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Coupling Loss, Interstrand Contact Resistance, and. Magnetization of Nb3. Sn Rutherford Cables With. Cores of MgO Tape and S-Glass Ribbon. E. W. Collings ...
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011

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Coupling Loss, Interstrand Contact Resistance, and Magnetization of Nb3Sn Rutherford Cables With Cores of MgO Tape and S-Glass Ribbon E. W. Collings, M. D. Sumption, M. A. Susner, D. R. Dietderich, and A. Nijhuis

Abstract—Multistrand cables may exhibit two classes of parasitic magnetization both of which can distort the bore-field of an accelerator magnet: (1) a static magnetization (“hysteretic”) resulting from intrastrand persistent currents, and (2) a dynamic magnetization produced by interstrand coupling currents generated during field ramping. The latter, which are moderated by the interstrand contact resistances (ICR), can be controlled by the presence of an insulating core inserted between the layers of the cable. Stainless steel ribbon (with its associated native oxide coating) is a frequently used core. Recently, however, MgO-paper tapes and woven s-glass ribbons have been suggested by LBNL (Lawrence Berkeley National Laboratory) as alternative core materials in the interests of improved flexibility and compatibility with the cabling process. This paper reports on the results of calorimetric AC loss (hence ICR) measurements on a set of four such cables and presents the results within the context of previously measured cored and uncored Nb3 Sn cables. Also considered is a typical ramp-rate-induced coupling magnetization and its relationship to persistent-current magnetizations over the operating range of an accelerator magnet. Index Terms—AC loss, calorimetry magnetization, cored cables, interstrand contact resistance, MgO-paper tape, Nb3 Sn Rutherford cable, s-glass ribbon.

I. INTRODUCTION

C

OUPLING loss and interstrand contact resistance has been the subject of a long series of studies of Rutherford cables wound with bare- and coated NbTi, Nb Al, and Bi:2212 (for references see [1]), and subsequently Nb Sn [1]–[9]. The suppression of interstrand coupling currents (ICCs) and “supercurrents” [10] (i.e. boundary-induced coupling currents, BICCs [11]) is necessary for dipole- and quadrupole field quality and magnet stability. Both ICCs and BICCs may be suppressed by increasing the cables’ crossover and side-by-side (adjacent) interstrand contact resistances—the ICRs and . Specifically, is the resistance across one contact of two crossing stands

Manuscript received August 13, 2010; accepted September 27, 2010. Date of publication November 09, 2010; date of current version May 27, 2011. This work was supported by the U.S. Department of Energy, Division of High Energy Physics, Lawrence Berkeley National Laboratory under Grant DE-AC0205CH11231 and The Ohio State University under Grant DE-FG02-95ER40900. E. W. Collings, M. D. Sumption, and M. A. Susner are with the Laboratories for Applied Superconductivity and Magnetism (LASM), Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 34210 USA (e-mail: [email protected]; [email protected]). D. R. Dietderich is with the Superconducting Magnet Group, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 USA (e-mail: [email protected]). A. Nijhuis is with the Low Temperature Division, Faculty of Applied Science, University of Twente, 7500 AE Enschede, The Netherlands (e-mail: [email protected]). Digital Object Identifier 10.1109/TASC.2010.2083620

(one on the top of the cable, one on the bottom), and is the resistance between two parallel, touching strands (either top or bottom) along one lay pitch (1/2 of the twist pitch). Full strand insulation would suppress both varieties of coupling currents but to the detriment of current sharing and hence stability. So a compromise between ICC and BICC reduction and magnet stability is sought leading to the recommendations that should be very small, although not less than 0.2 [11], and that should be about 15 5 [12]. But the wind-and-react assembly of Nb Sn Rutherford cables in an accelerator magnet typically leads to s in the vicinity of 0.1–0.4 [1]–[9]. These are unacceptably low values, to correct for which Nb Sn Rutherford cables have been provided with metallic (albeit “insulating”) cores of various types and widths. As described in [1]–[9] stainless steel (SS) ribbons or Cu-SS laminates have been used with varying degrees of success. Then in seeking a more flexible core, and one that is more compatible with the cabling process, the Lawrence Berkeley National Laboratory (LBNL) suggested the use of MgO-paper tape and woven s-glass ribbon, respectively. This paper reports on the results of calorimetric AC loss measurements on a set of LBNL-wound LHC Accelerator Research Program (LARP) HQ-KC2 (High gradient Quadrupole—Keystone Cable specification 2) prototype cables, four cored and one uncored (as a “reference”) and magnetization measurements of samples of strand extracted from them. Under LHC operating conditions field errors will be acceptably low provided the cables meet the above-quoted and specifications. These resistances can be extracted from the results of AC-loss measurements purposely carried out, as described below, at relatively high applied-field ramp-rates or frequencies. As explained in [2] (see also [13], [14]) the coupling losses per cycle per m of a cable (width, , thickness, , strand count, , transposition pitch, ) exposed to fields linearly ramping at a rate to amplitude applied perpendicular (face-on, FO) and parallel (edge-on, EO) to the cable’s broad face are given by:

(1a) (1b) or the variant of (1a) relevant for sinusoidally varying fields (see [2]):

1051-8223/$26.00 © 2010 IEEE

(2)

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011

TABLE I STRAND AND CABLE DETAILS (AFTER LBNL CABLE MFG. SUMMARY)

(a) The core widths were 10.39 mm (MGO) and 9.96 mm (SG). (b) SB = s-glass braid, R = CTD 101 resin impregnation, B = ceramic binder.

0

Then recognizing that , (1) and (2) can be re-written explicitly in terms of coupling magnetizations, . Equations (1a) or (2) express the FO-measured loss or magnetization in terms of a pair of resistors-in-parallel and enabling an “equivalent” or “effective” to be defined as . It is clear that itself is not part of the resistive-network model of the cable, but regarded just as a number emerging from the loss experiment it is a useful index of magnetization. Thus it is this that should conform to the 20 FO-measured ICR prescription. Embodied in the above definition is that if is to then should be not less than 0.2 for be about 20 the following reason: Picture a 28-strand cable with an of 0.2 . The parallel-resistor model depicts an shunted by 0.2 220 , which does little to suppress the desired combined of 20 . The utility of is that it indexes the magnetizations of either uncored cables (controlled by ) or cored cables (controlled by the -modified ). II. EXPERIMENTAL

Segments of these cables each about 19 inches long were individually sheathed with s-glass braid and assembled into 5-high cable stacks (with alternating keystone angles) in a stainless steel fixture designed to apply side-constraint during uniaxial compaction. Preparation of all cables took place according to: (1) uniaxial compaction to 20 MPa, (2) reaction heat treatment (RHT) following an OST-recommended 210 C/48 h 400 C/48 h 665 C/50 h. But in addition to this a special pre-conditioning technique was applied to two of the cables. Following a procedure employed by LARP and by the Fermi National Accelerator Laboratory (FNAL) a sol–gel–pre-cursor mixture (“CTD-1202X-Ceramic Matrix”) was administered to the edges of cables MGO and SG prior to a first compaction to 20 MPa. The ceramic binder produced during a sintering 2 h/150 C (plus up- and heat treatment for 1 h/80 C down-ramps) served to cement the cable stacks (then named MGOB and SGB, respectively). Finally in a simulation of magnet construction procedures, the pressure was released and then re-applied to 20 MPa prior to the above RHT. After RHT all five cable packs were: (1) wrapped in Teflon film, installed in silicone-greased aluminum molds, (2) uniaxially loaded and retained at 5 MPa, (3) vacuum impregnated with CTD-101 resin, (4) cured following CTD’s recommendations, (5) trimmed to length in readiness for AC loss and magnetization measurement. B. The Calorimetric AC Loss Measuring Technique Calorimetric measurements of AC loss were made at 4.2 K by helium-boil-off calorimetry ([11], p. 94) using facilities of the Low Temperature Division, Faculty of Applied Physics, University of Twente (UoT). The total AC loss per cycle, , where is the strand’s “persistent is the interstrand coupling loss, current” loss and was generated by transverse AC fields of amplitude 400 mT and frequencies, , of up to 90 mHz. For comparison with in-cable results, hysteretic losses, the extrapolated , and the associated persistent current magnetizations, , were measured at 4.2 K on pieces of strand extracted from the ends of the heat treated cable packs. These measurements were made at Ohio State University’s Center for Superconducting 400 mT and 13 T and Magnetic Materials (CSMM) to by vibrating sample magnetometry (VSM) using a Quantum Design Model 6000 “physical property measuring system” (PPMS). III. RESULTS AND ANALYSIS

A. Sample Materials and Preparation For this research LBNL fabricated four lengths of LARP HQ-KC2 prototype 35-strand Rutherford cables using Nb Snstrand manufactured by Oxford Superconducting Technology (OST, Table I), two with cores of MgO paper (MGO) and two with cores of woven s-glass ribbon (SG). Also wound for reference was a 34-strand uncored cable (NC). After the initial pass through the machine, the cables were annealed for 4h/200 and then re-rolled.

A. Coupling Loss and Interstrand Contact Resistance If the ICR is relatively large the coupling loss is directly proportional to over the frequency range of the experiment in is obtained from the reciprocal which case, following (2), hence . But when ICR is small the full slope of comes into play. In such frequency dependence of cases and at sufficiently high frequencies departs from linearity and eventually passes through a maximum at a critical

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Fig. 2. Unpenetrated M–B loops measured to 400 mT on extracted strands, showing a strong similarity of the response (overlapping curves). Fig. 1. Total per-cycle loss in AC fields applied FO (upper five curves) and EO (lower cluster of 5 lines)—calorimetric data and fitted curves. TABLE II MEASURED CALORIMETRIC RESULTS (B

(

! 0)

= 400 mT, 0 ! 90 mHz)

( )=

+ Q (f=f )=[1+

(a) From the intercept f of the fitted Q f Q f=f . (b) From the initial raw Q f data. (c) From the initial slope f of the fitted Q f=f , i.e. Q =f . Q f=f =

)]

(

(

) [1 + (

)]

() (

!

0)

(f ) = Q +

frequency (where is the corresponding relaxation time). In this case the FO loss calls for a modification of (2) and hence a total FO loss of the form:

(3) , where is a function of In (3) and the number of cables in the stack and is a function of the (Verweij [11]). individual-cable properties: and Hence, as detailed in previous papers on the subject (e.g. [6] are obtainable using (i) the slope of the and [8]), values of versus , (ii) the “raw” initial slope of a nonlinear linear , (iii) the initial slope after fitting the data to (3) even if the maximum frequency of the experiment is less than . The results of both the FO and EO calorimetric AC loss measurements are shown in Fig. 1. The FO results, in terms of ) and the persistent-current losses (“hysteretic”, s are presented in Table II. The of cable NC, at 0.33 , agrees well with all pres have been vious results on uncored Nb Sn cables whose [1]–[9]: well below found to be in the range of 0.1–0.4 [12]. Inclusion of the plain MgO and the optimal 15 5 s-glass cores raised to about 9 , a value that dropped after the ceramic binder was introduced. The cores, to 6.8

6

TABLE III UNPENETRATED HYSTERETIC LOSSES, Q (FOR 400 mT), AND HYSTERETIC SHIELDING MAGNETIZATIONS, M (at 4.2 K,12 T) FOR EXTRACTED STRANDS

0

about 10 mm wide, covered only about 75% of the available internal width of the cable (15–1.6 mm) leaving room for the use to 20 or of a wider core and the possibility of raising beyond. B. Unpenetrated Hysteretic Losses of Extracted Strands and Cables The AC loss experiment is intended to measure the fre, quency dependence of total loss, and the latter being a measure of and hence dipole or quadrupole field error. The zero- extrapolation of yields a persistent current loss, , corresponding to the measuring field amplitude of 400 mT. Since the strands are unpenetrated at this low field amplitude the result has no direct relevance to magnet operation. Nevertheless it is instructive , with those of extracted to compare the cable losses, 400 mT in the PPMS-VSM (Fig. 2; strands measured to Table III). The average FO and EO cable loss intercepts (measured at UoT) are 4.94 0.80 10 J/m and 2.31 0.08 10 J/m , respectively. These bracket the average VSM-measured extractedstrand loss, viz: 3.55 0.09 10 J/m (reduced from the measured 4.44 0.11 10 J/m by a factor 0.8 to take into account falls the packing factor of the parent cable). Thus the strand roughly midway between the FO and EO cable values, which can be compared to previous results [9]. Qualitatively confirmed by separate experiment and calculation this effect is attributed to the demagnetizations associated with a flat superconductor (e.g. a cable) in FO and EO applied fields. C. Operating-Field Magnetizations of Extracted Strands and Cables Extrapolating from the 400 mT results we assume that the and fully penetrated magnetic properties of the cable (

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Fig. 3. PPMS-VSM-measured M–B loops measured to 13 T on extracted strands showing a strong similarity of the response (overlapping curves).

hence ) under operating conditions can also be derived from those of the component strands. Of interest are the relaand shielding-persistive magnitudes of the coupling tent-current magnetizations at the injection- and storage segments of an accelerator’s operating cycle. For example, the 9 ) at present cable’s coupling magnetization (taking . an LHC ramp rate of 6.5 mT/s is To estimate the shielding magnetizations, we make use of the average 4.2 K extracted-strand magnetization (Fig. 3; Table III), and from it, we derive the 1.9 K, 12 T and 1.9 K, injection-field (e.g. 1.0 T) magnetizations using well-known conversion formulae [16]–[18]. The strands are all very similar of 3.23 10 A/m yields as expected, and an of 4.11 10 A/m and hence (at an operating an [9] and a cable fill factor of 80%) an reduced current of 11.8 kA/m. This is a large value for an accelerator magnet at its operating field but even larger, by an order of magnitude, is the magnetization at low fields near . injection, e.g. IV. SUMMARY A. Coupling The uncored value of 0.27 conforms well to several previous results obtained under collaborations with LBNL [4], [5], 0.24 and FNAL: 0.15, 0.16, 0.30, 0.33, and 0.36 [3], and 0.4 [6]. Such unacceptably low values stemming from the small crossover contact resistances, , characteristic of wind-and-react Nb Sn have called for the introduction of a core to separate the “upper and lower” parts of the cable s. of from winding. Stainless steel (SS) ribbons have led to [1]–[9]. To achieve comparable results tens to hundreds of but with a more flexible core the use of MgO paper tape and woven s-glass ribbon was suggested. The results are summarized in Fig. 4. For the present cable set the presence of the cores from 0.33 (bare cable) to 9.1 (average, no increased binder). Both MgO- and s-glass tapes provided comparable values although MgO (9.6 ) was slightly better than s-glass ). Although these values are significantly less than the (8.6 goal an increase is possible by increasing the core stated 20 width. The present cores of widths 10.39 mm (MgO) and 9.96

Fig. 4. Calorimetrically measured R for Nb Sn cables with cores of MgO paper and s-glass woven tape both with and without the injection of the ceramic binder. The eight data points are from Table II.

(s-glass) cover only 75% of the available internal cable width 13.4 mm). So based on previous experience with ( “variable-width” SS cores [15] we predict that an of over would be achievable with a full-width MgO or s-glass 30 core. To stiffen a magnet winding before it is transferred between fixtures FNAL recommends the use of a sol–gel-based ceramic binder. Accordingly the effect of this binder on the external s-glass-braid cable sheathing and the core-moderated was investigated. An apparent mechanical interstrand degradation of the insulation was observed. Furthermore, the s of both the MgO- and s-glass-filled binder reduced the cables but in so doing also reduced the difference between them (Fig. 4). B. Magnetization As discussed in [19] the coupling- and injection-field (0.54 T) persistent-current magnetizations of NbTi-wound 2.0 kA/m and LHC-inner cable are 7.31 kA/m. Bore-field magnetizations at this level can be cancelled by activating sets of compensating of 7.40 coils. With the present Nb Sn cored cables the kA/m could likewise be electrically compensated or reduced by the introduction of a wider core. But its persistent-current magnetization near an injection field of, say, 1.0 T would be 109 kA/m. A result of Nb Sn’s large product, this is an order of magnitude too high and will and the introduction likely call for significant reductions in of some form of passive magnetic compensation [20]. ACKNOWLEDGMENT The cables were fabricated at LBNL by H. C. Higley and N. L. Liggins. Both stages of pre-RHT compaction were performed at OSU with the assistance of R. Baldwin. The RHT took place at LBNL. The CTD-1202X-Ceramic binder mix was supplied by M. Whitson, (FNAL) who also advised on its application. J. Yue of Hyper Tech Research Ltd performed the vacuum impregnation and curing of the cable packs.

COLLINGS et al.: COUPLING LOSS, ICR, AND MAGNETIZATION OF Nb Sn RUTHERFORD CABLES

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