A Proposal for a 50 T HTS Solenoid

1. A Proposal for a 50 T HTS Solenoid Steve Kahn Muons Inc. August 10, 2006 S. Kahn -- 50 T HTS Solenoid

2. Alternating Solenoid Lattice for Cooling • We plan to use high field solenoid magnets in the near final stages of cooling. • The need for a high field can be seen by examining the formula for equilibrium emittance: • The figure on the right shows a lattice for a 15 T alternating solenoid scheme previously studied. S. Kahn -- 50 T HTS Solenoid

3. From R. Palmer From R. Palmer S. Kahn -- 50 T HTS Solenoid

4. S. Kahn -- 50 T HTS Solenoid

5. A Proposal for a High Field Solenoid Magnet R&D • The availability of commercial high temperature superconductor tape (HTS) should allow significantly higher field that can produce smaller emittance muon beams. • HTS tape can carry significant current in the presence of high fields where Nb3Sn or NbTi conductors cannot. • We would like to see what we can design with this commercially available HTS tape. S. Kahn -- 50 T HTS Solenoid

6. S. Kahn -- 50 T HTS Solenoid

7. S. Kahn -- 50 T HTS Solenoid

8. From D. Summers presentation on July 14, ‘06 S. Kahn -- 50 T HTS Solenoid

9. Comparison of JE for HTS Conductors We have chosen to use Bi2223 since it is available as a reinforced tape from AMSC The conductor can carry significant current at very high fields. NbTi and Nb3Sn can not. S. Kahn -- 50 T HTS Solenoid

10. High Strength Tape used for calculations New and Improved High Strength Plus Tape Properties of American Superconductor’s High Temperature Superconductor Wire • 6% more current per turn • 10 % more turns per radial space S. Kahn -- 50 T HTS Solenoid

11. Cross Sections of AMSC HTS Tape High Current Tape High Compression Tape High Strength Tape React and Wind S. Kahn -- 50 T HTS Solenoid

12. Some Mechanical Properties of Oxford BSSCO-2212 Strain Degradation at 0.4% Wind and React Ultimate Strength~130 MPa Young’s Modulus E~51-63 GPa S. Kahn -- 50 T HTS Solenoid

13. Why Do We Want to Go to Liquid Helium? The parallel field orientation is the most relevant for a solenoid magnet. Previous calculations had used the perpendicular field. (We can view this not as a mistake, but as a contingency). S. Kahn -- 50 T HTS Solenoid

14. Current Carrying Capacity for HTS Tape in a Magnetic FieldScale Factor is relative to 77ºK with self field S. Kahn -- 50 T HTS Solenoid

15. Field Quadratic Linear 30 1.5378 1.5454 40 1.3091 1.3384 50 1.0685 1.1314 60 0.816 0.9244 Fit to High Field to Extrapolate Beyond 27 T • We are using BSSCO 2223 which has been measured only to 27 T in the perpendicular configuration. We are using it in the parallel configuration. • We have to extrapolate to high field. • We know that BSSCO 2212 has been tested to 45 T, so we think that the AMSC tape will work. • The high field measurements of BSSCO 2212 has a different falloff from BSSCO 2223. • We certainly will need measurements of the AMSC tape at high field S. Kahn -- 50 T HTS Solenoid

16. A Vision of a Very High Field Solenoid • Design for 40 Tesla. • Inner Aperture Radius: 2.5 cm. • Axial Length chosen: 1 meter • Use stainless steel ribbon between layers of HTS tape. • We will vary the thickness of the SS ribbon. • The SS ribbon provides additional tensile strength • HTS tape has 300 MPa max tensile strength. • SS-316 ribbon: choose 660 MPa (Goodfellow range for strength is 460-860 MPa) • Composite strength = SS SS + (1-SS) HTS (adds like parallel springs). • We use the Jeff associated to 40 Tesla. • We operate at 85% of the critical current. • All parameters used come from American Superconductor’s Spec Sheets. S. Kahn -- 50 T HTS Solenoid

17. Constraining Each Layer With A Stainless Steel Strip • Instead of constraining the forces as a single outer shell where the radial forces build up to the compressive strain limit, we can put a mini-shell with each layer. Suggested by R. Palmer, but actually implemented previously by BNL’s Magnet Division for RIA magnet. (See photo) S. Kahn -- 50 T HTS Solenoid

18. Using Stainless Steel Interleaving for Structural Support • Case 1: Use constant thickness interleaving between layers for structural support. • The high strength HTS tape comes with ~2.7 mils stainless steel laminated to the tape. Additional SS is wound between the layers. • The effective modulus of the HTS/SS combination increases with increased SS fraction. • Figure shows strain vs. radial position for a 40 Tesla magnet. • The maximum strain limit for the material is 0.4%. • This is achieved with 5 mil SS interleaving. • The use of constant thickness SS interleaving is not effective for magnets with fields much above 40 Tesla. S. Kahn -- 50 T HTS Solenoid

19. A Slightly More Aggressive Approach • Bob Palmer has suggested that we can vary the amount of stainless steel interleafing as a function of radius. • At small radius where we have smaller stress, we could use a smaller fraction of stainless steel. (See previous slide) • In the middle radial region we would use more stainless where the tensile strength is largest. • Following this approach we can build a 50 Tesla solenoid. • I will show you results for two cases: • Case 2: 40 Tesla solenoid with SS interleaving varied to achieve 0.4% strain throughout. • Case 3: 50 Tesla solenoid with SS interleaving varied to achieve 0.4% strain throughout. • A 60 Tesla solenoid may be achieved by increasing the current as the field falls off with radius by using independent power supplies for different radial regions. S. Kahn -- 50 T HTS Solenoid

20. Varying SS Interleaving to Achieve Maximum Strain • The thickness of the stainless steel interleaving is varied as a function of radius so as to reach the maximum allowable strain through out the magnet. • This minimizes the outer solenoid radius (and consequently the conductor costs). • This also brings the center of current closer to the axis and reduces the stored energy. • This is likely to increase the mechanical problems. S. Kahn -- 50 T HTS Solenoid

21. Case Comparisons • The tables on the left summarize the parameters and results of the three cases presented. • The analysis assumes the solenoid length is 70 cm • The top table shows the dimensional parameters: • Inner/outer radius • Conductor length and amp-turns. • The bottom table shows the results from the magnetic properties: • Stored enegy • Radial and Axial Forces S. Kahn -- 50 T HTS Solenoid

22. Comments on Stored Energy • The 70 cm length was chosen to be consistent with the decay of ~100 MeV muon. It is also the minimum solenoid length where there is some “non-fringing” central field. • The stored energy of the 50 Tesla magnet (case 3) is 20 Mega-Joules (for 70 cm). • This can be compared to 7 Mega-Joules for the 10 m long LHC 2-in-one dipole. • The LHC quench protection system actually handles a string of dipoles in a sextant (?). • There are differences between HTS and NbTi that need to be considered for quench protection. • HTS goes resistive at a slower rate than NbTi. • A quench propagates at a slower velocity in HTS than for NbTi. • We will have to perform computer simulations of quench protection for the HTS system to determine how to protect the magnet in case of an incident. S. Kahn -- 50 T HTS Solenoid

23. What about Axial Forces? • There is a significant contribution to the axial forces from the fringing radial fields at the ends. • In the 50 Tesla solenoid shown we will see a fringing field of 9 Tesla • We have seen that there is a total axial compressive force at the center of ~30 Mega-Newtons. S. Kahn -- 50 T HTS Solenoid

24. More on Compressive Forces • The top figure shows the Lorentz force density at the end of the solenoid as a function of radius for the three cases. • The axial pressure on the end is P=JBrt where t is the tape width. This peaks at 10 MPa. • The lower figure shows the Lorentz force density along the length for the peak radial position. • It is largest at the end and falls to zero at center as expected. • These stresses are not large. Do we have to worry about compressive strain along the axial direction? • The maximum allowable compressive strain for the tape is 0.15%. S. Kahn -- 50 T HTS Solenoid

25. Formulate R&D Plan • Initial measurements of material properties. • JC measurements under tensile and compressive strain. • Modulus measurements of conductor. • Thermal cycling to 4K. • Formulate and prepare inserts for high field tests. • Design insert for test in 30 Tesla magnet. • This magnet has a reasonable size aperture. • At 30 Tesla, some part of the insert should be at the strain limit. • Program for conductor tests at 45 Tesla. • 45 Tesla magnet has limited aperture (3.1 cm). • It has a warm aperture. S. Kahn -- 50 T HTS Solenoid

26. 50 Tesla MagnetReferees’ Reports, etc. Steve Kahn June 1, 2006 Local Thusday Meeting S. Kahn -- 50 T HTS Solenoid

27. Referees’ Reports • The referees were generally fairly critical of the high field solenoid proposal. • They did not feel that we understood the problems. • We did not list references to other projects such as the NHFML • We ignored the NRC COHMAG report that calls for a 30 T magnet costing 10-12 M$ • They were not confident in our HTS experience. • They did not believe that we could pull it off after phase 1. • I cannot argue with their lack of confidence in our ability, but I can address the technical issues that they posed, all of which we had considered when writing the proposal. S. Kahn -- 50 T HTS Solenoid

28. Technical Issues: 1. Why did we choose to use BSCCO 2223 or YBCO ("which is not technically sound") instead of BSCCO 2212 ("which is the preferred material of high field solenoids ...")? It is true that Bi2212 does have a higher Je. We had chosen to use Bi2223 in the initial evaluation since it was available from the manufacturer in a version that was reinforced so that it could withstand the high tensile strains that would be present. It is clear that bare "isotropic" Bi2212 could not withstand the tensile stresses. It is not clear how to laminate or reinforce the isotropic Bi2212 material. We did present a scenario in the proposal based on Bi2223 which shown that it could reach 40-50 Tesla with its advertised Je. We should also point out that we wanted to avoid doing conductor development ourselves. The technical properties of the ASCM HTS superconductor were documented by the manufacturer. Certainly during phase I we would have evaluated what the best superconductor to do the job would be. S. Kahn -- 50 T HTS Solenoid

29. Technical Issues (cont.) 2. Referee comment: If Bi2223 conductor is wound at a diameter just below its allowed strain, then there is no allowable strain remaining for the Lorentz forces. Firstly, the minimum radius of the improved ASCM conductor is now 19 mm and we use 25 mm for the inner solenoid radius. The minimum bending radius is where there is a 5% degradation of current carrying capability. We did allow a 15% current contingency in our calculations. Secondly, in the 40 Tesla model where we have used a constant thickness stainless steel interleaving, the maximum tensile strain from the Lorentz forces does not occur at the inner radius, it occurs at 10 cm from the center. The Lorentz stress is maximum at the inner radius since the B field is and falls off with radius. However, because of the hoop stress relation, the tensile strain on the conductor increase with radius. The maximum tensile strain is seen in approximately the center of the magnet. When we go to the 50 Tesla model where we vary the stainless steel interleaving thickness, we adjust the tensile strain to be approximately constant with radius. We must of course include the bending stress in this optimization. The likely effect would be to increase the overall magnet radius by a relatively small amount. S. Kahn -- 50 T HTS Solenoid

30. Technical Issues (cont.) 3. Proposed measurements and material properties. Referee 1 says they would be valuable. Referee 2 says they are available from the manufacturer and the literature. Referee 3 says manufacturer data should be taken with a "grain of salt." My comment: No further justification is needed. S. Kahn -- 50 T HTS Solenoid

31. Technical Issues (cont.) 4. Referee Comment: Even if the magnet can reach 50 T when it is charged to full field (a very big if), the conductor will come apart (including the stainless steel clad conductor that is behind the proposal), because the conductor absorbs helium, which causes the conductor to swell and no longer carry current in the superconducting state. This is a reference to the concern that if helium comes into contact with the BSSCO filaments it will seriously degrade its performance. This was observed as a thermal cycling problem causing micro-cracking that lets in nitrogen in their case (and certainly helium in ours). We did not appreciate this at the time of the proposal. If this becomes an issue, the approach would be not allow the helium to come into direct contact with the conductor. We can interleave some copper foil with the stainless steel for a thermal path to an external cooling source such as cryo-coolers or an external helium source. S. Kahn -- 50 T HTS Solenoid

32. Technical Issues (cont.) 5. Referee comment: I would also encourage Muons Inc. to look at the quench characteristics of any high Tc superconductor. Yes. We will need an active quench protection system. A 40 Tesla magnet of 1 meter length will have 8-11 Mega Joules of stored energy!! 50 Tesla would be even higher (20 Mega Joules). This kind of study would be necessary! S. Kahn -- 50 T HTS Solenoid

33. Marketing Issues: 1. We should probably have resisted putting "50 Tesla" in the title. The bold title may have damaged our credibility. The referees are likely to be experts in the field and are aware that the highest field HTS insert magnet went to 25 Tesla. We, who are newcomers, should not say that we can build a 50 Tesla magnet when the experts have not been able to do it. We should have taken the approach that we think that we can advance the technology with certain techniques that we have proposed. We should have proposed a more modest 30 Tesla magnet which could be used as one component for the final stage of muon cooling, even though are preliminary estimates support the possibility of a 40-50 Tesla magnet. This could also be used as a technological step to finally building the 50 Tesla magnet for the final component of the muon cooling. 2. We should have understood and referenced other R & D for high field solenoid magnets. One referee pointed this out and this is valid. • Some of the referees did not think there would be a market for 50 T magnets other than muon colliders. I find that hard to imagine. S. Kahn -- 50 T HTS Solenoid