Analysis of HIE-ISOLDE cavity results

Transcription

1 Analysis of HIE-ISOLDE cavity results A. Miyazaki 1,2, Y. Kadi 1, K. Schirm 1, A. Sublet 1, S. Teixeira 1, M. Therasse 1, W. Venturini Delsolaro 1 1 Organisation européenne pour la recherche nucléaire (CERN), Switzerland 2 School of Physics and Astronomy, the University of Manchester, UK Akira.Miyazaki@cern.ch Milano

2 HIE-ISOLDE Nb/Cu Quarter-wave resonators (1MHz) Prototype: rolled sheet + a number of welding Series production: machined + one welding New design: fully machined + no welding Seamless cavity Beam port nose: Punch pressed Beam port nose: Machined Beam port nose: Removed (conical wall) 2

3 Q vs E cooled down under a compensated magnetic field H "#$ ~5 µt (50mG) Based on the discussion in TTC topical workshop 2017 in Fermilab Very small Q-slope was found in the seamless cavity

4 Q vs E cooled down H "#$ ~0 µt (00 mg) Typical Q-slope in Nb/Cu cavities

5 Function of Q-slope (seamless cavity): empirical Rs vs E fitting B-field compensated when cavity crossed Tc B-field enhanced when cavity crossed Tc enlarged 4.6K 2.4K 4.6K 2.4K Intrinsic Q-slope is temperature dependent curvature component Q-slope by trapped vortex is close to linear at low fields and weakly temperature dependent

6 Trapped vortex effect by the collective weak pinning RF field oscillates the trapped vortex under statistical sum of many pinning centers D. B. Liarteʼs (Cornell) analytical approximation resulted in R./ 4 3 fλ 5 μ 7 B * 5 ξ J 7 J * H "#$ H +, R./ H "#$ H +, ~1. 7?3 nω mt?f µt?f On the other hand, experiment showed R./ H "#$ H +,.H"IJ ~3?3 nω mt?f µt?f à Good agreement! Only a factor of two! J +, Preliminary J * Different material parameters ξ 7, λ L, R M, J * à Different sensitivity to the trapped vortices à Parameter determination is important! (See A. Miyazakiʼs presentations in topical TTC at FNAL) Curtesy of D. B. Liarte

7 [nω] R s Welded cavity à sensitive to thermal gradient DT Uniform cooldown when cavity crossed Tc B peak [MV/m] E acc [mt] enlarged DT=35mK 4.6K 2.4K [nω] R s The best possible cooldown still contains linear term à Severe trapped vortex contamination? Thermal gradient when cavity crossed Tc B peak [mt] DT=470mK K K E acc [MV/m] The physics from DTà trapped vortex is still a missing link (only speculations)

8 200 Comments on the trapped flux effect 180 Our findings Linear Q-slope in residual resistance caused by trapped flux A similar phenomenon was produced by thermal gradient when crossing T c Commonly found in historical Nb/Cu cavities (Q-slope problem) Bulk Nb cavity [G. Ciovati and A. Gurevich SRF2007] Linear Q-slope caused by trapped lux Nb 3 Sn/Nb cavity [D. Hall SRF2017] Linear Q-slope caused by trapped flux Thermal gradient effect This linear Q-slope might be a universal phenomenon in SRF cavities Just a different material parameters and environment De-pinning current, mean free path, B-shield, Thermal gradient problem seems a unique problem of bimetal cavities R fl /B ext (nω/g) B p (mt)

9 Intrinsic Q-slope (non-linear)

10 T-dependent Q-slope is a universal phenomenon in QWRs 140 [nω] R s global D. Longuevergne SRF2015 Z.A. Conway et al., NIM B 350 (2015) HIE-ISOLDE QSS2 4.5K 1MHz SPIRAL2 MB09 4.2K 88MHz ATLAS QWRS 4.5K 73MHz HIE-ISOLDE QSS2 2.3K 1MHz SPIRAL2 MB09 2.1K 88MHz B peak [mt] ATLAS QWRS 2.0K 73MHz

11 Vaglio-Palmieri model Surface resistance increased by quenched hot spots can be expressed as [nω] R s [MV/m] R N T, H = Q R,R N T 7, H, R R f R B dr R, E acc 7 V. Palmieri and R. Vaglio, Supercond. Sci. Technol, 29, (2016) W Distribution function of thermal boundary resistance can be obtained from Q-slope 4.6K Convert ) B f(r K 2.3K K R B 4 One order of magnitude different 5 2 [cm KW This model is not consistent with the T-dependence of this Q-slope -1 ]

12 [nω] R s An empirically found formula to fit the data (A,, R a"n ) from Rs vs T data χ 2 / ndf / 249 A 1830 ± ± R ± res R N T, B = A T exp k R T + αb + R a"n Low RF field H peak =3 mt [nω] R s Fit Rs vs H and determine α T [K] a [T -1 ] K 2.3K T [K] [mt] Such an exponential dependence has been reported by others (bulk Nb and Nb/Cu) 1. R. L. Geng (Cornell) Thermal analysis of a 200MHz Nb/Cu cavity SRF2001 [ad hoc] 2. D. Longuevergne (IPNO) Magnetic dependence of the energy gap: SRF2013 [exp(b 2 )] H peak

13 [nω] R s Temperature dependence of a K K K K K [mt] B peak ] -1 α [T α 1 T α T?F from the data à change the parameter by α = M k R T R N T, B = A T exp k R T + MB k R T + R a"n R N T, B = A MB exp T k R T This new constant M has a dimension of magnetic moment [JT -1 ] + R a"n -1 1/T [K ]

14 Comparison of magnetic momenta formula Value [JT -1 ] ref. This experiment M = α T k R T 9.8?55 Pair breaking by RF supercurrent Bohr magneton (electron spin) Trapped flux quantum NC core Magnetic permeability μ 7 = 4π?~ Area A supercurrent p, v N λ 7ev, > 2.7 ρ?5f V. Palmieri SRF2005 N v N = 7 T. Jungingerʼs p, v λ 7 = 30nm N thesis 2012 μ R = eħ 2m " 9.3?5y 1 2 μ 7φ 7 l 1.3?5F l Flux quantum φ 7 = 2.07?F Wb Flux length l [m] v, = 0.57 l m/s 0 < ρ N < 1 Total energy of one flux quantum stored in the magnetic field in the NC core U = 1 2 μ 7B 5 Al Average flux density in the NC Core B = φ 7 A Magnetic momentum m = U B = 1 2 μ 7φ 7 l

15 Comments on gap reduction Our findings in the HIE-ISOLDE Nb/Cu cavity tion of field at many temperatures, as well as the low-field Q 0 and resonant frequency f 0 as a function of bath temperature T 0. 7,11,20,21 We used the change in resonant frequency f 0 to determine the change in RF penetration depth k using methods described previously by Ciovati and others. 22,23 We used the quality factor Q 0 to determine total surface resistance R s using the relation in Eq. (1). We performed a com- The naïve gap reduction bined fit explains of R s ðt 0 Þ andfield DkðT 0 Þand to the temperature BCS theory using dependence very well SRIMP; 13 fits from cavity C4(P1) are given in Fig. 2 and serve as representative examples of the procedure followed Frequency ~ 0MHz for all cavities. This BCS fitting yielded the mean free path Mean free path >50, nm theenergygapd, [A. Miyazaki thecoherencelengthn, TTC Topical 2017 FNAL] resistance R 0.FittingtobothR s ðt 0 Þ and DkðT 0 Þ was very Quarter-wave resonator helpful for determining precise values for the fit coefficients as the two fits are more sensitive to energy gap and mean Similar phenomenon in bulk Nb QWRs (high RRR) as well free path, respectively. More information on these fitting techniques is available in previous reports of work at Cornell by Meyers, Valles, and others. 6,21,24 26 Equipped Relation to the N-doped bulk Nb cavities The pair breaking effect with R 0 is, weoverwhelmed were then able to calculate by the DoS BCS resistance smearing R BCS as a function of field and temperature using the relation in Eq. (2). àanti-q-slope [in the dirty limit; Gurevich PRL ] Frequency >> 0 MHz [M. Martinello TTC Topical 2017@FNAL] Mean free path < 50 nm [J.T. Maniscalco et al., J. Appl. Phys (20)] Elliptical cavity We might see different aspects of the same physics Different parameters à different observable Q-slope face resistance as a function of surface field and temperature, using the overheating parameter a as a free fitting parameter in Eq. (3), with no additional constraints. We found it necessary to use an additional field-independent fitting parameter s as a scaling factor, with the relation s ¼ R BCS;meas =R thy. Here, R BCS;meas is the BCS surface resistance extracted experimentally and R thy is the predicted surface resistance from Gurevich s theory as described above. For a given cavity, s was fixed for all temperatures. The scaling factor s was typically near unity; we believe that this accounted for systematic experimental errors that vary from cavity to cavity (e.g., uncertainty in G, the geometry factor), which we usually cite as %. We discuss this further below. It is important to note l = 34nm here that the theory does not include any explicit dependence of the field-dependent resistance on the mean free path; in our analysis, we sought to investigate any possible dependence of the overheating parameter on. C. R BCS results and theoretical fits Figure 3 shows typical results of the BCS surface resistance as a function of applied RF magnetic field, as well as FIG. 3. R BCS as a function of peak surface magnetic field for several representative 1.3 GHz TESLA cavit theoretical predictions with given overheating parameter a. Error bars have been omitted for visual clarit l = 200nm tematic errors that have been accounted for by the scaling parameter s. (a) Test of cavity C3(P2), with ¼ ¼ 346 nm, að2:1 KÞ ¼0:44. (c) Test of cavity C5(P2), with ¼ nm, að2:11 KÞ ¼1:7.

16 Conclusion The Q-slope in the seamless Nb/Cu cavity was decomposed into The linear term caused by the trapped flux The more intrinsic T-dependent exponential term The linear term can be explained by the collective weak pinning model Thermal gradient causes the similar result but the effect of cooldown dynamics to trapped flux is not yet known This term was seen in most of the Nb/Cu cavities and also in other cavities The intrinsic Q-slope seems a universal problem of low frequency QWRs The similar T-dependences were found in bulk Nb The function can be fitted by exponential but the naïve model of gap reduction deserves deeper theoretical consideration Frequency dependence is the key à Harmonics measurement, QPR, The Q-slope may not be the limiting factor of Nb/Cu technology Just a matter of different material parameters and environmental condition Optimizing for lower residual resistance and compatibility to optimized RF design will be the next steps