1. E821 SC Inflector and Beyond Wuzheng Meng (meng@bnl.gov) 12 June 2008

2. I. Design Constrains – a brief history E821 (originally) proposed a pulsed inflector. R&D was performed up to late 1989 (g-2 note No.32). DC SC inflector was proposed in 1988 (g-2 note No.25), and finally approved by collaboration in late 1990 (or early 1991?). By that time, the design of the storage ring magnet was almost completed (cross-section and conductor type), except some controversial shimming methods. E821 SC inflector final design had to fit this pre-defined limited space.

3. Down-stream – Vertical limit: storage ring magnet gap (180 mm) Horizontal: must as close as possible to the muon storage center (77 mm)

4. Up-stream --- Limited in radial direction, by storage ring outer coil cryostat

5. Could we make it shorter? Could we make it curved, so that L eff could be longer? ByBy S In order to cancel 2.55 T-m Fringe field from storage ring, Bo = 1.5 T and L= 1.7 m are comfortable for a low Tc NbTi SC septum magnet ----- We did not feel comfortable about Lorentz force constrains (in the inner side)

6. II. Design Principle – truncated double cosθ Single cosθ distribution (R. Beth, BNL AADD-102,1966) Field Produced by Cylindrical Current Arrays K 1 cosθ

7. Double cosθ Distribution and Truncation along Vector-potential lines --- Frank Krienen (NIM A283(1989)5) K 1 cosθ -K 2 cosθ

8. Conductor -- Astromag/g2Inf Configuration (NbTi:Cu:Al): 1: 0.9: 3.7 Processor: Co-extrusion NbTi/Cu composite: diameter 1.6 mm (monolith) NbTi Finament: diameter 0.02 mm Twist pitch: 31 mm Conductor dimension: 2 x 3 mm (bare); 2.3 x 3.3 mm (insulated) Critical current density Jc > 2500 A/mm 2 @ 5 T, 4.2 K Stabilizer purl Al: 99.997%; RRR=750 NbTi area = 1.06 mm 2

9. Prof. Akira Yamamoto (KEK) and Tokin Co. Cold mass: 60 kg Cooling power: 11 W Stored energy: ~9000 J Inductance: 0.002 H

10. Conductor positions were modified to avoid technical difficulties

11. III. Choices of Ends – Open-end Closed-end

12. Based upon following arguments, E821 chose Closed End (July 1991): (1)Easier for fabrication, force constrains (large quench margin); (2)Physical dimension is shorter; (3)Smaller integral fringe field (~1/6) Although closed-end has disadvantage – Less muons (~ 1/1.44) are injected and stored due to Multiple scatterings through materials (11mm Al; 0.8mm NbTi; 0.8mm Cu): ---- 20 turn (x2 layer) conductors; ---- coil caps; ---- windows on the mandrel and cryostat

13. IV. Fringe Field Issues – Sources of fringe field: (a) continue current distribution is replaced by discrete individual conductor winding; (b) end effect (principle is based on 2d potential theroy) Consequence of fringe field: Total integrated fringe field (~7ppm); peak field (in storage region) >200 Gauss and high gradients are beyond stable range of NMR probes. Special regional measurements introduce additional systematical errors (0.2 ppm). Magneto-static shimming did not work! SC shield is the solution!

14. Superconductivity -- (T<Tc; J< Jc; B<Bc) (1)Zero Electric Resistivity (2)Diamagnetism Type I Type II κ = λ(T)/ξ(T) 1/ Pure state (H < Hc) Mixed state (H c1 < H < H c2 ) Meissner effect Perfect conductor Can tolerate low flux density Can tolerate high flux density No use for magnets Good for magnets and flux shields λ(T) --- magnetic penetration depth ξ(T) --- coherence length κ ---- Ginzburg-Landau parameter

15. Type I SC Type II SC T = 300 K T = 4 K Figure from W. H. Warnes: Principles of Superconductivity (Red Text added by W. Meng) B = 0 B = Ba Ba = 0 B = Ba

16. Multilayer SC Sheet Nippon Steel Corporation Advanced Technology Research Lab Dr. Ikuo Itoh Jc > 1200 A/mm 2 @1.5 T, 4.2 K, H NbTi layer B = μ 0 Jc d (d = Total thickness of NbTi layers)

17. Working Procedure -- Main magnet powered Flux penetrating Inflector stays warm Un-powered Main magnet stable Cool down inflector Main flux are trapped by the SC shield 10 K 4.6 K (1) (2)(3) Power Inflector slowly (Io 2850 A; 2 A/sec) Main flux are trapped Fringe flux are blocked by the SC shield

18. V. Possible Modification & Improvement– Open both ends: Prof. Akira Yamamoto & Tokin Co Contributions – 1 prototype (L=0.5 m) and 2 full length (1.7 m) SC inflectors Prototype was tested up to 3057 A In KEK (with zero external field) Prototype was tested up to 3000 A In BNL with Ba=1.45 T (inside 18D72 magnet) Figure from Tokin Technical Review No.20 March 1993July 1994

19. Encouraged facts – Open-end has been tested in the external field. SC performance was very stable. Open-end gives additional magnetic field along beam axis. (further detailed study is needed) Although open-end gives more integral fringe field (x 6); peak field on inflector cold surface is estimated ~ 0.1 T. Existing SC sheet has enough shielding capability (0.23 T).