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CERN Accelerator School Superconductivity for Accelerators Case study 3

CERN Accelerator School Superconductivity for Accelerators Case study 3. Paolo Ferracin ( paolo.ferracin@cern.ch ) European Organization for Nuclear Research (CERN ). Case study 3. High field - large aperture magnet for a cable test facility Introduction

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CERN Accelerator School Superconductivity for Accelerators Case study 3

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  1. CERN Accelerator SchoolSuperconductivity for AcceleratorsCase study 3 Paolo Ferracin (paolo.ferracin@cern.ch) European Organization for Nuclear Research (CERN)

  2. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • Introduction • High field (Bbore>10 T) magnets are needed to upgrade existing accelerators in Europe and to prepare for new projects on a longer timescale. • Nb3Sn is today the right candidate to meet those objectives, because of its superconducting properties and its industrial availability. • On the very long term, further upgrades could require dipole magnets with a field of around 20 Tesla (T): a possible solution is to combine an outer Nb3Sn coil with an inner coil of High Critical Temperature (HTS) conductor, both contributing to the field. • In addition, an high-field dipole magnet with a large aperture could be used to upgrade the Fresca test facility at CERN, in the aim of meeting the strong need to qualify conductor at higher fields. • Goal • Design a superconducting dipole with an 100 mm aperture and capable of reaching 15 T at 1.9 K (~90% of Iss).

  3. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 Case study 3 • 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 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionMaximum field and coil size Case study 3 • The max. field that one could reach with 60 mm wide coil is about 16.5 T

  7. Case study 3 solutionMaximum gradient and coil size Case study 3 • With a w/r of 60/50 = 1.2 λof 1.04

  8. Case study 3 solutionMaximum gradient and coil size Case study 3

  9. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionCable and strand size • We assume a strand diameter of 0.80 mm • We assume a pitch angle of 17 Case study 3

  11. Case study 3 solutionCable and strand size • We assume • Thick. Comp. = -12 % • Width. Comp. = -1.5 % • 35 strands • Ins. Thick. = 150 μm • We obtain • Cable width: 15 mm • Cable mid-thick.: 1.4 mm Case study 3

  12. Case study 3 solutionCable and strand size Case study 3 • Summary • Strand diameter =0.80 mm • Cu to SC ratio =1.1 • Pitch angle  =17 • N strands = 35 • Cable width: 15 mm • Cable mid-thickness: 1.4 mm • Insulation thickness = 150 μm • Area insulated conductor = 26.0 mm2 • We obtain a filling factor • k = area superconductor/area insulated cable = 0.31

  13. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionMargins Case study 3 • Let’s work now on the load-line • The bore field is given by • So, for a Jsc= 1000 A/mm2 • jo = jsc * k = 465 A/mm2 • Bbore = 12.8 T • Bpeak = Bbore * λ= 12.8 * 1.04 = 13.3 T

  15. Case study 3 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 3

  16. Case study 3 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 3

  17. Case study 3 solutionMargins Nb3Sn Case study 3 • Let’s assume  = 0.000 • The load-line intercept the critical (“short-sample” conditions) curve at • jsc_ss = 1230 mm2 • jo_ss = jsc_ss* k = 381 mm2 • Iss = jo_ss* Ains_cable= 9900 A • Bbore_ss = 15.8 T • Bpeak_ss = 16.4 T

  18. Case study 3 solutionMargins Nb3Sn Case study 3 • The operational conditions (80% of Iss) • jsc_op = 984 mm2 • jo_op = jsc_op* k = 305 mm2 • Iop = jo_op* Ains_cable= 7930 A • Bbore_op = 12.7 T • Bpeak_op = 13.2 T

  19. Case study 3 solutionMargins Nb3Sn Case study 3 • In the operational conditions (80% of Iss) • 4.6 K of T margin • (3000-984) A/mm2 of jscmargin • (17.2-13.2) T of field margin

  20. Case study 3 solutionMargins Nb-Ti Case study 3 • “Short-sample” conditions • jsc_ss = 850 mm2 • jo_ss= jsc_ss* k = 264 mm2 • Iss = jo_ss* Ains_cable= 6900 A • Bbore_ss = 11.0 T • Bpeak_ss = 11.4 T • The operational conditions (80% of Iss) • jsc_op = 680 mm2 • jo_op = jsc_op* k = 244 mm2 • Iop = jo_op* Ains_cable= 6350 A • Bbore_op = 8.8 T • Bpeak_op = 9.1 T • 2.1 K of T margin • (1850-680) A/mm2 of jscmargin • (11.5-9.1) T of field margin

  21. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionCoil layout Case study 3 • One wedge coil sets to zero b3 and b5 in quadrupoles • ~[0°-48°, 60°-72°] • ~[0°-36°, 44°-64°] • Some examples

  23. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionE.m. forces and stresses Case study 3 • 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 3 solutionE.m. forces and stresses Case study 3 • In the operational conditions (Bbore_op = 12.7 T) • Fx (quadrant) = +5.68 MN/m • Fy (quadrant) = -4.89 MN/m • The accumulates stress on the coil mid-plane is

  26. Case study 3 Case study 3 • High field - large aperture magnet for a cable test facility • 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 3 solutionDimension of the yoke Case study 3 • The iron yoke thickness can be estimated with • Therefore, being • Bbore = 14.2 T (at 90% of Iss ) • r = 50 mm and • Bsat= 2 T • we obtain • tiron = ~360 mm

  28. Case study 3 solutionDimension of the support structure Case study 3 • We assume a 25 mm thick collar • Images not in scale

  29. Case study 3 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 = +14.4 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~ 36 mm Case study 3

  30. Case study 3 solutionMagnet cross-section Case study 3 • Coil inner radius: 50 mm • Coil outer radius: 110 mm • The operational conditions (80% of Iss) • jsc_op = 984 mm2 • jo_op = jsc_op* k = 305 mm2 • Iop = jo_op* Ains_cable= 7930 A • Bbore_op = 12.7 T • Bpeak_op = 13.2 T • Collar thickness: 25 mm • Yoke thickness: 330 mm • Shell thickness: 36 mm • OD: 1 m

  31. Comparison Case study 3

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