HFM References (v. 2)

EuroCirCol (2015-2020): general references

1. D. Tommasini, et al., “The 16 T dipole development program for FCC” IEEE Trans. Appl. Supercond. 27 (2017) 4000405 – Presenting CERN magnet development program and Eurocircle for first time – RMC, ERMC and RMM program, aiming at 16 T, in 2017 and 2018 respectively; table of specifications : 1500 A/mm², 16% margin, 1.9 K, <200 MPa, <350 K at 105% of nominal. Selection of final design by 2017, construction of 3 to 4 models in 2022.

2. D. Schoerling, et al., “Considerations on a Cost Model for High-Field Dipole Arc Magnets for FCC” IEEE Trans. Appl. Supercond. 27 (2017) 4003105 – 2300 A/mm² at 16 T and 1.9 K justification of 1.9 K – table with margins in temp, enthalpy for 11 T MQXF and 16 T –final cost of 1.3 MEUR per magnet, 700 kEUR of assembly and components (scaled on LHC), and 600 kEUR of conductor – hybrid Nb-Ti option is also considered but small savings – targert price for Nb₃Sn is 5 EUR/ kA m at 16 T and 4.2 K, or is 3.4 EUR/ kA m at 16 T and 1.9 K

3. D. Tommasini, et al., “Status of the 16 T development program for a future hadron collider” IEEE Trans. Appl. Supercond. 28 (2018) 4001305 – Summary of coil cross-sections, cos theta, block (CEA), common coil (CIEMAT), CCT (PSI) – reduction of diameter from 800 to 600 mm (to fit HE-LHC), reduction of beam distance from 250 mm to 204 mm – ERMC and RRM foreseen for 2018 and 2019 – first estimate of cost, with 400 k for components, 500 k for assembly, and 500 k for conductor.

4. D. Schoerling, et al., “The 16 T dipole development program for FCC and HE-LHC” IEEE Trans. Appl. Supercond. 29 (2019) 4003109 – design changes : magnet diameter back to 800 mm, interbeam distance to 250 mm, first estimate of cold mass weight 55 tons, first estimate of heat losses 5 kJ/m during ramp, – 37 MJ of stored energy, inductance of 570 mH, current of 11.3 kA, costheta as baseline – block 4% more, common coil 25% more conductor – conductor cost of 670 kEUR per magnet, total of 1.7 To 2.0 MEUR interesting plot of degradation of critical current vs stress (fig 3), ERMC under manufacturing, to be tested in 2019, results from LBNL CCT : 9.1 T in 90 mm bore for CCT4.

Nb₃Sn conductor development (2015 to today)

1. L. Bottura, et al., “Targets for R&D on Nb₃Sn Conductor for High Energy Physics” IEEE Trans. Appl. Supercond. 25 (2015) 6000906 – Setting the requirements for jc 1500 A/mm² at 4.2 K and 16 T (based on 600 A/mm² engineering operational current, 1.5 of Cu, and zero margin for operation at 4.2 K – not so clear to me). Magnetization target 150 mT (five times the LHC) – dependence of j_c on subelement size (fig. 3). Cost is given as 10 EUR/ kA m at 12 T and 4.2 K. A reduction of a factor 3 is considered realistic for larger productions (end of 4^th page) – first proposal of 5 EUR/kA m at 16 T and 4.2 K (beginning of last page)

2. A. Ballarino, et al., “The CERN FCC Conductor Development Program: A Worldwide Effort for the Future Generation of High-Field Magnets” IEEE Trans. Appl. Supercond. 29 (2019) 6001709 – Description of the conductor development program (Fig. 1) – stage 1 aims at 1000 A/mm² at 4.2 K and 16 T, with 60 mm sub-elements, stage two at 1500 A/mm², same sub-element – Institutes : KAT (Korea), TVEL (Russia), JASTEC (Japan) reach the 1000 A/mm² deliveries of 20 km from KAT and 5 km from JASTEC are expected – HTS program: iron based, BSCCO, MgB₂

3. S. Hopkins, et al., “Quantitative Analysis and Optimization of Nb₃Sn Wire Designs Toward Future Circular Collider Performance Targets” IEEE Trans. Appl. Supercond. 29 (2019) 6001307 – Analysis of productions of JASTEC, KAT and TVEL – a path to 1200 A/mm² at 16 T and 4.2 K is identified.

4. S. Hopkins, et al., “Design, Performance and Cabling Analysis of Nb₃Sn Wires for the FCC Study” J. Phys.: Conf. Ser. 1559 (2020) 012026 – Deliveries of 12 km from TVEL, 1 km from JASTEC, 6 km from KAT, studies on degradation due to cabling – TVEL and JASTEC exceed 1000 A/mm² at 16 T and 4.2 K – characteristics given in Table I : TVEL has 1.0 mm diamater and 1.2 Cu 150 mm d_eff, (but 60 mm is given in the IEEE paper of 2021) JASTEC 0.8 mm diaeater and 1.0 Cu, 55 mm d_eff

5. S. Hopkins, et al., “Phase Evolution During Heat Treatment of Nb₃Sn Wires Under Development for the FCC Study” IEEE Trans. Appl. Supercond. 31 (2021) 6000706 – Analysis of heat treatment for TVEL, JASTEC and Bruker (0.7, 0.85 and 1.0 mm diameter) wires

6. S. Hopkins, et al., “Design Optimization, Cabling and Stability of Large-Diameter High Jc Nb₃Sn Wires” IEEE Trans. Appl. Supercond. 33 (2023) 6000609 –

7. S. Hopkins, et al., “Deformation Behavior and Degradation on Rutherford Cabling of Nb3Sn Wires ” IEEE Trans. Appl. Supercond. 34 (2024) 6001308 –

Nb₃Sn demonstrator program SMC and RMM (2015 to today)

1. E. Fornasiere, et al. “Status of the Activities on the Nb₃Sn Dipole SMC and of the Design of the RMC” IEEE Trans. Appl. Supercond. 23 (2013) 4002308 – design of SMC and RMC, with test results on SMC with PIT and RRP, with test results of SMC3a (90% of short sample at 1.9 K, and 95% at 4.5 K); plans forn SMC3b and SMC4-5: design of RMC, a 15 T peak field assembly at 1.9 K and at short sample without aperture (one or two double pancakes);

2. S. Izquierdo Bermudez, et al. “Design of ERMC and RMM, the base of the Nb3Sn 16 T magnet development at CERN IEEE Trans. Appl. Supercond. 27 (2017) 4002004 – design of ERMC (8 mm aperture) and RMM (50 mm aperture) both without flared ends; 16 T demonstrators at 80% loadline fraction, with 250-280 A/mm² overall current density

3. E. Rochepault, et al., “3-D magnetic and mechanical design of coil ends for the racetrack model magnet RMM” IEEE Trans. Appl. Supercond. 28 (2018) 4006105 – mechanical design of coil ends

4. M. Garcia Perez, et al., “Mechanical tests. analysis, and validation of the support structure of the ERMC and RMM magnets of the FCC R&D at CERN”, IEEE Trans. Appl. Supercond. 30 (2020) 4004507 – verification of the mechanical structure of RMM and eRMC on mock-up at r.t. and at 80 K, and comparison to FEM;

5. J. C. Perez, et al., “Construction and Test of the Enhanced Racetrack Model Coil, First CERN R&D Magnet for the FCC”, IEEE Trans. Appl. Supercond. 32 (2022) 4005105 – Design, assembly and power tests of ERMC, reaching 16.3 T

6. E. Gautheron, et al., “Assembly and Test Results of the RMM1a,b Magnet, a CERN Technology Demonstrator Towards Nb₃Sn Ultimate Performance”, IEEE Trans. Appl. Supercond. 33 (2023) 4004108 – Design, assembly and power tests of RMM1a and RMM1b, reaching 16.5 T

Nb₃Sn magnet BOND (2025 to today)

1. J. C. Perez, et al., “Conceptual Design of BOND: A 14 T Dipole for FCC-hh”, IEEE Trans. Appl. Supercond. 35 (2025) 4002506 – First paper on BOND, a 14 T dipole for FCC-hh with block coils and flared ends

Nb₃Sn common coil from CIEMAT (2017 to today)

The EuroCirCol works on 16 T common coil

1. F. Toral, et al., “ EuroCirCol 16T common-coil dipole option for the FCC,” IEEE Trans. Appl. Supercond. 27 (2017) 4001105 – first design of common coil for 16 T with 18% margin – coil width of about 41 mm for option 10, with 550 A/mm²

2. F. Toral, et al., “Magnetic and mechanical design of a 16 T common coil dipole for FCC,” IEEE Trans. Appl. Supercond. 28 (2018) 4004305 – Second iteration of common coil design, including mechanics

The HFM works on demonstrators (ISAAC) and 14 T common coil (DAISY)

3. J. Garcia Matos, et al., “Design of a Common Coil Magnet Using Existing Racetrack Model Coils (RMC),” IEEE Trans. Appl. Supercond. 34 (2024) 4300105 – First proposal of ISAAC, a demonstrator for achieving 12 T in a 10 mm aperture using RMC coils with 0.80 loadline fraction – second phase with 34 mm aperture, 12 T with 0.85 loadline:

4. C. Martins Jardim, et al., “Mechanical Design of a Common Coil Magnet With RMC Coils (ISAAC),” IEEE Trans. Appl. Supercond. 35 (2025) 4002705 – Second paper on ISAAC, with focus on mechanical structure

5. J. Garcia Matos, et al., “ Magnetic Design of a 14 T Common Coil Demonstrator Magnet (DAISY),” IEEE Trans. Appl. Supercond. 35 (2025) 4002705 – First paper on common coil at 14 T – simplified magnetic design without corrective coils for field quality, first exploration of hybrid Nb-Ti/Nb₃Sn (options A and B)

6. J. Garcia Matos, et al., “ Exploring Hybrid Designs for a 14 T Common Coil Demonstrator Magnet (DAISY)” IEEE Trans. Appl. Supercond. 36 (2026) in press – Second paper on common coil at 14 T – magnetic design, proposal for hybrid Nb-Ti/Nb₃Sn

Nb₃Sn block coil from CEA (2017 to today)

The EuroCirCol works on 16 T block coil

1. C. Lorin, et al., “EuroCirCol 16 T block-coils dipole option for the future circular collider,” IEEE Trans. Appl. Supercond. 27 (2017) 4001405 – first design with 1.1 mm and 0.7 mm diameter strand – 8500 tons of total need of conductor, equivalent coil width is 53 mm

2. C. Lorin, et al., “Design of a Nb3Sn 16 T Block Dipole for the Future Circular Collider” IEEE Trans. Appl. Supercond. 28 (2018) 4005005 – iteration on design, reduction of the conductor mass from 8500 to 7500 tons

3. M. Segreti, et al., “2-D and 3-D Design of the Block-Coil Dipole Option for the Future Circular Collider” IEEE Trans. Appl. Supercond. 29 (2019) 4000404– two in one mechanical design – same parameters as 2018 – outer yoke 616 mm

The research line based on R2D2 and F2D2 demonstrators

4. H. Felice, et al., “F2D2: A Block-Coil Short-Model Dipole Toward FCC” IEEE Trans. Appl. Supercond. 29 (2019) 4001807– F2D2: new name for the block option – external splices – collaboration agreement signed to build F2D2 – bore field of 15.5 T with enhanced HL-LHC (1200 A/mm² at 16 T and 4.2 K)

5. E. Rochepault, et al., “3D Conceptual Design of F2D2, the FCC Block-Coil Short Model Dipole” IEEE Trans. Appl. Supercond. 30 (2020) 4001005 – Same design, 14 T gives 150 MPa of max stress– two intermediate steps proposed : R2D2 with single layer coils

6. V. Calvelli, et al., “R2D2, the CEA Graded Nb₃Sn Research Racetrack Dipole Demonstrator Magnet” IEEE Trans. Appl. Supercond. 31 (2021) 4002706– First presentation of the design of R2D2: single layer coil, with field of 11.5 T – many aspects look critical (protection, 1.9 K and 4.5 K mechanics)

7. E. Rochepault, et al., “The Use of Grading in Nb₃Sn High-Field Block-Coil Dipoles” IEEE Trans. Appl. Supercond. 31 (2021) 4001510 – A paper giving analytical forumales for block design

8. E. Rochepault, et al., “3D Conceptual Design of R2D2, the Research Racetrack Dipole Demonstrator” IEEE Trans. Appl. Supercond. 32 (2022) 4004605– second paper about design of R2D2 – cannot be powered to short sample – max 12 T will be achieved

9. D. Liu, et al., “CLIQ Protection Design for the Graded Nb₃Sn Research Racetrack Dipole Demonstrator (R2D2)” IEEE Trans. Appl. Supercond. 33 (2023) 4701105– …

10. T. Salmi, et al., “Quench Protection of Nb₃Sn High Field Magnets Using Heaters, a Strategy Applied to the Graded Racetrack Dipole R2D2” IEEE Trans. Appl. Supercond. 33 (2023) 4701606– (protection work, from Tampere University)

11. T. Salmi, et al., “A Numerical Simulation of Quench Propagation in Nb3Sn Cables Covered With Protection Heaters” IEEE Trans. Appl. Supercond. 34 (2024) 4701205– (protection work, from Tampere University)

12. E. Fernandez Mora, et al., “Longitudinal and Transverse Dimensional Changes During Heat Treatment of the Nb₃Sn Cables for the Graded Research Racetrack Dipole Demonstrator (R2D2)” IEEE Trans. Appl. Supercond. 34 (2024) 8800505–

13. F. Nunio, et al., “CoCaSCOPE-Mesh Generator: A Tool to Generate 3D Numerical Models of Rutherford Cables” IEEE Trans. Appl. Supercond. 34 (2024) 4904005– (not directly related to R2D2)

Nb₃Sn cos theta coil from INFN (2017 to today)

The EuroCirCol works on 4 layers

1. M. Sorbi et al., “The EuroCirCol 16 T cosine-theta dipole option for the FCC,” IEEE Trans. Appl. Supercond. 27 (2017) 4001205. – update of previous design: loadline fraction from 0.82 to 0.86, reduction of coil equivalent width from 55 to 50 mm, 1.1 mm and 0.7 mm strand used, but less strand per cable (inner: previously 28, then 22 – outer is kept at 36)

2. V. Marinozzi et al., “Quench protection study of the eurocircle 16 T cos theta dipole for FCC,” IEEE Trans. Appl. Supercond. 27 (2017) 4702505– stored energy 1.3 MJ/m per aperture – max. hotspot of 350 K – it puts in evidence that less copper can give lower hotspot for inner layer

3. V. Marinozzi et al., “Conceptual design of a 16 T cosθ bending dipole for the future circular collider,” IEEE Trans. Appl. Supercond. 28 (2018) 4004205. – iteration on the design (strands per cable from 22/36 to 22/37), reduction of the iron diameter to 600 mm, 2.6 MJ/m for wo apertures

4. B. Caiffi, et al., “Update on a mechanical desing of a cos-theta 16 T bending dipole for the FCC,” IEEE Trans. Appl. Supercond. 28 (2018) 4006704. – Mechanical structure of the dipole: 600 mm diameter, 204 mm intrabeam, extra-large notch on the pole – B&K – max stress of 211 MPa during cool-down, considered acceptable – fabrication of a mechanical design under study

5. R. Valente, et al., “Baseline design of a cos-theta 16 T bending dipole for the FCC,” IEEE Trans. Appl. Supercond. 29 (2019) 4003005 – to reduce b₂ from 25 to 5 units,, asymmetric coil is used, beam interdistance goes from 204 to 250 mm, iron diameter from 600 to 660 mm, strand per cable changed from 22/36 to 22/38, all stresses below 200 MPa.

The HFM works on 2 layers (since 2020) and 4 layers (since 2025)

6. R. Valente, et al., “Electromagnetic and Mechanical Study for the Nb₃Sn Cos-Theta Dipole Model for the FCC,” IEEE Trans. Appl. Supercond. 30 (2020) 4001905 – first proposal for a two layer design (FalconD): 34 strands 1.1 mm diameter, 14 T at 86% with 1500 A/mm² – mechanical analysis at 14 T gives a max stress of 170 MPa

7. A. Pampaloni, et al., “Preliminary Design of the Nb₃Sn cosθ Short Model for the FCC,” IEEE Trans. Appl. Supercond. 31 (2021) 4900905 – Strand diameter from 1.1 to 1 mm, number of strands from 34 to 40, new target of 12 T and 14 T is set as ultimate, use of 1200 A/mm², 24% margin on loadline, peak stress on the conductor at 125 MPa – stored energy of 1.1 MJ/m at 12 T, and 1.5 MJ/m at 14 T.

8. R. Valente, et al., “Study of Superconducting Magnetization Effects and 3D Electromagnetic Analysis of the Nb₃Sn cosθ Short Model for FCC,” IEEE Trans. Appl. Supercond. 31 (2021) 4002205 – first estimate of the hysteresis losses on a up-down cycle 5.7 kJ/m (to be checked, it appears in contradiction to other results giving 20 kJ/m) – impact of ferromagnetic shimming to reduce b3 at injection from 45 to 20 units

9. A. Pampaloni, et al., “Mechanical Design of FalconD, a Nb₃Sn Cosθ Short Model Dipole for the FCC,” IEEE Trans. Appl. Supercond. 32 (2022) 4000605 – analysis of longitudinal preload : 25% at 12 T and 50% at 14 T of e.m. forces

10. R.U. Valente, et al, “Update on the Electromagnetic Design of the Nb3Sn Cos-Theta Dipole Model for FCC-hh,” IEEE Trans. Appl. Supercond. 32 (2022) 400105 – Update of coil end design, study of sextupolar insert to minimize b3

11. F. Levi, et al., “Updates on the Mechanical Design of FalconD, a Nb₃Sn Cosθ Short Model Dipole for FCC-hh,” IEEE Trans. Appl. Supercond. 33 (2023) 4000805 – results of the 2022 review – reduction of ultimate field from 14 to 13.5 T – mainly focused on mechanical analysis

12. R. Valente, et al., “Optimization of Electromagnetic Design After Winding Tests for the Nb₃Sn Cos-Theta Dipole Model for FCC-hh,” IEEE Trans. Appl. Supercond. 33 (2023) 4601107 – Important paper on the winding tests ; some aspects to be clarified (was the test complete, i.e. done on the whole first layer ? with the final FalconD cable ?) – for some aspects it looks in contradiction with later results

13. R. Valente, et al., “Status on the Development of the Nb₃Sn 12 T Falcon Dipole for the FCC-hh,” IEEE Trans. Appl. Supercond. 34 (2024) 4900405 –status of the project, a value of 230 mJ/cm³ given for enthalpy margin probably a misprint, shold be 10 times less), no changes in design

14 S. Farinon, et al. “Advancements in Nb₃Sn 12 T Cos-Theta Dipole Development for Next-Generation Accelerators: The INFN-CERN Collaboration on the FalconD Project”, IEEE Trans. Appl. Supercond. 35 (2025) 4001905 – status of the project, recap of design, activities in ASG.

15. R. Valente, et al., “Design of a Four-Layer Nb3Sn Cos-Theta Dipole in the CERN High Field Magnet R&D Program,” IEEE Trans. Appl. Supercond. 35 (2025) 4100105 – First revamping of studies on four layers – strand 1.0 and 0.7 mm, 22 and 38 strands per cable, eq. Coil width from 50 to 55 mm, margin between 20% and 25 %

16. M. Elisei, et al., “Design Comparison of Four-Layer Full-Nb₃Sn and Hybrid Nb₃Sn/NbTi Cos-Theta Dipoles for the CERN High Field Magnet R&D Programme,” IEEE Trans. Appl. Supercond. 36 (2026) 4000305 – Review of Valente design with strand of 0.85 mm, 40 strands cable, and considering also hybrid design – full Nb₃Sn: 55 mm equivalent width, 20% margin – Hybrid : 59mm equivelent coil width (25+35 I guess), but inner layers with 13.5 % margin only – outer layer very large. Not clear to me the large loss in margin since the inner cable is the same for hybrid and for the full Nb₃Sn (to be discussed)

Nb₃Sn magnets with CCT design (LBNL, PSI)

1. S. Caspi, et al., “Design of a Canted-Cosine-Theta Superconducting Dipole Magnet for Future Colliders,” IEEE Trans. Appl. Supercond. 27 (2017) 4001505 – design for 16 T, reducing from 8 to 4 layers – with 87% on loadline – also two in one – estimate of 6.7 ktons total conductor – protection to be clarified

2. B. Auchmann, et al., “Electromechanical design of a 16-T CCT twin-aperture dipole for FCC,” IEEE Trans. Appl. Supercond. 28 (2018) 4000705

3. P. Ferracin, et al., “Towards 20 T Hybrid Accelerator Dipole Magnets,” IEEE Trans. Appl. Supercond. 32 (2022) 4000906

4. D. Arbelaez, et al., “Status of the Nb3Sn Canted-Cosine-Theta Dipole Magnet Program at Lawrence Berkeley National Laboratory,” IEEE Trans. Appl. Supercond. 32 (2022) 4003207

5. J. L. Rudeiros Fernandez, et al., “Assembly and Mechanical Analysis of the Canted-Cosine-Theta Subscale Magnets,” IEEE Trans. Appl. Supercond. 32 (2022) 4006505

6. L. Brouwer, et al., “Design of CCT6: A Large Aperture, Nb3Sn Dipole Magnet for HTS Insert Testing,” IEEE Trans. Appl. Supercond. 32 (2022) 4001805

7. P. Ferracin, et al., “Conceptual Design of 20 T Hybrid Accelerator Dipole Magnets,” IEEE Trans. Appl. Supercond. 33 (2023) 4002007

8. X. Wang, et al., “An Initial Look at the Magnetic Design of a 150 mm Aperture High-Temperature Superconducting Magnet With a Dipole Field of 8 to 10 T,” IEEE Trans. Appl. Supercond. 33 (2023) 4000608

9. P. Ferracin, et al., “Electromechanical Analysis for the Integration of a Nb3Sn and a Bi-2212 CCT Dipole Magnet for a Hybrid Magnet Test,” IEEE Trans. Appl. Supercond. 33 (2023) 4901005

The IHEP dipoles for SPPC

1. C. Wang, et al., “Electromagnetic Design, Fabrication, and Test of LPF1: A 10.2-T Common-Coil Dipole Magnet With Graded Coil Configuration,” IEEE Trans. Appl. Supercond. 29 (2019) 4003807 –

2. K. Zhang, et al., “Mechanical Design, Assembly, and Test of LPF1: A 10.2 T Nb3Sn Common-Coil Dipole Magnet With Graded Coil Configuration,” IEEE Trans. Appl. Supercond. 29 (2019) 4000108 –

3. K. Zhang, et al., “Mechanical Design and Stress Analysis of LPF2: A 12-T Hybrid Common-Coil Dipole Magnet,” IEEE Trans. Appl. Supercond. 30 (2020) 4002205 –

4. C. Wang, et al., “Electromagnetic Design and Fabrication of LPF2: A 12-T Hybrid Common-Coil Dipole Magnet With Inserted IBS Coil”, IEEE Trans. Appl. Supercond. 30 (2020) 4000205 –

5. C. Wang, et al., “Development of superconducting model dipole magnets beyond 12 T with a combined common-coil configuration,” SUST 36 (2023) 065006 –

6. J. Shi, et al., “Design, Simulation and Test Results of Quench Protection System for a 13-T Twin-Aperture Superconducting Dipole Magnet,” IEEE Trans. Appl. Supercond. 34 (2024) 4701405 –

7. C. Wang, et al., “Design and Fabrication of a 13-T Twin-Aperture Superconducting Dipole Magnet With Graded Common-Coil Configuration,” IEEE Trans. Appl. Supercond. 34 (2024) 4000805 –

8. Y. Wang, et al., “Mechanical Design, Assembly and Strain Measurement Results of a 13-T Superconducting Dipole Magnet,” IEEE Trans. Appl. Supercond. 34 (2024) 4000705