1. Development of non-Nb coatings for SRF accelerator cavities Alex Gurevich Old Dominion University, Department of Physics and Center for Accelerator Science, Norfolk, VA 23529, USA Future Circular Collider Study, Washington DC, March 24, 2015 Supported by DOE under grant No. DE-SC0010081

2. Why new SRF materials are needed? Best Nb cavities have reached the breakdown fields close to the fundamental limit H c  200 mT at which penetration of vortices destroys superconductivity. Higher T c superconductors may offer a great reduction of the BCS surface resistance, and higher Q: R s  exp ( - 1.76T c /T) + R i But higher T c superconductors have the lower critical field H c1 much lower than 200 mT and usually higher residual resistance R i Multilayer coating – a possibility to increase penetration field beyond 200 mT up to H c = 0.5-1T of the coating material while avoiding the H c1 penalty Choice of the optimum SRF materials: Nb 3 Sn, NbN, pnictides or alloyed Nb. Possibility of developing high Q cavities operating at 4.2 K and high fields H’(0) = H s /λ

3. Multilayer coating Nb insulating layers higher-T c SC: NbN, Nb 3 Sn, etc Magnetic screening of the Nb cavity without vortex penetration Multilayer coating of SC cavities: alternating SC and I layers with d < The breakdown field could be increased up to the superheating field H s of the coating: 450 mT for Nb 3 Sn No thermodynamically stable parallel vortices due to the enhancement of H c1 in thin films with d < (Abrikosov, 1964 ) A. Gurevich, APL. 88, 012511 (2006) Pushes the accelerating gradient above 100 mV/m

4. Recent progress  Experimental evidences of the enhancement of the parallel H c1 in thin films L. Civale, T.K. Worthington, A. Gupta, Phys. Rev. B 48, 7576 (1993). C. Antoine, et al Phys. Rev. ST-AB 13, 121001 (2010). T. Tajima, et al. J. Phys. Conf. Ser. 234, 012043 (2010); AIP Conf. Proc. 1435, 297 (2012). DB Beringer, C Clavero, T Tan, XX Xi, WM Roach, RA Lukaszew IEEE Trans. Appl. Supercond. 23, (2013)  Increasing the high-field performance and reduction of R s by a NbN overlayer C.Z. Antoine, J.-C. Villegier, G. Martinet, APL 102, 102603 (2013). WM Roach, DB Beringer, Z Li, C Clavero, RA Lukaszew, IEEE Trans. Appl. Supercond. 23 (2013)  NbTiN/Al 2 O 3 /Nb thin film bilayers at Jlab (A-M. Valente)  Nb 3 Sn and pnictide multilayers are being developed (ODU/UW) What’s next?  Is there an optimum thickness of layers which maximizes the breakdown field? ✔  If yes, how far can the maximum screening field H m be increase by multilayers? Can the optimized H m exceed the superheating field of the layer? ✔  Do we know how to select the best layer material? Can dirty Nb multilayers do the job? ✔  Are the insulating layers really necessary to protect the cavity and to suppress thermal quench caused by local penetration of vortices at defects? ✔

5. Outline  There is an optimum thickness of multilayers at which it can screen the magnetic field exceeding the superheating field of both Nb and the layer material.  MLs provide best protection of cavities against surface defects which lower the Bean- Livingston barrier and open gates for local penetration of vortices.  Dielectric layers are instrumental to suppress vortex dissipation and dendritic thermomagnetic avalanches which trigger the cavity quench.  Dielectric layers suppress thermoelectric currents which generate trapped vortices during the cavity cooldown  Implementation of the optimized Nb 3 Sn or NbN multilayers could double the maximum accelerating gradient, pushing it above 100 MV/m.  Pnictides could potentially quadruple the accelerating gradient.  New opportunities of using dirty Nb multilayers to push H m up to 280-300 mT

6. Superheating field  Meissner state becomes unstable above the superheating field H > H s as the current density J s = H/ at the surface reaches the depairing current density J d = H s /  H s close to T c : ( Matricon and Saint-James, 1967, Chapman 1995 )  B s decreases as the surface gets dirtier and the GL parameter κ = λ/ξ increases. Nb At T > 1 has been calculated in the clean limit (Galaiko 1966, Catelani and Sethna, 2008) and for arbitrary impurity concentration (Lin and Gurevich, 2012)  Surface barrier for penetration of vortices vanishes at H = H s

7. Possible multilayer materials Material T c (K) H c [T] H c1 [mT] H c2 [T] [nm ]  [meV] Nb9.20.21700.4401.5 pnictides30-550.5-0.930>10020010-20 Nb 3 Sn180.545030853.1 NbN16.20.2320152002.6 MgB 2 400.43303.5-601402.3; 7.2 YBCO 931.410>10015020 Large gap Δ (good for SRF) is usually accompanied by low H c1 (bad for SRF ) d-wave high-T c cuprates with nodal gap and are not useful for SRF

8. Screening field in a multilayer  Solutions of London equation for a layer with the penetration depth λ on a substrate with the penetration depth λ 0  Important parameters where c and b are given by: for the SC substrate (Nb) with λ 0 < λ, both c and k are positive J(x)/J(0) Meissner state breaks down at the surface of either ML or Nb where the current densities J(0) = h’(0) and J(d) = h’(d) are maximum T. Kubo, Y. Iwashita, and T. Saeki, APL 104, 032603 (2014); A. Gurevich, AIP Advances, 5, 017112 (2015)

9. Current counterflow induced by the Nb substrate  Current density in the layer J(x) = - h’(x):  Current density at the surface J(0) is reduced by the substrate with λ 0 < λ: Counterflow induced by the substrate reduces the current density at the ML surface, allowing the Meissner state in the ML to survive up to fields exceeding the bulk superheating field H s For a thick ML with d >> λ, the maximum field H m is limited by H s : at optimum thickness d m the field H m exceeds both H s and H s0

10. Optimum thickness  The Meissner state is stable if the screening current density at the surface of both the ML and the substrate is smaller than the depairing limit: J(0) < J d = H s /λ and J(d) < J d0 = H s0 /λ 0 for H s = 2H s0 and k = ½, d c = ln[μ + (μ 2 – k) 1/2 ] The Meissner state is below both blue and red lines. The crossing point defines the optimum thickness d m for maximum H m which exceeds the superheating fields of both the layers and the substrate d/λ

11. Maximum screening field  The maximum screening field H m corresponds to d = d m for which H m at the optimum thickness exceeds the bulk superheating fields of both Nb and the layer material. For λ >> λ 0, practically for λ > 160 nm for a SC layer on the Nb cavity with λ 0 = 40 nm, H m approaches the limit Let us evaluate H m for a ML on clean Nb with λ 0 = 40 nm and H s0 = 1.2H c = 240 mT (the GL result for clean Nb) and different layer materials, such as Nb 3 Sn, NbN, pnictides, and also dirty Nb A.Gurevich, AIP Advances, 5, 017112 (2015)

12. Estimates of H m and d m  Nb 3 Sn: H s = 0.84H c = 454 mT and λ = 120 nm (moderately dirty): H m = 507 mT, d m = 1.1λ = 132 nm doubles the superheating field of clean Nb  Ba 0.6 K 0.4 Fe 2 As 2, T c = 38 K, H c = 0.9T, H s =756 mT, λ = 200 nm H m = 930 mT, d m = 1.78λ = 356 nm. almost quadruples the superheating field of clean Nb  dirty Nb layer: H c = 200 mT, H s = 170 mT, l = 2 nm, and λ =λ(ξ 0 /l) 1/2 = 180 nm H m = 288 mT, d m = 0.44λ = 79 nm. 20% gain as compared to H s = 240 mT of clean Nb

13. Can a cavity be protected only by the surface barrier? H0H0 u J H = H c1 H < H c1 H > H c1 H = H c u G Thermodynamic potential G(u) as a function of the position u: MeissnerImage Vortices have to overcome the surface barrier even at H > H c1 (Bean & Livingston, 1964) Surface barrier disappears at the overheating field H = H s > H c1. Meissner state is metastable at H c1 < H < H s Image to ensure J ┴ = 0 Inevitable surface defects weaken the surface barrier which vanishes at H = H p where H c1 < H p < H s Scanning laser confocal microscopy of a BCP Nb cavity (Jlab), P. Lee, 2006 Probes ≈ 0.3-3 μm scales

14. Are dielectric layers really necessary? Once a vortex breaks through a defect, it triggers penetration of avalanche of vortices causing a thermo-magnetic flux jump and the cavity quench Poor thermal conductivity of Nb 3 Sn: a 2-3 μm thick film doubles the thermal impedance of the Nb cavity wall, facilitating local overheating and branching vortex avalanches H λ λ H Why cannot we just deposit a thick Nb 3 Sn film without I layers and hope that the surface barrier would block penetration of vortices? (S. Posen et al, 2011; T Kubo, 2014) Surface defects in SRF cavities are unavoidable. Dielectric layers prevent global quench and make local vortex dissipation at H > H p tolerable Inconsistent with experiments. Premature penetration of vortices on surface defects at H < H s due to grain boundaries, topographic defects, local nonstoichiometry, etc..

15. Magneto-optical imaging of magnetic field penetration MOI reveals vortex penetration along weak linked grain boundaries  (x,y)=VH z (x,y)d Faraday rotation of the light polarization angle P A H z (x,y) YBCO film (A. Polyanskii, ASC/NHMFL)

16. What happens if vortex avalanches propagate (MO image of Nb film by M.Welling and R. Wijngaarden, U. Amsterdam)

17. Theory of dendritic flux penetration  Coupled equations for the temperature T and electric field E E JJcJc  Two characteristic times: - t m =  0 L 2 /  - time of magnetic flux diffusion - t h = CL 2 /  - time of thermal diffusion  Thermal bistability and nonlocal flux diffusion  Propagation of dendritic flux structures of hot normal phase I. Aranson, A. Gurevich, V. Vinokur, Phys. Rev. Lett. 87, 0976003 (2001); 94, 037002 (2005). Becomes particularly violent at low temperatures < 4 K as the specific heat C(T) = C 0 T 3 decreases

18. Dendritic flux propagation in a film with surface defects Branching thermomagnetic flux jump Successive waves of dendritic flux propagation I. Aranson, A. Gurevich, V. Vinokur, Phys. Rev. Lett. 87, 94, 037002 (2005). For the SRF cavities, this happens during 0.1 ns Hot magnetic flux branches penetrating with supersonic velocity, > 1-10 km/s Triggers cavity quench at the breakdown field

19. Arresting penetration of vortices in a multilayer Parallel H c1 in a thin film multilayer is irrelevant (no longer a problem) I layer intercepts propagating vortex loops, turning them into two short vortices of opposite polarity. No propagation in the bulk if h(d) < H c1 Great reduction of the RF vortex power q localized in a thin S layer. Upper limits of q and the amplitude of V-AV oscillations u m Nb 3 Sn: ρ n = 0.2 μΩm, d/λ = 0.2, κ = 20, λ = 100 nm, β = H p /H s = 1/2, ν = 2GHz For Nb 3 Sn, u m ≈ 4 μm, and q ≈ 2 μW Unlike thick Nb 3 Sn films, a thin ML only slightly (by ≈ 5%) increases the thermal impedance of the cavity wall. No deterioration of thermal quench stability.

20. Ti or N-alloyed dirty Nb multilayers A. Grasselino et al, SUST 26, 102001 (2013) P. Dhakal et al, PR. ST-AB 16, 042001 (2013) H c1 ? Ti or N alloyed Nb film of optimum thickness Cavity grade bulk Nb A few nm thick Al 2 O 3 spacer  Optimized impurity profile at the surface  To combine the extended Q(B) rise and compensate reduction of H c1 in alloyed Nb  Use a bilayer of multilayer to push the breakdown field above 250 mT Enhancement of breakdown field by a Nb/Al 2 O 3 bilayer deposited onto a Nb cavity: R. Russo et al, IEEE Trans. Appl. Supercond. 19, 1394 (2009)

21. Conclusions  Multilayer S-I-S-I-S coating: breaking the Nb monopoly by taking advantage of superconductors with much higher H c without the penalty of lower H c1  Possibility to double the accelerating gradients and move from 2K to 4.2K  Optimum thickness at which the breakdown field is maximum  Multilayers with optimum thickness can reach breakdown fields exceeding the bulk superheating field of the layer material  Most promising ML materials: Nb 3 Sn, NbN and possibly pnictides  Dirty Nb multilayers could reach the breakdown field up to 30% higher than the superheating field of 200-240 mT for the cavity-grade Nb  New possibility of combination of the extended Q-rise in N or Ti-alloyed Nb and increased breakdown field