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

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 30412.8 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

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

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

2D load lines & harmonics Peak Coil Field Modulus [T] Main Component Modulus @ 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

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

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

Dodecapole integrated harmonics Mesh: 252567 (70250 in HPZ) Mesh: 180372 (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 10000 -9.9 -14.1 15.0 5.1 Giovanni Volpini CERN, 15 May 2014

Giovanni Volpini CERN, 15 May 2014 Dodecapole Mesh: 252567 (70250 in HPZ) Mesh: 180372 (7239 in HPZ) Giovanni Volpini CERN, 15 May 2014

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

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 field @ operating current peak field @ s.s. limit Design integrated strength 90 mT∙m Giovanni Volpini CERN, 15 May 2014

Giovanni Volpini CERN, 15 May 2014 Operating point Magnet stored energy @ operating current 3.4 kJ Giovanni Volpini CERN, 15 May 2014

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 = 179 A @ 5 T, 4.2 K (0.5 mm)

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

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

Iron yoke total length 700 mm - 800 mm HX hole D60 @ r = 185 mm round bore return flux plate Symmetric return flux plate

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

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 Aturns @ Iop [At] 71812 57674 Bpeak @ ssl [T] 8.05 6.56 Stored energy @ Iop [J] 30882 24569 Inductance @ 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

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≡ 1 2 𝐿 𝐼 𝑜𝑝 2 ∝ 𝐵 0 2 ∙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

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

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

Procurement & Construction Activity Giovanni Volpini CERN, 15 May 2014

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

Giovanni Volpini CERN, 15 May 2014 procurement and activity status @ 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

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 D60 @ 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

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

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