1. Large aperture Q4 M. Segreti, J.M. Rifflet
DSM/IRFU/SACM
M. Segreti, J.M. Rifflet
The HiLumi LHC Design Study (a sub-system of HL-LHC) is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement
HiLumi LHC videoconference, 5 November 2012

2. Parameters and specifications
Within the framework of HiLumi LHC - Task n° Sub-task “Large aperture Q4”, CEA/Saclay is studying the conceptual design of a large aperture two-in-one quadrupole for the outer triplet
Field quality must be optimized in the domain boundary (1/3 of aperture radius) with consideration of cross-talk due to double aperture
Nominal gradient could be low and compensated by magnetic length: value of [Nominal gradient × Magnetic length] can be the same than that of actual MQY magnet, i.e. 160 T/m × 3.4 m = 544 T
Margin to quench must be at least 20% at nominal current
Magnetic designs uses one layer or two layers of MQM cable or one layer of MQ cable
For all studies, cable insulation and inter-pole insulation thicknesses were assumed to be the same than those of actual MQM or MQ magnets

3. Parameters and specifications
Kind of cables
Width (mm)
Min thick (mm)
Max thick (mm)
Nb strands
Transp (mm)
Degrad (%)
Fil
MQM
8.8
0.78
0.91 36 66 5
NbTi MQ
15.1
1.362
1.598
100
Strand
Diam (mm)
Cu/sc
RRR
Tr (K)
Br (T)
BrTr
dJc/dB
MQM
0.48
1.75 80
1.9 5
2800
600 MQ
0.825 9
1953
550

4. Optimized solutions (ROXIE) with 1 layer of MQM cable (1/2)

5. Optimized solutions (ROXIE) with 1 layer of MQM cable (2/2)

6. Optimized solutions (ROXIE) with 2 layers of MQM cable

7. Optimized solutions (ROXIE) with 1 layer of MQ cable

8. Mechanical computation Thermo-mechanical properties
Due to symmetries, the 2D CASTEM model is restricted to one octant
2 levels of collars to simulate effect of stacking in alternated layers
Boundary conditions imposed at symmetry planes
Thermo-mechanical properties
In this example is presented the 90 mm aperture design using 2 layers of MQM cable

9. Mechanical computation
Collaring, relaxation due to insulation creep, cool-down and energization are simulated with the CASTEM software package:
The collaring process is simulated by prescribing an azimuthal gap between the sides of the keys and collar keyways (gap angle θ)
The relaxation due to insulation creep is in first assumed to be 20 %. Creep is modeled by a 20 % reduction of the gap angle θ which is maintained for the next steps (cooling and energization)
The cooling is modeled by an applied thermal body force over the entire structure (by the use of integrated thermal shrinkages of each material from 300 K to 2 K)
The magnetic forces induced at 110 % of nominal current are computed at each coil node using the magneto-static module of CASTEM software package
In this example is presented the 90 mm aperture design using 2 layers of MQM cable

10. Mechanical computation
Mag. configuration
Ø aper
(mm)
Nominal
current (A)
110% of nominal
Mag. forces sum/octant (MN/m)
Coil azim. stress at collaring (MPa) Fx Fy
Peak stress
Average (pre-stress)
1 layer MQM cable 85
7124
7836
0.267
-0.378
-98
-64 90
7043
7747
0.279
-0.387
-94
-66 95
6908
7599
0.286
-0.391
100
6900
7590
0.303
-0.408
-95
-67
105
6767
7444
0.310
-0.410
-96
110
6758
7434
0.327
-0.426
-101
-68
115
6656
7322
0.336
-0.430
120
6626
7289
0.361
-0.446
-104
-69
2 layers MQM cable
4945
5440
0.490
-0.670
-141
-73
4865
5352
0.524
-0.703
-130
-72
4877
5365
0.538
-0.721
-145
-74
4718
5190
0.599
-0.773
-121
-70
1 layer MQ cable
16602
18262
0.403
-0.576
-105
16188
17807
0.436
-0.612
-108
15485
17033
0.450
-0.622
-109
15199
16719
0.488
-0.659
-111
-71
Main results: in yellow the three “preselected” 90 mm aperture designs

11. Mechanical computation
For each magnetic design, mechanical study allowed to verify that the following objectives were reached:
during all phases, coils remained in compression and peak stress in coils was below 150 MPa (arbitrary, but reasonable value) to avoid any possible degradation of the cable insulation
all parts of coils remained in compression at 110% of nominal current with a security margin of 10 MPa at coil polar plane to avoid any separation from collars
coil radial displacement due to magnetic forces during excitation was low (below 50 µm)

12. Mechanical computation
MQM 1
MQM 2 MQ
90 mm design
MQM 1 layer
MQM 2 layer
MQ 1 layer
Main steps
Collaring
Creep
(20%)
Cool down
Energization
Azimuthal stress in coil (MPa)
Max
-94
-75
-56
-63
-130
-104
-107
-98
-108
-86
-65
Average
-66
-52
-44
-46
-72
-57
-51
-68
-55
-40
-42
Min on polar plane
-10
Average on polar plane
-14
-23
-12
Coil radial displacement due to Lorentz forces (µm)
Point A 16 40 25
Point B 2 12 8
Point C 13 23 17
Point D -2 -1
Max von Mises stress (MPa)
In collars
621
497
530
605
1112
890
909
1043
840
672
617
721
In keys
166
133
165
186
303
242
271
304
231
184
191
219

13. Mechanical computation
MQM 1
MQM 2 MQ
Azimuthal stress distribution in coil just after collaring (Mpa)

14. Mechanical computation
MQM 1
MQM 2 MQ
Azimuthal stress distribution in coil at 2 K (Mpa)

15. Mechanical computation
MQM 1
MQM 2 MQ
Azimuthal stress distribution in coil at 110 % of nominal current (Mpa)

16. Mechanical computation
MQM 1
MQM 2 MQ
Coil radial displacement due to magnetic forces during energization up to 110 % of nominal current (µm)

17. Needed cable lengths It is scheduled the fabrication of:
one 2-m-long trial coil 0
one 2-m-long single-aperture model
one 2-m-long double-aperture model
one real-length cold mass prototype
Five real-length cold masses for the series
If the 2-m-long single-aperture model is used for the 2 m long double-aperture model (1 trial coil + 2 x 4 coils = 9 model coils)
and if the real-length cold mass prototype is used for the 5 real-length cold masses for the series (5 x 4 x 2 = 40 real-length coils)
If the 2-m-long single-aperture model is not used for the 2 m long double-aperture model (1 trial coil + 2 x 4 coils = 13 model coils)
and if the real-length cold mass prototype is not used for the 5 real-length cold masses for the series (5 x 4 x 2 = 48 real-length coils)

18. Conclusions
Optimized magnetic designs for the large aperture Q4 have been briefly recalled with MQM cable (1 or 2 layers) and with MQ cable (1 layer) cable with 85, 90, 95 and 100 mm apertures
Mechanical simulations of each main phase (collaring, relaxation due to cable insulation creep, cooling and energization) have been realized and have validated all magnetic designs by taking into use 110 % of nominal current
Needed cable lengths have been estimated for each magnetic design. Because development of a new cable for the large aperture Q4 is not envisaged, the quantities of existing cable lengths available at CERN will influence the choice of the final design which will be used as baseline for further studies