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 284404. HiLumi LHC videoconference, 5 November 2012

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

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) Jc @ BrTr dJc/dB MQM 0.48 1.75 80 1.9 5 2800 600 MQ 0.825 9 1953 550

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

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

Optimized solutions (ROXIE) with 2 layers of MQM cable

Optimized solutions (ROXIE) with 1 layer of MQ cable

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

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

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

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)

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

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

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

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

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

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)

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