Transcript RF breakdown in multilayer coatings: a possibility to

RF breakdown in multilayer
coatings: a possibility to
break the Nb monopoly
Alex Gurevich
National 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.
Motivation
• Why Nb?
BCS surface resistance: Rs  4exp (-/kBT)
Minimum Rs implies maximum , that is,
maximum Tc 1.87/kB and minimum
London penetration depth 
Nb3Sn has maximum Tc and minimum  to
provide the optimum Rs
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
Background
KEK&Cornell
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 …
Superconducting Materials
Very weak
dissipation
-M
Very weak dissipation
at H < Hc1 (Q = 1010-1011)
Q drop due to vortex
dissipation at H > Hc1
Strong vortex
dissipation
0
Hc1 Hc
Hc2 H
Higher-Hc SC
Nb
Material
Tc (K)
Hc(0)
[T]
Hc1(0)
[T]
Hc2(0)
[T]
(0)
[nm]
Pb
7.2
0.08
na
na
48
Nb
9.2
0.2
0.17
0.4
40
Nb3Sn
18
0.54
0.05
30
85
NbN
16.2
0.23
0.02
15
200
MgB2
40
0.43
0.03
3.5
140
YBCO
93
1.4
0.01
100
150
Nb has the highest
lower critical field Hc1
H c1 

0  
ln

0
.
5


2 
4  

Thermodynamic critical
field Hc (surface barrier
for vortices disappears)
0
Hc 
2 2
2
Single vortex line
• Core region r < 
where (r) is suppressed
B
• Region of circulating
supercurrents, r < .

2


r
• Each vortex carries the
flux quantum 0
Important lengths and fields
• Coherence length  and magnetic (London) penetration depth λ
Bc1 

0  

,
ln

0
.
5
2 
4  

Bc 
0
,
2 2
Bc 2 
For clean Nb, Hc1  170 mT, Hc  180 mT
0
2 2
Surface barrier: How do vortices get in a
superconductor at H > Hc1?
J
Two forces acting on the vortex at the surface:
H0
image
to ensure
J = 0
G
- Meissner currents push the vortex in the bulk
- Attraction of the vortex to its antivortex image pushes
the vortex outside
b
Thermodynamic potential G(x0) as a function of the position x0:

G(b)  0[H0e x0 /   0.5Hv (2 x0 )  Hc1  H0 ]
Meissner
H < Hc1
H = Hc1
H > Hc1
H = Hc
x0
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 < 
London screening is weak so 22B = - 0(r)
B ( x, y ) 
0
42




cosh ( y  y0 )  cos ( x  x0 )
d
d
ln
cosh ( y  y0 )  cos ( x  x0 )
d
d
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
  
G ( x0 )   0 
 4 
2
  2d
 H0d 2  4 x02  J0 x0
x0 
1  2  
cos
  0.38 
ln
2 
d 
d 
c
  
 32 
Self-energy
Magnetic
energy
G. Stejic, A. Gurevich,
E. Kadyrov, D. Christen,
R. Joynt, and D.C.
Larbalestier,
Phys. Rev. B49, 1274 (1994)
Lorentz
force  x0
Enhanced lower critical field and
surface barrier in films
Use thin films with d <  to enhance
the lower critical field
H c1 

20  d
ln

0
.
07


2 
d  

Field at which the surface barrier
disappears
0
Hs 
2d
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 Hc1 in SC
cavities with Tc > 9.2K? AG, Appl. Phys. Lett. 88, 012511 (2006)
Higher-TcSC: NbN,
Nb3Sn, etc
Multilayer coating of SC
cavities: alternating SC and
insulating layers with d < 
Higher Tc thin layers provide
magnetic screening of the
bulk SC cavity (Nb, Pb)
without vortex penetration
Nb, Pb
For NbN films with d = 20
nm, the rf field can be as
high as 4.2 T !
Insulating
layers
No open ends for the cavity
geometry to prevent flux
leaks in the insulating layers
How many layers are needed for a
complete screening?
H0 = 2T
Hi = 50mT
Example: N Nb3Sn layers with d = 30nm
0 = 65 nm and Hc1 = 2.4T
Peak rf field H0 = 2T < Hc1
Internal rf field Hi = 50 mT (high-Q regime)
H 0 exp(
dN
0
)  Hi

N
0
d
ln
H0
Hi
Nb
N = (65/30)ln(40) = 8
d
Strong reduction of the BCS resistance by Nb3Sn layers due to larger
 and shorter :

02 24 n0    
 



Rs 
ln

C
exp



0


k BTpF
   

 k BT 
A minimalistic solution
H0 = 324mT
Hi = 150mT
A Nb cavity coated by a single Nb3Sn
layer 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
H 0  H i exp(d / 0 ) 
d
150exp(50 / 65)  323.7m T
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 resistance
~
2 L / 
2 L / 
Rs  (1  e
) R0  e
Rb
layer
bulk
Nb3Sn coating of thickness L = 50 nm, RNb3Sn(2K)  0.1RNb
~
Rs  0.3RNb
Screen the surface of Nb cavities using multilayers with lower
surface resistance
Why is Nb3Sn on Nb cavity much better
than Nb3Sn on Cu cavity?
vortices
H(t)
H(t)
H
Nb
Cu
w
Nb3Sn/Nb cavity is much better protected against small transverse
field components than Nb3Sn/Cu cavity
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
Vortex penetration in a screen
Dynamic equation for a vortex
02
u
u 
tan  0 J
2
40 d
d
Vortex flight time and energy release

2d02
n
,
02d
q0 
402
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:
0
Hc
Hm 

4
2
Nb3Sn coating more than doubles
vortex penetration field for Nb
Analytical thermal breakdown model
T

T 1 2
 (T )
 H  Rs (Tm ) ( x )  0
x
x 2
Tm
H(t)
coolant
Ts
T0
d
Equations for Tm and Ts
x
Thermal runaway due to
exponential increase of Rs(T)
Kapitza thermal flux: q = (T,T0)(T – T0)
1 2
H 0 Rs (Tm )   (T0 )(Tm  Ts ) / d ,
2
Ts
For a general case of thermal quench, see
Gurevich and Mints,
Reviews of Modern Physics 59, 941 (1987),
  (T )dT  d (T , T )(T
s
T0
0
s
 T0 )
Maximum temperature
BCS + residual surface resistance Ri
A 2
 
Rs 
exp    Ri
T
 T
Since Tm – T0 << T0 even Hb, we may
take  and h at T = T0, and obtain the
equation for H(Tm):
~
2
T
(
T

T
)

m
m
0
H 02 
,
2
[ A exp( / Tm )  Tm Ri ]
~ 

1  d / 
Thermal feedback stability for multilayers
Breakdown field as a function of the
total overlayer thickness L
teHb20
H 
,
(1  s )r exp(t )  s exp(t )
2
b
r (t  1)
s
r (t  1)  (1  t ) exp[(1   )t ]
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.