CERN Accelerator School Superconductivity for Accelerators Case study

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 High field (Bbore>10 T) magnets are needed to upgrade existing accelerators in Europe and to prepare for new projects on a longer timescale. Nb 3 Sn 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 Nb 3 Sn 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). Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 2

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 3

Case study 3 Additional questions Evaluate, compare, discuss, take a stand (… and justify it …) regarding the following issues High temperature superconductor: YBCO vs. Bi 2212 Superconducting coil design: block vs. cos Support structures: collar-based vs. shell-based Assembly procedure: high pre-stress vs. low pre-stress Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 4

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 5

Case study 3 solution Maximum field and coil size The max. field that one could reach with 60 mm wide coil is about 16. 5 T Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 6

Case study 3 solution Maximum gradient and coil size With a w/r of 60/50 = 1. 2 λ of 1. 04 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 7

Case study 3 solution Maximum gradient and coil size Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 8

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 9

Case study 3 solution Cable and strand size We assume a strand diameter of 0. 80 mm Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 We assume a pitch angle of 17 Case study 3 10

Case study 3 solution Cable 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 11

Case study 3 solution Cable and strand size 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 mm 2 We obtain a filling factor k = area superconductor/area insulated cable = 0. 31 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 12

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 13

Case study 3 solution Margins Let’s work now on the load-line The bore field is given by So, for a Jsc= 1000 A/mm 2 jo = jsc * k = 465 A/mm 2 Bbore = 12. 8 T Bpeak = Bbore * λ = 12. 8 * 1. 04 = 13. 3 T Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 14

Case study 3 solution Margins Nb 3 Sn parameterization Temperature, field, and strain dependence of Jc is given by Summers’ formula where Nb 3 Sn is 900 for = -0. 003, TCmo is 18 K, BCmo is 24 T, and CNb 3 Sn, 0 is a fitting parameter equal to 60800 AT 1/2 mm-2 for a Jc=3000 A/mm 2 at 4. 2 K and 12 T. Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 15

Case study 3 solution Margins Nb-Ti parameterization Temperature and field dependence of BC 2 and TC are provided by Lubell’s formulae: where BC 20 is the upper critical flux density at zero temperature (~14. 5 T), and TC 0 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/mm 2) and CNb-Ti (27 T), Nb-Ti (0. 63), Nb-Ti (1. 0), and Nb-Ti (2. 3) are fitting parameters. Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 16

Case study 3 solution Margins Nb 3 Sn Let’s assume = 0. 000 The load-line intercept the critical (“short-sample” conditions) curve at jsc_ss = 1230 mm 2 jo_ss = jsc_ss * k = 381 mm 2 Iss = jo_ss * Ains_cable= 9900 A Bbore_ss = 15. 8 T Bpeak_ss = 16. 4 T Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 17

Case study 3 solution Margins Nb 3 Sn The operational conditions (80% of Iss) jsc_op = 984 mm 2 jo_op = jsc_op * k = 305 mm 2 Iop = jo_op * Ains_cable= 7930 A Bbore_op = 12. 7 T Bpeak_op = 13. 2 T Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 18

Case study 3 solution Margins Nb 3 Sn In the operational conditions (80% of Iss) 4. 6 K of T margin (3000 -984) A/mm 2 of jsc margin (17. 2 -13. 2) T of field margin Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 19

Case study 3 solution Margins Nb-Ti “Short-sample” conditions jsc_ss = 850 mm 2 jo_ss = jsc_ss * k = 264 mm 2 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 mm 2 jo_op = jsc_op * k = 244 mm 2 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/mm 2 of jsc margin (11. 5 -9. 1) T of field margin Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 20

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 21

Case study 3 solution Coil layout One wedge coil sets to zero b 3 and b 5 in quadrupoles ~[0°-48°, 60°-72°] ~[0°-36°, 44°-64°] Some examples Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 22

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and the accumulated stress on the coil midplane 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 23

Case study 3 solution E. m. forces and stresses For a dipole sector coil, with an inner radius a 1, an outer radius a 2 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 24

Case study 3 solution E. m. forces and stresses 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 25

Case study 3 High field - large aperture magnet for a cable test facility Questions 1. 2. Determine maximum gradient and coil size (using sector coil scaling laws) Define strands and cable parameters 1. 2. 3. 4. 3. Determine load-line (no iron) and “short sample” conditions 1. 4. 2. 6. 7. 8. Compute jsc_ss , jo_ss , Iss , Bpeak_ss Determine “operational” conditions (80% of Iss ) and margins 1. 5. Strand diameter and number of strands Cu to SC ratio and pitch angle Cable width, cable mid-thickness and insulation thickness Filling factor κ Compute jsc_op, jo_op , Iop , 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 Fy and 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 26

Case study 3 solution Dimension of the yoke 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 27

Case study 3 solution Dimension of the support structure We assume a 25 mm thick collar Images not in scale Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 28

Case study 3 solution Dimension 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 29

Case study 3 solution Magnet cross-section Coil inner radius: 50 mm Coil outer radius: 110 mm The operational conditions (80% of Iss) jsc_op = 984 mm 2 jo_op = jsc_op * k = 305 mm 2 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 30

Comparison Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study 3 31