1. A model superconducting helical undulators wound of wind and react MgB2 and Nb3Sn multifilamentary wires
Center for Superconducting & Magnetic Materials
M. Majoros
M. D. Sumption
E. W. Collings
M. Susner
C. Kovacs
Hyper-Tech Research, Inc.
M. Tomsic
X. Peng
M. Rindfleisch
D. Doll
D. Lyons

2. Outline
Experiments (250 mm long, 14 mm period) undulators tested in LHe bath
- MgB2 undulator
- Nb3Sn (Fusion wire) undulator
- Nb3Sn (Tube-type wire) undulator
FEM Modeling
Nb3Sn 12 mm period undulator
Nb3Sn 10 mm period undulator

3. Model undulator design
TABLE I Design Parameters for the Undulator Models
Period (λ) (mm) 14
Winding bore (mm) 8
Beam aperture (mm) 7
Coil width in axial direction (mm) 5
Coil thickness in radial direction (mm)
Pole width (mm) 2
Coil length (mm)
250

4. Model undulator design
Beam aperture = 7.0 mm
Winding bore, 2ro = 8.0 mm
OD of coil winding = 18.0 mm
OD of pole (flange) = 19.05mm
Period, λ = 14 mm
Coil width, a = 5.0 mm
Coil thickness, b = 5.0 mm
One period, λ = 14 mm
63 turns,
0.5 mm wire
2.0
5.0
5.0
windings
3.5
4.0
9.0
9.53
Pole,1010 Fe
Total length of coil = 250 mm
Beam, SS

5. Optical cross-section of the 0.47 mm strand
MgB2 wire design
7 filament strand with Mg-rich powders and a Glidcop (a high alumina content grade of dispersion strengthened Cu) outer sheath drawn to 0.47 mm in diameter
The multifilament wire was constructed with Nb barriers, Cu matrix, and Glidcop outer heath, and with six MgB2 filaments around one center Cu filament
The wire was reacted at 675 ºC for 20 or 40 minutes
The MgB2 multifilament strands were insulated with s-glass braid. The wire diameter including insulation was mm Cu
Glidcop Nb
MgB2
Optical cross-section of the 0.47 mm strand

6. Model MgB2 undulator design
Undulator parts assembled into a former
A total of 66.6 meters in six layers were wound on the model undulator coil (39 turns)
The undulator coil was heat treated at 675°C for 20 minutes in an oven with flowing argon
The day following heat treatment it was epoxy impregnated with mixed Stycast 1266 epoxy heated in a vacuum
After removal from the epoxy bath the curing continued in air at room temperature. The coil was placed on a slow rotating shaft for an hour, and then remained stationary for another 8 to 12 hours
End piece with conductor wound on ends

7. Model MgB2 undulator design
4-turn undulator:
FEM modeling
Iron:
- initial µr = 150
- M (saturation) = 1.6 Tesla
Maximum field on z-axis: 0.25 T
Ic (0.15 µV/cm) = 250 A

8. Model MgB2 undulator design
A short model helical undulator, 250 mm long, with a period of 14 mm made of MgB2 6 filament wire was designed, fabricated and tested in liquid helium bath
A bore field of 0.25 Tesla in radial direction was achieved on the axis
To reach a desired value of 0.8 T, it is needed to improve MgB2 strand and increase fill factor of the conductor, packing factor of the winding, and Jc for the MgB2 conductor
The works toward reducing the particle size of the Mg and B powder mixture in order not to lose current density when processing the wire to a small diameter with small filaments and higher fill factor are in progress

9. Nb3Sn wire (fusion type internal-Sn strand) and undulator design
An out-of-spec gun-drilled fusion conductor:
Bare wire diameter: 0.7mm
No. filaments in an individual sub-element: 162
No. sub-elements: 19
Total number of filaments: 3078
Filament size: about 5 microns
Parameters of Nb3Sn model undulator:
Insulated Nb3Sn wire diameter = 0.85 mm
Number of turns per layer = 5
Number of layers = 5
Total number of turns = 25
Iron: - initial relative permeability = 150
- saturation magnetization = 1.6 Tesla

10. Model Nb3Sn (fusion strand)undulator design
Nb3Sn undulator (25x500A) – field in central plane
Max. on-axis field: 1.1 T

11. After epoxy impregnation
Model Nb3Sn (fusion strand)undulator design
As wound
After epoxy impregnation

12. Model Nb3Sn (fusion strand)undulator design
A short model helical undulator, 250 mm long, with a period of 14 mm made of Nb3Sn 19 strand wire was designed, fabricated and tested in liquid helium bath
A bore field of Tesla in radial direction was achieved on the axis
To reach a desired value of 1 T, it is needed to prevent epoxy cracking and probably to improve Nb3Sn strand stability

13. Model Nb3Sn (tube-type strand)undulator designCu
Nb-7.5wt% Ta
Nb3Sn strand parameters.
Outside diameter (mm)
0.5
Number of filaments
217
Filament diameter (µm) 24
Effective diameter (µm) 35
SC fraction (%)
45.6
12 T Jc,non-Cu (A/mm2)
2200
4 T Jc,non-Cu (A/mm2)
7650
4 T Je (A/mm2)
3825
4 T Ic (A) for 0.5 mm OD
622.22
insulation
s-glass

14. Model Nb3Sn (tube-type strand)undulator design
Ic of the undulator = 832 A

15. Current ramp rate (A/s)
Model Nb3Sn (tube-type strand)undulator design
Run No.
Iq, A
Current ramp rate (A/s) 1
640.3
0.4 to 150 A; 0.7 from 150 A to A 2
718.8
2 to 650 A; 0.25 from 650 A to A 3
814.5
2 to A; 0.25 from A to A 4
842.6
2 to A; 0.25 from A to 842.6A 5
740.0
2 to A
- The undulator reached the target field of 0.8 T on the axis
Also, the coil exhibits the same critical current (Ic) as the short sample, a significant achievement, especially considering that it was made with a Tube type wire (a newer Nb3Sn wire fabrication technique).
- After measurement, the undulator emerged with no obvious cracking.
- The strand exhibited increased stability as compared to previous undulators, suggesting that a less aggressive HT is beneficial for this application.
It is note that while the overall performance was good, substantial training of the coil was present; this training eventually became negative after the fifth quench, a point which needs to be improved.
- We speculate that this training could be due to the level of epoxy around the end turn legs being insufficient.
Finally, we note that the winding pack was not filled. The performance would have been significantly enhanced has the full winding height been employed.

16. Model Nb3Sn 12mm period undulator – FEM modelingλ ri w th
thFe
winding
Pole, Fe
Beam tube
wFe
MAXIMUM ON-AXIS FIELDS OF THE MODELED 12 mm-PERIOD UNDULATORS (in Tesla)
Model 1
Model 2
Model 3
FW-S glass
0.986
1.0445
1.182
FW-nGimat
1.157
1.246
1.393
TW-S glass
1.233
1.319
1.477
TW-nGimat
1.442
1.5026
1.688
FTW-nGimat
1.67
1.759
1.9208
PARAMETERS OF THE MODELLED UNDULATORS WITH A PERIOD OF 12 mm
Model 1
Model 2
Model 3
ri (mm) 4
th (mm)
thFe (mm) 2
w (mm) 5 7 10
wFe (mm)
5.53
7.53
10.53
Poles Fe

17. Model Nb3Sn 10mm period undulator – FEM modelingλ ri w th
thFe
winding
Pole, Fe
Beam tube
wFe
PARAMETERS OF THE MODELLED UNDULATORS WITH A PERIOD OF 10 mm
MAXIMUM ON-AXIS FIELDS OF THE MODELED 10 mm-PERIOD UNDULATORS (in Tesla)
Model 1
Model 2
Model 3
Model 4
ri (mm) 3 4
th (mm)
thFe (mm) 2
w (mm) 11 6
wFe (mm) 12 - 7
Poles Fe
air
Model 1
Model 2
Model 3
Model 4
FW-S glass
1.216
1.053
0.998
0.697
FW-nGimat
1.422
1.244
1.162
0.807
TW-S glass
1.504
1.340
1.217
0.875
TW-nGimat
1.750
1.600
1.025
FTW-nGimat
2.023
1.873
1.641
1.203

18. Conclusion
A short model helical undulators, 250 mm long, with a period of 14 mm made of MgB2 and Nb3Sn strands (FW and TW) were designed, fabricated and tested in liquid helium bath
A bore field of 0.25, and 0.8 Tesla in radial direction was achieved on the axis of MgB2 and Nb3Sn (FW and TW) model undulators, respectively
A field > 1 Tesla is achievable in undulators with a period of 12mm and10 mm wound using Nb3Sn wires
The works toward reducing the particle size of the Mg and B powder mixture in order not to lose current density when processing the MgB2 wires to a small diameter with small filaments and higher fill factor are in progress