1. Nb3Sn wiggler development
Laura García Fajardo
CERN
Low Emittance Rings 2014 Workshop
17-19 September. INFN-LNF, Frascati, Italy

2. Outline Overview Nb3Sn wiggler model. 2D optimization
CLIC DR requirements, Nb3Sn wiggler background…
Nb3Sn wiggler model. 2D optimization
Selection of the main wiggler parameters (winding configuration, coil thickness, gap, B in gap, period length…)
Design of the impregnation mould
Conclusions
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

3. Overview - CLIC damping rings requirements
Plots and specifications by Fanouria Antoniou
From the point of view of the magnet design, to get low emittances we should reach the highest Bw at the lowest possible λw, considering the IBS effect
CLIC damping rings
26 wigglers per each straight section of the DR (52 wiggler per DR, 104 wigglers in total for CLIC)
Bw: Maximum magnetic field density in the gap
λw: Period length
Lw: Total length of wigglers in the damping rings
εr: Emittance with effect of intra-beam scattering
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

4. Overview - Wiggler design
Pictures taken from Daniel Schoerling Ph.D. Thesis
Vertical design
Important wiggler’s parameters
Vertical design advantages
Period length not limited by the bending radius
Possibility of continuous winding
Bw: Maximum mag. field dens. in the gap
Bp: Mag. field dens. in the pole tip
Bs: Maximum mag. field dens. in the conductor’s surface
By: Vertical component of the mag. field dens.
Bmod: Norm of the mag. field dens.
λw: Period length
g: Magnetic gap
zc: Width of the square aperture
Superconducting material (Nb3Sn) advantages
Larger parameter space available (than with NbTi)
Higher T and enthalpy margin (than with NbTi)
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

5. First vertical racetrack magnet (5 coils) tested in 2011
Overview - Background
Photos courtesy of Jacky Mazet
Short model sample
First vertical racetrack magnet (5 coils) tested in 2011
Strand: OST, RRP
Period length: 41.8mm
Strand’s diameter [mm]
0.81
Jc SC [A/mm2]
at B=12T and T=4.3K
2963
Magnet test interrupted after reaching 75% of max. current because of short circuit between the conductor and the iron parts (shorts to ground)
Need to increase the insulation thickness between the poles and the cables
This implies either increasing the period length or using a more efficient strand
Short model sample inside the impregnation mould
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

6. Overview - Strand options
Technology: RRP
Provider: OST
Price: ≈5€/m
Strand insulation:
Fiberglass braiding, 0.07mm thick
Strand specification
Strand specification
d [mm]
0.70
# of filaments
132/169
Sub-element size [µm] 41
Jc SC [A/mm2] at B=10T and T=4.3K
3421
Jc SC [A/mm2] at B=12T and T=4.3K
2176
SC fraction
44.44%
d [mm]
0.85
# of filaments
132/169
Sub-element size [µm] 48
Jc SC [A/mm2] at B=12T and T=4.3K
2450
Jc SC [A/mm2] at B=15T and T=4.3K
1400
SC fraction
45.45%
d: Strand diameter
Jc SC: Critical current density of the superconducting material
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

7. Nb3Sn model. 2D optimization - Selection of the winding configuration
Photos courtesy of Jacky Mazet and Paolo Ferracin
Goal: Finding the most efficient way to wind the magnet
It means: the winding configuration with the highest packing factor
It means: the highest ration between the area occupied by the cables and the area of the square aperture
Winding configuration of the short model:
Odd number of layers that have the same number of turns
Insulation layers will be added between the wire bundle and the iron poles
Plasma coating + fiberglass = 0.5mm
Cross section of the short model
Square aperture of the short model
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

8. Nb3Sn model. 2D optimization - Selection of the winding configuration
Comparing the packing factor (f) of different winding configurations
f(2) is always greater than f(1)
f(3) is greater than f(4) if n < 2m+1
Finally, f(3) is greater than f(2) if n < 2m
It means that the winding configuration #3 has the highest packing factor if the height and width of the square aperture meet the following relation:
(1) Centred layers – even number
(2) Displaced layers – even number
n: number of layers
m: number of turns of the lowest layer
a: height of the square aperture
b: width of the square aperture
D: diameter of the insulated strand
Winding configuration selection
(3) Centred layers – odd number
(4) Displaced layers – odd number
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

9. Cable unit length saving ≈19%
Nb3Sn model. 2D optimization - Selection of the wire bundle thickness
Previous studies (Schoerling, 2012) have shown that the optimal cross-section dimension in terms of maximum Bp* is
yc ≈ zc ≈ 0.30*λw
Cable saving. Comparing the maximum Bw for R=0.30 and R=0.27 (R=zc/λw):
R=0.30
R=0.27
Bw gain ≈1%
Cable unit length saving ≈19%
Ratio of Bp achieved with a cross-section yc and zc to the maximum Bp* for a given period length λw.
But zc has to be an integer multiplier of the insulated strand’s diameter!
Period length vs. maximum Bw for R=0.27 and R=0.30. Strand diameter=0.70mm
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

10. Nb3Sn model. 2D optimization - Selection of the magnetic gap
Fix ratio: R=0.27
As zc has to be an integer multiplier of the cable’s diameter, for different strand diameters we get different period lengths
Magnetic gap selection: g=15mm
(clear bore gap=10mm)
1-period Bwy profile for different period lengths
Strand diameter 0.70mm
1-period Bwy profile for different period lengths
Strand diameter 0.85mm
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

11. 2 possible options using Nb3Sn:
Nb3Sn model. 2D optimization - Selection of the max. magnetic field density in the gap
Magnetic gap: 15mm
Working point: 80%
Nb3Sn strand
Diameter: 0.85mm
Jc SC at B=12T and T=4.3K:
2450 A/mm2
NbTi Bochvar strand
Jc SC at B=5T and T=4.3K:
3088A/mm2
2 possible options using Nb3Sn:
Bw=3.5T
Bw=4.0T
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

12. Period length selection: Cable unit length saving
Nb3Sn model. 2D optimization - Selection of the period length and the strand
Period length selection:
λw=44mm for a maximum Bwy ≈3.5T
λw=48mm for a maximum Bwy ≈4.0T
Period length: λw=40, 42, 44, 46, 48, 50mm
Ratio: 0.27 ≤ R ≤ 0.30
λw [mm]
Bw [T]
Cable unit length [m]
d-strand:
0.70mm
0.85mm 44
3.63
3.58 99 69 48
4.06
119 93
λw [mm]
Bw gain
Cable unit length saving
d-strand: 0.70mm
d-strand: 0.85mm 44
≈1%
≈30% 48 0%
≈22%
Strand selection:
Diameter=0.85mm
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

13. Nb3Sn model. 2D optimization - Bw profile in one period of the wiggler
λw=44mm
λw=48mm
Air
Iron yoke
Coil
Winding pole
Side pole
Half gap
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

14. Nb3Sn model. 2D optimization - Parameters of the selected options
CS: Critical surface; WP: Working point; L: Cable unit length; CC: Critical current
Parameters of the selected options
λw [mm]
L [m] R
% of CC
I-strand [A]
J-strand [A/mm2]
Bs [T]
Bw [T]
Bw/Bs 44 69
0.27
100 %
1365
2406
7.81
4.32
55 %
80 %
1092
1925
6.26
3.58
57 % 48 93
0.29
1232
2172
8.40
4.92
59 %
986
1737
6.73
4.06
60 %
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

15. Nb3Sn model. 2D optimization - Behaviour of the maximum Bw respect to λw
Red plots: R=0.27
Blue plots: 0.27 ≤ R ≤ 0.30
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

16. Design of the impregnation mould
Drawings by Javier Parrilla Leal
This piece does not compress the cables
Wiggler prototype on the bottom piece of the mould
Assembly of the top piece of the mould
Assembly of the side pieces of the mould
Assembly of the front and back pieces of the mould
Previous wiggler prototype inside its impregnation mould, 2011
Wiggler prototype inside its impregnation mould
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

17. Conclusions
It is possible to build a wiggler magnet using Nb3Sn strand, that meets the emittance requirements of the CLIC DR
In this work, the 2D optimization of a Nb3Sn wiggler that aimed at reaching the highest Bw at the lowest possible λw, was presented
Important parameters of the wiggler’s configuration were set:
Winding configuration (odd number of centred layers)
Wire bundle thickness (~0.27*period length)
Magnetic gap (15mm)
Maximum magnetic field density in the gap (3.5T or 4.0T)
Strand (OST RRP, d=0.85mm)
Period length (44mm or 48mm)
Two possible scenarios were selected for constructing the 5 coils wiggler prototype:
Period length=44mm for a maximum field density in gap ≈3.5T (better for total wiggler length decrease)
Period length=48mm for a maximum field density in gap ≈4.0T (better for IBS effect decrease)
The final design of the impregnation mould allows avoiding leaks during the impregnation process (o-rings), eases its manufacturing (box shape) and protects the coils during assembly (curved pieces on the sides)
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

18. People involved in the project at CERN
Laura García Fajardo
Paolo Ferracin
Jacky Mazet
Javier Parrilla Leal
Thomas Sahner
Daniel Schoerling
References
A Multi-TeV Linear Collider Based on CLIC Technology. CLIC Conceptual Design Report. Geneva, 2012
Ferracin, P. et al., Report on CLIC Nb3Sn wiggler magnet. Local report, CERN.
Schoerling, D., Superconducting wiggler magnets for beam-emittance damping rings. Ph.D. Thesis, CERN.
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014

19. THANK YOU FOR YOUR ATTENTION!
Nb3Sn wiggler development. Low Emittance Rings 2014 Workshop. Frascati, Italy
18/09/2014