http://www.surfacetreatments.it/thinfilms RF Losses due to incomplete Meissner-Ochsenfeld effect: difference between bulk Nb and Nb/Cu (Enzo Palmieri - 20') Speaker: Enzo Palmieri - Legnaro National Laboratories of INFN and University of Padua | Duration: 20 min. Abstract Experimentally it is found that for Nb/Cu Sputtered Resonators, conrary to bulk Niobium Cavities the residual resistance due to magnetic flux trapped into the superconductor is independent of the magnetic induction intensity B at the moment of cooling. Because of the large demagnetization factor of the extended surface of a resonator, an incomplete Meissner-Ochsenfeld effect happens, favouring the trapping into the superconductor of any external fied present during the cooling phase as for instance the earth magnetic field or its unscreened fraction. For Bulk Nb cavities the trapped vortexes dissipate energy since depinned by radiofrequency, while for Nb sputtered cavities the vortexes are frozen on pinning centers and there is no flow resistance.

1. RF Losses due to incomplete Meissner – Ochsenfeld effect:Difference between Bulk Nb and Nb/CU Enzo Palmieri Legnaro National Laboratories ISTITUTO NAZIONALE DI FISICA NUCLEARE and UniversityofPadua

2. Because of the Large dimensions of a cavity Mesoscopic effect Policristallinity of the SC (Grain Boundaries) Pin-holes and defects in the film Large Demagnetization factor due to steps and protrusions however present Unavoidably slight inhomogheneities of the superconductor However small, Incomplete Meissner-Ochsenfeld effect will be always present due to Partially Unscreened Earth Magnetic Flux Trapping

3. Residual Resistance versusthe magnetic field left during cooling 500 MHz 4,2 K After W. Weingarten 1986 CERN

4. Twomechanismsofdissipation: The RF dissipationof the vortexnormalcore The energydamping due tofluxonsdynamical flow

5. In case oftrappedearthmagneticfieldH << HC1 Vortex density is so low, thatthereis no Abrikosov Lattice Vortexes are single insulatedflux quanta oscillating under RF

6. Bardeen and Stephen - Phys Rev 140 A1197 (1965) but also Kim, Hempstead and Strnad- Phys Rev 139 A1163 (1965) have shown that The well known equation of the damped forced oscillator can be used for describing the oscillation of a vortex from and to a pinning center

7. Ifuis the displacementof a single fluxlinerespectto the pinning center Where M is the effective Mass of the Vortex per unitlenght his the flow Viscosity K is the elasticconstantof the linearizedpinningforce in the approximationofsmalldisplacements Fo is the vortex quantum Jis the current densityinducedbyrffields

8. For single non interactingvortexes, the pinningconstant the viscosity beings the low temperature conductivitybefore SC transition Kim, Hempstead and Strnad - Phys Rev 139 A1163 (1965) A. Schmid,W. Hauger, J. Low Temp. Phys., 11,667, (1973)

9. for Frequencies lower than the electron collision frequency w << 1/t The effective mass M has no appreciable dynamical effect Then the motion equation get simplified into: Then setting and Since

10. Wearriveto the Ohm law Fromwhich the flux flow conductivityisfound

11. Discussing the oscillatorymotionoffluxoids in type II superconductros, De Gennes and Matriconintroduced the notionofa depinningfrequency belowwhich(w << w0) the motionislargelyinhibitedbypinningtocrystal lattice defects abovewhich(w >> w0) pinningisrelativelyuneffective

12. The depinningfrequencyw0: depends on the ResidualResistivityRatiob indeed Shown by Eileberger (Phys Rev 153, 584 (1967) that the max difference between K and K1 is less than 9% and mean free path

13. Attentionmustbepaiedto JCthatindeedisnot the expressionfoundbyBardeenfor a thin film that is the depairing current but the depinning current that is definitely smaller

14. To estimate the depinningcurrentlet’s useLarkin-OvchinikovExpressions ( JLTP, 34, P409 (1979) for the pinningforceexertedby a grainboundaryofthicknesstparallelto the vortex being n the density ofstates g1the deviationof the electron phononinteractionconstant t the density od states

15. Free to move Pinned by Grain Boundaries Vortex Vortex Bulk Niobium Niobium film High depinning frequency w0 Low depinning frequency w0

16. Tinkhamdemostratedthat the SurfaceimpedanceZnfor a normal metal in the normal regime can be extended to SC by simply substituting the Mattis and Bardeen complex conductivity at the place of s in the Znformula sn = 1 / rn = dc conductivity at T d = skin depth s1-is2 in place of sn

17. Analogously, we introduce sf in changeofsnforcalculating the residualterm due to the vortex flow sn = 1 / rn = dc conductivity at T d = skin depth sfin place of sn

18. Hencethe penetrationdepthbecomes or betterwritten

19. Hencethe SurfaceResistancebecomes or betterwritten

20. Whose real part reduces to

21. w / w0

22. For w >> w0, practically all vortexes are depinnedand Rf reaches his saturation value For w << w0, the flux flow losses decrease as w3/2 since less and less vortexes have enough energy to overcome the pinning attraction.

23. Residual Resistance versusthe magnetic field left during cooling 500 MHz 4,2 K After W. Weingarten 1986 CERN

24. Since the criticalparameteris the ratiow / w0the Flux flow losses increase both when working at higher frequanciesw and when increasing the RRR value b, i.e. decreasing the depinning frequency. In Conclusion: If for low frequency RF Structures, thin films coated cavities do not require magnetic screenings, it is not said that at higher frequencies, thin films will pin the vortexes, being the ratiow / w0the criticalparameter