1. 1 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Hansestadt Hamburg around 1400… …pirates, the “Vitalienbrüder” or “Likedeelers” based at Helgoland Klaus Störtebecker and Godeke Michels

2. Critical Surfaces A comparison between LTS and HTS Arno Godeke Lawrence Berkeley National Laboratory, Berkeley, CA, USA WAMHTS-1 workshop – DESY Hamburg – May 23, 2014 This work was partly supported by the Director, Office of Science, High Energy Physics, U.S. Department of Energy under contract No. DE-AC02-05CH11231

3. 3 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Motivation: Record dipole fields HE-LHC and MAP: 20+ T dipoles HTS: High Tesla Superconductors (Bi-2212, YBCO, Bi-2223) Nb-Ti 18 T (1.9 K) Nb 3 Sn 10.5 T Dietderich and Godeke, Cryogenics 48, 331 (2008) Nb 3 Sn quality and quantity in wires Magnet technology 1 decade ago 2 decades ago 20+ T dipoles require High Tesla Superconductors (at least presently) Nb 3 Sn

4. 4 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg How much current density is needed? J W : In windingsJ E : In wire 2 layer, 40 mm bore, 25 mm Rutherford – R 1 = 20 mm, R 2 = 70 mm,  0 H = 20 T – J W = 637 A/mm 2 Maximum stress Meuser, LBNL Eng. note M5254 (1978) Caspi and Ferracin, Proc. PAC-2005 Godeke, et al., Unpublished J E = 600 A/mm 2 & J W = 450 A/mm 2 (if stress = OK) J E = 600 A/mm 2 & J W = 450 A/mm 2 (if stress = OK) Meuser, LBNL Eng. note M5256 (1978) Caspi and Ferracin, Proc. PAC-2005 Increase R 2 Drop J W Reduce stress Bottura and Godeke, Rev. Accel. Sci. Techn. 5 25 (2012) R max

5. 5 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg LTS intrinsic limits and dipole performance Field – temperature limitations and achieved dipole fields NbTi – 10.5 T – 80% of H c2 (1.8 K) Nb 3 Sn – 16 T – 65% of H c2 (4.5 K) – 80% of H c2 (4.2 K) = 20 T? – 80% of H c2 (1.8 K) = 22 T? ? Can Nb 3 Sn be pushed higher? Godeke, et al., IEEE Trans. Appl. Supercond. 17 1149 (2007) Godeke, et al., J. Appl. Phys. 97 093909 (2005)

6. 6 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Prospects for A15 quality and quantity (LTSW 2003) 25% 40% 10% 25% Non-Cu: Ternary 64h/675°C C.M. Fischer MS thesis UW-Madison PIT measured: ~140nm, 40% A15 in non-Cu OI-ST: ~170nm, ~60% A15 (?), 24%Sn PIT, all = best bit, ~140nm, 40% A15 PIT, + = 65% A15, ~140nm, ~24%Sn PIT, + = 65% A15, ~140nm, all best bit Sn CONTENT Nb 3 Sn FRACTION AND Sn CONTENT Nb 3 Sn FRACTION Simulations on SMI-PIT (Nb,Ta) 3 Sn for J c (12T,4.2K) Godeke, LTSW (2003) Godeke, et al., J. Appl. Phys. 97 093909 (2005) Achieved: Bruker PIT: 2600 A/mm 2 (2008) OST IT: >3000 A/mm 2 (since 2003) Hypertech IT: 3400 A/mm 2 (2008) Academic limit = 5000 A/mm 2 Practical limit = 4000 A/mm 2 (2003) 3800 A/mm 2 measured in OST-RRP (2011) Unless pinning can be improved! Academic limit = 5000 A/mm 2 Practical limit = 4000 A/mm 2 (2003) 3800 A/mm 2 measured in OST-RRP (2011) Unless pinning can be improved!

7. 7 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Pinning optimizations? Comparison between NbTi and Nb 3 Sn J E (H) Godeke, et al., IEEE Trans. Appl. Supercond. 17 1149 (2007) H c2 (1.9K) NbTi is more efficient approaching H c2 → WHY?

8. 8 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg What determines J c ? J c is determined by the achievable pinning force F P And thus by the average grain size in Nb 3 Sn Grain boundaries are the main pinning centers in Nb 3 Sn Godeke, Supercond. Sci. Techn. 19, R68 (2006) After Fischer M.Sc. Thesis U. Wisconsin – Madison (2002) No pinning F L < F P F L > F P EcEc JcJc

9. 9 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg What is an optimal grain size? Ideal is 1 pinning center per flux-line Schematic: Cubic grains and flux-lines Ideal: d av = a 0 Flux-line spacing a 0 is field dependent E.g. at 12 T a 0 = (3/4) ¼ (  0 /  0 H) ½ = 12 nm Grain size in Nb 3 Sn wires → 100 – 200 nm NbTi: Nanometer scale α-Ti precipitates Nb 3 Sn: Grain size determines F P,MAX Grain size determines F P (H) Grain size Nb 3 Sn factor 10 too large Pinning in Nb-Ti is fully optimized Nb 3 Sn: Grain size determines F P,MAX Grain size determines F P (H) Grain size Nb 3 Sn factor 10 too large Pinning in Nb-Ti is fully optimized Lee, et al., Wire J. Int. Feb. 2003 Godeke, et al., IEEE Trans. Appl. Supercond. 17 1149 (2007) Godeke and Dietderich, Unpublished

10. 10 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg What happens when Nb 3 Sn grains are refined? Pinning force predicted gains 12 T, 4.2 K J c increases by factor 3.6 (!) – A factor 3.4 is measured in thin films that were made and tested at LBNL Critical current 20 – 25 T field regime is opened up – Much more efficient approaching H c2 Finer grains are emerging for wires… Dietderich and Godeke, Cryogenics 48 331 (2008) Godeke, et al., Unpublished (2014) Gains confirmed on thin films. How to do in wires is emerging… Gains confirmed on thin films. How to do in wires is emerging… 3225 A/mm 2 11,567 A/mm 2 E.g. Xu, et al., Appl. Phys. Lett. 104 (2014) F P normalized to non-Cu J c

11. 11 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Wrap-up: What are the present dipole limits using LTS? Nb-Ti reaches 80% of H c2 (T)  -Ti precipitates form pinning centers Nb 3 Sn reaches 65% of H c2 (T) Inefficient high field pinning Geometric and stress limitations Limits: 10.5 T at 1.9 K for Nb-Ti 16 T at 4.5 K for Nb 3 Sn (or ~18 T at 1.9 K) Limits: 10.5 T at 1.9 K for Nb-Ti 16 T at 4.5 K for Nb 3 Sn (or ~18 T at 1.9 K) Needed for 20+T 1 flux line per pinning site (core pinning) 10 flux lines per pinning site (collective pinning)

12. 12 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Three paths towards higher dipole fields… 1.Use High Tesla Superconductors for inserts Requires compatible magnet technology 2.Improve high field pinning in Nb 3 Sn Requires clever material science; might reduce H c2 3.Increase H c2 in Nb 3 Sn Is 35 T the limit of Nb 3 Sn H c2 (0)? Cooley, et al., Appl. Phys. Lett. 88 142506 (2006) Mentink, Ph.D. Thesis Univ. of Twente (2014) Godeke, Supercond. Sci. Techn. 19 R68 (2006) ? Still more to expect from Nb 3 Sn!

13. 13 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg What dipole fields are possible using HTS? Bi-2212 is available as a round wire …with significant potential! Bi-2212 is available as a round wire …with significant potential! H c2 (0) [T]T c (0) [K] NbTi149.5 Nb 3 Sn3018 MgB 2 3.5-3532-40 YBa 2 Cu 3 O 7 >10093 Bi-2223>100108 Bi-2212>10095 No field limitations 7 m of cable in a coil

14. 14 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg What about intrinsic limitations: H c2 (T) or H irr (T)? Irreversibility field? Irreversible magnetization i.e. no more pinning! Godeke, Ph.D. thesis, Univ. of Twente (2005) Thermal de-pinning can be severe H irr swamped by inhomogeneities SC but no pinning

15. 15 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Pinning defines practical phase boundary Actual phase boundaries HTS compared to LTS Larbalestier, et al., Nat. Mater. 13 375 (2014) Severe lack of pinning? Saved by BZO? MacManus-Driscoll, et al., Nat. Mater. 3, 439 (2004) “Spontaneous” nano-distribution of nano-dots and nano-rods (Nb 3 Sn…?) Large C P Large T-margin Low NZP Bi-2212 (Bi-2223) inserts Do we really want good pinning for Bi-2212 inserts at 4.2 K? (We do want good pinning for Nb 3 Sn at 4.2 K!) Do we really want good pinning for Bi-2212 inserts at 4.2 K? (We do want good pinning for Nb 3 Sn at 4.2 K!)

16. 16 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg So: Are there enough pinning sites in Bi-2212 at 4.2 K? Miao, et al., IEEE Trans. Appl. Supercond. 15 2554 (2005) 1 bar reaction, 4 cm sample, 2005! 1 flux line per pinning site (core pinning) 10 flux lines per pinning site (collective pinning) Weak links Linearity at high field suggests core pinning for strong links at 4.2 K => Sufficient density of pinning sites? Linearity at high field suggests core pinning for strong links at 4.2 K => Sufficient density of pinning sites?

17. 17 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg How do 4.2 K LTS and HTS pinning strengths compare? 2005 1 bar Bi-2212: J E (45 T, 4.2 K) = 266 A/mm 2 25 % Bi-2212: F P-max = 48 GN/m 3 in Bi-2212 2012 100 bar (OP) Bi-2212 F P-max ≈ (650/450)*48 = 70 GN/m 3 at 45 T NbTi and REBCO Trociewitz, et al., 2005 NHMFL report 297 Nb 3 Sn ~5000 A/mm 2 at 12 T – F P-max = 93 GN/m 3 at 5 T “APC” Nb 3 Sn: F P-max = 215 GN/m 3 at 12 T (?) Applied magnetic field [ T ] Normalized pinning force 4.2 K = 1700 GN/m 3 (“flat” from 8 – 32 T) OP Bi-2212 at 4.2 K seems comparable to present Nb 3 Sn but at much higher field REBCO is still far better OP Bi-2212 at 4.2 K seems comparable to present Nb 3 Sn but at much higher field REBCO is still far better Xu, et al., Appl. Phys. Lett. Mater. 2 046111 (2014)

18. 18 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Comparison of superconductor fractions NbTi: 50% of wire is SC Nb 3 Sn (PIT): 20% of wire is SC Bi-2212: 25% of wire is SC NB: Price Ag = 630 $/kg, Nb (G1) = 350 $/kg REBCO: 1% of tape is SC 25% 40% 10% 25% Non-Cu: Ternary 64h/675°C C.M. Fischer MS thesis UW-Madison Larbalestier, et al., Nat. Mater. 13 375 (2014) P.J. Lee, Applied Superconductivity Center (2003) Larbalestier, et al., Nat. Mater. 13 375 (2014) A lot to gain in HTS SC fraction

19. 19 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Uniaxial strain (e.g. CTE differences in accelerator magnets) Generic plot of axial strain sensitivity Not much happens for NbTi until >1% strain Nb 3 Sn, YBCO are reversible in compression – Cracks when loaded too far into tension Bi-2212, Bi-2223 are crack dominated – Limited reversible linear region YBCO under strain depends on direction… …which is beneficial for certain cable layouts Bottura and Godeke, Rev. Accel. Sci. Techn. 5 25 (2012) Van der Laan, et al., Supercond. Sci. Techn. 24 115010 (2011)

20. 20 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Uniaxial strain sensitivity of porous and dense Bi-2212 1 bar reacted, porous Bi-2212 wires Generic behavior since mid 1990’s 100 bar reacted, dense Bi-2212 wires Godeke, et al, submitted to Appl. Phys. Lett. (2014) Cheggour, et al., Supercond. Sci. Techn. 25 015001 (2011) Densification does not improve strain margin Will densification reduce buckling?

21. 21 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Cables and stress (e.g. Lorentz load in accelerator magnets) Nb 3 Sn: 200 MPa Bi-2223: Cables? REBCO: 45 MPa (Roebel) … 1 GPa (CORC) Dietderich, et al., IEEE Trans. Appl. Supercond. 11 3577 (2001) Hasegawa, et al., IEEE Trans. Appl. Supercond. 11 3034 (2001) Transverse pressure measurements on modern Bi-2212 cables are urgently needed! (Experiments at 65 K and self-field are probably sufficient) Transverse pressure measurements on modern Bi-2212 cables are urgently needed! (Experiments at 65 K and self-field are probably sufficient) Bi-2212 ? about 0.3% ⊥ strain

22. 22 May 23, 2014A. Godeke – Critical Surfaces – WAMHTS-1 workshop – DESY Hamburg Summary Nb 3 Sn is far from exhausted! 20 T dipoles might be possible with engineered pinning center Nb 3 Sn – Huge benefit: Utilization of proven Nb 3 Sn magnet technology! R&D in academia needed for development (bring on your Ph.D. students!) If only REBCO was a multi-filamentary round wire available in km length Crazy pinning strength Low strain sensitivity at 4.2 K No reaction! BUT… If only Bi-2223 was available as cable without crack dominated strain dependence Bi-2212 is a multi-filamentary round wire available in km length Comparable pinning to Nb 3 Sn, but at 10x the field Magnet designers need high J E cables and these have been proven W&R: One order more complex than Nb 3 Sn, but proven 0.3% strain margin is small but workable, transverse pressure still unknown