1. RF breakdown in multilayer coatings: a possibility to break the Nb monopoly Alex Gurevich National High Magnetic Field Laboratory, Florida State University "Thin films applied to Superconducting RF: Pushing the limits of RF Superconductivity" Legnaro National Laboratories of the ISTITUTO NAZIONALE DI FISICA NUCLEARE, in Legnaro (Padova) ITALY, October 9-12, 2006.

2. Motivation Why Nb? BCS surface resistance: R s  4 exp (-  /k B T) Minimum R s implies maximum , that is, maximum T c  1.87  /k B and minimum London penetration depth Exceptions: Does not work for the d-wave high-T c superconductors for which R s  T 2 due to nodal lines in  (k) = 0. Two gap MgB 2 with    2.3 meV    7.2 meV: T c is proportional to  , while R s  exp (-   /k B T) is limited by   Vanishing  (k) = 0 along [110] directions in HTS Nb 3 Sn has maximum T c and minimum to provide the optimum R s

3. Background Best KEK - Cornell and J-Lab Nb cavities are close to the depairing limit (H  H c = 200 mT) How far further can rf performance of Nb cavity be increased? Theoretical SRF limits are poorly understood … KEK&Cornell

4. H c2 H c1 0 H Strong vortex dissipation HcHc Very weak dissipation - M Superconducting Materials Material T c (K) H c (0) [T] H c1 (0) [T] H c2 (0) [T] (0) [nm] Pb7.20.08na 48 Nb9.20.20.170.440 Nb 3 Sn180.540.053085 NbN16.20.230.0215200 MgB 2 400.430.033.5140 YBCO931.40.01100150 Very weak dissipation at H < H c1 (Q = 10 10 -10 11 ) Q drop due to vortex dissipation at H > H c1 Nb has the highest lower critical field H c1 Thermodynamic critical field H c (surface barrier for vortices disappears) Nb Higher-H c SC

5. Single vortex line 22 2  B r  Core region r <  where  (r) is suppressed Region of circulating supercurrents, r <. Each vortex carries the flux quantum  0 Important lengths and fields Coherence length  and magnetic (London) penetration depth λ For clean Nb, H c1  170 mT, H c  180 mT

6. Surface barrier: How do vortices get in a superconductor at H > H c1 ? Two forces acting on the vortex at the surface: - Meissner currents push the vortex in the bulk - Attraction of the vortex to its antivortex image pushes the vortex outside H0H0 b J image to ensure J  = 0 H = H c1 H < H c1 H > H c1 H = H c x0x0 G Thermodynamic potential G(x 0 ) as a function of the position x 0 : Meissner Image Vortices have to overcome the surface barrier even at H > H c1 (Bean & Livingston, 1964) Surface barrier disappears only at the overheating field H = H c > H c1 at which the surface J becomes of the order of the depairing current density

7. Vortex in a thin film with d < Vortex in a thin film with d < Vortex field in a film decays over the length d/  instead of (interaction with many images) Vortex free energy as a function of the position x 0 Self-energy Magnetic energy Lorentz force  x 0 London screening is weak so 2  2 B = -  0  (r) G. Stejic, A. Gurevich, E. Kadyrov, D. Christen, R. Joynt, and D.C. Larbalestier, Phys. Rev. B49, 1274 (1994)

8. Enhanced lower critical field and surface barrier in films Use thin films with d < to enhance the lower critical field Field at which the surface barrier disappears Example: NbN (  = 5nm) film with d = 20 nm has H c1 = 4.2T, and H s = 6.37T, Much better than H c = 0.18T for Nb

9. How one can get around small H c1 in SC cavities with T c > 9.2K? How one can get around small H c1 in SC cavities with T c > 9.2K? AG, Appl. Phys. Lett. 88, 012511 (2006) Nb, Pb Insulating layers Higher-T c SC: NbN, Nb 3 Sn, etc Higher T c thin layers provide magnetic screening of the bulk SC cavity (Nb, Pb) without vortex penetration For NbN films with d = 20 nm, the rf field can be as high as 4.2 T ! No open ends for the cavity geometry to prevent flux leaks in the insulating layers Multilayer coating of SC cavities: alternating SC and insulating layers with d <

10. How many layers are needed for a complete screening? H 0 = 2T H i = 50mT d Example: N Nb 3 Sn layers with d = 30nm 0 = 65 nm and H c1 = 2.4T Peak rf field H 0 = 2T < H c1 Internal rf field H i = 50 mT (high-Q regime) N = (65/30)ln(40) = 8 Nb Strong reduction of the BCS resistance by Nb 3 Sn layers due to larger  and shorter :

11. A minimalistic solution H 0 = 324mT H i = 150mT d A Nb cavity coated by a single Nb 3 Sn layer of thickness d = 50nm and an insulator layer in between If the Nb cavity can withstand H i = 150mT, then the external field can be as high as Lower critical field for the Nb 3 Sn layer with d = 50 nm and  = 3nm: H c1 = 1.4T is much higher than H 0 A single layer coating more than doubles the breakdown field with no vortex penetration, enabling E acc  100 MV/m

12. Global surface resistance Nb 3 Sn coating of thickness L = 50 nm, R Nb3Sn (2K)  0.1R Nb Screen the surface of Nb cavities using multilayers with lower surface resistance layer bulk

13. Why is Nb 3 Sn on Nb cavity much better than Nb 3 Sn on Cu cavity? NbCu H(t) Nb 3 Sn/Nb cavity is much better protected against small transverse field components than Nb 3 Sn/Cu cavity vortices Meissner state persists up to H  < H c1 (Nb) Meissner state is destroyed for small H  < (d/w)H c1 (Nb3Sn) << H c1 (Nb3Sn) due to large demagnetization factor w/d  10 3 -10 5 w HH

14. Vortex penetration in a screen Dynamic equation for a vortex Vortex flight time and energy release For a 30 nm Nb 3 Sn film,   10 -12 s, much shorter than the rf period  10 -9 s Maximum rf field at which the surface barrier disappears: Nb 3 Sn coating more than doubles vortex penetration field for Nb

15. Analytical thermal breakdown model H(t) T TmTm T0T0 TsTs coolant x d For a general case of thermal quench, see Gurevich and Mints, Reviews of Modern Physics 59, 941 (1987), Equations for T m and T s Kapitza thermal flux: q =  (T,T 0 )(T – T 0 ) Thermal runaway due to exponential increase of R s (T)

16. Maximum temperature BCS + residual surface resistance R i Since T m – T 0 << T 0 even H b, we may take  and h at T = T 0, and obtain the equation for H(T m ):

17. Thermal feedback stability for multilayers Breakdown field as a function of the total overlayer thickness L Here s = exp(-2L/ ), r = R 0 /R b,  =  0 /  b 50 nm Nb 3 Sn overlayer triples Q at low field 100 nm overlayer more than doubles the thermal breakdown field

18. Conclusions: Multilayer S-I-S-I-S coating could make it possible to take advantage of superconductors with much higher H c, than those for Nb without the penalty of lower H c1 Strong increase of H c1 in films allows using rf fields > H c of Nb, but lower than those at which flux penetration in grain boundaries may become a problem Strong reduction of BCS resistance because of using SC layers with higher  (Nb 3 Sn, NbN, etc) The significant performance gain may justify the extra cost.