Vincent Roger, Siarhei Yurevich, Cecilia G. Maiano, Mario Sapinski CASE STUDY 2 Goal Design a Nb-Ti superconducting quadrupole with an 120 mm aperture for the upgrade of the LHC interaction region operating at 1.9 K Vincent Roger, Siarhei Yurevich, Cecilia G. Maiano, Mario Sapinski

CASE STUDY 2 Determination of the maximum Gradient :

CASE STUDY 2 Determination of the maximum Gradient : 150 T/m Coil’s parameters choosen : 2 layers of 15.2 mm width Strand diameter Ø 0,8 mm 38 strands per cable Cu to SC Ratio 1,6 Pitch angle 15,19 deg keystone angle 0.64 deg Coil’s parameter calculated : 2 layers of 14,8 mm width Cable’s thickness 1,45 mm Add: Keystone angle Thickness compaction : -9,375 % Width compaction : -4,56 % K = 0,28

CASE STUDY 2 Determination of the Short sample conditions : j sc_ss : 1766 A/mm2 j o_ss : 500 A/mm2 I ss : 13212 A G ss : 144,5 T/m B peak_ss : 9,4 T

CASE STUDY 2 Determination of the Operational conditions (80% of jss) : j sc_op : 1413 A/mm2 j o_op : 400 A/mm2 I op : 10570 A G op : 115,3 T/m B peak_op : 7,5 T Margin : j o_margin : 400 A/mm2 B peak_margin : 2,5 T T margin : 2,3 K

CASE STUDY 2 Margin with NbTi strands : j o_margin : 400 A/mm2 B peak_margin : 2,5 T T margin : 2,3 K Margin with Nb3Sn strands : j o_margin : 600 A/mm2 B peak_margin : 3,2 T T margin : 4,8 K

CASE STUDY 2 Determination of the Lorentz forces : Fx : 630 kN/m Fy : -1300 kN/m Accumulated stress on the coil mid-plane : σθ max : -52 MPa Thickness of the yoke : t=r2*Gss/2Bsat t : 130 mm Thickness of the collar: t : 40 mm