1. Current Sharing and AC losses in Coated Conductor Roebel Cables -- HEP Applications
M.D. Sumption, M. Majoros, E.W. Collings
Center for Superconducting and Magnetic Materials, MSE, The Ohio State University
Nick Long, IRL, New Zealand
EUCAS 2011 Centennial Den Haag
W. Goldacker
A. Nijhuis, E Kershoop, The University of Twente, EMS Group
This work was funded by the U.S. Dept. of Energy, Division of High Energy Physics, under Grant No. Grant No. DE-FG02-95ER40900 (University Program)

2. Outline Roebel Cables in the context of HEP
Roebel Cables as Topological transformations of Rutherford Cables
Loss Expressions, Contact Resistance Expressions
Direct I-V measurements of Interstrand Contact Resistance
AC Loss and Its relation to ICR
Measurements of Roebel with Helium gas flow induced temperature gradients
G. Levin

3. YBCO Roebel in HEP Context
It is useful to consider YBCO for HEP magnets for very high field devices, like 50 T solenoids for muon colliders, because they are enabling. Worth considering for other HEP magnets as well
Large magnets need cables, typically tens of kAs
Cables need current sharing between the strands for stability and protection reasons in LTS, as well as current distribution uniformity considerations
Strand to strand contacts must be low resistance enough to allow this, but high enough to keep low loss
These same considerations needed for Rutherford cables will need to be applied to Roebels, and it is easy to see why since …….

4. The Roebel is a topological transformation of a Rutherford Cable
i.e., no cutting or pasting operations allowed
Operation 2 flatten
Operation 1 rotate
Operation 3 flatten some more

5. Roebel as Topological transformation of Rutherford II
This fact is long known, although perhaps not well known
So what?
The important point is that the loss current paths, the losses of which have been calculated in detail, transform topologically as well

6. Topological equivalence of coupling current paths in Roebel and Rutherford cables
FO Coupling loop, involves R
R, this is a connection between “top”and “bottom” layer strands
In the Roebel cable this would mean left and right side connections, and these don’t exist
dB/dt
dB/dt
EO Loop, R//
Old EO Loop Transformed, would imply strand 1 having continuous contact with strand 2, and 2 with 3, and 3 with 4 etc, all on the strand faces. In fact this is true, but the R involved can be high

7. Use of Rutherford Expressions for Roebel
For Rutherford cables the AC Loss expressions for coupling loss per cycle per m3 are EO FO EO FO
Realizing that Rc is infinite, then both field applied to the face and field applied to the edge of the Roebel cable will follow
With different proportionality constants in front for cable face and cable edge orientations and Ra refers to nearest strand contact, e.g., 1-2, 2-3, etc

8. Similarity in Problems, similarity in solutions
In Rutherford cables, the main item controlling contact resistance is the oxide layer on the Cu (or other surface metal) – this is also true for YBCO
One way of overcoming this in Rutherford cables was by controlled low temperature sintering of the cables to break down the surface oxide layers, we could try that (did not work so well, see below)
Another was of overcoming this was the use of a Ag-Sn solder, which was ductile, and pressure responsive, and replaced the heavy CU oxide with a lighter one –this is our motivation for using a Sn sheet for contacts in Roebel below
In some cases, contacts were soldered, we also tried this
We start out by seeing how simple pressure effects the contacts

9. Attempt to Create Current Sharing in YBCO Roebel Cables
Oxide layers on Cu stabilizer suppress current sharing, as they did for NbTi cables used in accelerator magnets
There, the problem was solved with low temperature “cures” under slight pressure to sinter Cu surfaces (140C/1/2 h, 25 MPa)
We recently attempted 170C for 2 h, but low pressure (< 5 MPa), and then measured via helium boiloff calorimetry

10. IBAD Based Roebel (Cables 1 and 2)
Measurements at 77 K and 4 K
Two different Cables
R1 from IRL
R2 from KFK
Nick Long, IRL, New Zealand
W. Goldacker

11. 4.2 K Calorimetric Loss Measurements Cable 1
AC losses are hysteretic, independent of frequency
Cable Results for Cable 2 done at higher Freq also no coupling loss

12. Results of Try #1 -- loss section
For As-received Roebel cable the strands have no coupling
This means no eddy current loss, but also no current sharing
This is due to the native oxide layers on the Cu stabilizer
Mild Curing of the cable of the kind which worked to control ICR in NbTi Rutherford cables did not work – at least at the low pressures we used

13. Trial # 2 -- Contact Resistance Measurements in Roebel Cables by Direct I-V
We used a direct I-V measurement to obtain contact resistance, Rc, between strands in a cable
We used the method described by Verweij
Measurements are made at RT, at 77 K, and then with
applied pressure
applied pressure with Soft metal pressure contact
soldered contacts

14. Direct Contact Method for ICR
We can adopt the direct I-V technique used by Arian Verweij in his measurement of ICR in Rutherford cables, see “Electrodynamics of Superconducting cables in Accelerator Magnets, Thesis, University of Twente 1995
Rmax
R// only
Rc as well
Another way to see this is that we have N resistors in parallel, and N/2 series segments of these
Our case corresponds to his Eq 4.46 b, except that the Ra used there is slightly different, and given that our cable length is equal to Lp, we get
Ra = 2Rmax

15. Wiring of the cable Number of tapes: 15
Current contact on one end of the cable – tape no. 2
Current contact on the other end of the cable – tape no. 10
DC power supply: HP6634 A (1 A – 100 V)
Voltmeter: Keithley 2182A nanovoltmeter
Pairs of the potential taps used for voltage measurements: 1-2, 1-3, 1-4, …. 1-15
Cable Provided by Industrial Research Limited, IRL

16. Pressure application
Pressure was applied by adding stainless steel plates on top of the G-10 top plate, both were free to move up and down but stabilized laterally by guide rods

17. (baseline) 77 K Results for zero Applied Pressure
I = 500 mA
Vmax = 225 mV
Rmax = 450 m
Liquid nitrogen bath (77.3 K) data (no pressure applied): contact no. 1 = potential taps 1-2, contact no. 2 = potential taps 1-3, …… contact no. 14 = potential taps 1-15.

18. (a) Effect of Pressure Application 77 K – no interlayer metal
No Pressure 77 K
I = 500 mA
Vmax = 225 mV
Rmax = 450 m
Max Pressure 77 K
Vmax = 70 mV
Rmax= 140 m
Max Pressure is 95 kPA
Pressure is applied to the wide face of the cable by stacking metal plates, the weight of which cause a pressure

19. (b) Roebel Cable with Soft metal interlayer under pressure
Max Pressure is 95 kPA
Effect of pressure on transverse resistance of the cable with Sn foil on its top, measured in liquid nitrogen bath (77.3 K). Pressure measured in number of steel “bricks” used as a load.
Sn+ 1 brick 77 K
I = 500 mA
Vmax = 30 mV
Rmax = 60 m
Sn+ 4 brick 77 K
I = 500 mA
Vmax = 16 mV
Rmax= 32 m

20. (b) Roebel Cable with Soft metal interlayer under pressure
Max Pressure is 95 kPA
Effect of presence of Sn foil on transverse resistance of the cable at maximum pressure of 4 steel bricks, measured in liquid nitrogen bath (77.3 K).
No Sn+ 4 brick 77 K
I = 500 mA
Vmax = 55 mV
Rmax = 110 m
Sn+ 4 brick 77 K
I = 500 mA
Vmax = 16 mV
Rmax= 32 m

21. ICR Results so Far

22. Roebel Cable with Indium Soldered Cu bridges
The above techniques has induced some contact, but not enough – how about in soldered Cu shunts? Inspired both by previous soldering work, and work done at IRL (Long)

23. (c) Roebel with Indium Soldered Cu shunts – 77 K data
Roebel cable IRL (2011) with In soldered Cu bridges –– LN2 data. (contact no. 1 = potential taps 1-2, contact no. 2 = potential taps 1-3, …… contact no. 14 = potential taps 1-15). I=0.5 A Vmax=50 Rmax = 100 

24. ICR Results with Solder addition

25. New Series of Loss Measurements on Soldered cable
We might expect increased coupling loss to now be seen for Roebels with soldered junctions
Let’s see …

26. AC Loss Results for Roebel with Indium soldered Cu shunts
No apparent increase in loss! ICR would appear not to have changed!

27. Higher frequency loss at 77 K for Roebel with soldered contacts
Roebel cable from IRL (2011) indium-soldered Cu bridges –– LN2 in-field ac losses at different frequencies

28. What are the expected resistances of the contacts?
Resistance of Solder contacts R = L/A = 15 cm*10*10-4cm/1cm2 = 15 n Resistance of 0.1 mm thick Cu strip (1cm sq) R = L/A = (1.6 cm/RR(T))*1 cm/0.01cm2 = at 77 K, RR(T)=5, and R = 160  Reasonable agreement with the direct ICR at 4 K, RR(T) = 100, and R = 8  Similar to what might be a target for a Rutherford accelerator strand

29. 4.2 K NbTi Rutherford cables, FO
M.D. Sumption,E.W. Collings,, R.M. Scanlan, S.W. Kin, M. Wake, T. Shintomi, A. Nijhuis, and H.H.J. Ten Kate, Cryogenics 41, 2001, 733

30. Coupling Loss
We can compare this 10 * 104 J/m3 to the scale for the Roebel cable – No such loss slope appears –why? ?
Lets calculate the coupling current, I=/R, and note that the cable would have coupled strands when most of their Ic is taken up in coupling, rather than hysteretic shielding, currents.

31. Coupling Schematic in Bean Terms
For this to be true the current flowing from strand to strand must be a relatively high percentage of the strand current, or they will flow in circles in the strands
A cable has coupled strands when most of their Ic is taken up in coupling, rather than hysteretic shielding, currents
Green regions are strands
Black lines are flux profiles
Dashed line is flux in coupled state
Blue lines are uncoupled (hysteretic shielding) current
Red lines are coupled current
dB/dt

32. Calculating the Loss slope II
= -d/dt = AdB/dt, and dB/dt max is  0.1 Hz*4*.4T=0.16 T/s
NbTi Rutherford cable
A  Lay pitch*cable width/2=50*15= m2
I=/R=(6*6-3V)/(2*10*10-6)= 300 A, factor of
5 or so less than NbTi Ic at measurement,
strands are partially coupled
YBCO Roebel
A  Lay pitch*slit width=1 cm * 1 mm = 1 * 10-5 m2
0.15 * 10-5 V, I = 0.15 A
Since Ic for YBCO is roughly 2000 A at 4 K and low fields, a cross current I of 0.15 leads to essentially no coupling So – The hysteretic losses dominate
THESE ARE EDGE LOOPS SO THE AREA IS MINIMAL

33. Summary
A reminder that Roebel cables are topological transformation of Rutherford cables
Current loops are directly transferrable from Rutherford after transforming FO and EO and setting R to infinity
Direct I-V techniques from LTS can be used to advantge for these cables
Pressure and pressure with soft metal reduce ICR, but do not give great contact. Soldering reduces ICR, but does not induce much loss because flux coupling area is small
Large hysteretic losses still present

34. YBCO Splice Under Helium Flow (SUHF) Probe
A helium gas flow probe for YBCO strand and small cable has been completed and initial testing with a single tape (without splice) has been performed
Studying concepts related to possible future CERN uplink
See also 4LB04-G Levin Talk this conference

35. 3: G-10 flow channel connection
1: Top Flange 1
3: G-10 flow channel connection
1 ¼” NPT threaded
304 S.S. Plate 2 3
Weld to 304 S.S. Sanitary Tee
(Tube OD: 2 ½”)
Type E TC
feed-throughs
sealed with Stycast
1 ¼” NPT nipple 4
2: Side Flange
Support tube feedthrough (OD: ¼”) and helium gas flow to flowmeter.
Stycast Bond
G-10 Flow Tube
(OD: 1 3/8”)
Support tube with inlets for helium gas flow
G-10 Sheathed
300A Current Feed-throughs
Voltage/CERNOX wire feed-throughs

36. Photos of SUHF probe Mk.I
Type E thermocouples (5)
Bottom Thermocouple
Bottom Cernox sensor
Voltage taps
SIDE VIEW
Kapton Tape below and above Type E thermocouple
Pb-Sn Soldered onto Alloy 101 OFHC Cu plate
TOP VIEW

37. Imposed Thermal Gradient Measurement
TOP
BOTTOM V1 V2 V3 V4 V7 V5 V6
V11 V9 V8
V10
V12
V13
V14
TC1
TC2
TC3
TC4
TC5 3”
13.5” 3”

38. Further details - Future Work
Perform Splice experiment: Balance current transport through two tapes then transfer all to a single tape. Measuring and balancing contact resistances
See talk 4LB04-By G Levin For further details