1. Challenges in understanding Q(E acc ) dependence in SRF cavities Alex Gurevich Dept. Physics & Center of Accelerator Science Old Dominion University, Norfolk, VA, USA TTC Meeting, Jlab, Nov. 5-8 (2012). A.Gurevich, Rev. Accel. Sci. Technol, 5, xx 2012

2. Challenges How does the SC physics and materials science affect Q(B) of the best performing cavities? Understanding mechanisms of:  Q at low fields  Low-field increase of Q(B)  Medium-field Q - slope  High-field Q - slope  Maximum breakdown field G. Ciovati, G. Myneni, F. Stevie, P. Maheshawari, D. Griffis, Phys. Rev. ST-AB 13, 022002 (2010)  Impurity and defect management by heat treatments to optimize Q(B) curves.  Fundamental limits of Q(B) at low and high fields B. How far can Q(B) be increased?

3. Outline  Surface resistance at low fields. Mechanisms of residual resistance - impurities and subgap states - trapped vortex hotspots - grain boundaries and segregation of impurities  High field surface resistance and superheating field at low temperatures - Effect of impurities on B sh - Effect of impurities on the density of states: reduction of current pairbreaking and the high-field Q slope by impurities - Baking effect  Theory of surface resistance at high rf fields has not been developed  Effect of impurities on the surface resistance at high fields is not understood Clean or dirty? The key effect of impurities on the electron density of states at high rf fields

4. BCS surface resistance D.C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958)  Decreases exponentially to 0 as T  0. No thermal dissociation of Cooper pairs E. Palmieri

5. Residual resistance subgap states BCS T. Proslier, J.F. Zasadzinskii, J. Moore, L. Cooley, C. Antoine, M. Pellin, J. Norem, K. Gray, Appl. Phys. Lett. 92, 212505 (2008). BCSResidual Semi-empirical Dynes formula for the density of states:  Finite R i indicates subgap states at  < . No energy gap for thermal activation of quasiparticles.  yields nonzero N(  ) at  <   Finite residual resistance : Here  /   10 -2 yields R i  10-20 n  for Nb with = 40 nm, f = 1.5 GHz, and  n = 10 9 1/  m

6. Mechanisms of subgap states  Electron damping due to strong electron-phonon coupling in Nb (Eliashberg generalization of BCS ) Intrinsic Extrinsic  Nonsuperconducting precipitates – hydrides, metallic suboxides at the Nb surface  Trapped vortices – well established  Grain boundaries – inconclusive evidence A.Gurevich, Rev. Accel. Sci. Technol, 5, xx 2012

7.  Proton irradiation produces point atomic radiation defects (vacancies and interstitials)  BCS part of the surface resistance slightly decreases after irradiation  Residual resistance significantly increases after irradiation

8. Electromagnetic granularity Magnetic granularity caused by grain boundaries PRB, 46, R3187 (1992); PRB 48, 12857 (1993); PRB 50, 13563 (1994); PRB 65, 214531 (2002). PRL 88, 097001 (2002 ).  Only small currents can pass through GBs Fragmentation of uniform current flow into decoupled current loops in the grains  Serious problem for high-T c cuprates and Nb 3 Sn, but not so much for Nb  The highest breakdown fields were observed on small-grain Nb cavities Polyanskii, 2001 MO imaging of YBCO

9. Midgap states in vortex cores   40 nm λ  40 nm Vortex core region of suppressed superconductivity Region of circulating supercurrents H.F. Hess, et al, Phys. Rev. Lett. 62, 214 (1989) vortex bulk vortex core bulk

10. Trapped vortices in cavities Cooldown in field from T > T c to 2K  Vortices can be trapped in a cavity upon cooling below T c  Vortices trapped at the inner cavity surface oscillate under the RF field producing hotspots RF field Nb H(t) λ London penetration depth of superconducting currents ≈ 40 nm << d = 3mm  A bundle of trapped vortex bundles can produce RF power comparable to the exponentially small BCS dissipation: Δ ≈ 17.5 K for Nb

11. Moving vortex hotspots by thermal gradients  Critical gradient to unpin trapped vortices: Any change of thermal maps after applying local heaters (laser beams) indicates that hotspots are due to trapped vortices rather than fixed defects For clean Nb with B c1 = 0.17 T, J c = 1kA/cm 2 and T = 2K: |  T| c = 1.6 K/mm Ciovati and Gurevich, Phys. Rev. ST-AB 11, 122001 (2008) – outside heaters; G. Ciovati et al, Rev. Sci. Instr. (2012) – scanning laser beam.

12. Parallel vortices near the oscillating surface barrier Gurevich and Ciovati, Phys. Rev. B 77, 104501 (2008) Onset of vortex penetration B v  B c Vortex time constant: τ = μ 0 λ 2 B c2 /B v ρ n ≅ 1.6×10 -12 s for Nb 3 Sn, ρ n = 0.2 μΩm, B c2 = 23T, B c = 0.54T, λ = 65 nm Supersonic vortex velocity v = λ/τ ≅ 400 km/s Penetration times much shorter than the rf period (instant for the SRF cavities) Bardeen-Stephen viscous vortex drag is inadequate for high velocities; jump-wise instabilities (Larkin-Ovchinnikov and overheating) of vortex oscillations x ℓ d H0H0 u(t) dmdm Oscillations of trapped vortices under the rf field M. Rabinovitz, J. Appl. Phys. 42, 88 (1971).

13. Wagging vortex tail Vortex viscous drag coefficient Nonlocal vortex line tension 22 λ H(t) u(z,t)

14. Dissipated power Short segments,  <<  l Long segments,  >   /   1/2 22 P/P   Low frequencies. Entire vortex segment vibrates  Intermediate and high . Only a smaller vortex tip vibrates. Power becomes independent of the length of the vortex segment For Nb, we get f  40 GHz and f l = ( /l) 2 f 200 nm. In this case P  0.13  W at B = 100 mT and 2 GHz. The cleaner the better Hotspots revealed by thermal maps require regions  few mm with  10 6 vortices

15. Residual resistance due to trapped vortices For Nb with  n = 10 -9  m, B c = 200 mT, we obtain that R i = 5 n  can be produced by the residual magnetic field B 0  0.7  T much smaller than the Earth field B E = 20-60  T. Field dependent R i due to thermal feedback  Can contribute to the medium-field Q slope  Thermal feedback makes R i (H) interconnected with R BCS  Vortex hotspots can ignite lateral thermal quench propagation

16. Superheating field  Meissner state can only exist below the superheating field H < H s  Periodic vortex instability of the Meissner state as the current density J s = H s / at the surface reaches the depairing limit Hernandez and Dominguez, PRB 65, 144529 (2002)  GL calculations of the superheating field H s at T  T c (Matricon and Saint-James, 1967) Nb  T > 1: ( Galaiko, 1966; Catelani and Sethna, 2009) B s  0.84B c

17. Pairbreaking at H sh At H = H sh, the velocity of Cooper pairs reaches the critical value v c =  /p F. Maximum screening current density Some 4 orders of magnitude higher than typical critical current densities J c  0.1 - 0.01 MA/cm 2 to unpin vortices in Nb

18. Effect of nonmagnetic impurities on H sh

19. Effect of the rf currents on the density of states  g (H) Dirty limit: The gap  g (H) closes at H larger than H sh H sh is the maximum field at which R s at H = H sh remains much smaller than R s in the normal state

20. Decrease of high-field R s by impurities Gap  g (H) at H = H sh opens up as the impurity parameter exceeds  c Impurities reduce the high-field Q slope because they reduce the drop of  g (H) with H and preserve the gap  g (H) even at H = H sh. Field-dependent surface resistance:

21. Mechanism of the baking effect Pollution of a thin  10-20 nm surface layer with impurities strongly reduces the field dependence of the surface resistance Diffusion of extra impurities (O or H) from the pentoxide layer by the distance L = (Dt) 1/2  5-20 nm at 120 C for 20-40 hrs  This mechanism is insensitive to particular impurities (O, H, or else)  Consistent with the fact that the backing effect can be reversibly undone by anodizing which removes a thin layer of Nb at the surface, returning it to the pristine (less polluted) state

22. Conclusions  Understanding the effect of impurities on the surface resistance at high rf fields is the key issue which underlines the ways of improving the SRF cavity performance by different heat treatments  A thin (5-20 nm) dirty layer at the surface can significantly improve Q at high fields  Physics of the subgap states at strong rf fields  Theory of Rs under nonequilibrium conditions of high rf fields  Reducing the density of trapped vortices in the SRF cavities – a “cheap” way of improving the SRF performance Scientific challenges: