SUPERCONDUCTIVITY IN ACCELERATORS PART II : MIXED STATE

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1 SUPERCONDUCTIVITY IN ACCELERATORS PART II : MIXED STATE Cours supraconductivité M2 GI Claire ANTOINE MAGNETS AND RF CAVITIES

2 WY DO VORTICES ARE SO IMPORTANT? Magnets RF Cavities!!!!!!!! Magnet (DC) : One aims at very high current densities with 0 resistance It means: Mixed state Non moving vortices, trapped (medium fields: < irr ) Defects are voluntarily introduced to pinning and l ( C1 et C2 ) J < J C <<< J D Cavities One aims at very high field with minimal dissipation (but 0 ) variable, max ~ S (= f( C )) Vortices cannot keep pinned at this frequency => very high dissipations (!), One is close to J D (at least in Nb) One has to prevent Vx entering: keep in Meissner state! Reduce # of defects (promoting early Vx penetration), => C1 Good SC for magnet application are bad for cavities! And vice versa! C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 2

3 VORTICES (I): PENETRATION INSIDE TE SUPERCONDUCTOR C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 3

4 > C1 : VORTEX = ENERGETICALLY FAVORABLE Magnetic energy Condensation energy Free energy dg m ~ µ 2 0 (1 e 2 dg c ~ mµ 0 C 2 n(x) 2 n s x λ L ) B 0 over l ns grows over x SC type I λ L < ξ, Ici k ~ = 0,7 c SC type II λ L > ξ, Ici k ~ = 0,7 c N λ L ξ SC 0 G 1 2 µ 0 c µ 0 c 2 N λ L ξ SC 0 G 1 2 µ 0 c µ 0 c 2 Cost in condensation energy Gain in surface free energy x/l L Free energy < x/l L Creation of a normal/sc interface is energetically favorable in type II SC At equilibrium (transition) g n = g s except close to the surface C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 4

> C1 : VORTEX = ENERGETICALLY FAVORABLE Thin sample, field Minimization of free energy: Normal zone as small as possible ( ~ 2x); Magnetic size ~2 l (VX = normal zone w.

5 > C1 : VORTEX = ENERGETICALLY FAVORABLE Thin sample, field Minimization of free energy: Normal zone as small as possible ( ~ 2x); Magnetic size ~2 l (VX = normal zone w. 1 flux line + screening current). This holds only for x< l => Type II SC Number of Vx is the one that minimize G/L (depends on applied ) Vortices repels each other (but attract antivortices) Surface stabilizes the apparition of the SC mixed state Nucleation always occur at surface In field : boundary conditions are unchanged Surf Bulk In // field : E nucleation < E nucleation surface superconductivity can be observed in specific geometries (B C3 ) (on a thickness << l L ). C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 5

6 VORTEX PENETRATION WIT B // Surface barrier (Bean & Livingston, 1964) J Boundary condition. (J = 0) image vortices Supercurrent tends to push Vx inside 0 Image antivortex tends to pull it out G Before entering the material Vx have to cross a surface barrier: Vx thermodynamic Potential : x G x = φ 0 0 e λ v 2x + C1 0 Image Image Vortex J = 0 x l 0 < c1 Meissner Ideal surface 0 = c1 0 > c1 x Rationale used to predict SRF limits BUT If localized defect w.: c Local bulk c (or Tc Local Barrier disappears only at S ~ C > C1 0 = c 0 T c bulk ) => early penetration of 1 or several Vx there C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 6

7 DEMAGNETIZATION COEFFICIENT Geometrical effects Elliptical samples : = C everywhere Arbitrary shape : consider local deformation of flux lines B = μ 0 ( + M ) => B = μ 0 ( +(1-D) M ) Infinitively thin strip D 1 Sphere : D = 1/3 Infinite cylinder: D = 0 Strong influence of geometry, orientation edge effects be careful with measurements!!! Classical magnetometry gives P not C1 (convolution of SC properties with geometrical effects) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 7

8 VORTEX & (NEARLY) PERFECT MATERIAL In field : demagnetization effect, local field depends on the shape Nb 2 Se (Abrikosov Vx lattice) Dark contrast: B=> 0 Light contrast : B C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 8

EFFECTS TAT PROMOTES V X PENETRATION Morphologic defects Grain boundary weak links

5 mm : notch has small impact on flux distribution even at higher T Josephson Vortex:

. Sung et al, FNAL/FSU] 0.8 0.6 0.4 0.2 @ 4.

W B W B MO contrast is double at the groove, when in-plane field perpendicular to

9 EFFECTS TAT PROMOTES V X PENETRATION Morphologic defects Grain boundary weak links (GB) Magnetic impurities. MonoX Nb =40 mt T=7K GB #1 0.5 mm : notch has small impact on flux distribution even at higher T Josephson Vortex: Pinned on interface (GB) Current line distortion Resistance [A. Polyanskii,.. Sung et al, FNAL/FSU] K 0 GB ~ 32 mt 0 bulk ~ 150 mt Magnetic field R0 double contrast W B W B MO contrast is double at the groove, when in-plane field perpendicular to groove // surface T=5.6K W B No MO contrast at the groove, when in-plane field parallel to groove C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 9

10 GRAIN BOUNDARIES IN Nb Preferential G.B. ( G.B) P GB << P bulk GB #1 Josephson Vortex: Pinned on interface (GB) Current line distortion Resistance K 0 GB ~ 32 mt 0 bulk ~ 150 mt Magnetic field R0 Dominant mechanism (see below) if boundary is thick (e.g. YBCO) if boundary is clean (local SC properties only modified over a few interatomic distances) Nb : rather (clean boundaries, large x) NB monoxtal cavities ~ polyxtal cavities Same behavior : Qslope, performance Monocrystalline cavities [A. Polyanskii,.. Sung et al, FNAL/FSU] C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

DEFECTS AND AVALANCES Localized defect effect YBa 2 Cu 3 O 7 film w. one single defect B http://www.mn.uio.

RF period (ns) flux jumps avalanche penetration, observed in transient state (so also expected in RF) MgB 2 http://www.nature.

11 DEFECTS AND AVALANCES Localized defect effect YBa 2 Cu 3 O 7 film w. one single defect B tivity/mo/ Vx penetration (~100 µm) during 1! RF period (ns) flux jumps avalanche penetration, observed in transient state (so also expected in RF) MgB 2 l?message-global=remove&wt.ec_id=srep C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 11

12 VORTEX IN PRESENCE OF ELECTRIC FIELD AND/OR CURRENT ( ) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 12

MOVING VORTEX Influence of ԦJ Vx submitted to Lorentz force ԦF = ԦJ B Vx lattice moves at speed v under the action of J (collective movement) Generate electrical field E = - v B (//ԦJ) Ohm law : if

13 MOVING VORTEX Influence of ԦJ Vx submitted to Lorentz force ԦF = ԦJ B Vx lattice moves at speed v under the action of J (collective movement) Generate electrical field E = - v B (//ԦJ) Ohm law : if potential difference, then R => non negligible resistivity: flux flow resistivity r ff Lattice viscosity : movement limited by / viscous force (Magnus force) Origin: normal zone dissipation r ff = r n BΤB C2 (B/B C2 => vol. fraction of normal e-) Viscosity η = φ 0 BΤB C2 Constant speed v = E/B Elastic energy: Tends to keep Vx equidistant in absence of defects (reminder: inter-vortex distance depends on applied field) See also : k/english/research/groups/ amks/superconductivity/sv/ NbSe 25x35 µm V J C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 13

$VORTICES AVALANCES https://www.eurekalert.org/multimedia/pub/145764.php\ Dr.$

14 VORTICES AVALANCES Dr. Yonathan Anahory Racah Institute of Physics The ebrew University of Jerusalem Lead films scanning SQUID-on-tip microscopy technique allows magnetic imaging at magnetic sensitivity and high resolution (~50 nm) At high currents (high drives) vortices move at 20 km/s and appear as smeared line. C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 14

15 CRITICAL CURRENT DENSITY J C For type II SC In practice R 0 only for J>J C For J<J C R=0 (for J<< JC, close to J C : some flux creep) Vx are pinned on defects E J C : current at which flux flow starts No dissipation => pin Vx => artificially create defects (inclusions, grooves, alloying, damaging ) For J C : defect density => l x, l, k and C1, C2 J C (extrinsic) << J D (intrinsic) J C J RF Cavities : pinning is inefficient, J C meaning less: always in the flux flow regime (that is why we want to prevent early Vx penetration!) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 15

A COMPLEX PASE DIAGRAM Applications type II SC : 3 main Phases Cavities Coils

State thousands of SC In practice: <10 are actually used They are all type II :

16 A COMPLEX PASE DIAGRAM Applications type II SC : 3 main Phases Cavities Coils Meissner state (SC, B=0 ) Mixed state (SC + vortices (B 0) ) Normal conducting State thousands of SC In practice: <10 are actually used They are all type II : low C1 and high C2 => mixed state EXCEPT Nb! (RF appli.) NB : J D depairing current dens. (intrinsic) J C critical current density (technical limit) Jc has no meaning in RF C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 16

A COMPLEX PASE DIAGRAM Vortex behavior is conditioning the application limits Vortex (Vx) centered hexagonal lattice (triangular) can be pinned on cryst.

17 A COMPLEX PASE DIAGRAM Vortex behavior is conditioning the application limits Vortex (Vx) centered hexagonal lattice (triangular) can be pinned on cryst. defects (see part II) Several states > M => R 0 M Irr Vx glass Vx Liquid C2 Vx Lattice C1 T 2 C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 17

18 VORTEX (II): PINNING ON CRYSTALLINE DEFECTS (Introduction) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 18

19 EXAMPLES OF CRYSTALLINE DEFECTS Punctual: Vacancy 1D: Edge dislocation 2D : Surfaces, interfaces (GB) Substitutional atom Screw dislocation 3D : Inclusions Interstitial atom Surface faceting Voids Dislocation cells C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 19

MORE DETAILS ON PINNING MECANISMS Matsushita : 4 mechanisms from the SC point of view - Condensation energy variation (one saves condensation energy if ⱻ already a normal zone) -

In normal state, NB => interacts strongly with lattice elastic deformation due to crystalline defects-see below) -Magnetic interaction (if defects >>l, you can treat it like an

!!! (=>2 fluids model not fully OK) 2 kinds of pinning : Strong pinning (surface magnetic pinning) : twinning, voids, non SC aggregates, irradiation defects (columnar),

20 MORE DETAILS ON PINNING MECANISMS Matsushita : 4 mechanisms from the SC point of view - Condensation energy variation (one saves condensation energy if ⱻ already a normal zone) - Elastic interactions (lattice elastic moduli in SC state < elastic Mod. In normal state, NB => interacts strongly with lattice elastic deformation due to crystalline defects-see below) -Magnetic interaction (if defects >>l, you can treat it like an interface: image vortex + surface barrier => very strong effect) - Kinetic interaction (areas with x => in Vx velocities?) IN BRIEF : local effects!!!! (=>2 fluids model not fully OK) 2 kinds of pinning : Strong pinning (surface magnetic pinning) : twinning, voids, non SC aggregates, irradiation defects (columnar), nano-indentations : Dominant mechanism: then Weak pinning centers but many of them: «volume core pinning» Dominant mechanism: ; less efficient than but if they are many pinning centers => results into strong pinning Mechanism efficiency Interface (G.B) dislocation punctual defects C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 20

21 FORCES AT PLAY Pinning Force vs elasticity Efficient pinning: F P (r) small for r << 2x et r >> x r~ defects F P (r), J C maximum for Vx // defects w. size ~2 x (columnar defects, plane interfaces) For inclusions ~ x, interspace d, J C => J C ~J C L/d (length fraction. L occupied by pinning centers w. d interspace) In general: if volume fraction f with aleatory defects w. a 0 : Gain : g ~( C2 µ 0 /2)fpx 2 per length u.. L, i.e. force F~ g/l ~( C2 µ 0 /2)fpx 2 /L J C = f/f 0 ~( C2 µ 0 /2)fpx (for L~x) J C = f/f 0 ~( C2 µ 0 /2)fpx 2 /a 0 (for L~a 0 ) (ad minima, but in practice J C is very difficult to predict) E elastic ~ C ii 2 u 2 d 3 r (u ~ Vx displacement /its ideal position, C ii : elastic constants /length unit) C 11 : compression ~ B 2 /µ 0 C 44 : torsion ~ B 2 /µ 0 C 66 : shear ~ BF 0 /16pµ 0 l L F P 2x Pinning Force r Usually: C 44 >>C 66 Periodicity of the Vx Abrikosov lattice is lost => Vx polycrystal, even Vx glass or liquid ⱻ complex phase diagrams of Vx states Weird dynamic properties (80% of SC literature ) In some SC (TC): a new material state was discovered: Bragg glasses C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 21

22 EFFECT OF DEFECTS Importance of the elastic strain Pinning center: chemical or topological defect with locally depleted SC, or even NC. The lattice deforms to accommodate to the pinning, but pays in elastic energy. 3D 2D 1D Strain on the crystalline lattice 0D Plays on SC parameters: l, k... Interfaces (oxide layer, inclusions) > GB > cells > (=dislocations) > vacancies or interstitials Vacancies, interstitials If uniformly distributed : typical of weak pinning (=volumic core pinning) if V = pinning potential and r Vx = density: E pinning ~ V r ρ r d 3 r Generally l>a 0 : one can work with mean values over l (continuum model/ Larkin volume) (a 0 ~ pinning center) collective pinning theory Larkin and Ovchinnikov J. Low Temp. Phys (1979) Mostly studied with irradiation defects e.g. Nb + => 1 vacancy + I self-interstitial. Expected F P /U. Length ~ 10-9 N/m Fp with density of defect, but not monotonically => non uniform distribution (elastic interaction only) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

INDIVIDUAL DISLOCATIONS Source of the hysteresis in DC magnetometry Local elastic distortion of the lattice

net/vamsikrishna393950/stress-fields-around-dislocation/ Dominant mechanism 1!

well recrystallized Non linear behavior => Dislocation repartition is not uniform (not 1D anymore) Nb F P

23 INDIVIDUAL DISLOCATIONS Source of the hysteresis in DC magnetometry Local elastic distortion of the lattice [Bahte et al PAC 98] + 1 GPa 0-1 GPa Stress map around an edge dislocation Dominant mechanism 1! Disloc = (effect < GB) but [Narlikar A, Dew ughes D 1964 #1542] They are many dislocation inside Nb, even if well recrystallized Non linear behavior => Dislocation repartition is not uniform (not 1D anymore) Nb F P /unit lenth or vol 1 (//) ~10-6 N/m 5% deformed ~ cm N/m 3 C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

DISLOCATION CELLS in Nb Dislocations gather in cells (as soon as 3-5% strain) Stress on

(~ to x,=> stronger pinning) Etching figures revealing dislocation arrays on as received Nb

(Abrikosov lattice visualization) In well recrystallized: Abrikosov Lattice everywhere In

24 DISLOCATION CELLS in Nb Dislocations gather in cells (as soon as 3-5% strain) Stress on dislocation pill-up = stress on 1! Disloc n x 20!!! => 2D defects, analogous to G.B. (ⱻ many more dislocations than GB) Expend over a distance larger than G.B. (~ to x,=> stronger pinning) Etching figures revealing dislocation arrays on as received Nb sheet after light etch Monocrystal, RRR = 5000 [Narlikar, 1964, #1542] «Bitter decoration» (Abrikosov lattice visualization) In well recrystallized: Abrikosov Lattice everywhere In deformed Nb: Abrikosov Lattice only in the core of D. cells, but all Vx close to dislocations cells are attracted and pinned there ) [erring, 1974, #1544] C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

SURFACE/INTERFACE PINNING (II) Surfaces/Interfaces : NC precipitate Image vortices formalism (J = 0) Supercurrent tends to push Vx inside Image antivortex tends to pull it out Condensation energy

25 SURFACE/INTERFACE PINNING (II) Surfaces/Interfaces : NC precipitate Image vortices formalism (J = 0) Supercurrent tends to push Vx inside Image antivortex tends to pull it out Condensation energy savings => Strong pinning centers NC precipitate can trap several vortices superconductivity/melt.htm Surfaces/Interfaces : Grain boundaries Disordered area over n atomic distances => local SC parameter affected Compare with x TC SC : for some orientations n is ~10 (~3 nm) and x AB ~ 2 nm => strong pinning Nb : n ~2-3 (~<1 nm) and x ~ 40 nm => weak pinning YBCO Material Nb (// GB) Nb 3 Sn MgB nm F P /unit length N/m N/m N/m C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 25

26 SURFACE/INTERFACE PINNING (I) Surfaces/Interfaces : strong pinning Boundary conditions : ԦJ S n=0 (J = 0) => Vx always exit to the surface Equilibrium : pinning force = elastic force (line tension) If the Vx is curved, its length and thus the elastic return force also. Equilibrium => pinning force also increases as a consequence. Macro. scale : Vx must curve to satisfy B.C. (Vx is to surface). Micro. scale : strong surface state influence SC sphere q cr n s.org/prb/abstract / /PhysRe vb ԦJ S IC can increase with increasing surface roughness (=> thin films applications!!!) Roughness scale in concern depends on the applied field (µm at low, nm at high!) I S ~ M(B, T) sinq C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 26

CONSEQUENCIES OF GB/GRAIN SIZE Depinning frequency Theory: see e,g, Palmieri TFSRF 2010 http://fr.slideshare.

pinning force in SC cables Easy to measure: l b Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements Pautrat 2003 φ ac

27 CONSEQUENCIES OF GB/GRAIN SIZE Depinning frequency Theory: see e,g, Palmieri TFSRF ri-rf-losses-trapped-flux Measurement of complex (/effective) penetration depth: l AC = l + il Typically used to determine pinning force in SC cables Easy to measure: l b Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements Pautrat 2003 φ ac = b ac ds ~ 2λ ac l b b 0 At low frequency : l ~ d RF (d RF = penetration depth in normal state) At high frequency l ~ l ~ l L << d RF C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

28 SENSITIVITY TO TRAPPED MAGNETIC FLUX/DEPINNING FREQUENCY Pinning is very efficient for bulk but not for thin films Nb in the 100 Mhz-1 Ghz range Lütke-Entrup et al /condmat/ pdf Thin films Nb Depends on quality, can reach some 10 Gz; e.g. here 26 Gz, Bulk monox Nb: 10 kz Gittleman et al See also D. Janjušević et al S. all igh depinning frequency: measured on various SC, various film deposition technique, but can vary with quality of the films. e.g.: measurements from Glitterman on Nb 3 Sn : w 0 ~300 Gz!!! All thin films show low sensitivity to trapped magnetic flux: because all the flux is efficiently trapped!!! C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II)

29 SENSITIVITY TO TRAPPED FLUX IS RELATED TO PINNING Observations 100% trapped flux on Nb samples /cavities (cf C. Vallet PhD + recent work) Sensitivity to trapped flux of bulk Nb varies From lab to lab ( measurement geometries, shielding, environment???) From supplier to supplier (cf FNAL proto series) From sheet to sheet (recrystallization varies from batch to batch, and even in the same batch if the Tp in furnace is not perfectly uniform) ighest sensitivity for: N doped cavities Nb 3 Sn Lowest sensitivity for: Thin film Nb (at least at low field) Comparative measurements of niobium sheet and sputter coated cavities Arnold Mayer & Weingarten 1987 (here measured field is not RF field, but external field) C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 29

30 MORE ON PINNING IN NIOBIUM IN TE LECTURE: "MATERIAL AND SURFACE ASPECTS IN SRF TECNOLOGY" C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 30

31 NEXT: PART III : APPLICATIONS IN ACCELERATORS MAGNETS & RF CAVITIES C.Z. ANTOINE Lecture on Superconductivity in accelerators (part II) 2018 PAGE 31

Introduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO Conclusions. Flux pinning.

Department of Physics and Astronomy 14.6.2011 Contents Introduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO Type II superconductors and vortices Type I ξ < λ S/N