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CERN Accelerator School Superconductivity for Accelerators Case study 4

CERN Accelerator School Superconductivity for Accelerators Case study 4. Paolo Ferracin ( paolo.ferracin@cern.ch ) European Organization for Nuclear Research (CERN ). Case study 4. 11 T Nb 3 Sn dipole for the LHC collimation upgrade Introduction

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CERN Accelerator School Superconductivity for Accelerators Case study 4

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  1. CERN Accelerator SchoolSuperconductivity for AcceleratorsCase study 4 Paolo Ferracin (paolo.ferracin@cern.ch) European Organization for Nuclear Research (CERN)

  2. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Introduction • The second phase of the LHC collimation upgrade will enable proton and ion beam operation at nominal and ultimate intensities. • To improve the collimation efficiency by a factor 15–90, additional collimators are foreseen in the room temperature insertions and in the dispersion suppression (DS) regions around points 2, 3, and 7. • To provide longitudinal space of about 3.5 m for additional collimators, a solution based on the substitution of a pair of 5.5-m-long 11 T dipoles for several 14.3-m-long 8.33 T LHC main dipoles (MB) is being considered. • Goal • Design a Nb3Sn superconducting dipole with an 60 mm aperture and a operational field (80% of Iss) at 1.9 K of 11 T.

  3. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  4. Case study 4 Case study 4 • Additional questions • Evaluate, compare, discuss, take a stand (… and justify it …) regarding the following issues • High temperature superconductor: YBCO vs. Bi2212 • Superconducting coil design: block vs. cos • Support structures: collar-based vs. shell-based • Assembly procedure: high pre-stress vs. low pre-stress

  5. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  6. Case study 4 solutionMaximum field and coil size Case study 4 • With a 30 mm wide coil one could reach a bore field of 13-14 T.

  7. Case study 4 solutionMaximum gradient and coil size Case study 4 • With a w/r of 30/30 = 1 λof 1.04

  8. Case study 4 solutionMaximum gradient and coil size Case study 4

  9. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  10. Case study 4 solutionCable and strand size • We assume a strand diameter of 0.70 mm • We assume a pitch angle of 16 Case study 4

  11. Case study 4 solutionCable and strand size • We assume • Thick. Comp. = -10.5 % • Width. Comp. = -4 % • 40 strands • Ins. Thick. = 150 μm • We obtain • Cable width: 14.5 mm • Cable mid-thick.: 1.25 mm Case study 4

  12. Case study 4 solutionCable and strand size Case study 4 • Summary • Strand diameter =0.70 mm • Cu to SC ratio =1.1 • Pitch angle  =16 • N strands = 40 • Cable width: 14.5 mm • Cable mid-thickness: 1.25 mm • Insulation thickness = 150 μm • Area insulated conductor = 22.9 mm2 • We obtain a filling factor • k = area superconductor/area insulated cable = 0.32

  13. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  14. Case study 4 solutionMargins Case study 4 • Let’s work now on the load-line • The bore field is given by • So, for a Jsc= 1000 A/mm2 • jo = jsc * k = 320 A/mm2 • Bbore = 6.7 T • Bpeak = Bbore * λ= 6.7 * 1.04 = 7.0 T

  15. Case study 4 solutionMargins • Nb3Sn parameterization • Temperature, field, and strain dependence of Jc is given by Summers’ formula • where Nb3Snis 900 for  = -0.003, TCmois 18 K, BCmois 24 T, and CNb3Sn,0is a fitting parameter equal to 60800 AT1/2mm-2 for a Jc=3000 A/mm2 at 4.2 K and 12 T. Case study 4

  16. Case study 4 solutionMargins • Nb-Ti parameterization • Temperature and field dependence of BC2 and TC are provided by Lubell’s formulae: • where BC20 is the upper critical flux density at zero temperature (~14.5 T), and TC0 is critical temperature at zero field (~9.2 K) • Temperature and field dependence of Jc is given by Bottura’s formula • where JC,Ref is critical current density at 4.2 K and 5 T (~3000 A/mm2) and CNb-Ti (27 T), Nb-Ti (0.63), Nb-Ti (1.0), and Nb-Ti (2.3) are fitting parameters. Case study 4

  17. Case study 4 solutionMargins Nb3Sn Case study 4 • Let’s assume  = 0.000 • The load-line intercept the critical (“short-sample” conditions) curve at • jsc_ss = 2120 mm2 • jo_ss = jsc_ss* k = 678 mm2 • Iss = jo_ss* Ains_cable= 15500 A • Bbore_ss = 14.1 T • Bpeak_ss = 14.7 T

  18. Case study 4 solutionMargins Nb3Sn Case study 4 • The operational conditions (80% of Iss) • jsc_op = 1696 mm2 • jo_op = jsc_op* k = 543 mm2 • Iop = jo_op* Ains_cable= 12430 A • Bbore_op = 11.2 T • Bpeak_op = 11.8 T

  19. Case study 4 solutionMargins Nb3Sn Case study 4 • In the operational conditions (80% of Iss) • 4.6 K of T margin • (4100-1700) A/mm2 of jscmargin • (15.3-11.8) T of field margin

  20. Case study 4 solutionMargins Nb-Ti Case study 4 • “Short-sample” conditions • jsc_ss = 1450 mm2 • jo_ss= jsc_ss* k = 464 mm2 • Iss = jo_ss* Ains_cable= 10630 A • Bbore_ss = 9.6 T • Bpeak_ss = 10.0 T • The operational conditions (80% of Iss) • jsc_op = 1160 mm2 • jo_op = jsc_op* k = 371 mm2 • Iop = jo_op* Ains_cable= 8500 A • Bbore_op = 7.7 T • Bpeak_op = 8.0 T • 2.1 K of T margin • (2500-1160) A/mm2 of jscmargin • (10.8-8.0) T of field margin

  21. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  22. Case study 4 solutionCoil layout Case study 4 • One wedge coil sets to zero b3 and b5 in quadrupoles • ~[0°-48°, 60°-72°] • ~[0°-36°, 44°-64°] • Some examples

  23. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  24. Case study 4 solutionE.m. forces and stresses Case study 4 • For a dipole sector coil, with an inner radius a1, an outer radius a2 and an overall current density jo , each block (quadrant) see • Horizontal force outwards • Vertical force towards the mid-plan • In case of frictionless and “free-motion” conditions, no shear, and infinitely rigid radial support, the forces accumulated on the mid-plane produce a stress of

  25. Case study 4 solutionE.m. forces and stresses Case study 4 • In the operational conditions (Bbore_op = 11.2 T) • Fx (quadrant) = +2.54 MN/m • Fy (quadrant) = -2.26 MN/m • The accumulates stress on the coil mid-plane is

  26. Case study 4 Case study 4 • 11 T Nb3Sn dipole for the LHC collimation upgrade • Questions • Determine maximum gradient and coil size (using sector coil scaling laws) • Define strands and cable parameters • Strand diameter and number of strands • Cu to SC ratio and pitch angle • Cable width, cable mid-thickness and insulation thickness • Filling factor κ • Determine load-line (no iron) and “short sample” conditions • Compute jsc_ss, jo_ss, Iss, Bss, Bpeak_ss • Determine “operational” conditions (80% of Iss) and margins • Compute jsc_op, jo_op, Iop, Bop, Bpeak_op • Compute T, jsc, Bpeak margins • Compare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technology • Define a possible coil lay-out to minimize field errors • Determine e.m forces Fx and Fyand the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss) • Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss

  27. Case study 4 solutionDimension of the yoke Case study 4 • The iron yoke thickness can be estimated with • Therefore, being • Bbore = 12.7 T (at 90% of Iss ) • r = 30 mm and • Bsat= 2 T • we obtain • tiron = ~190 mm

  28. Case study 4 solutionDimension of the support structure Case study 4 • We assume a 25 mm thick collar • Images not in scale

  29. Case study 4 solutionDimension of the support structure • We assume that the shell will close the yoke halves with the same force as the total horizontal e.m. force at 90% of Iss • Fx_total = Fx_octant * 2 = +6.4 MN/m • Assuming an azimuthal shell stress after cool-down of • shell = 200 MPa • The thickness of the shell is • tshell = Fx_total/2/1000/ shell~ 16 mm Case study 4

  30. Case study 4 solutionMagnet cross-section Case study 4 • Coil inner radius: 30 mm • Coil outer radius: 60 mm • The operational conditions (80% of Iss) • jsc_op = 1696 mm2 • jo_op = jsc_op* k = 543 mm2 • Iop = jo_op* Ains_cable= 12430 A • Bbore_op = 11.2 T • Bpeak_op = 11.8 T • Collar thickness: 25 mm • Yoke thickness: 190 mm • Shell thickness: 16 mm • OD: 582 m

  31. Comparison Case study 4

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