RF Losses due to incomplete Meissner – Ochsenfeld effect:Difference between Bulk Nb and Nb/CU<br />Enzo Palmieri<br />Legn...
Because of the<br />Large dimensions of a cavity <br />Mesoscopic effect <br />Policristallinity of the SC (Grain Boundari...
Residual Resistance versusthe magnetic field left during cooling<br />500 MHz <br />4,2 K <br />After W. Weingarten 1986 C...
Twomechanismsofdissipation:<br />The RF dissipationof the vortexnormalcore<br />The energydamping due tofluxonsdynamical f...
In case oftrappedearthmagneticfieldH << HC1<br />Vortex density is so low, <br />thatthereis no Abrikosov Lattice<br />Vor...
Bardeen and Stephen  - Phys Rev 140 A1197 (1965) <br />but also <br />Kim, Hempstead and Strnad- Phys Rev 139 A1163 (1965)...
Ifuis the displacementof a single fluxlinerespectto the pinning center <br />Where<br />M  is the effective Mass of the Vo...
For single non interactingvortexes,  <br />		the pinningconstant<br />		the viscosity<br />beings the low temperature cond...
for Frequencies lower than the electron collision frequency  w << 1/t<br />The effective mass M has no appreciable dynamic...
Wearriveto the Ohm law<br />Fromwhich the flux flow conductivityisfound<br />
Discussing the oscillatorymotionoffluxoids in type II superconductros, De Gennes and Matriconintroduced the notionofa depi...
The depinningfrequencyw0:<br />depends on the ResidualResistivityRatiob<br />indeed<br />Shown by Eileberger (Phys Rev 153...
Attentionmustbepaiedto JCthatindeedisnot<br />the expressionfoundbyBardeenfor a thin film <br />that is the depairing curr...
To estimate the depinningcurrentlet’s useLarkin-OvchinikovExpressions ( JLTP, 34, P409 (1979) for the pinningforceexertedb...
Free to move<br />Pinned by Grain Boundaries<br />Vortex<br />Vortex<br />Bulk Niobium <br />Niobium film <br />High depin...
Tinkhamdemostratedthat the SurfaceimpedanceZnfor a normal metal in the normal regime can be extended to SC by simply subst...
Analogously, we introduce sf in changeofsnforcalculating the residualterm due to the vortex flow<br />sn = 1 / rn = dc con...
Hencethe penetrationdepthbecomes<br />or betterwritten<br />
Hencethe SurfaceResistancebecomes<br />or betterwritten<br />
Whose real part reduces to <br />
w / w0<br />
For w >> w0, practically all vortexes are depinnedand Rf reaches his saturation value  <br />For w << w0, the flux flow lo...
Residual Resistance versusthe magnetic field left during cooling<br />500 MHz <br />4,2 K <br />After W. Weingarten 1986 C...
Since the criticalparameteris the ratiow / w0the Flux flow losses increase both when  working at higher frequanciesw and w...
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Palmieri - RF losses trapped flux

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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.

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Palmieri - RF losses trapped flux

  1. 1. RF Losses due to incomplete Meissner – Ochsenfeld effect:Difference between Bulk Nb and Nb/CU<br />Enzo Palmieri<br />Legnaro National Laboratories<br />ISTITUTO NAZIONALE DI FISICA NUCLEARE<br />and <br />UniversityofPadua<br />
  2. 2. Because of the<br />Large dimensions of a cavity <br />Mesoscopic effect <br />Policristallinity of the SC (Grain Boundaries)<br />Pin-holes and defects in the film<br />Large Demagnetization factor due to steps and protrusions however present<br />Unavoidably slight inhomogheneities of the superconductor<br />However small, Incomplete Meissner-Ochsenfeld effect will be always present due to <br />Partially Unscreened Earth Magnetic Flux Trapping <br />
  3. 3. Residual Resistance versusthe magnetic field left during cooling<br />500 MHz <br />4,2 K <br />After W. Weingarten 1986 CERN<br />
  4. 4. Twomechanismsofdissipation:<br />The RF dissipationof the vortexnormalcore<br />The energydamping due tofluxonsdynamical flow<br />
  5. 5. In case oftrappedearthmagneticfieldH << HC1<br />Vortex density is so low, <br />thatthereis no Abrikosov Lattice<br />Vortexes are single insulatedflux quanta oscillating under RF<br />
  6. 6. Bardeen and Stephen - Phys Rev 140 A1197 (1965) <br />but also <br />Kim, Hempstead and Strnad- Phys Rev 139 A1163 (1965) <br />have shown that <br />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<br />
  7. 7. Ifuis the displacementof a single fluxlinerespectto the pinning center <br />Where<br />M is the effective Mass of the Vortex per unitlenght<br />his the flow Viscosity<br />K is the elasticconstantof the linearizedpinningforce in the approximationofsmalldisplacements<br />Fo is the vortex quantum <br />Jis the current densityinducedbyrffields<br />
  8. 8. For single non interactingvortexes, <br /> the pinningconstant<br /> the viscosity<br />beings the low temperature conductivitybefore SC transition<br />Kim, Hempstead and Strnad - Phys Rev 139 A1163 (1965) <br />A. Schmid,W. Hauger, J. Low Temp. Phys., 11,667, (1973)<br />
  9. 9. for Frequencies lower than the electron collision frequency w << 1/t<br />The effective mass M has no appreciable dynamical effect<br />Then the motion equation get simplified into:<br />Then setting and<br />Since <br />
  10. 10. Wearriveto the Ohm law<br />Fromwhich the flux flow conductivityisfound<br />
  11. 11. Discussing the oscillatorymotionoffluxoids in type II superconductros, De Gennes and Matriconintroduced the notionofa depinningfrequency<br />belowwhich(w << w0) the motionislargelyinhibitedbypinningtocrystal lattice defects<br />abovewhich(w >> w0) pinningisrelativelyuneffective<br />
  12. 12. The depinningfrequencyw0:<br />depends on the ResidualResistivityRatiob<br />indeed<br />Shown by Eileberger (Phys Rev 153, 584 (1967) that the max difference between K and K1 is less than 9%<br />and mean free path <br />
  13. 13. Attentionmustbepaiedto JCthatindeedisnot<br />the expressionfoundbyBardeenfor a thin film <br />that is the depairing current<br />but the depinning current that is definitely smaller<br />
  14. 14. To estimate the depinningcurrentlet’s useLarkin-OvchinikovExpressions ( JLTP, 34, P409 (1979) for the pinningforceexertedby a grainboundaryofthicknesstparallelto the vortex<br />being<br />n the density ofstates<br />g1the deviationof the electron phononinteractionconstant<br />t the density od states<br />
  15. 15. Free to move<br />Pinned by Grain Boundaries<br />Vortex<br />Vortex<br />Bulk Niobium <br />Niobium film <br />High depinning frequency w0<br />Low depinning frequency w0<br />
  16. 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 <br />sn = 1 / rn = dc conductivity at T<br />d = skin depth<br />s1-is2 in place of sn<br />
  17. 17. Analogously, we introduce sf in changeofsnforcalculating the residualterm due to the vortex flow<br />sn = 1 / rn = dc conductivity at T<br />d = skin depth<br />sfin place of sn<br />
  18. 18. Hencethe penetrationdepthbecomes<br />or betterwritten<br />
  19. 19. Hencethe SurfaceResistancebecomes<br />or betterwritten<br />
  20. 20. Whose real part reduces to <br />
  21. 21. w / w0<br />
  22. 22. For w >> w0, practically all vortexes are depinnedand Rf reaches his saturation value <br />For w << w0, the flux flow losses decrease as w3/2 since less and less vortexes have enough energy to overcome the pinning attraction.<br />
  23. 23. Residual Resistance versusthe magnetic field left during cooling<br />500 MHz <br />4,2 K <br />After W. Weingarten 1986 CERN<br />
  24. 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.<br />In Conclusion: <br />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<br />
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