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The Superheating Field of Niobium: Theory and Experiment
Nicholas Valles Cornell University
Laboratory for Elementary-Particle Physics
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February 20, 2012 N. Valles. 15th International Conference on RF Superconductivity (2011) 2
Outline
• Critical Fields of Superconductors • Survey of Previous Work • New Results from Cornell on the
Superheating Field
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February 20, 2012 3
• Critical Fields of Superconductors • Survey of Previous Work • New Results from Cornell on the
Superheating Field
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Critical Fields of Superconductors
• Type-I: Meissner State below applied field Hc, normal above
• Type-II: Meissner State below Hc1. Energetically favorable to enter mixed state below Hc2. Normal above Hc2.
• Hc3 is a surface effect: bulk is normal, but surface layer (~ξ) superconducting.
February 20, 2012 4 N. Valles. 15th International Conference on RF Superconductivity (2011)
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Critical Fields of Superconductors
February 20, 2012 5
Critical Field Value at 0K (mT) Reference Bc 200 Finnemore; Casalbuoni
Bc1 174 Finnemore
Bc1 190 C. Vallet
Bc2 390 Casalbuoni
Bc2 400 Finnemore
Bc2 410 Saito
Bc2 450 C. Vallet
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Superheating Field: Metastability and Nucleation
February 20, 2012 6
Raindrops: the Liquid-Gas Transition
“Superheating” like 110% humidity
Metastable energy barrier B
droplet nucleation R2 surface tension cost
R3 bulk energy gain
Gas phase metastable for Tc > T > Tsp, spinodal temperature
Tc
Tsp
J. Sethna, Cornell University N. Valles. 15th International Conference on RF Superconductivity (2011)
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Superconductors & Magnetic Fields
February 20, 2012 7
Type II (Nb and Nb3Sn) Type I (Pb)
Can we calculate the phase diagram for Hsh? J. Sethna, Cornell University
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Metastability Threshold and Hsh
February 20, 2012 8
Why a superheating field?
Why is there a barrier to vortex penetration?
ξ
Λ> ξ
Costly core ξ enters first; gain from field Λ later
Barr
ier
J. Sethna, Cornell University N. Valles. 15th International Conference on RF Superconductivity (2011)
ξ
Λ
Coherence length: Decay of Ψ
Penetration depth: Decay of Η
Energy cost
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Motivation
• Why do we care? – Hsh sets the ultimate physical limit for surface fields – Hsh can be effected by surface treatments – Metastability is an interesting phenomenon to study
February 20, 2012 9 N. Valles. 15th International Conference on RF Superconductivity (2011)
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February 20, 2012 10
• Critical Fields of Superconductors • Survey of Previous Work • New Results from Cornell on the
Superheating Field
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Hsh: Temperature Dependence
• Most Hsh work based on Ginzburg-Landau Theory
• GL solved in 1D case
– Asymptotic expansion (Dolgert et. al.)
February 20, 2012 11
( )
−=
2
1)(c
csh TTHcTH κ
N. Valles. 15th International Conference on RF Superconductivity (2011)
H/Hc
κ = λ/ξ
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First Evidence Hsh > Hc
February 20, 2012 12
Magnetization curves of Nb cylinders at 4.2K showing Hsh > Hc
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Hsh Measurements: Midrange κ
February 20, 2012 13
Type-I and Type-II superconducting spheres near Tc. Yogi (1976)
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Hsh: First measurement of Temperature Dependence
February 20, 2012 14
Hays Measurement of Hsh(T) for Nb (1995) N. Valles. 15th International Conference on RF Superconductivity (2011)
[mT]
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February 20, 2012 15
• Critical Fields of Superconductors • Survey of Previous Work • New Results from Cornell on the
Superheating Field
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Theories of Superconductivity
February 20, 2012 16
Validity versus complexity Ginzburg-Landau (GL) • ψ(r), H(r) order parameters • Spatial dependence OK • Valid only near Tc
Ginzburg-Landau valid
Bardeen Cooper Schrieffer (BCS) theory • Pairing k, -k within vibration energy • Excellent for traditional superconductors • Hc1(T), Hc2(T) done • Hsh(T) hard (spatial dependence)
n kF
ħωd
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J. Sethna, Cornell University
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Ginzburg-Landau
Underestimate for Hsh
MgB2 Nb3Sn
Theories of Superconductivity
February 20, 2012 17
Validity versus complexity Eilenberger Equations • Valid at all temperatures • Assumes ∆(r), H(r) vary slowly
Eliashberg equations • Needs electronic structure • Never done before for Hsh
Eilenberger equation results
N. Valles. 15th International Conference on RF Superconductivity (2011)
J. Sethna, Cornell University
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Ginzburg-Landau Eilenberger near Tc – Mark Transtrum
February 20, 2012 18
Theoretical Hsh Work
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Hsh(T), Large κ
February 20, 2012 19
Eilenberger Eqns, κ >> 1. Sethna , Catelani
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Hsh(T), Intermediate κ
• Solving the Eilenberger equations are hard, especially for moderate or small κ
• Experimental measurements are necessary to help guide theory
February 20, 2012 20 N. Valles. 15th International Conference on RF Superconductivity (2011)
Hsh(κ ~ 1), convergence
100 101 102 1031
1.5
2
2.5
Number of points on Fermi Surface
c(κ
~ 1)
≡ H
sh/H
c
T = 0.200 TcT = 0.975 Tc
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Hsh(T) Measurement
February 20, 2012 21 LR1-3 to measure Superheating Field
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Hsh(T) Measurement
February 20, 2012 22 LR1-3 to measure Superheating Field
Re-entrant cavity prep: •Vertical EP •2 hr HPR , clean assembly •120C bake for 48 hr
N. Valles. 15th International Conference on RF Superconductivity (2011)
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Pulsed Power Measurements
February 20, 2012 23 N. Valles. 15th International Conference on RF Superconductivity (2011)
Boeing Klystron supplies high power pulses • Pf ~ 1.5 MW • Qext ~ 6×106
• Ramp up power quickly (100 μs) to minimize thermal effects
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Calculating Q0 vs Time
• Following Hays we can write:
February 20, 2012 24
dtdU
QUPP rf ++=0
ω
extfr Q
UPP ω−=
extext
f
QU
dtdU
QUP
QU ωωω
−−= 20
extext
f
QdtUd
QP
UQ121
0
−
−=
ωω
and
which gives
N. Valles. 15th International Conference on RF Superconductivity (2011)
or
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Measuring Hsh
February 20, 2012 25 N. Valles. 15th International Conference on RF Superconductivity (2011)
110 115 120 125 130 135 140105
106
107
108
Time [µs]In
trins
ic Q
ualit
y Fa
ctor
0 50 100 150 200 250 3000
200
400
600
800
1000
Sur
face
Mag
netic
Fie
ld [O
e]
0 50 100 150 200 250 3000
0.3
0.6
0.9
1.2
1.5
Time [µs]
Kly
stro
n P
ower
[MW
][mT]
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Measuring Hsh
February 20, 2012 26 N. Valles. 15th International Conference on RF Superconductivity (2011)
110 115 120 125 130 135 140105
106
107
108
Time [µs]In
trins
ic Q
ualit
y Fa
ctor
0 50 100 150 200 250 3000
200
400
600
800
1000
Sur
face
Mag
netic
Fie
ld [O
e]
0 50 100 150 200 250 3000
0.3
0.6
0.9
1.2
1.5
Time [µs]
Kly
stro
n P
ower
[MW
]
90% SC
[mT]
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Measuring Hsh
February 20, 2012 27 N. Valles. 15th International Conference on RF Superconductivity (2011)
110 115 120 125 130 135 140105
106
107
108
Time [µs]In
trins
ic Q
ualit
y Fa
ctor
0 50 100 150 200 250 3000
200
400
600
800
1000
Sur
face
Mag
netic
Fie
ld [O
e]
0 50 100 150 200 250 3000
0.3
0.6
0.9
1.2
1.5
Time [µs]
Kly
stro
n P
ower
[MW
]
90% SC
120 μs
[mT]
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RBCS vs Temperature
February 20, 2012 28
SRIMP Fit: MFP = 27 nm. κ = 3.5 N. Valles. 15th International Conference on RF Superconductivity (2011)
Determining κ in CW
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Hsh(T) Measurement
February 20, 2012 29
Fit: c(κ) = 1.04 ±0.01
( )
−=
2
1)(c
csh TTHcTH κ
N. Valles. 15th International Conference on RF Superconductivity (2011)
[mT]
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Transtrum: Hsh(κ)
February 20, 2012 30
κ = 3.5
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Transtrum: Hsh(κ)
February 20, 2012 31
κ = 3.5
κ = 1.0
Possibility for 20% increase by changing κ N. Valles. 15th International Conference on RF Superconductivity (2011)
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c(κ) vs Mean Free Path
February 20, 2012 15th International Conference on RF Superconductivity (SRF 2011) 32
κ = 3.5
κ = 1.0
( )2/3
0
0
+
=
ξξλκ L
Baking lowers mean free path (and thus κ) by introducing surface impurities
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Hsh(T) Measurement
February 20, 2012 33 LR1-3 to measure Superheating Field
Re-entrant cavity prep: • 800 C bake, 2 hr • Vertical EP • 2 hr HPR , clean assembly • NO 120C bake
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Q vs E (CW), for LR1-3
February 20, 2012 34
Severe Q drop at low fields. Small radiation, no quenches
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Hsh(T) Measurement
February 20, 2012 35
c(κ) = 1.28±0.06 (Theory predicts 1.30) κ clearly changed!
N. Valles. 15th International Conference on RF Superconductivity (2011)
[mT]
( )
−=
2
1)(c
csh TTHcTH κ
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Conclusions
• We now have a measurement showing the full temperature dependence of Hsh
• GL theory is suprisingly accurate over the full temperature range
• Surface treatments strongly influence Hsh • There appears to be a trade-off between removing
high field Q-slope and high superheating field – Alternative to 120C bake?
February 20, 2012 36 N. Valles. 15th International Conference on RF Superconductivity (2011)
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The Future of Hsh
• Eilenberger theory appears to give a small increase to Hsh at low temperatures
• Hsh measurements are a place where experiment can really drive theory
• More work needs to be done to ensure the convergence of the Eilenberger eqns for T << Tc
• Can we reproduce these results for new materials such as Nb3Sn or MgB2?
February 20, 2012 37 N. Valles. 15th International Conference on RF Superconductivity (2011)
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The Future of Hsh
• Eilenberger theory appears to give a small increase to Hsh at low temperatures
• Hsh measurements are a place where experiment can really drive theory
• More work needs to be done to ensure the convergence of the Eilenberger eqns for T << Tc
• Can we reproduce these results for new materials such as Nb3Sn or MgB2?
February 20, 2012 38
Sam Posen at Cornell is currently making Nb3Sn. THPO066 Hsh measurements to follow
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Thanks
• Special thanks: – Matthias Liepe, Hasan Padamsee, and Zachary Conway
for great help with experimental measurements – James Sethna and Mark Transtrum for temperature
dependence from Eilenberger Theory
February 20, 2012 39 N. Valles. 15th International Conference on RF Superconductivity (2011)
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the 1995 U.S. Particle Accelerator Conference. 25 Holmes, S. D. (2009), in Particle Accelerator Conference. 26 J.A. Crittenden, e. a. (2009), in Particle Accelerator Conference. 27 Joseph, A. S., and W. J. Tomasch (1964), Phys. Rev. Lett. 12 (9), 219. 28 Kneisel, P. (2004), in Pushing the Limits of RF Superconductivity. 29 Padamsee, H., J. Knobloch, and T. Hays (1998), RF Superconductivity
for Accelerators (Wiley). 30 Padamsee, H., J. Knobloch, and T. Hays (1998), “Rf superconductivity
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