RF breakdown in multilayer coatings: a possibility to break the Nb monopoly

Alex GurevichNational High Magnetic Field Laboratory, Florida State University

"Thin films applied to Superconducting RF: Pushing the limits of RF Superconductivity"

Legnaro National Laboratories of the ISTITUTO NAZIONALE DI FISICA NUCLEARE, in Legnaro (Padova) ITALY, October 9-12, 2006.

MotivationMotivation• Why Nb?

BCS surface resistance: Rs 4exp (-/kBT)Minimum Rs implies maximum , that is, maximum Tc 1.87/kB and minimum London penetration depth

Exceptions:• Does not work for the d-wave high-Tc

superconductors for which Rs T2 due to nodal lines in (k) = 0.

• Two gap MgB2 with 2.3 meV 7.2 meV: Tc is proportional to , while Rs exp (- /kBT) is limited by

Vanishing (k) = 0 along [110] directions in HTS

Nb3Sn has maximum Tc and minimum to provide the optimum Rs

Background

Best KEK - Cornell and J-Lab Nb cavities are close to the depairing limit (H Hc = 200 mT)

How far further can rf performance of Nb cavity be increased? Theoretical SRF limits are poorly understood …

KEK&Cornell

Hc2Hc10 H

Strong vortex dissipation

Hc

Very weak dissipation - M

Superconducting Materials

Material Tc (K) Hc(0) [T]

Hc1(0) [T]

Hc2(0) [T]

(0) [nm]

Pb 7.2 0.08 na na 48Nb 9.2 0.2 0.17 0.4 40

Nb3Sn 18 0.54 0.05 30 85NbN 16.2 0.23 0.02 15 200MgB2 40 0.43 0.03 3.5 140YBCO 93 1.4 0.01 100 150

Very weak dissipation at H < Hc1 (Q = 1010-1011)Q drop due to vortex dissipation at H > Hc1

Nb has the highest lower critical field Hc1

Thermodynamic critical field Hc (surface barrier for vortices disappears)

5.0ln

4 20

1

cH

22

0cH

Nb Higher-Hc SC

Single vortex lineSingle vortex line

2

2

B

r

• Core region r < where (r) is suppressed

• Region of circulating supercurrents, r < .• Each vortex carries the flux quantum 0

Important lengths and Important lengths and fieldsfields

• Coherence length and magnetic (London) penetration depth λ

20

20

20

1 2,

22,5.0ln

4

ccc BBB

For clean Nb, Hc1 170 mT, Hc 180 mT

Surface barrier: How do vortices get in a Surface barrier: How do vortices get in a superconductor at H > Hsuperconductor at H > Hc1c1??

Two forces acting on the vortex at the surface:

- Meissner currents push the vortex in the bulk- Attraction of the vortex to its antivortex image pushes the vortex outside

H0

b

J

imageto ensure J = 0

])2(5.0[)( 010/

000 HHxHeHbG cvx

H = Hc1

H < Hc1

H > Hc1

H = Hc

x0

GThermodynamic potential G(x0) as a function of the position x0:

Meissner Image

Vortices have to overcome the surface barrier even at H > Hc1 (Bean & Livingston, 1964)

Surface barrier disappears only at the overheating field H = Hc > Hc1 at which the surface J becomes of the order of the depairing current density

Vortex in a thin film with d < Vortex in a thin film with d <

)(cos)(cosh

)(cos)(coshln

4),(

00

00

20

xxd

yyd

xxd

yydyxB

Vortex field in a film decays over the length d/ instead of (interaction with many images)

Vortex free energy as a function of the position x0

cxJ

dxdH

dxdxG 00

2

20

2

200

20

041

3238.0cos2ln

4)(

Self-energy Magnetic energy

Lorentzforce x0

London screening is weak so 22B = - 0(r)

G. Stejic, A. Gurevich,E. Kadyrov, D. Christen,R. Joynt, and D.C. Larbalestier, Phys. Rev. B49, 1274 (1994)

Enhanced lower critical field and Enhanced lower critical field and surface barrier in filmssurface barrier in films

07.0ln2

20

1 dd

Hc

d

H s 20

Use thin films with d < to enhance the lower critical field

Field at which the surface barrier disappears

Example: NbN ( = 5nm) film with d = 20 nm has Hc1 = 4.2T, and Hs = 6.37T,Much better than Hc = 0.18T for Nb

How one can get around small HHow one can get around small Hc1c1 in in SC cavities with TSC cavities with Tcc > 9.2K? > 9.2K? AG, Appl. Phys. Lett. 88,

012511 (2006)

Nb, Pb

Insulating layers

Higher-TcSC: NbN, Nb3Sn, etc

Higher Tc thin layers provide magnetic screening of the bulk SC cavity (Nb, Pb) without vortex penetration

For NbN films with d = 20 nm, the rf field can be as high as 4.2 T !

No open ends for the cavity geometry to prevent flux leaks in the insulating layers

Multilayer coating of SC cavities: alternating SC and insulating layers with d <

How many layers are needed for a complete screening?

ii H

Hd

NHdNH 00

00 ln)exp(

H0 = 2T

Hi = 50mT

d

Example: N Nb3Sn layers with d = 30nm0 = 65 nm and Hc1 = 2.4T

Peak rf field H0 = 2T < Hc1

Internal rf field Hi = 50 mT (high-Q regime)

N = (65/30)ln(40) = 8Nb

Strong reduction of the BCS resistance by Nb3Sn layers due to larger and shorter :

Tk

CTpk

nRBFB

s expln 00

4220

A minimalistic solutionA minimalistic solution

H0 = 324mTHi = 150mT

d

A Nb cavity coated by a single Nb3Snlayer of thickness d = 50nm and an insulator layer in between

If the Nb cavity can withstand Hi = 150mT,then the external field can be as high as

mTdHH i

7.323)65/50exp(150)/exp( 00

Lower critical field for the Nb3Sn layer with d = 50 nm and = 3nm: Hc1 = 1.4T is much higher than H0

A single layer coating more than doubles the breakdown field with no vortex penetration, enabling Eacc 100 MV/m

Global surface resistanceGlobal surface resistance

bLL

s ReReR /20

/2 )1(~

Nb3Sn coating of thickness L = 50 nm, RNb3Sn(2K) 0.1RNb

Nbs RR 3.0~

Screen the surface of Nb cavities using multilayers with lower surface resistance

layer bulk

Why is Nb3Sn on Nb cavity much better than Nb3Sn on Cu cavity?

Nb Cu

H(t) H(t)

Nb3Sn/Nb cavity is much better protected against small transverse field components than Nb3Sn/Cu cavity

vortices

Meissner state persists up to H < Hc1

(Nb)Meissner state is destroyed for small H < (d/w)Hc1

(Nb3Sn) << Hc1(Nb3Sn)

due to large demagnetization factor w/d 103-105

w

H

Vortex penetration in a screen

Jdu

du 02

0

20 tan

4

2

0

20

0

20

4,2 dqd

n

Dynamic equation for a vortex

Vortex flight time and energy release

For a 30 nm Nb3Sn film, 10-12 s, much shorter than the rf period 10-9 s

Maximum rf field at which the surface barrier disappears:

240 c

mHH

Nb3Sn coating more than doubles

vortex penetration field for Nb

Analytical thermal breakdown modelAnalytical thermal breakdown model

))(,()(

,/))(()(21

00

020

0

TTTTddTT

dTTTTRH

ss

T

T

smms

s

H(t)

T

Tm

T0

Ts

coolant

xd

For a general case of thermal quench, see Gurevich and Mints, Reviews of Modern Physics 59, 941 (1987),

0)()(21)( 2

xTRH

xTT

x ms

Equations for Tm and Ts

Kapitza thermal flux: q = (T,T0)(T – T0)

Thermal runaway due to exponential increase of Rs(T)

Maximum temperatureMaximum temperature

/1~,

])/exp([

~)(22

020 dRTTA

TTTHimm

mm

BCS + residual surface resistance Ri

is RTT

AR

exp

2

Since Tm – T0 << T0 even Hb, we may take and h at T = T0, and obtain the equation for H(Tm):

Thermal feedback stability for multilayers

Breakdown field as a function of the total overlayer thickness L

])1exp[()1()1()1(

,)exp()exp()1(

202

tttrtrs

tstrsteHH b

b

Here s = exp(-2L/), r = R0/Rb, = 0/b

• 50 nm Nb3Sn overlayer triples Q at low field• 100 nm overlayer more than doubles the thermal breakdown field

Conclusions:• Multilayer S-I-S-I-S coating could make it possible to take advantage

of superconductors with much higher Hc, than those for Nb without the penalty of lower Hc1

• Strong increase of Hc1 in films allows using rf fields > Hc of Nb, but lower than those at which flux penetration in grain boundaries may become a problem

• Strong reduction of BCS resistance because of using SC layers with higher (Nb3Sn, NbN, etc)

• The significant performance gain may justify the extra cost.