Block design status EuroCirCol Clément Lorin, Maria Durante 16 may 2017 Acknowledgements:

Critical surface Nb3Sn Jc (1.9 K, 16 T) = 2245 A/mm² no cabling degr. C0 = 267845 AT/mm² where t = T/Tc0 and b = B/Bc2(t) with B the magnetic flux density on the conductors. Tc0 = 16 K, Bc20 = 29.38 T, α = 0.96, are fitting parameters computed from the analysis of measurements on the conductor. Similarly: Jc (1.9 K, 16 T) = 2312 A/mm² 3% cabling degr. C0 = 275880 AT/mm²

Design evolution bore tip th. decrease Quantity ASC2016 v20ar v1ari204 Unit strand diameter 1.1 – 0.7 1.155 – 0.705 1.15 – 0.70 mm nb of strands 24 – 39 21 – 35 20 – 34 N/A width 14.25 13.05 12.6 average thickness 2.0 – 1.25 2.1 – 1.25 Cu/nonCu 0.8 – 1.6 0.8– 2.3 0.8– 2.0 Inom 10930 10990 10465 A Bpeak 16.81 16.74 16.72 T LL margin (1.9 K) 13.95 14.01 13.94 % Inductance diff. (2 ap) 48.06 39.80 44.2 mH/m Stored energy (2 ap) 3016 2518 2542 kJ/m Nb of turns 114 = 3+3+9+9 +22+22+23+23 104 = 5+5+10+10 +18+18+19+19 108 = 5+5+9+9 +19+19+21+21 - Fx & Fy (per ½-coil) 8473 & -3572 8042 & -3347 8042 & -3329 kN/m Hotspot 348 349 351 K Bore thickness 6.3 1.75 1.6 Midplane shim 1.45 2.25 LdxI (1 aperture) 263 218 232 HA/m I/Ic HF-LF 0.47 – 0.61 Conductor area (2 ap) 151.9 133.7 130.3 cm² 4578 x 14.3 x 8.7 weight 8652 7614 7420 tons = v20ar v1ari204 bore tip th. decrease interbeam decrease (250mm -> 204 mm) insulation = 0.15 mm

Harmonic contents v1ari204: higher cross-talking (b2 = 24 units) at nominal 16 T: 1 T 3.3 T 16 T

Fringe field R = 1 meter -> Bnorm ~ 3 mT R = 1 m 0° 90°

Emag 3D Opera model: Bpss-Bpends = 0.4 T Lyoke = Lcoil = 1780 mm Lpads = 1100 mm Lmag = 1498 mm 141 mm 340 mm Harmonics from 560 mm to 960 mm (orange box) b3 can be easily tuned Bpss-Bpends = 0.4 T

Emag 3D - Optics Question asked to beam guys (WP2, A. Chance, B. Dalena): No straight section length effect What we usually do: Optimization depends on the SS length 14 m with b3 = 6 units 2x0.15 m with b3 = -300 units To get more compact ends for block design Is that feasible?

Need validation/correction Graded: how? Need validation/correction by Etienne et Susana Two options: External connexions vs Internal connexions Courtesy from Etienne Rochepault CERN Development program CERN, CEA, PSI,…? Pros&Cons: -Coil assembly: cable to take care -End parts: cable path outwards -Additional connexion box -Shorter ends -Connexion length -Splice in low field area Pros&Cons: -Length of the splice (not long enough < Tp) -Gap between LF&HF: longer ends -Splice in high field area -Coil assembly easier -End parts simpler

Mechanics v1ari204 63 mm thick shell 700 µm ← 50 µm ↓ 1.6 mm thick bore tip Ryoke = 273 mm Contacts/symmetry: sliding; 0.2 friction glued: coils with pole vertically and with shoes rail is a block for rigidity

Coil stress v1ari204 Contact at 105% σ von Mises σhorizontal Keys in 106 MPa -117 MPa 190 MPa -203 MPa 185 MPa -186 MPa Contact at 105% 16.8 T central field 105 % nominal -19 MPa +145 MPa 16.0 T central field 100 % nominal +11 MPa +98 MPa

Coil displacement Before key insertion to nominal powering 16 T x horizontal disp. y vertical disp. 1 2 3 4 5 6 1 2 3 4 5 6 u1x_nominal = -68 µm u2x_nominal = -85 µm u3x_nominal = -27 µm u4x_nominal = -10 µm u5x_nominal = -440 µm u6x_nominal = -368 µm u1y_nominal = -17 µm u2y_nominal = -146 µm u3y_nominal = -171 µm u4y_nominal = -255 µm u5y_nominal = -192 µm u6y_nominal = -17 µm compaction ~ 1% of cable width

Aluminum shell Cold – 4.2 K 16.8 T (105% nominal) Key σ theta Rp0.2 RT 480 MPa 690 MPa Cold – 4.2 K 16.8 T (105% nominal) Key σ theta

Iron yoke Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises Rp0.2 RT cold/tension Magnetil 180 MPa 230 MPa 723 MPa/200 MPa 723 MPa/380 MPa Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises σI – tension max

Iron pad1 Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises Rp0.2 RT cold/tension Magnetil 180 MPa 230 MPa 723 MPa/200 MPa 723 MPa/380 MPa Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises σI – tension max

Iron pad2 Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises Rp0.2 RT cold/tension Magnetil 180 MPa 230 MPa 723 MPa/200 MPa 723 MPa/380 MPa Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises σI – tension max

Titanium pole Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises Rp0.2 RT cold/tension Ti-6Al-4V 827 MPa 1624 MPa Cold – 4.2 K 16.8 T (105% nominal) Key σ von Mises 489 MPa 891 MPa 1140 MPa

Conclusion Bore tip to be modified Vertical pad to be modified 1.75 mm / ground ins. taken into account Vertical pad to be modified Roundish angle -> Emag impact Double aperture Split vertical key to improve coil-pole contact and reduce peak stress (230 MPa*) Start working on 204 mm interbeam Shall we stop working with 1.15 mm strand? Demonstrator strands? *260 MPa: H. Felice et al. Performance of Nb3Sn quad under high stress https://www.osti.gov/scitech/biblio/1048936

Key position 18 mm 20 mm 27 mm 25 mm Single aperture:

extra Coil stress v1ari204 Contact at 100% σ von Mises σhorizontal Keys in 1.8 K 16.8 T σ von Mises σhorizontal 91 MPa -101 MPa 175 MPa -187 MPa 159 MPa -175 MPa Contact at 100% 16.0 T central field 100 % nominal -3 MPa 131 MPa About 10 to 15 MPa less than a contact at 105% σeq (100%,4.2K) = 175 MPa σx (105%, 4.2K) = -203 MPa