1. Coupling- and Persistent-Current Magnetizations of Nb3Sn Rutherford Cables with Cores of Stainless Steel and Woven Glass-Fiber Tape Measured by Pick-up Coil Magnetometry
3LPT-08
E.W. Collings1, M.D. Sumption1, M.A. Susner1, D.R. Dietderich2, E. Krooshoop3 and A. Nijhuis3
Center for Superconducting & Magnetic Materials (CSMM), Department of Materials Science & Engineering, The Ohio State University, USA
Lawrence Berkeley National Laboratory (LBNL), University of California, USA
Energy, Materials, and Systems Group, University of Twente, NL
Concluding Discussion on Coupling Loss and ICR
Sources of Cable Magnetization
Coupling Theory
Results
A. Magnetically Determined AC Loss, ICR, and Coupling Magnetization
crossover, Rc
side-by-side, Ra
Coupling currents
Persistent currents
The results of the magnetic FO loss measurements are shown in Figure 2 and the derived values of Reff (both from the slopes dQt/df and from fc are presented in Table III. Then based on Equation (1a), the measured Reff values, and a specified value of dB/dt it is possible to estimate the coupling magnetizations, Mcoup = Qcoup/4Bm, generated in the present 35-strand cables by an LHC-specified charging ramp-rate of 6.5 mT/s for comparison with that of a typical NbTi-based LHC-inner cable, viz 2.7 kA/m. The results given in Table IV emphasize the excessive coupling loss that will be generated by the narrow-SS-cored cable, SS2.
Analysis of Coupling Loss
The Stainless Steel Cored Cables
With the original uncored 28-strand LHC-inner cable a compromise between coupling magnetization and stability (current sharing) was achieved with an Rc of 15 ± 5 μΩ. But given that FO coupling magnetization is proportional to (w/t)LpBm2N2 a cable of the present dimensions would require an Reff of 25 ± 8 μΩ to achieve the same level of magnetization. With a fitted Reff of 23 μΩ (Table III) Cable SS1, with an almost full-width SS core (W = 93%, Table II), is close to achieving this result. But Reff is very sensitive to core width. Thus we estimate, based on previous studies of variable width cores, that the 8 mm core of Cable SS2 (W = 59%) should provide an Reff of ~4 μΩ . We attribute the lower measured value of ~1 μΩ (comparable to those of the uncored Nb3Sn cables referred to in the Introduction) to the fact that the core is not centrally positioned, leaving 1.5 strands uncovered on one side and 5.5 strands on the other. Previously measured cables with narrow off-center SS cores have also provided low Reff values.
The coupling losses per cycle per m3 of a cable (width w, thickness t, strand count N, transposition pitch 2Lp) exposed to fields linearly ramping at a rate dB/dt to amplitude Bm applied perpendicular (face-on, FO, leading to Qcoup-FO) and parallel (edge-on, EO, Qcoup-EO) to the cable’s broad face are given by:
Table III. Summary of Magnetically Measured Reffs
(1a)
Cable
name
Core
width, mm
Reff
init(a), μΩ
init-fit(b),
fc,
mHz
from fc,
EG1
12.7 56 47 50
2.0
EG2 38 67 78
3.1
SG1
103
118
129
5.0
SG2 48 64 96
3.8
SS1 14 23
215
8.6
SS2 8
0.9
1.1 20
0.8
(1b)
or the “frequency-dependent” variant of (1a)
(2)
Since Mcoup=Qcoup/4Bm, Equations (1) and (2) can be re-written in terms of the FO coupling magnetization, Mcoup-FO (1a); likewise for the EO coupling magnetization (1b)
Equations (1) and (2) express a linear dependence of Qt(f)=Qh+Qcoup(f) on frequency, f, in which case Reff is obtained from the reciprocal slope of Qt(f) and Qh is the intercept. But when ICR is small (e.g μΩ for uncored Nb3Sn cables) Qcoup(f) will depart from linearity within the frequency range of the present experiments (90 mHz) and pass through a maximum at some critical frequency fc.
The Glass-Tape-Cored Cables
Analysis of the coupling loss data, Table III, provides insights into the structures of the glass-tape-cored cables. Based on the fitted slopes, dQ/df, three of the present cables, EG1, EG2 and SG2, provided an average Reff of 53 ± 11 μΩ. Although this is not the true ICR (see below), the cable magnetizations are in fact small so that the primary goal of core introduction seems to have been achieved. But, starting with the fitted values of Q0 we deduce that magnetization reduction will have been achieved at the expense of reduced current sharing: (1) First of all we note that for a “standard” Rutherford cable with the parameters of Table II the fitted values of dQ/df would lead to plots of Qt vs f that are linear within the confines of Fig.2 but associated with implied values of fc in the range of several thousand mHz (Table VI). (2) But the Qt vs f curves for the glass-cored cables are not linear and rise to anomalously low maxima, Q0/2. Then recognizing that Q0  N2 we deduce that only a small number of the strands, Neff « N, are coupled. The estimated values of Neff are listed in Table VI. (3) When these new strand-count numbers are inserted into the calculations we find dQ/df-based values of Reff of 1.9 to 4.7 μΩ and fc-based values of 0.04 to 0.10 μΩ. These may be compared to the sintered crossover-contact Rc values of 0.09 μΩ to 0.4 μΩ measured previously on uncored Nb3Sn cable. Taken together, these results suggest that the woven-glass-cored cables are loose Rutherford-like assemblies of strands with relatively few points of strong (i.e. low resistance) interstrand contact.
Table I. Strand Details and Cable Assignments
LBNL Cable
1007R
1009
The Strand
OST-RRP Billet ID No.
11976
11588
Strand type (element #)
108/127
54/61
Filament count
108 54
Strand diameter, mm
0.802
Non-Cu content, %
49.0
Av. Filament outside diameter*, d0, μm
61.8
84.8
Prior internal-Sn diameter*, di, μm
31.2
43.2
Effective Filament diameter**, deff, μm
72.2
99.4
*Measured at OSU by SEM
**Based on deff = d0[(1-R3)/(1-R2)] with R = di/d0
The Cable
Cable Type
LARP High Gradient Quadrupole
Anneals
Cable anneal,
(206oC max,
4 hrs > 195oC)
Strand anneal,
(180oC max,
4 hrs > 170oC)
From line fitted to the initial (low-f) data
From a data fit to Qt(f)=Qh+Q0(f/fc)/[1+(f/fc)2]
Figure 2. Total AC loss vs. frequency measured FO magnetically (blue) and EO calorimetrically (red)
(FO)
(3)
Table IV. Estimated Coupling Magnetization at 6.5 mT/s
In which 2π(DE)≡Reff/fc where E is a function of (w/t) and the number of cables in the stack and D is a function of the individual-cable properties, N and Lp. Finally, after defining
Cable Name
EG1
EG2
SG1
SG2
SS1
SS2
Reff, μΩ
46.9
67.1
118.4
64.0
22.6
1.11
Mcoup, kA/m.
1.4
1.0
0.6
3.2
64.6
(4)
Equation (3) may then be rewritten in abbreviated form:
(FO)
(5)
B. Persistent-Current Loss, Qh
The hysteresis loops for several representative strands extracted from ends of the reacted cables were measured at ± 400 mT, the amplitude, Bm, of the AC loss measurements. By way of example the M-B loops (area Qh) for strands from EG1and SS1 are shown in Figure 3. Table V compares the losses, Qh, of strands EG1, SG1, SS1, and SS2 magnetically measured at OSU with those of the corresponding cables measured magnetically (FO) and calorimetrically (FE and EO) at UoT. In comparing the calorimetrically measured FO and EO losses we notice that Qh,FO/Qh,EO = 2.1 ± 0.1 in response to demagnetization associated with a highly aspected (w/t ~10) superconducting cable. For the same reason the “strand-estimated” Qh,cable lies between Qh,FO and Qh,EO.
These results indicate that by taking demagnetization into account the persistent-current cable properties can be deduced from magnetic measurements on the individual strands.
Equations (2), (3), and (5) provide ways of deriving Reff from the loss data:
From the reciprocal of the linear Qt(f) versus f, Equation (2)
From the reciprocal initial slope of the full Qt(f) versus f, Equation (3) or what is the same thing, from (Q0/fc)-1
With reference to Figure 1, we note some other properties of the above equations:
Qt(f) or Qcoup(f) maximizes at Q0/2.
2π(DE), a function of the cable stack geometry, is a constant which makes Q0 a constant and independent of Reff. It follows that: (a) all the FO coupling loss curves maximize at the same value of Q0/2 and (b) Reff  fc, such that when Reff is small (uncored Nb3Sn cables) the FO coupling loss maximizes at low frequencies of the applied field..
Table VI. Q0 (104 J/m3), fc(Hz), and Estimated Effective Strand Counts, Neff, and ICRs
Cable Name
EG1
EG2
SG1
SG2
Calculated Q0(1) 88 90 92 89
Estimated fc(2), Hz
1.3
0.6
3.4
1.7
Fitted Q0(3)
3.8
3.5
4.9
Neff 7 8
Reff from (dQ/df), μΩ, (4)
1.9
2.7
4.7
3.3
Reff, from fc, μΩ(5)
0.04
0.06
0.10
0.08
Table II. Cable Details
Annealed Cable, Reroll 2nd Pass
Annealed Strand, one pass
CSMM Name
EG1
EG2
SG1
SG2
SS1
SS2
LBNL Name
1007R
1009C
1009B
Strand Count 35
Pitch 2Lp, mm
102
Width, w, mm
15.07
15.21
15.22
15.25
Thickness, t, mm
1.559
1.520
1.578
1.534
1.442
1.438
Keystone deg.
0.715
0.678
0.703
0.640
0.722
Pack Factor*, %
78.3
80.6
76.6
78.6
83.8
84.0
Core Material
E-glass
S-glass
316 SS
304 SS
Core Width, mm
12.7 8
Core Cover, W** 93 59
Cables in Pack 5
Cable insulation***
SB+ri
* Average packing factor, not accounting for core volume
** W%, based on available internal width (mm) = x = 13.60
*** SB = S-glass braid, ri = CTD-101 resin vacuum-impregnation
Table V. Persistent Current Losses of Cables and Extracted Strands, 104 J/m3
From Equation (4)
Based on Equation (2), Reff, Iinit-fit (Table III), and (dQ/df)=Q0/fc
From a data-fit to Qt(f)=Qh+Q0(f/fc)/[1+(f/fc)2]
Based on Neff and (dQ/df)init-fit
From Reff=2πDEfc and an Neff-based recalculation of DE, c.f. Table III
Cable Name
EG1
EG2
SG1
SG2
SS1
SS2
Qh, FO, Cal.
7.1
6.5
6.8
4.8
4.7
Qh, FO, Mag.
6.9
7.6
7.5
5.7
3.7
Qh, EO, Cal.
3.2
3.4
3.3
2.3
2.6
Qh,FO/Qh,EO (Cal.)
2.2
1.9
2.1
Qh, strand
6.2
6.0
4.0
Qh, cable
4.6
2.8
Acknowledgements
The cables were wound at LBNL by H.V. Higley. All stages of uniaxial compaction were performed at OSU with the assistance of R.J. Baldwin. The RHT took place at LBNL. J. Yue of HyperTech Research Inc. performed the vacuum impregnation and curing of the cable packs. SEM-based measurements of cable and strand were performed at OSU by M.A. Kuldell.
Funding was provided by the U.S. Dept. of Energy, Office of High Energy Physics, under Grants No. DE-FG02-95ER40900 (OSU) and DE-AC02-05CH11231 (LBNL).
Figure 3. CSMM-measured unpenetrated hysteresis loops for two representative strands extracted from ends of the reacted cables measured at ± 400 mT (the amplitude, Bm, of the UoT AC loss measurements)
Figure 1. Computed dimensionless frequency dependence of coupling loss based on Equation (5) for given Q0 and 4 values of fc (10-500)
13-17 October 2012