1. Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009

2. 2 Requirements: ring

3. 3 Requirements: IR

4. 4 Baseline conductor: Nb 3 Sn  Nb 3 Sn is superior to NbTi at all fields and temperatures and has a potential for further improvement  Nb 3 Sn is superior to HTS at the fields fits well in the present optics requirements From P. Lee  Nb 3 Sn has a lower critical temperature than HTS (18K vs. >85K). However, our (LARP) experience with measuring thermal margin in Nb 3 Sn magnets shows that even the 18K margin is unlikely to be explored in a collider because of the cryogenic constraints

5. 5 Thermal potential of Nb 3 Sn  The 120-mm Nb 3 Sn quads in the LHC IR triplets CAN operate at the luminosity of 10 36 cm -2 s -1 with ~20% margin IF the cryogenic system is able to extract the heat (~3kW per 6-m long Q1 magnet at 1.9K)  But it is an order of magnitude above the available cryogenic capacity V. V. Kashikhin, R. Bossert, G. Chlachidze, M. Lamm, N. V. Mokhov, I. Novitski, A.V. Zlobin, “Performance of Nb 3 Sn Quadrupole Magnets Under Localized Thermal Load”, CEC/ICMC 2010.

6. 6 Magnet design concept  Based on the well known and proven (now also for Nb 3 Sn) shell- type magnet technology  Avoid dumping all the heat in the cryogenic system by opening the midplanes, using absorbers, optimizing magnet length, etc.  Uniform assumptions for all magnets: Jc(12T,4.2K)=2700A/mm 2, scaled with the operating temperature as necessary. Cu/nonCu ratio 1.17. These parameters were achieved in the Nb 3 Sn conductors for LARP  Use HTS only where Nb 3 Sn cannot work

7. 7 IR quads  90-mm Nb 3 Sn quads were tested by LARP  120-mm quad will be tested next year  There are certain issues, but the way is more or less clear

8. 8 Opening midplane in cos-theta coil  Field quality gets destroyed quickly as the midplane gap increases  But, is there way to approach the ideal field with such geometry?

9. 9 Analytical concept of an open midplane dipole Let’s consider the following two statements:  “Cos-theta” magnet cannot be made with an open midplane  Technology used for the “cos-theta” magnets cannot be applied in the open midplane magnets -Somewhat true -Fundamentally wrong! +=

10. 10 Open-midplane ring dipole  Based on two double-shells to minimize the number of splices  Keystoned cable to ease winding of coil ends  Aperture available for the beam – 60mm  B op ~10T with ~15% margin at 4.5K.  Midplane gap: Coil-coil – 30mm Clear – 20mm  As the conductor is removed from the coil midplanes, it can no longer be referred to as the “cosine-theta” geometry. Although it may look that way, the optimization employs different (from the “cosine-theta”) criteria to compensate for the missing turns

11. 11 Combined-function ring dipole  Different left and right gaps to create gradient  Asymmetric coils to optimize the field quality (work in progress)  The B/G ratio is built into the design, but can be adjusted for the specific requirements  B op ~10T, G op ~23T/m with ~15% margin at 4.5K  Midplane gap: Coil-coil – 30/42mm Clear – 20mm

12. 12 Ultimate case – gradient C-dipole  Naturally provides dipole field and relatively large gradient  B op ~10T, G op ~50T/m with ~10% margin at 4.5K  Midplane gap: Coil-coil – 60mm Clear – 50mm  BUT the quadrupole component CANNOT be reversed without reversing the dipole OR reversing the open midplane  It is a limitation of that design,… but before we discard it – would anyone be interested in such magnet? ByBy x

13. 13 IR BE1 magnet  One of the most challenging magnets in the list: large midplane gap and unusual aperture requirements  Same concept as for the ring dipole, but field quality optimized for the vertically elongated beam  Two double-shells or shell/block hybrid  B op ~ 8T with ~22% margin at 4.5K in either case.  Midplane gap: Coil-coil – 60mm Clear – 50mm

14. 14 IR BE1 magnet: FQ zone FQ optimized for the 1:2 beam ratio. ~Elliptical good field area Shell magnet Shell/block hybrid 10 -3 limit: 118x56mm 10 -4 limit: 108x26mm 10 -3 limit: 120x64mm 10 -4 limit: 84x37mm

15. 15 IR BE1 magnet: iron yoke  800-900 mm outer diameter is required to contain the flux  Can be reduced if fringe field is not a concern

16. 16 Coil ends Shell type geometry allows the “traditional” coil ends even in case of the open midplane magnet. Benefits:  The winding stresses are minimized as the cable takes the most natural position corresponding to the minimum strain energy;  All conductors are contained within the cylindrical shells that allows the same mechanical structure throughout the coil. It avoids structural discontinuity between the straight section end ends that may cause premature quenches and degradation;  The end length in minimized;  30+ years of polishing this type of superconducting technology starting from Tevatron and continuing in LARP.

17. 17 BE1 dipole ends Midplane gap and open aperture are maintained throughout the magnet

18. 18 IR dipole structural analysis Assumptions and constraints:  Coil elasticity modulus is 40GPa  Coil can move within its envelope and separate from the collar  All prestress is provided by the collar  The collar is registered with respect to the vertically split iron yoke using two keys (per quadrant)  No thermal contraction was considered

19. 19 IR dipole: forces 23% of total 17% of total 6.6% of total 16% of total

20. 20 Shell type IR dipole  The mechanical structure is not optimized  If the coil motion is unrestricted, the stresses approach 300MPa in the coil corners and the maximum vertical displacement is 335  m  If the inner layer spacer is locked with respect to the collar, the stresses are below 200 MPa and the maximum vertical displacement is 240  m  It may be possible to reduce the stress to 150MPa (considered the reversibility limit for Nb 3 Sn) after the shim and keys geometry is optimized  However, the Nb 3 Al conductor having the stress tolerance up to 500MPa can work right away

21. 21 Hybrid IR dipole  The hybrid allows vertical support at the center of the coil midplane  The peak coil stress is ~120MPa and the maximum vertical displacement is ~260  m (no spacer locking is needed)

22. 22 Summary Some of the ring and IR magnets were preliminary studied:  The aperture and gradient requirements for the IR quadrupoles are close to those considered by LARP. These magnets can directly benefit from the LARP experience.  The open midplane ring dipole can provide the required field with a sufficient margin. Can be made as the combined function magnet with both midplanes open or as a C- type magnet  Because of the large midplane gap and unusual aperture requirements, the open midplane IR dipole appears to be one of the most challenging magnets  Two IR dipole concepts based on shell and shell/block geometry were considered: - The good field quality can be obtained within the vertically elongated area in either design - The stresses approach 200MPa in the shell type design, but may be reduced after optimization of the support structure. The stresses in the hybrid are comfortably low  The shell type magnet technology is an attractive option for either type of the open midplane magnet