Transcript Diapositiva 1 - LNL-INFN

The International Workshop on Thin films and new ideas
for pushing the limits of RF Superconductivity
Q-drop:
Enzo Palmieri
ISTITUTO NAZIONALE DI FISICA NUCLEARE
Laboratori Nazionali di Legnaro
&
Padua University, Science Faculty, Material Science Dept
Work supported by the European Community Research Infrastructure Activity
under the FP6 “Structuring the European Research Area” programme
(CARE, contract number RII3 CT-2003- 506395)
Low field Q-Slope
Medium field Q-Slope
High field Q-drop
11
Q0
10
10
10
2K
1,8 K
1,6 K
9
10
0
10
20
30
40
Eacc [MV/m]
Best 9-cell cavity result (after electro-polishing)
(Courtesy D. Proch)
Low field Q-Slope
11
Q0
10
10
10
2K
1,8 K
1,6 K
9
10
0
10
20
Eacc [MV/m]
30
40
Nb/Cu sputtered
cavity at CERN
Courtesy C. Benvenuti et al
Since first cavities were baked in the cryostat at ~150°C for ~48 hours
the low field Q-slope was also reported for bulk Nb cavities
Cavity spun at LNL and treated/measured at KEK
Courtesy
G. Ciovati
(Courtesy G. Bisoffi)
Presented at the 9-th RF Superconductivity Workshop, Santa Fè, NM, 1999
Renzo Parodi - RF SUPERCONDUCTIVITY AT INFN_GENOA
Typical plot of Qo vs Eacc for cavities treated by Dry Oxidation
of the surface after a medium temperature annealing
Let us suppose that:
on bulk niobium (SC 2 ) we put an overlayer of a different superconductor (SC 1)
SC 2
SC 1
Vacuum
l1
Hz
l2
a
a is the tickness of the SC 1
l2 is the penetration depth of the SC 2
l1 is the penetration depth of the SC 1
THE ELECTROMAGNETIC RESPONSE OF A METAL
x
For a semi-infinite conductor that
E
H
fills the +
metal
z
x
half-space and
has a plane surface at
x=0
Vacuum
y
H(x) = H(0) e (ikx-wt)
the Surface Impedance is defined as:
E ( 0)
E
( 0)
4 y
y
Z 

c H ( 0)
 J y( x )dx

0
z
SC 2
SC 1
l1
l2
a
Vacuum
Hz
Two Superconductors:
SC 2 + SC 1
SC 2
SC 1
l1
l2
a
Vacuum
Hz



l a
ll 
J
(
x
)
dx

J
(
x
)
dx
c

|

H
H


z
z |a 
0
0
a





4  E 0  
z
E 0 
y
y


a
1
|
a
a l
c H z( 0 )
c
H
(
0
)
 .
.( 1  e 1 )  .
e l1
Z
4 E y( 0 )
4 E y( 0 )
||
1
Z
1
Z

1
Z1
.( 1  e
Q  Q(1 1  e
a l
1
)
a l 1
1
Z2
e
a l
1
)  Q 2e
a l 1
SC 2
SC 1
l1
l2
Vacuum
For a “2 Superconductor system”
Hz
1 10
10
a
Q2
Q
Q( x)
Q
91
1 10
5
10
l120
/a
15
x
Q  Q(1 1  e
a l 1
)  Q 2e
a l 1
 Q1 ( Q 2  Q1 )e
 Q1  Q e
.
a l 1
a l 1
Medium field Q-Slope
11
Q0
10
10
10
2K
1,8 K
1,6 K
9
10
0
10
20
Eacc [MV/m]
30
40
SC 2
SC 1
l1
l2
Vacuum
Hz
Q  Q1 ( Q 2  Q1 )e
a l 1
1 10
10
Q2
a
Q( x)
Q
91
1 10
5
10
x
15
20
l1/a
An hypotesis:
Gap and Penetration depth depends on magnetic field
( B )   0  kB
l
l( B )  l0 
B  ...  l0  B
B
0
SC 2
SC 1
l1
l2
Vacuum
( b )   0  kb
Hz
Q 2  Q 0,2e
b  B / BC
k 2b
l( b )  l0  b
a
1 10
10
Q2
Q( x)
Q9 1
1 10
5
10
15
x
(eQk22b Q
)e
QQ
 Q1Q
(1Q
Q
1
2
1
a
a
 l 1
( l 1b )
20
l1/a

Q1 )e
Kenzo6
1E11
Q0
Q  Q1 ( Q 2e
k 2b
a

( l 1b )
Data: Foglio1_B
Model: Palmieri5
1E10
Chi^2
R^2
= 2.1868E17
= 0.99494
P1
P2
P3
P4
P5
25826656840.20985
±-75222961773.57346
±-0.02683
±0.00036
1E-14 ±-2.97457
±0.04402
1E9
0
5
10
15
20
25
30
35
Eacc [MV/m]
40
Q  Q1 ( Q 2e
= Q (* 1  e
1
1 10
Why Q increases
q1( B)
with field?
a

( l 1b )
k 2b

Q1 )e
) + Q2 * e
a

( l 1b )
k 2b
e

a

( l 1b )
11
Q2
Q2e-k2b
q2( B)
( B)
TheqTmore
l1
Q1
increases
vs field
Q2
Q2 exp(  k2  B)
Q1
t
The Q1
more
SC2 ( low
 ( Q2 Q1)  exp

 c 
losses) is involved
1 10
10
5
10
15
20
25
B
30
35
40
45
b
50
Q  Q1 ( Q 2e
= Q (* 1  e
1
1.1 10

121 10
a

( l 1b )
k 2b

Q1 )e
) + Q2 * e
a

( l 1b )
k 2b
e

a

( l 1b )
13
The ticker is SC 1, the smoother is the Q-rise
qT ( B  0.1)
qT ( B  0.5)
qT ( B  1)
a/l
qT ( B  1.5)0
Q2
qT ( B  2)
O
Q1
0.1
Q2
1
Q2 exp(  k2  B)
10
1 10
12
  t Q1

 c 
Q1 ( Q2 Q1)  exp
11
1 10 1 1011
0.04
2
4
6
8
10
B
12
14
16
18
b b
20
20
( B )   0  kB
?
 = 0 - pfvs
I.I. Kulik, V. Palmieri, "THEORY OF DEGRADATION AND NON LINEAR
EFFECTS IN Nb-COATED SUPERCONDUCTING CAVITIES",
Proceedings of the Eight Workshop on RF Supercoductivity, Abano,
Italy, October 1997, V. Palmieri, A. Lombardi eds.
Special Issue of Particle Accelerators, Vol. 60,(1998)p.257-264
The Ginzburg-Landau result
= 0 (1 – H2/HC2)
does not apply!!!
This formula has done a lot of
= 0 (1 – H2/HC2)
damage to our community for
the understanding of the Q-Slope
R.H. White and M. Tinkham, Magnetic-Field Dependence of Microwave
Absorbtion and Energy gap in Superconducting Films, Phys Rev, vol
136, 1A, (1964), p. A203
“…..The qualitative features of /0 dependences like (1 – h2) and (1-h2)1/2
arevery different from those of the experimental absorption curves
reported here …. due to the disagreement between these results and
previous theory and experiment, it must be concluded that the above
procedure for determining an effective energy gap parameter as a function
of H is too naive.”
Y. Nambu, S.F. Tuan, Phys, Rev. Lett. 11, 119 (1963); Phys.Rev.133, A1, (1964)
“…Electrons moving parallel to the surface play a special role: since the magnetic
filed will confine such an electron and the one with which it is paired to opposite
surfaces of the film, they contribute little to the superconductivity pairing energy…”
This relation goes back to first principles
 = 0 - pfvs
It means to take into account the supercurrent!
If for Superconducting Magnets the fundamental and
indipendent parameters are 3: TC, HC and JC, …..
why for Superconducting cavities, JC disappeared?
Is 40 MV/m (1600 G) a field not strong enough?
REVIEWS OF MODERN PHYSICS
VOLUME 34, NUMBER 4
OCTOBER 1962
Critical Fields and Currents in Superconductors*
JOHN BARDEEN
UNIVERSITY OF ILLINOIS, Urbana, Illinois
…
II.THERMODYNAMIC RELATIONS
To discuss the thermodynamics of a superconductor in a magnetic field or with
current flow, it is most convenient to take the external field H and the
superfluid velocity vs as independent variables. ……
The displacement of the pairs causes an increase in free energy of the system
which may be expressed simply in terms of Js……
APPENDIX B. DIRECT CALCULATION OF CHANGE OF GAP WITH CURRENT
... In the low temperature limit, there are no excitations formed and thus no
change in D until the velocity vs reaches the value for which it is favorable to
form pairs of excitations, corresponding to transfer of an electron from one side
of the Fermi sea to the other.This criterion is (depairing condition)
1 pf
1 pf
m( m  v s )  m( m  v s )  2
2
2
2
2
or
p f  2
RBCS  e


kT
e
p f v s B l0 * e v F n 12

(
)
kT
KT
ns

pv
 0 f s
kT
*
kT
l 12
pf v s B l0 * e v F

( cot gh )
kT
KT
0
*
*
*
pf v s B l0 * e v F
l 12

( cot gh )
kT
KT
0
*
*
The parasitic term PfVs is neglectable at high value of
the pure bulk Nb case
l
It becomes important at low
0
- thin film case
- contaminated surface after low temp baking
l
0
Courtesy C. Benvenuti et a
l
0
Is a key parameter; low values give:
- high Q
- higher slope
For film coated cavities there is no hope to get rid of the slope, unless
RRR is increased, but in this case Q values will be lower than the actual
High field Q-drop
11
10
Q0
10
10
2K
1,8 K
1,6 K
9
10
0
10
20
Eacc [MV/m]
30
40
In local electrodynamics of superconductivity,
j = j1+j2
vs
Where J is the Meissner current
j 1  n s ev s( 1  2 )
vc
At small supercurrent
j 1  n s ev s
2
1
but at larger Vs, GL theory foresees a deparing effect by the current

Js
Vm
Vs
ns
Vs
Vs
Over Vm the superconducting state become unstable
Conclusions:
• Low field - The hypotesis of an overlayer explains the Q rise
Q  Q(1 1  e
a l 1
)  Q 2e
a l 1
• Medium field – The gap decrease linearly vs field
  0 – pf vs
This effect is neglectable for high
l
0
but is felt when
l
0
is reduced
Film coated cavities: no hope to get rid of the slope, unless RRR is increased, but
in this case Q values will be lower than the actual
• High
field – The gap closes at VC, but js start decreasing at
Vm< Vc. Between Vm and VC, there is instability