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Thermal Boundary Resistance
Enzo Palmieri1,2, A.A. Rossi1, R. Vaglio3
1 Legnaro National Laboratories of the INFN2 Università degli Studi di Padova3 Università degli Studi di Napoli
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RS = RBCS+ RRes
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0.2 0.3 0.4 0.5 0.6
1E-6
1E-5
1E-4
RS Nb 122 After ATM Annealing
f(T) @ 2MV/m FitRs1 (User) Fit of Sheet1 Rs
RS [
]
1/T [K-1]
Model FitRs1 (User)
Equation C+(x*A*exp(-B*x))/((1+exp(-B*x))^2)
Reduced Chi-Sqr 3.55369E-13
Adj. R-Square 0.99425
Value Standard Error
Rs A 0.00367 4.32631E-4
Rs B 14.47994 0.51509
Rs C 1.22522E-6 3.56914E-7
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Qo
Eacc [Mv/m]
5 10 20 25
Cons
tant
fiel
d
T = 4.2 K
T = 1.8 KCo
nsta
nt p
ower
108
109
1010
1011
120 m
W
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Constant W means that, apart Eacc only T is changing
Constant Eacc means that both T and W are changing
Q is function of 3 variables (T, Eacc, W), and only 2 of them are independent
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0.2 0.3 0.4 0.5 0.61E-7
1E-6
1E-5
RS Nb 122 After 3rd UHV Annealing
100 mW R
s fit
Rs
[]
1/T [K-1]
Model Rs (User)
Equation C+(x*A*exp(-B*x))/((1+exp(-B*x))^2)
Reduced Chi-Sqr 7.85399E-15
Adj. R-Square 0.99727
Value Standard Error
Rs
A 0.00265 2.52241E-4
B 17.57752 0.36563
C 7.37002E-8 3.96425E-8
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If we cooled the cavity in 3He instead then in 4He, should we wait a different RRES?
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.. in other words, RRES depends on heat transfer to Liquid He and not only on Nb material?
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Rs vs 1/T (termometro Ge)
0,25 0,30 0,35 0,40 0,45 0,50 0,551E-7
1E-6
1E-5
25 mW 50 mW 75 mW 100 mW 125 mW 150 mW 175 mW 200 mW 400 mW 600 mW 1000mWR
s [
]
1/T [K-1]
Termometro Ge
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You have the choice:
• One curve of RS(T) at constant Eacc
• A family of curves of RS(T) at constant W
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R =RS (T) and Q=Q (Eacc),
so we can
join the 2 curves into 1 graph
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0 2 4 6 8 10 12 14107
108
109
@ 4.2K @ 1.8K 25 mW 50 mW 75 mW 100 mW 125 mW 150 mW 175 mW 200 mW 400 mW 600 mW 1000mW
Q
Eacc
[MV/m]
Nb117
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Rs vs 1/T vs P (Cernox X63398)
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Masked data
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Rs vs 1/T [P=100mW]
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.6010-7
10-6
10-5
Termometro: Cernox X62101
Rs(P=100mW)
1/T
Rs
[]
1/T [K-1]
1/T
At -point:
Rs = 1.350810-7
T = 0.039K
{
Nb123
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Kapitza conductance
=
This quantity has a strong Tn temperature dependence with n varying betwen 2 and 4
NbRF
field
s h𝐾 0
Liquid He
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Whenever we neglect the jump at Tl, we
extract a false value of the strong
coupling factor S
𝑅𝐵𝐶𝑆=𝐴𝑇𝑒− 𝒔2𝑇𝐶
𝑇
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)(2
exp)(00
2
0 TT
sT
T
ATTR C
BCS
000
2
0 12
exp)(T
T
T
sT
T
ATTR C
BCS
00
2
0 2exp)(
T
sT
T
ATR C
BCS
𝒔𝒎𝒆𝒂𝒔=𝒔 (𝟏−∆𝑻𝑻 𝟎
)
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What often we forget is that…
RS = RBCS + RRes
is an approximation
valid only at zero-field
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000
2
0 12
exp)(T
T
T
sT
T
ATTR C
BCS
) exp[
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RS (T+ DT) = f(DT/T2) RBCS + RRes
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0 2 4 6 8 10 12 14107
108
109
@ 4.2K @ 1.8K 25 mW 50 mW 75 mW 100 mW 125 mW 150 mW 175 mW 200 mW 400 mW 600 mW 1000mW
Q
Eacc
[MV/m]
Nb117
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0 2 4 6 8 10 12 14107
108
109
@ 4.2K @ 1.8K 25 mW 50 mW 75 mW 100 mW 125 mW 150 mW 175 mW 200 mW 400 mW 600 mW 1000mW
Q
Eacc
[MV/m]
Nb117
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the Q-factor decreases linearly with W,
but at a certain point it becomes almost
constant!
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The critical power where the losses change slope do correspond to the He boiling nucleation?
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0 1 2 3 4 5 6 7 8 9 10106
107
108
109
Nb 122 After ATM Annealing
4,2K f(T) 1,8K
Q
EAcc
[MV/m]
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Is it possible that
He-II will have memory of the
boiling nucleation of He-I ?
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1.8 K is very close to T ,l
so at 1.8K rn is ~34%