drop: Q-drop Enzo Palmieri (CARE, contract number RII3 CT ) The 12-th Workshop on RF Superconductivity, Cornell University
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1 Q-drop drop: The -th Workshop on RF Superconductivity, Cornell University Enzo Plmieri ISTITUTO NAZIONALE DI FISICA NUCLEARE Lbortori Nzionli di Legnro & Pdu University, Science Fculty, Mteril Science Dept Work supported by the Europen Community Reserch Infrstructure Activity under the FP6 Structuring the Europen Reserch Are progrmme (CARE, contrct number RII3 CT
2 0 Low field Q-Slope Medium field Q-Slope High field Q-drop Q0 0 0 K,8 K,6 K E cc [MV/m] Best 9-cell cvity result (fter electro-polishing (Courtesy D. Proch
3 0 K,8 K,6 K E cc [MV/m] Q Low field Q-Slope
4 Questions: Is the low-field Q-slope clibrtion problem? If not, which is its physicl reson? nd in such cse.. Is something pulling up the Q? (if understood, it could be beneficil The Q is originlly higher, but for some reson t low field, it decys? 0 Q0 0 0,6 K Ecc [MV/m]
5 Before Abno/Snt fè Workshops (997/999: the low field Q-slope ws reported only for Nb/Cu cvities Nb/Cu sputtered cvity t CERN Courtesy C. Benvenuti et l Since first cvities were bked in the cryostt t ~50 C for ~48 hours the low field Q-slope ws lso reported for bulk Nb cvities
6 Cvity spun t LNL nd treted/mesured t KEK
7 Courtesy G. Ciovti
8 (Courtesy G. Bisoffi
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10 Presented t the 9-th RF Superconductivity Workshop, Snt Fè, NM, 999 Renzo Prodi - RF SUPERCONDUCTIVITY AT INFN_GENOA Typicl plot of Q o vs E cc for cvities treted by Dry Oxidtion of the surfce fter medium temperture nneling
11 Let us suppose tht: on bulk niobium (SC we put n overlyer of different superconductor (SC SC SC Vcuu m λ H z λ is the tickness of the SC λ is the penetrtion depth of the SC λ is the penetrtion depth of the SC
12 Only one Superconductor: No overlyer SC Vcu um E y (0 λ
13 THE ELECTROMAGNETIC RESPONSE OF A METAL x For semi-infinite conductor tht E y H H metl z Vcuum ( ( i( kx ω t x H 0 e fills the +x hlf-spce nd hs plne surfce t x 0 the Surfce Impednce is defined s: Z 0 E ( 0 y 4 π J ( x dx c y E H y z ( 0 ( 0
14 Two Superconductors: SC + SC ( y E dx x J dx x J z ( ( ( y H H E c ll z l z π ( ( ( ; ( ( ; ( ( ; ( ( ( e e H e H H e H H e H H H x ll z x ll z ll z l z l z x l z l z z x X X x X x λ λ λ λ λ SC SC λ λ Vcuu m H z
15 SC λ SC λ Vcuu m H z 0 z J ( x dx + E y ( 0 J ( x dx l ll c H z π E y H z ( 0 H ( 0.( Z 4 π E y ( 0 4 π E c λ c H ( 0 z Z λ. e +. e y( 0 λ λ Z.( e + Z Z e Q λ e + Q e λ Q (
16 SC λ Q SC λ Q Vcuu m H z For Superconductor system. 0 Q 0 Q Q ( x Q x λ / λ λ λ e + Q e Q + ( Q Q e ( Q + Q. e λ
17 0 Medium field Q-Slope K,8 K,6 K Ecc [MV/m] Q
18 SC λ SC λ Vcuu m H z. 0 Q 0 Q Q + ( Q Q e λ Q ( x.0 9 Q λ/ x An hypotesis: Gp nd Penetrtion Penetrtion depth depth depends depends on on mgnetic mgnetic field λ ( B kb ( λ B λ + B +... λ + α B B 0
19 SC λ SC λ Vcuu m H z Q ( x Q Q ( 0 b kb b B / B C k Q Q e 0, b ( λ b λ 0 + α b. 0 Q Q λ/ x b Q Q + ( Q + ( e Q Q e k λ + λ α b (
20 E Q0 Q Q + ( Q e Q e ( λ + k b α b Kenzo6 E0 Dt: Foglio_B Model: Plmieri5 Chi^.868E7 R^ P ±-- P ±-- P ± P4 E-4 ±-- P ± E Ecc [MV/m]
21 Q Q Q ( *. 0 Why Q increses q ( B with field? q ( B Q qt ( B The more λ increses Q vs field Q Q exp ( k B Q The more SC ( t low Q + ( Q Q exp losses is involved c e ( ( Q e k b ( λ + α b Q e λ +α b + Q * e ( λ + k b α e b Q e -kb B b
22 Q Q + ( Q e k b ( λ + α b Q e Q ( * e ( λ +α b + Q * e k b ( λ + α e qt ( B, The ticker is SC, the smoother is the Q-rise qt ( B, 0.5 qt ( B, qt ( B,.5 qt ( B, O Q 0. Q Q exp ( k B 0 /λ 0 Q + ( Q Q exp t c Q.0 Q B b 0 b
23 SC 3 SC SC Vcuu m λ 3 λ λ H z Three Superconductors: SC 3 + SC + SC λ λ + λ Q Q + ( Q Q e λ + ( Q 3 Q e λ λ Generliztion to n lyers: SC n + SC n- + + SC + SC lim 0 n Q n Q + ( Q Q e i + i i J i λ j x dq ( x 0 (x λ 0 e dx d x dx
24 0 ( B kb? 0 - p f v s I.I. Kulik, V. Plmieri, "THEORY OF DEGRADATION AND NON LINEAR EFFECTS IN Nb-COATED SUPERCONDUCTING CAVITIES", Proceedings of the Eight Workshop on RF Supercoductivity, Abno, Itly, October 997, V. Plmieri, A. Lombrdi eds. Specil Issue of Prticle Accelertors, Vol. 60,(998p The Ginzburg-Lndu result 0 ( H /H C does not pply!!!
25 This formul hs done lot of 0 ( H /H C dmge to our community for the understnding of the Q-Slope R.H. White nd M. Tinkhm, Mgnetic-Field Dependence of Microwve Absorbtion nd Energy gp in Superconducting Films, Phys Rev, vol 36, A, (964, p. A03..The qulittive fetures of / 0 dependences like ( h nd (-h / revery different from those of the experimentl bsorption curves reported here. due to the disgreement between these results nd previous theory nd experiment, it must be concluded tht the bove procedure for determining n effective energy gp prmeter s function of H is too nive. Y. Nmbu, S.F. Tun, Phys, Rev. Lett., 9 (963; Phys.Rev.33, A, (964 Electrons moving prllel to the surfce ply specil role: since the mgnetic filed will confine such n electron nd the one with which it is pired to opposite surfces of the film, they contribute little to the superconductivity piring energy
26 This reltion goes bck to first principles 0 - p f v s It mens to tke into ccount the supercurrent! If for Superconducting Mgnets the fundmentl nd indipendent prmeters re 3: T C, H C nd J C,.. why for Superconducting cvities, JC disppered? Is 40 MV/m (600 G field not strong enough?
27 REVIEWS OF MODERN PHYSICS VOLUME 34, NUMBER 4 OCTOBER 96 Criticl Fields nd Currents in Superconductors* JOHN BARDEEN UNIVERSITY OF ILLINOIS, Urbn, Illinois II.THERMODYNAMIC RELATIONS To discuss the thermodynmics of superconductor in mgnetic field or with current flow, it is most convenient to tke the externl field H nd the superfluid velocity v s s independent vribles. The displcement of the pirs cuses n increse in free energy of the system which my be expressed simply in terms of J s APPENDIX B. DIRECT CALCULATION OF CHANGE OF GAP WITH CURRENT... In the low temperture limit, there re no excittions formed nd thus no chnge in D until the velocity vs reches the vlue for which it is fvorble to form pirs of excittions, corresponding to trnsfer of n electron from one side of the Fermi se to the other.this criterion is (depiring condition p p ( s s f m + v m ( v > > f or m m p f
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33 R BCS e kt e p v B λ p v * 0 * * f s + f s 0 F kt kt ( kt KT e v n n s p v B * * e v s F f kt λ l KT ξ * 0 (cot gh 0
34 λ l KT ξ p v B * * e * v f s 0 F (cot gh kt 0 The prsitic term P f V s is neglectble t high vlue of the pure bulk Nb cse l It becomes importnt t low - thin film cse ξ 0 - contminted surfce fter low temp bking l ξ 0
35 0 - p f v s p v B * λ * e * v (cot gh f s 0 F l ξ 0 h * v f ξ This will ffect λ 0 0 nd B c π *
36 Courtesy C. Benvenuti et l Is key prmeter; low vlues give: ξ 0 - high Q - higher slope For film coted cvities there is no hope to get rid of the slope, unless RRR is incresed, but in this cse Q vlues will be lower thn the ctul
37 0 Q High field Q-drop K,8 K,6 K E cc [MV/m]
38 In locl electrodynmics of superconductivity, j j +j Where J is the Meissner current At smll supercurrent j n ev s s v s n ev ( s s j v c but t lrger V s, GL theory foresees depring effect by the current J s n s V m V s V s V s Over V m the superconducting stte become unstble
39 Conclusions: Low field - The hypotesis of n overlyer explins the Q rise Q λ λ e + Q e Q ( Medium field The gp decrese linerly vs field 0 p f v s l This effect is neglectble for high but is felt when is reduced ξ 0 Film coted cvities: no hope to get rid of the slope, unless RRR is incresed, but l ξ 0 in this cse Q vlues will be lower thn the ctul High field The gp closes t V C, but j s strt decresing t V m < V c. Between V m nd V C, there is instbility
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