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Large aperture Q4M. Segreti, J.M. Rifflet

HiLumi LHC videoconference, 5 November 2012

DSM/IRFU/SACM

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 284404.

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Parameters and specifications

• Within the framework of HiLumi LHC - Task n° 3.5 - 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

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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 36 100 5 NbTi

Strand Diam (mm) Cu/sc RRR Tr (K) Br (T) Jc @ BrTr dJc/dBMQM 0.48 1.75 80 1.9 5 2800 600MQ 0.825 1.9 80 1.9 9 1953 550

Parameters and specifications

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

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

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Optimized solutions (ROXIE) with 2 layers of MQM cable

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Optimized solutions (ROXIE) with 1 layer of MQ cable

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Mechanical computation

• 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 propertiesMaterials Temp. Elastic Yield Ultimate Integrated

Componants Modulus Strength Strength Thermal Shrinkage(K) E (GPa) (MPa) (MPa) a (mm/m)

yus 130 S Nippon Steel 300 190 445 795Collars 2 210 1023 1595 2.4

316L Stainless Steel 300 205 275 596Keys 2 210 666 1570 2.9

Copper 300 136Angular wedges 2 136 3.3Kapton Foils 300 2.5

inter-layer & inter-pole insulations 2 4 6.0 insulated NbTi conductor blocks 300 7.50 *

Coils with MQM cable 2 11.25 * 5.0 * insulated NbTi conductor blocks 300 10.00

Coils with MQ cable 2 15.00 4.9* For MQM insulated conductor, it is assumed that: E 2K = 1.5 × E 300K and a = 5.0 mm/m (see in red)

A C

B

D

q

O

qFront collar

Back collar keyway

Collars mid-plane

Perfect contactbetween layers

In this example is presented the 90 mm aperture design using 2 layers of MQM cable

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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

A C

B

D

q

O

qFront collar

Back collar keyway

Collars mid-plane

Perfect contactbetween layers

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Mechanical computation

Mag. configuration Ø aper(mm)

Nominalcurrent (A)

110% of nominalcurrent (A)

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 -94 -66

100 6900 7590 0.303 -0.408 -95 -67

105 6767 7444 0.310 -0.410 -96 -67

110 6758 7434 0.327 -0.426 -101 -68

115 6656 7322 0.336 -0.430 -101 -68

120 6626 7289 0.361 -0.446 -104 -69

2 layers MQM cable

85 4945 5440 0.490 -0.670 -141 -73

90 4865 5352 0.524 -0.703 -130 -72

95 4877 5365 0.538 -0.721 -145 -74

100 4718 5190 0.599 -0.773 -121 -70

1 layer MQ cable

85 16602 18262 0.403 -0.576 -105 -67

90 16188 17807 0.436 -0.612 -108 -68

95 15485 17033 0.450 -0.622 -109 -69

100 15199 16719 0.488 -0.659 -111 -71

Main results: in yellow the three “preselected” 90 mm aperture designs

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Mechanical computationFor 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)

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MQM 1 MQM 2 MQ

Mechanical computation

90 mm design MQM 1 layer MQM 2 layer MQ 1 layer

Main steps Collaring Creep(20%) Cool down Energization Collaring Creep

(20%) Cool down Energization Collaring Creep(20%) Cool down Energization

Azimuthal stress in coil (MPa)

Max -94 -75 -56 -63 -130 -104 -107 -98 -108 -86 -56 -65

Average -66 -52 -44 -46 -72 -57 -51 -52 -68 -55 -40 -42

Min on polar plane

-10

-10

-10

Average on polar plane -14 -23 -12

Coil radial displacement due to Lorentz forces (µm)Point A

16 40 25Point B 2 12 8Point C 13 23 17Point D -2 2 -1Max von Mises stress (MPa)In collars 621 497 530 605 1112 890 909 1043 840 672 617 721In keys 166 133 165 186 303 242 271 304 231 184 191 219

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Mechanical computation

Azimuthal stress distribution in coil just after collaring (Mpa)

MQM 1 MQM 2 MQ

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Mechanical computation

MQM 1 MQM 2

Azimuthal stress distribution in coil at 2 K (Mpa)

MQ

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Mechanical computation

MQM 1 MQM 2 MQ

Azimuthal stress distribution in coil at 110 % of nominal current (Mpa)

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Mechanical computation

MQM 1 MQM 2 MQ

Coil radial displacement due to magnetic forces during energization up to 110 % of nominal current (µm)

A

B

C

D

A

B

C

D

A

B

C

D

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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

Ø aper Mag. Length Nr of turns Cable length per coil number of 2m Cable length per number of real- Total needed(mm) (m) per coil for 2m model (m) coils (model) coil for series (m) length coils cable (m)

1 layer MQM cable 90 5.33 24 96 9 256 40 110982 layers MQM cable 90 4.25 51 204 9 434 40 19176

1 layer MQ cable 90 4.53 14 56 9 127 40 5578

Mag. configuration

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)

Ø aper Mag. Length Nr of turns Cable length per coil number of 2m Cable length per number of real- Total needed(mm) (m) per coil for 2m model (m) coils (model) coil for series (m) length coils cable (m)

1 layer MQM cable 90 5.33 24 96 13 256 48 135282 layers MQM cable 90 4.25 51 204 13 434 48 23460

1 layer MQ cable 90 4.53 14 56 13 127 48 6816

Mag. configuration

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)

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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