TUOLP03

超伝導空洞の物理
高Q値・高加速勾配空洞の実現に向けて
Physics of superconducting cavity: towards
realizations of high-Q and high gradient cavities

KEK / 総研大#17H04839
久保 毅幸
KUBO, Takayuki

第14回日本加速器学会年会（2017年8月1日）
Picturehttp://www.linearcollider.org/ILC/Press/Images-and-graphics

12
http://www.linearcollider.org/ILC/Press/Images-and-graphics

electron

3
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Large accelerating
electric field

Eacc

http://www.linearcollider.org/ILC/Press/Images-and-graphics

Large accelerating
electric field

Eacc
small
surfaceresistanceRs

or Large Quality factor
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Q0∝1/RsNb cavity processed by thestandard ILC recipe

High Eacc(standard ILC recipe)

T= 2 [K]6

Nb cavity processed by
the N or Ti doping recipe
A. Grassellino et al, Supercond. Sci. Technol. 26, 102001 (2013)
P. Dhakal et al., Phys. Rev. ST Accel. Beams 16, 042001 (2013); in proceedings of IPAC2012, New Orleans, Louisiana, USA (2012), p. 2426, WEPPC091

High Q(Nitrogen doping)High Eacc(standard ILC recipe)

T= 2 [K]7

We want to go beyond the limits ofthe present technologies!
High Q(Nitrogen doping)High Eacc(standard ILC recipe)

T= 2 [K]8

We want to go beyond the limits ofthe present technologies!
High Q(Nitrogen doping)High Eacc(standard ILC recipe)?

How

T= 2 [K]9

Basics towards high gradients10
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Magnetic field
distribution11
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Low field (Meissner state)

Magnetic field
distribution12
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Low field (Meissner state)

Magnetic field
distribution

High field (vortex state)13
http://www.linearcollider.org/ILC/Press/Images-and-graphics

Vortex Avalanche
Magnetic field
distribution

http://www.linearcollider.org/ILC/Press/Images-and-graphics

J. I. Vestgården, D. V. Shantsev, Y. M. Galperin & T. H. Johansen,
14
Scientific Reports 2, 886 (2012)

Magnetic field
distribution

To achieve a highfield, a material
that can withstandagainst the vortex
penetration up toa high magnetic
field should be
used.
15

http://www.linearcollider.org/ILC/Press/Images-and-graphics

So we use Nb as the material of SRF cavity.
The lower critical field of pure Nb is

Bc1～170 mT (Eacc～40MV/m for TESLA cavity),
which is larger than other superconductors.

※ The other reason is

the thermal conductivity.
Today I do not talk about this topic

16

Interactions.org, Particle Physics News and Resources, http://www.interactions.org/cms/?pid=1900

So we use Nb as the material of SRF cavity.
The lower critical field of pure Nb is

Bc1～170 mT (Eacc～40MV/m for TESLA cavity),
which is larger than other superconductors.

T=2K
40MV/m35
MV/m

30MV/mT. Kubo (2017)17

Interactions.org, Particle Physics News and Resources, http://www.interactions.org/cms/?pid=1900

Even if ultra pure Nb wasused, achieving Bc1～170 mT(Eacc～40MV/m) was not astraight forward task.

18

Even if ultra pure Nb wasused, achieving Bc1～170 mT(Eacc～40MV/m) was not astraight forward task.
How did SRF researchers
achieve Eacc>40MV/m?
19

ILC recipe

20Electropolish

C. Antoine

21

Electropolish

Electropolish

C. Antoine

Electronbeam

22Electropolish

Electropolish

C. Antoine

23

Electropolish

Electropolish

If we skip this step, cavities suffer“Q-disease” due to niobium hydride“Q-disease”

B. Aune et al.,in proceedings of LINAC1990, Albuquerque, New Mexico, USA (1990)

C. Antoine

24

Electropolish

Electropolish

C. Antoine25

If we skip this step, Q would degrade
due to the field emissions.
Electropolish

Electropolish

C. Antoine

P. Bernard et al.,In proceedings of EPAC1992, Berlin, Germany (1992)26

Electropolish

Electropolish

C. Antoine

What is the 120℃-48hours bake?
L. Lilje et al., in Proceedings of SRF1999, Santa Fe, New Mexico, USA (1999), p. 74, TUA001.

Without
bakingHigh field
Q-dropWhat is the 120℃-48hours bake?
L. Lilje et al., in Proceedings of SRF1999, Santa Fe, New Mexico, USA (1999), p. 74, TUA001.

With
baking

E. Kako et al., in Proceedings of SRF1995, Gif-sur-Yvette, France(1995), p. 425, SRF95C12.
P. Kneisel et al., in Proceedings of SRF1995, Gif-sur-Yvette, France(1995), p. 449, SRF95C17.
M. Ono et al., in Proceedings of SRF1997, Abano Terme (Padova),
Italy (1997), p. 472, SRF97C08.
L. Lilje et al., in Proceedings of SRF1999, La Fonda Hotel, Santa Fe,
New Mexico, USA (1999), p. 74, TUA001.

At the present day, we know
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)

By using Low Energy muon spin rotation techniqueFermilab news at work
http://news.fnal.gov/wp-content/uploads/2016/09/11-0233-27D.jpg

30

At the present day, we know
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)

The baked Nb has alayered structurethat consists of31

At the present day, we know
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)

The baked Nb has alayered structurethat consists of1.

dirty Nb layer

Dirty Nb32

At the present day, we know
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)

The baked Nb has alayered structurethat consists of1.

dirty Nb layerand2. clean bulk Nb.

Dirty Nb

Clean Nb
33

At the present day, we know
The baked Nb has alayered structurethat consists of1.

dirty Nb layerand2. clean bulk Nb.
Dirty Nb

Clean Nb34

①

Since excited quasiparticles increase and contribute to the surface
resistance as the gap decreases, a larger gap is desired. The gap in the

dirty layer is rather well behaved at a high field!
→ cure the high field Q drop
Note here Bc1 is a bulk property and given by the bulk clean SC:

Bc1～170mT remains after layered.

clean

dirty

Gap under a current (narrow!)

Gap under a current(wider than clean case!)

Becomes gapless before arriving at
 F. P-J. Lin and A. Gurevich, Phys. Rev. B 85, 054513 (2012)
the superheating field!
 A. Gurevich, Rev. Accel. Sci. Technol. 5, 119 (2012)

The surface current is suppressed.

②The current suppression means an enhancement of the field limit,
because the theoretical field limit is determined by the current density.
The gap reduction due to the current is further prevented.

λ1 (> λ2)

λ2This slope corresponds tothe current density.
The surface current issuppressed!

SS case: T. Kubo, in Proceedings of LINAC2014, p. 1026, THPP074.
SIS case: T. Kubo et al., Appl. Phys. Lett. 104, 032603 (2014).
 A. Gurevich, AIP Advance 5, 017112 (2015).
 S. Posen et al., Phys. Rev. Applied 4,044019 (2015).
Figures from T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

This is SIS case.
SS case is similar.

③

Vacuum sidesuperconductor side

Bean-Livingston
barrier

Vortices are expelled by the boundary ifλ(layer)> λ(bulk). (left figure) T. Kubo, Supercond. Sci. Technol. 30, 023001(2017)
 T. Kubo, in Proceedings of LINAC2014, p. 1026, THPP074.
 M. Checchin et al., in Proceedings of IPAC2016, p. 2254,
WEPMR002

References(recent findings related to the ILC recipe)F. P-J. Lin and A. Gurevich, Phys. Rev. B 85, 054513 (2012)
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)
T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)
解説 T. Kubo, in proceedings of the International Workshop on Future Linear Colliders(LCWS2016), Morioka, Japan (2016).
 T. Kubo, Journal of the Particle Accelerator Society of Japan, 14, 35 (2017).[日本語]38NitrogendopingA. Grassellino

P. Dhakal

Ti-doping

Fermilab today

https://www.jlab.org/news/ontarget/target-december-201139
http://www.fnal.gov/pub/today/archive/archive_2014/today14-06-03_Readmore.html

Electropolish

Electropolish

C. Antoine

40

Electropolish

Electropolish

C. Antoine

41

Inject N2 gas(～3×10-5 Pa)

Electropolishat 800℃
for 2 minutes

Electropolish

C. Antoine

42

Inject N2 gas(～3×10-5 Pa)

Electropolishat 800℃
for 2 minutes

Electropolish

C. Antoine

43

Inject N2 gas(～3×10-5 Pa)

Electropolishat 800℃
for 2 minutes

Electropolish

C. Antoine

44

Inject N2 gas(～3×10-5 Pa)

Electropolishat 800℃
for 2 minutes

Electropolish

C. Antoine

45

Electropolish

Electropolishby 5-7μm

Electropolish

C. Antoine

46

Then we obtain a “high Q”
N dopeILC recipe

A. Grassellino et al, Supercond. Sci. Technol. 26 102001 (2013)47

Why does Q increase as the field increases?

48

Why does Q increase as the field increases?
Let us begin with a brief review of thesurface resistance of SRF cavity.

49

Why does Q increase as the field increases?
Let us begin with a brief review of thesurface resistance of SRF cavity.
ε
The gap is much larger than RF:
RF (～GHz) cannot break Cooper
pair.

Gap～O(102) GHz

50

Why does Q increase as the field increases?
Let us begin with a brief review of thesurface resistance of SRF cavity.
ε
The gap is much larger than RF:
RF (～GHz) cannot break Cooper
pair.

However, when T > 0,
Quasiparticles (normal electrons)
necessarily exist above the gap.

Quasiparticles

Gap～O(102) GHz

51

Why does Q increase as the field increases?
Let us begin with a brief review of thesurface resistance of SRF cavity.
ε
The gap is much larger than RF:
RF (～GHz) cannot break Cooper
pair.

However, when T > 0,
Quasiparticles (normal electrons)
necessarily exist above the gap.
They absorb RF→ P≠0→ 𝑅𝑠 ≠ 0

𝑅𝑠 ~ න 𝑑𝜖 𝑁 𝜖 𝑁(𝜖 + ℏ𝜔)𝑒 −𝜖/𝑘𝑇

Quasiparticles

1.3GHzGap～O(102) GHz

52

Why does Q increase as the field increases?
1
𝑅𝑠 ∝ ln𝑝𝑒𝑎𝑘 𝑤𝑖𝑑𝑡ℎZero field

𝑁(𝜀)A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)53

Why does Q increase as the field increases?
1
𝑅𝑠 ∝ ln𝑝𝑒𝑎𝑘 𝑤𝑖𝑑𝑡ℎFinite field

𝑁(𝜀)A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)

The broaden
DOS peakreduces Rs!

54 Rs of ideal dirty SC generally decreases as
the field increases: the Q-increase
phenomenon is rather natural behavior of
dirty SC.
 However, very low RRR(〜10) Nb cavities,
which are also dirty SC, do not show the“Q-increase”. What is the difference
between N and other impurities? What is
the role of N?
55

Disadvantage of N-dope:

Q increases but gradient decreases.
N dopeILC recipe

A. Grassellino et al, Supercond. Sci. Technol. 26 102001 (2013)

56

The reason is obvious!
Interstitial N reduces mean free path:
RRR=300 (mfp > 700nm) material → mfp～50nm
N-dopeM. Martinello et al, Appl. Phys. Lett. 109, 062601 (2016)

Then Bc1=170mT → Bc1=130mT
N-dopeEacc=40MV/m

which corresponds to Eacc=30MV/m!!

57

※Tesla空洞の35MV/m
は150mTに対応

Bc1 around here

T. Kubo,Prog. Theor. Exp. Phys. 2015, 063G01 (2015).

Superheating field Bs of dirty Nb

58

※Tesla空洞の35MV/m
は150mTに対応

Bc1 around here

N-dope is not really suited tohigh gradient application!
T. Kubo,Prog. Theor. Exp. Phys. 2015, 063G01 (2015).

Superheating field Bs of dirty Nb

59

References(related to the N-dope)
A. Grassellino et al, Supercond. Sci. Technol. 26 102001(2013)
P. Dhakal et al., Phys. Rev. ST Accel. Beams 16, 042001(2013)
G. Ciovati, P. Dhakal, and A. Gurevich, Appl. Phys. Lett. 104,
092601 (2014)
A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)
T. Kubo, Prog. Theor. Exp. Phys. 2015, 063G01 (2015)
M. Martinello et al, Appl. Phys. Lett. 109, 062601 (2016)60

N infusion(new ILC recipe?)

A. Grassellino

http://td.fnal.gov/

https://www.jlab.org/news/ontarget/target-december-2011

61

They knew
1. The dirty-clean layered
structure realized in ILC
recipe (120℃-48hours bake)is the key to high gradients.
A. Romanenko et al., Appl. Phys. Lett. 104, 072601 (2014)

2. Nitrogen doping is the key
to high Q.
A. Grassellino et al, Supercond. Sci. Technol. 26 102001 (2013)

They considered“Let us combine 1 and 2”→ Nitrogen infusion

62

Electropolish

Electropolish

C. Antoine

63

Inject N2 gas(～3×10-5 Pa)

Electropolishat 120℃
for 48 hours

Electropolish

C. Antoine

64

Inject N2 gas(～3×10-5 Pa)

Electropolishat 120℃
for 48 hours

ElectropolishNochemistry

C. Antoine

65

Inject N2 gas(～3×10-5 Pa)

Electropolishat 120℃
for 48 hours

ElectropolishNochemistry

C. Antoine

66

Then we obtain “high-Q & high gradient”

A. Grassellino et al.,arXiv:1701.06077 to be published in Supercond. Sci. Technol.
67

Nitrogen plays a role

NitrogenArgon
68

Why is the high gradient possible?

Let us remind the small Bc1 of N-dope comesfrom its dirtiness at the depth up to μm.

〜μm

69

Why is the high gradient possible?

RF

Regraded asa bulk dirty SC
Bc1=130mT(30MV/m)Screening
current

Let us remind the small Bc1 of N-dope comesfrom its dirtiness at the depth up to μm.

100nm

〜μm

70

Why is the high gradient possible?

In the N-infusion case, the dirty region is
confined in the first tens of nm.

A few tens of nm71

Why is the high gradient possible?

RF
RF sees
dirty and clean SC

Screening
current

In the N-infusion case, the dirty region is
confined in the first tens of nm.

100nm

Bc1=170mT(40MV/m) A few tens of nm

72

Why is the high gradient possible?

In the N-infusion case, the dirty region is
confined in the first tens of nm.
This effect may also
play a role in pushingup gradientVortices are expelled by the boundary ifλ(layer)> λ(bulk). (left figure)
T. Kubo,Supercond. Sci. Technol. 30, 023001 (2017)73

Why is the high Q possible?

Open Question
Probably the similar mechanism as N-dope:
remind the cavity behavior approaches Ndope behavior when baking T increases.
What is the role of N?

N induces high Q, but others do not. Thismight be the key to understand it.
74References(related to the N-infusion)

A. Grassellino et al., arXiv:1701.06077 to be published inSupercond. Sci. Technol.
F. P-J. Lin and A. Gurevich, Phys. Rev. B 85, 054513 (2012)
T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)
T. Kubo and A. Gurevich, “Unified Theory of surface
resistance and residual resistance of SRF cavities at low
temperatures”, SRF2017 invited talk.
75

A. Romanenko

Flux
expulsion76

http://www.fnal.gov/pub/today/images/images11/Romanenko.jpg

This is really excellent finding, but we
do not have enough time to introduce
this today. A. Romanenko, et al., Appl. Phys. Lett. 105, 234103 (2014)

References(related to the flux expulsion)
A. Romanenko, et al., Appl. Phys. Lett. 105, 234103 (2014)
T. Kubo, Prog. Theor. Exp. Phys. 2016, 053G01 (2016)
S. Huang, T. Kubo, and R. Geng, Phys. Rev. Accel. Beams
19, 082001 (2016)
S. Posen et al., J. Appl. Phys. 119, 213903 (2016)77

Further high-Q
and high-Grad

SRF201778

http://news.fnal.gov/2016/06/sam-posen-wins-2016-ieee-past-award/

(Ultra) High-Q

79

S. Posen and D. L. Hall,
Supercond. Sci. Technol. 30, 033004 (2017)

Nb3Sn has attracted
much attention as thenext generation “highQ” SRF material

80

S. Posen and D. L. Hall,
Supercond. Sci. Technol. 30, 033004 (2017)

Nb

Nb3Sn

81

4.2K
S. Posen and D. L. Hall,
Supercond. Sci. Technol. 30, 033004 (2017)82

Why so high Q?
The gap is large, so the number of normal
electrons at a given T is exponentially small.
ε

Nb

ε

Quasiparticles

1.3GHzNb3Sn
Quasiparticles

1.3GHzGap
Gap𝜋

Note that BCS’s relation ∆= 𝑒 𝛾𝐸 𝑘𝐵 𝑇𝑐 ≃ 1.76𝑘𝐵 𝑇𝑐

83

(Ultra) High-Gradient84

Stable Meissner state if B < Bc1=170mT

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)85Stable Meissner state if B < Bc1=170mTMetastable at B > Bc1=170mT

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)86Stable Meissner state if B < Bc1=170mTMetastable at B > Bc1=170mTThe world record exceeds B=200mT, which
is close to the ultimate limit!

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)87

We need to explore new materials!

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

100
MV/m
88

We need to explore new materials!

Candidate
0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

100
MV/m
89

However…

Stable Meissner state at B < Bc1〜50mT,
which corresponds to Eacc = 10-20MV/m

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

100
MV/m
90

However…

Stable Meissner state at B < Bc1〜50mT,
which corresponds to Eacc = 10-20MV/m
This region is not stable!

0
MV/m

20
MV/m

40
MV/m

T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

100
MV/m
91

Experimental results have been limited by
B〜70mT (Eacc=17MV/m)

S. Posen and D. L. Hall,
Supercond. Sci. Technol. 30, 033004 (2017)

70mT
92

Experimental results have been limited by
B〜70mT (Eacc=17MV/m)

70mT

93

Experimental results have been limited by
B〜70mT (Eacc=17MV/m)To go far awayfrom Bc1,
any tiny defects
must be removed!

94Experimental results have been limited by
B〜70mT (Eacc=17MV/m)To go far awayfrom Bc1,
any tiny defects
must be removed!

J. I. Vestgården, D. V. Shantsev, Y. M. Galperin & T. H. Johansen,
95
Scientific Reports 2, 886 (2012)

How to avoid the avalanches?

Further advanced layered structures
Dirty Nb3Sn(～100nm)

Clean Nb

 T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)
 T. Kubo, in Proceedings of LINAC2014, Geneva, Switzerland (2014), p. 1026,
THPP074.
 See also the discussion section of T. Kubo, Progress of Theoretical andExperimental Physics 2015, 063G01 (2015)
 T. Kubo, TTC meeting at Saclay France (2016)

The fourfold benefit of the layered structure will improve the maximum
Eacc and Q0 : (1) the reduction of gap is small in the dirty layer(2) suppress the surface current and enhance the theoretical field limit(3) prevent the vortex penetration by the additional barrier(4) In addition, since a part of current flows on the low loss surface,
Nb3Sn, dissipation decreases and Q increases.
96How to avoid the avalanches?

Further advanced layered structures
Dirty Nb3Sn(～100nm)insulator Clean Nb

 A. Gurevich, Appl. Phys. Lett. 88, 012511 (2006).
 T. Kubo, Y. Iwashita, and T. Saeki, Appl. Phys. Lett. 104, 032603(2014).
 A. Gurevich, AIP Advance 5, 017112 (2015).
 S. Posen et al., Phys. Rev. Applied 4,044019 (2015).
 T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)

Furthermore, introducing the insulator layer (1) prevent the vortex
penetration and (2) suppress vortex dissipation, because thevortex core disappears in the insulator layer.
97

e.g.)

Nb3Sn / thin insulator / Nb substrateor
Nb3Sn / Nb substrate

Note this shows just theoretical field limits. Whether we can achieve them depends on whether a gimmick to avoid vortex
penetration works well or not. See T. Kubo, TTC meeting at France (2016) or Supercond. Sci. Technol. to be published (arXiv:1607.01495)(116MV/m of TESLA)

100MV/m(93MV/m) A. Gurevich, AIP Advance 5, 017112 (2015).
 T. Kubo, talk at SRF2015, Whistler, Canada (2015), TUBA07.
 T. Kubo, TTC meeting at Saclay France (2016) T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017)(70MV/m)Bs(Nb3Sn)=0.84×540mT=450mT
λ1=120nm

Bs(substrateNb)=240mT
λ2=40nm98

References(related to Ultra high-Q & high-grad)

Nb3Sn

 S. Posen and M. Liepe, Phys. Rev. ST Accel. and Beams 17, 112001(2014).
 S. Posen, M. Liepe, and D. L. Hall, Appl. Phys. Lett. 106, 082601 (2015).
 S. Posen and D. L. Hall, Supercond. Sci. Technol. 30, 033004 (2017).

Layered structure A. Gurevich, Appl. Phys. Lett. 88, 012511 (2006).
 T. Kubo, Y. Iwashita, and T. Saeki, Appl. Phys. Lett. 104, 032603 (2014).
 A. Gurevich, AIP Advance 5, 017112 (2015).
 S. Posen et al., Phys. Rev. Applied 4, 044019 (2015).
 T. Kubo, Supercond. Sci. Technol. 30, 023001 (2017).
 C. Z. Antoine et al., Appl. Phys. Lett. 102, 102603 (2013).
 T. Tan et al., Scientiﬁc Reports 6, 35879 (2016).
99

Summary
Superficial introduction to hot topics in SRF
 Basics of SRF
 ILC recipe
 N-dope N-infusion
 Flux expulsion
 Nb3Sn for ultra high-Q SRF
 Layered structure for ultra high-G

Too short to introduce these topics!
Please read the references!
100Ultra high-Gradient for
the ILC 1TeV upgrade!!
“MgB2 on Nb” sample (2016)

N-infused
Baking (2010s)

BakingBare clean Nb (1990s)
T= 2 [K]100MV/m(20XX)