1. HL-LHC Corrector Magnet Design & Construction Activity Status
Giovanni Volpini
on behalf of the LASA team
CERN 15 May 2014

2. magnet specs Giovanni Volpini CERN, 15 May 2014 Name Orientation Order
Aperture
Int strenght at radius = 50 mm
Magnetic length
Wire diameter
Outer radius (construction)
Stored energy
TOTAL
[-]
[mm]
[Tm]
[m]
[J]
MCQSX S 2
150
1.00
0.789
0.7
230.0
MCSX
N/S 3
0.06
0.108
0.5
150.0
1200.5
MCOX 4
0.04
654.2
MCDX 5
0.03
0.122
588.7
MCTX N 6
0.09
0.456
2649.4
MCTSX
0.015
0.076
441.6
Giovanni Volpini CERN, 15 May 2014

3. Giovanni Volpini CERN, 15 May 2014
Dodecapole
Giovanni Volpini CERN, 15 May 2014

4. Giovanni Volpini CERN, 15 May 2014
dodecapole 2D
outer
air
High Precision Zone for harmonics computation boundary
iron
yoke
coil
bore
pole
Giovanni Volpini CERN, 15 May 2014

5. 2D load lines & harmonics
Peak Coil Field Modulus [T]
Main Component 50 mm
Stored Energy [J]
Inductance [H]
Current [A]
Current [A]
Harmonics w/ linear iron µr=4000 computed, in nice agreement with low-current real iron (b18 = -1.1)
Relative Compoents [x 10E4]
Current [A]
Giovanni Volpini CERN, 15 May 2014

6. Giovanni Volpini CERN, 15 May 2014
Dodecapole 3D
yoke
return flux
coil
Target integrated strenght b6 90 mT·m
Full iron length (not including the return flux plates) 500 mm (z=250 mm)
Air volume up to z=500 mm + infinite elements
Computations (2D & 3D) with COMSOL
Iron à la Roxie, with f.f. 98.5%, no anisotropy (so far)
Mesh 100k – 300 k tetrahedral elements
Giovanni Volpini CERN, 15 May 2014

7. Giovanni Volpini CERN, 15 May 2014
I = 150 A
Peak field on coil (150 A)
1.55
1.5
1.4
Giovanni Volpini CERN, 15 May 2014

8. Dodecapole integrated harmonics
Mesh: (70250 in HPZ)
Mesh: (7239 in HPZ)
Iron Yoke
Iop [A] b6
b18
b30
b42
b54 10
10000
-0.10
-0.15
-0.83
-0.50 50
-0.08
100
0.20
-0.16
-0.53
150
0.70
-0.84
-0.55
b6 b18 b30 b42 b54
Giovanni Volpini CERN, 15 May 2014

9. Giovanni Volpini CERN, 15 May 2014
Dodecapole
Mesh: (70250 in HPZ)
Mesh: (7239 in HPZ)
Giovanni Volpini CERN, 15 May 2014

10. Coil peak field location drift
I = 10 A
I = 50 A
Giovanni Volpini CERN, 15 May 2014

11. Giovanni Volpini CERN, 15 May 2014
Operating point
Design operating current ratio vs. s.s. limit (40%)
s.s. limit
n.o. turns
Operating
current
peak operating current
peak
s.s. limit
Design integrated strength
90 mT∙m
Giovanni Volpini CERN, 15 May 2014

12. Giovanni Volpini CERN, 15 May 2014
Operating point
Magnet stored operating current 3.4 kJ
Giovanni Volpini CERN, 15 May 2014

13. Ic low field extrapolation could be somewhat inaccurate
Caveat:
Ic low field extrapolation could be somewhat inaccurate
@ B = 2 T, top down
LB6
AD 1
LB1 BA
LB2
LB4
LB5 ~0.7
s.s. limit 6,8,10,12-pole
s.s. limit 4-pole
(w/ 0.7 mm wire)
Ic = T, 4.2 K (0.5 mm)

14. Giovanni Volpini CERN, 15 May 2014
Quadrupole
Giovanni Volpini CERN, 15 May 2014

15. Quadrupole 2D cross section
iron
yoke
High Precision Zone for harmonics computation boundary
coil
bore
pole
outer
air
HX hole
Giovanni Volpini CERN, 15 May 2014

16. Iron yoke total length
700 mm mm
HX hole r = 185 mm
round bore return flux plate
Symmetric
return flux plate

17. Giovanni Volpini CERN, 15 May 2014
Quadrupole load lines
700 mm
800 mm
Giovanni Volpini CERN, 15 May 2014

18. Optimized values for 700 mm and 800 mm case
𝑨 𝟐 𝒅𝒛=𝒄𝒐𝒔𝒕
700 mm
800 mm
40% load line
ssl limit [A]
338.6
456.6
n.o. turns
530.2
315.7
Iop [A]
135.4
181.9
Iop [At]
71812
57674
ssl [T]
8.05
6.56
Stored Iop [J]
30882
24569
Iop [H]
3.37
1.49
50% load line
455.7
578
315.2
199.5
227.8
289.0
6.60
5.36
1.19
0.59
245/III
Giovanni Volpini CERN, 15 May 2014

19. Length and operating point scaling laws
k fraction on the load line
l magnet length
q≈1
𝐵 0 𝑑𝑧=𝑐𝑜𝑠𝑡≈ 𝐵 0 ∙𝑙
𝐵 0 ∝ 𝐴 𝑡 𝑝 𝑝≈ 0.7
𝐵 𝑝 ∝ 𝐴 𝑡 𝑞 𝑘 −𝑞 𝑞≈ 0.7 – 1
𝐼 𝑐 ∝ 𝐵 𝑝 −1 (Kim-Anderson)
𝐼 𝑜𝑝 ≡ 𝑘∙𝐼 𝑐
𝑛 𝑡 ≡ 𝐴 𝑡 𝐼 𝑜𝑝
W≡ 𝐿 𝐼 𝑜𝑝 ∝ 𝐵 ∙𝑙
𝐿≡ 2𝑊/ 𝐼 𝑜𝑝 2
𝐵 0 ∝ 𝑙 −1
𝐴 𝑡 ∝ 𝑙 −1/𝑝
𝐵 𝑝 ∝ 𝑙 − 1 𝑝 ∙ 𝑘 −1
𝐼 𝑐 ∝ 𝑙 1 𝑝 ∙𝑘
𝐼 𝑜𝑝 ∝ 𝑙 1 𝑝 ∙ 𝑘 2
𝑛 𝑡 ∝ 𝑙 − 2 𝑝 ∙ 𝑘 −2
W ∝ 𝑙 −1 ∙ 𝑘 0
𝐿∝ 𝑙 − 𝑝+2 𝑝 ∙ 𝑘 −4
𝐵 0 ∝ 𝑙 −1
𝐴 𝑡 ∝ 𝑙 −1/𝑝
𝐵 𝑝 ∝ 𝑙 − 𝑞 𝑝 ∙ 𝑘 −𝑞
𝐼 𝑐 ∝ 𝑙 𝑞 𝑝 ∙ 𝑘 𝑞
𝐼 𝑜𝑝 ∝ 𝑙 𝑞 𝑝 ∙ 𝑘 𝑞+1
𝑛 𝑡 ∝ 𝑙 − 1+𝑞 𝑝 ∙ 𝑘 −𝑞−1
W ∝ 𝑙 −1 ∙ 𝑘 0
𝐿∝ 𝑙 − 𝑝+2𝑞 𝑝 ∙ 𝑘 −2(𝑞+1)
These scaling laws provide us with some understanding of the results found and guidance for magnet design .
Disclaimer: They give the general tendencies, not accurate forecasts!
246/III
Giovanni Volpini CERN, 15 May 2014

20. Fringe field with different choices for the flux return plate
Iron yoke half length 350 mm
No flux return plate
symmetric flux return plate
Flux return 40 mm
round hole flux
return plate
Giovanni Volpini CERN, 15 May 2014

21. 3D Quadrupole Harmonics
Likely operating range
Giovanni Volpini CERN, 15 May 2014

22. Procurement & Construction Activity
Giovanni Volpini CERN, 15 May 2014

23. Giovanni Volpini CERN, 15 May 2014
Impregnation mould
Giovanni Volpini CERN, 15 May 2014

24. Giovanni Volpini CERN, 15 May 2014
procurement and activity LASA
NbTi wire (8 km 0.5 mm dia + 8 km 0.7 mm dia, for all the corrector magnets) to be supplied by B-EAS. Delivery scheduled end of June;
Duratron plates delivered at LASA;
1st CTD-101 resin batch delivered (CERN order);
4 iron plates (580x3975 mm2) ex-LHC to be delivered from CERN to LASA for the sextupole manufacture;
Impregnation mould now being teflon coated at an external company; first impregnation test as soon as it is back!
Curing oven refurbished and tested with the CTD-101 resin;
Winding machine being upgraded with a new wire spool friction system;
1 year contract, HiLumi funded, for a physicist, Luca Somaschini, to follow corrector magnets manufacture QA and room temperature and cryogenic tests, started on May 5th, in addition to the established technical staff (~3 FTE) .
108/I
221/II
Giovanni Volpini CERN, 15 May 2014

25. Giovanni Volpini CERN, 15 May 2014
correctors outer envelope & interfaces
After a discussion concerning the integration in the CP, the following iron yoke outer radii were defined:
Quadrupole r = 230 mm
Higher orders r = 160 mm
Quadrupole design fits the HX hole r = 185 mm;
the design of the higher order magnets, strictly speaking, does not.
Provision for :
alignement reference;
longitudinal stops;
radial spacers to match the pressure vessel inner wall;
magnet handling;
wiring & bus bars;
will be made in the magnet design when the requirements are issued.
233/II
Giovanni Volpini CERN, 15 May 2014

26. Giovanni Volpini CERN, 15 May 2014
Summary
Conclusions:
3D e.m. designs for 4-pole and 12-pole
operating current close to 200 A in both cases
«limited» harmonic content
Next steps:
complete design for 8- and 10- pole (1st week of June)
discuss and define the baseline for the operating currents (mid-June)
complete the conceptual specification set
investigate the e.m. cross-talk and mechanical coupling between magnet (less simple than expected, full 2π model required for the most general case);
Q: the order of magnet is fixed? what are its constraints?
verify the space allocation in the CP
4-pole protection (higher multipoles appear safer)
mechanical design
Giovanni Volpini CERN, 15 May 2014

27. Giovanni Volpini CERN, 15 May 2014
the end
Giovanni Volpini CERN, 15 May 2014