1. Towards 50 T Solenoids MAP Meeting, Mar. 5, 2010
E. Barzi, A. Bartalesi (guest), V. Lombardo, E. Terzini (guest), D. Turrioni
MAP Meeting, Mar. 5, 2010

2. R&D Areas 1. HTS Conductor R&D 2. Magnet design studies
3. Coil technology
4. Coil test

3. 1. HTS Conductor R&D Wires BSCCO-2212 Rutherford-type Cables
YBCO Roebel Cables

4. HTS Wires

5. Wire R&D
Monitoring industry progress to provide input to magnet design.
This includes studies of the engineering current density (Je) as a function of:
magnetic field => up to 28 T (FNAL-NIMS)
temperature => from superfluid He to LN
field orientation (for tapes)
bending strain
longitudinal strain => fixture awaiting commissioning
transverse pressure => setup is available.

6. BSCCO Cables – HTS Coll. 100% pass rate in bending test

7. Ic Degradation vs. Packing Factor Samples Reacted at OST - Tested at Fermilab
Cabling level of degradation depends on powder and/or billet design.
for VHFSMC

8. FSU Results on Leak Test of FNAL Cable
Cabling did not cause leakage because there was no leakage at the edge of any cables, but random leakage on flat surface of BSCCO powders.
E. Hellstrom et al.

9. YBCO ROEBEL Cable from quality assessment to actual cabling
1 x 5 mm wide strand in 12 mm wide material
15/5
design
width
Ic uniformity can be evaluated performing a 2D magnetic measurement of the field penetration profile. There are seven Hall sensor readings at each position of the tape and the resolution in tape position is set at 1 mm. The field penetration profile at every specific location of the tape length reflects the uniformity across the width

10. Ic Inhomogeneities

11. 1. Summary HTS Conductor R&D
Round BSCCO-2212 wire can be cabled in Rutherford type cables or round cables.
Its major challenges are requiring a very stringent reaction schedule in Oxygen, the Jc, powder leaks and strain sensitivity.
YBCO can be used in Roebel cable R&D, has very high parallel Jc, and is very strong mechanically.
Its present challenges are anisotropy and Jc homogeneity.

12. 2. Magnet Design Studies
Analytical Study of Stress State in HTS Solenoids
A mesomechanic model to represent a wound and impregnated YBCO coil

13. Analytical Study of Stress State in HTS Solenoids
To produces Stresses as a function of a coil nominal field, the following was done:
Room temperature analytical model of BSCCO solenoid
Study of stress distribution in the coil for various constraint configurations
Comparison of the analytical results with FEM model
Coil size optimization for max σhoop=100 MPa
Study of max stress as a function of coil self-field
FERMILAB-TM-2448-TD

14. Parameters Main variables are: The engineering current density J
Ratio of outer and inner diameters, α=OD/ID
Dimensionless length of the solenoid, β= L/ID
The following was set:
ID = 50 mm
The length of the solenoid was chosen from the minimum volume curve β(α)

15. Examples of Constraint Cases
Cases analyzed:
Free coil => σrr(R1) = σrr(R2) = 0
Outer surface locked => σrr(R1) = u(R2) = 0
Outer SS skin (t=2 mm) => σrr(R1) =0, u_sol(R2)= u_skin(R2)
E_coil = 40 GPa
E_skin = 206 GPa
t = 2 mm 1. 2. 3.

16. Results of Stress Distributions
α=4 (β_opt= 2.52) ; J = 152 A/mm2.
B0 ≈ 10 T 1. 3. 2.
The critical location of the coil is on the inner surface (r=R1)

17. FEM comparison
Analytical model vs. FEM
FEM(300 K) vs. FEM (4.2 K)

18. Critical current characteristic
To study maximum stress values as a function of the solenoid magnetic field, FNAL/NIMS data up to 28 T were used for the Bi-2212 Ic characteristic.

19. Geometry vs. Self-field
Using J(B), the geometric parameters can be plotted as a function of the coil Self-Field.

20. Stress vs. Self-field Outer surface locked Outer SS skin No pre-load
t = 2 mm

21. Stress Sensitivity to Coil Young Modulus
Influence of elastic modulus of the solenoid on stress of coil and skin
For an elastic modulus of the solenoid 40<E<110 GPa
The “softness” of the coil impacts only the stress in the skin.

22. Stress Sensitivity to Pre-load
A radial interference, γ=Δ/R2, decreases the max hoop stress of the solenoid, but increases that on the skin.
Skin Max Hoop Stress & J vs. Self field

23. What maximum field could we achieve If BSCCO could take 100 MPa of tensile stress
Imposing σadm =100 MPa and R1=25 mm:
Cases
R2 [mm]
L [mm]
J [A/mm2]
B [T]
Max Hoop [MPa]
Max Radial [MPa]
Stresses distributions
[MPa]
Free (1) 65 77
286.1
9.5
100
3.37
Outer surface locked (2) 93
113
246.1
14.8
-47.9
With SS skin (3) 68 81
279.8
10.1
-5.78

24. Conclusions and next steps
It is clear that in order to use BSCCO for high field magnet applications a number of strengthening solutions, from strain management in the coil itself, to reinforcement of the cable and/or the strand, have to be explored.
Optimizing the design of the coil containment will minimize the stresses.
These analytical studies could be expanded to study coil reinforcement effects.
For actual magnet design, it will however be important to include anisotropic effects using finite element models.

25. Example of Reinforced SolenoidB
Coil radius, m
Basic Parameters
Inner bore diameter 50 mm
Length 1 meter
Fields 30 T or higher 
HTS materials
Key design issues:
superconductor type
Jc, effect of field direction in case of HTS tapes
stress management
quench protection
cost
Conceptual design:
hybrid coil design
coil sections
NbTi
Nb3Sn
BSCCO-2223
V.V. Kashikhin et al.

26. Modeling Anisotropy This section Kapton YBCO Tape insulation
A wound coil can structurally be seen as an anisotropic material
Two different materials are cowound for electrical insulation between turns
To better analyze it, a composite-oriented technique is proposed

27. The mesomechanic technique
Kapton
YBCO
Epoxy
With this analysis, we isolate and study an Elementary Cell, which repeats itself in the whole material.
This cell is modeled and loaded, and a material model is built upon the results.
FERMILAB-MASTERS

28. Rigidity matrix for a composite
Solving, we obtain the properties
Ansys outputs
Unitary explorative loads

29. Required Analyses (six)
For example, the x pressure
Mesomechanic
Analysis
Integrated Ansys output

30. Example of Mesomechanical analysis results
X axis
Load

31. Anisotropic Material Characterization
YBCO: E = 110 GPa, nu= 0.3
Kapton: E = 5.5 GPa, nu = 0.3
Epoxy: E = 4.5 GPa, nu = 0.3
Resulting anisotropic tensor
Err = 16.6 GPa, Eθθ = 26.8 GPa, Ezz = 28.0 GPa
nurθ = 0.30, nuθz = 0.27, nuzr = 0.32
Grθ = 2.77 GPa, Gθz = 4.97 GPa, Gzr = 2.84 GPa

32. Max 120 MPa in the coil @ self field
Original Analysis
Max 120 MPa in the self field
Hoop
Radial
Homogeneous material

33. Max 135 MPa in the skin @ self field
Anisotropic Analysis
Max 135 MPa in the self field
Steel skin
Hoop
Radial
Composite material

34. 2. Summary Magnet Design Studies
In the assumption that BSCCO can take 100 MPa tensile stress, it would produce 10 T max.
A 40 T solenoid produces 900 MPa + in the coil itself.
The analytical studies showed that a pre-load decreases somewhat the max hoop stress of the solenoid, but increases much more that on the skin.
Hence it is clear that strengthening solutions will have to be used.
Results of mesomechanic finite element models show that for an accurate stress representation it is important to include anisotropic effects.

35. 3. Coil Technology Winding process and tooling Impregnation techniques
Splicing procedures
R&D on thermally conductive insulation

36. Winding Process and Tooling
Co-Winding Machine for YBCO and Kapton Tape (commissioning stage)
19mm/62mm copper/kapton practice double pancake coil.

37. Tape&Insulation Co-winding Process

38. Impregnation tooling

39. 4. Coil Test
Thin coils to fit within 49 mm Variable Temperature Insert and within 77 mm magnet bore mounted on existing probe.
Thicker double pancakes mounted on modular Insert Test Facility and tested within 77 mm aperture 14 T solenoid.
Before testing whole assembly of 14 double pancakes to produce 20 T + on the conductor, the effects of mutual inductance between insert and outer magnet have to be calculated.

40. Test Equipment
Modular ITF
14 T solenoid with 77 mm bore

41. Summary of HTS coils tested in 49 mm Variable Temperature Insert for Temperature dependence studies
Wire Manufacturer
Conductor Type
Coil Geometry
Impregnation
Test Parameters
SSL(4.2K,14T)
Notes
American Superconductor
348 YBCO
Single Pancake
Stycast 2850FT
77K, 4.2K
0T-14T
98%
[Di:38mm-Do:43mm]
Tested at 4.2K,12K,22K,33K
Hermetic BSCCO2223
[Di:38mm-Do:43mm] Tested at 4.2K,12K,22K,33K
Double
Pancake
77K, 0T
67%
[Di:32mm-Do:43mm] Bad Splice due to small outer radius and stiffness of tape
SuperPower
YBCO M3-609 (R&D conductor) 0%
[Di:38mm-Do:43mm] Resistive Coil
YBCO M3-569 (spool 4)
29%
Low Ic, Low n values
YBCO M (spool 4)
Double Pancake
22%
[Di:32mm-Do:43mm]
Dry
76%
[Di:38mm-Do:43mm] Tested in compression

42. Summary of Double pancake 2G YBCO coils tested in 14 T, 77 mm bore magnet
Coil ID
Conductor
ID/OD
Coil Length (m)
Impregnation
Test Setup
SSL
Notes
DPY01
SP M3-569 (spool4)
60mm/62mm 2
dry
Individual
Top coil resistive, bottom ok
DPY02
Resistive after first quench in helium
DPY03
SSL(77K,0T)=100%
SSL(4.2K,0T)=100%
1000A in Self Field.
DPY04
SSL(4.2K,12T)=76%
Unsupported joints Ic(4.2K,12T) = 570 A
Joint degradation.
DPY05
CTD101 (whole coil)
Top pancake showed early quench
DPY06
CTD101 (last layer)
very thick epoxy (3mm) – ok in nitrogen, coil damaged before first test in helium
DPY07
SP M3-565 (spool5)
Impregnation thickness adjustments (1.5 to 0.5mm). Ic(4.2K,12T) = 400 A
DPY08
Replica of DPY07. Damaged during winding.
DPY09
ITF
High resistive Joint.
DPY10
Stycast (last layer)
SSL(4.2K,12T)=75%
Ic(14T)=523 A Ic(12T)=558 A Ic(10T)=604 A

43. Magnet Assembly (1)
Proprietary data

44. Magnet Assembly (2)
The magnet consists of a single Nb3Sn inner high field section 180 mm high, and of two outer lower field NbTi coils 262 mm high. The Nb3Sn coil is constrained with four layers of stainless steel (SS) wire. The innermost NbTi coil is made of three coils, whereas the outermost NbTi coil is made of two coils. Between each of the coil sections an inter-coil insulation material is present.
In short, the magnet assembly includes a total of seven coils.

45. Example of Stress State in Magnet Assembly
Coils 3 to 5

46. Results Comparison (1) Magnetic Field (contours plot) FNAL Model
Oxford Model

47. Results Comparison (2)
Hoop stresses
FNAL Model
Oxford Model

48. 4. Summary
Coil Test
Small coil tests are used to provide feedback to the Coil Technology area, including improving splicing techniques, and possible impregnation procedures.
Oxford proprietary magnet assembly and material properties were obtained and anisotropic model validated to perform mutual force calculations.