthe peak magnetic field for comparison purposes for thefollowing reasons: 1) The definition of the peak RF field isunique (as is not for the definition of the accelerating gradi-ent); 2) The magnetic field is more relevant than the electricfield when discussing losses of the RF surface. It is evident10810910100 100 200 300 400 500 600 700 800KEK-B Cavity#7 (LC)Cornell BB1-4Cornell BB1-6Cornell-SRRCBB1-4 after bakeQ0Peak Magnetic Field [Oe]Figure 6: The measurement results for cavities with differ-ent surface treatment. There is a strong effect of surfacetreatment on the low-field Q-slope.that the low-field Q-slope is different for the two class ofcavities. Cornell type cavities exhibit a milder Q-slope ascompared to the KEK type cavities. It is also shown thatbaking at 140 C has some effect on the Q-slope for Cor-nell cavities.The material used for manufacturing Cornell cavities isRRR250 sheet Niobium with a thickness of 3 mm, andRRR200 with a thickness of 2.5 mm for KEK-B cavities.The thermal impedance due to the wall thickness for thesecavities is estimated to be just about the same (note theproportionality between Niobium thermal conductivity andRRR). For this reason, the difference in the low-field Q-slope for these two class of cavities lies in nowhere but thedifference in the material property of the Niobium RF sur-face due to different surface treatment.Cornell Cavities are etched with BCP1:1:2 for a surfaceremoval of 120 m followed by high pressure water rinsing(HPR) for about 100 minutes. KEK cavities are preparedin a more involved manner [11] [12] [13]: Electropolish-ing for a surface removal of 80 m; Degassing at 700 Cfor 1.5 hours; Electropolishing for another 15 m of sur-face removal followed by rinsing with 3 ppm ozonized wa-ter (OWR); Baking at a temperature of 80 - 140 C prior totest. It is believed that the Niobium RF surface of KEK cav-ities is covered with a dense and uniform layer of Nb2O5due to ozonized water rinsing [14].For the convenience of comparison, we adopt anexponent-law formalism eHpk to quantify the field de-pendent of Q0. Hpk, in Oe, is the peak magnetic field. Theincrease of 1Q0, or the modified surface resistance Rs=G,as a function of the field amplitude is then proportional toeHpk. A steeper Q-slope is characterized by a larger fielddependent factor , which has a dimension of Oe 1.Table 1 lists the field dependent factors for cavities withdifferent treatment. The cavity labeled as KEK-B #7 LC isone out of the latest batch of Niobium cavities for the KEKB Factory. All the four cavities of this batch show the samefield dependent characteristics as can be seen from Fig. 1.The cavity labeled as Cornell BB1-4 is a Niobium cavityfor the upgrade of Cornell Electron-positron Storage Ring(CESR). This cavity was manufactured by the industry andthe surface treatment was finished at Cornell. In additionto the standard surface treatment, this cavity was baked at140 C for about 60 hours. The cavity labeled as CornellBB1-6 and Cornell-SRRC are Niobium cavities manufac-tured by the same company as for BB1-4. The surfacetreatment of these two cavities were finished at the com-pany with their own facilities, following the Cornell proce-dure. Totally, nine Cornell type Niobium cavities have beentested, all showing the same field dependent characteristcsafter a standard Cornell surface treatment. Also listed inTable 1 are the field dependent factors due to the effect ofthe Kapitza impedance as calculated by the ANSYS andHEAT model presented in Section 5.From Table 1, the following findings are made. 1) Theeffect of the Kapitza impedance contributes only a smallfraction to the overall low-field Q-slope of Niobium cav-Table 1: Comparison of field dependent factorsIdentity  Note10 3Oe 1KEK-B #7 LC 2.41 EP+700C+OWR+EP+BakingCornell-SRRC 1.38 BCP+HPRCornell BB1-6 1.38 BCP+HPRCornell BB1-4 1.38 BCP+HPRCornell BB1-4 1.20 BCP+HPR+BakingKapitza effect 0.23 ANSYS resultKapitza effect 0.40 HEAT resultities; 2) The major effect on the low-field Q-slope is at-tributable to the material property of the RF surface; 3) Thelow-field Q-slope is reduced by baking at 140 C 1.7 DISCUSSIONAccording to BCS theory, the surface resistance of su-perconductors is independent of the amplitude of the exter-nal RF field. This renders a constant quality factor up tothe onset gradient of field emission. However, experimentresults are at odd with this prediction.The effect of the Kapitza impedance across the inter-face between the Niobium and He-I has been blamed tobe responsible for this Q-slope. This were the case, a fieldindependent BCS resistance can still be preserved. How-ever, our calculation results show that the effect of Kapitzaimpedance contributes only a small part to this Q-slope.The surface treatment has a strong effect on the low-field Q-slope at 4.2 K. However, Q0virtually does not dropat lower temperatures, where the residual resistance dom-inates over the BCS resistance. This indicates that the Q-slope arises from the BCS resistance, rather than some ad-ditional loss mechanism. As shown in Section 6 the mate-rial property contributes to the major part of the Q-slope.We believe a field dependent term is somehow intrinsicallycoupled to the BCS resistance, through factors such as themean free path of electrons.It should be mentioned that film Niobium cavities [15]exhibit similar low-field Q-slope but at a rather pronounceddegree - field dependent factors being in the range of3.8 - 5.0 10 3 Oe 1. It has been also argued that theBCS resistance depends on the amplitude of the RF fieldfor these film Niobium cavities [16].8 CONCLUSIONSThe effect of Kapitza impedance contributes only a smallfraction to the low-field Q-slope of superconducting Nio-bium cavities cooled with He-I. The major contribution to1This appears to be an added bonus to the 140 C baking, which isproved to be effective in reducing the BCS resistance by a factor of asmuch as 2.this Q-slope arises from the material property of the Nio-bium RF surface. To fully account this Q-slope, the BCSresistance has to be dependent on the amplitude of the RFfield resonating in the cavity.9 ACKNOWLEDGMENTWe thank Dr. Tsuyoshi Tajima of LANL (formerly ofKEK) for providing the latest vertical test results of KEK-Bcavities. Dr. Jens Knobloch (now at BESSY) is acknowl-edged for many contributions to the treatment and test ofCornell cavities.10 REFERENCES[1] T. Tajima, Los Alamos National Laboratory Report, LA-UR-01-4058 (2001).[2] H. Padamsee, J. Knobloch, T. Hays, RF Superconductivityfor Accelertors, John Wiley & Sons, Inc., (1998).[3] K. Saito et. al., Proceedings of the 4th Workshop on RF Su-perconductivity, Tsukuba, Japan, p.635 (1989).[4] J. Halbritter, Z. Physik, 238, p.466 (1970).[5] S.W. Van Sciver, Helium Cryogenics, Chapter 6, PlenumPress (1986).[6] C. Schmidt, Stability of Superconductors, pp.17-32, Interna-tional Institute of Refrigeration Commission A 1/2, Saclay,France (1981).[7] http://www.ansys.com[8] R.L. Geng, Cornell University, Laboratory of Nuclear StudiesReport SRF010212-01 (2001).[9] A. Deniz and H. Padamsee, Cornell University, Laboratoryof Nuclear Studies Report CLNS-79/434 (1979). The codeHEAT has undergone continuous evolution over the years.The latest version, HEAT2000, was updated from the earlierversion HEAT63 in order to make simulations with He-I cool-ing possible.[10] G. Mu¨ller, Proceedings of the 3rd Workshop on RF Super-conductivity, Argonne, Illinois, USA, p.331 (1988).[11] T. Furuya et. al., Proceedings of the 5th Workshop on RFSuperconductivity, Hamburg, Germany, p.684 (1991).[12] T. Tajima et. al., Proceedings of the 1999 Particle Accelera-tor Conference, New York, New York, USA, p.440 (1999).[13] T. Furuya et. al., Proceedings of the 9th Workshop on RF Su-perconductivity, Santa Fe, New Mexico, USA, p.31 (1999).[14] K. Asano et. al., Proceedings of the 7th Workshop on RFSuperconductivity, Gif Sur Yvette, France. p.419 (1995).[15] E. Chiaveri, Proceedings of the 5th European Particle Ac-celerator Conference, Barcelona, Spain, p.200 (1996).[16] C. Benvenuti et. al., Physica C316, p.153 (1999).

On the Low-Field Q-Slope of RF Superconducting Niobium Cavities Cooled by Helium-I

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