Transcript Slide 1

CERN Accelerator School
Superconductivity for Accelerators
Case Study 5 – Case Study 6
Case Study Summary
Q5.1&5.2: f change with T
Why does the frequency change when cooling down?
Is the size changing? – no,
the curve is flat below 50 K.
But a varying penetration depth also is an effective change of
cavity size. This thickness becomes smaller with decreasing T, the
cavity becomes smaller – this consistent with the increase
frequency.
All 3 groups had that right! Congrats!
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Q5.1&5.2: f change with T
London penetration depth: 𝜆𝐿 =
𝑚
,
𝜇0 𝑛𝑠 𝑒 2
𝑛𝑠 ∝ 1 −
𝑇 4
𝑇𝑐
1
𝜆𝐿 𝑇 = 𝜆𝐿 0 ∙ 1 −
𝑑𝜆
𝑑𝑌
=
𝑑𝜆
𝑑𝑓
∙
𝑑𝑓
𝑑𝑌
=
−𝐺
𝜋𝜇0 𝑓 2
−
𝑇 4 2
𝑇𝑐
= 𝜆𝐿 0 ∙ 𝑌; 𝜆𝐿 0 =
𝑑𝜆
𝑑𝑌
∙ −1.6 kHz , so 𝜆𝐿 0 = 65 nm.
Why not 243mm?
Because 𝑇 → 𝑇𝑐 corresponds
to 𝑌 → ∞, so the point ∆𝑓 = 0
has no absolute meaning. Only
the slope
𝑑𝑓
𝑑𝑌
𝑇 → 𝑇𝑐
has.
Larger than bulk number (36 nm) since 𝜆 𝑙 = 𝜆𝐿 1 +
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𝜉0
𝑙
Case study Summary -- Superconducting RF
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This is used in real life
Junginger et al.: “RF Characterization of Superconducting Samples”,
https://cds.cern.ch/record/1233500
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Q5.3,5.4&5.5: Q-switch – hot spot
What happens here?
*
Because locally the film is in bad
thermal contact with copper, it is
not enough cooled and its surface
resistance increases.
Size of the defect?
Stored energy: 𝑈 =
𝑉𝑎𝑐𝑐 2
;
𝜔∙ 𝑅 𝑄
3 ∙ 109
1.5 ∙ 109
Size (assuming 𝑃 =
MV
m
assuming 𝐿𝑎𝑐𝑐 = 0.2 m: 34 mJ
Power loss into the (small) defect: 𝑃 =
𝑅𝑠
2
1.1
𝜔𝑈
:
𝑄
𝑅𝑠 2
2
𝐻 𝑑𝐴 ~ 𝐻 𝐴:
2
93 mW
𝐴 = 6 mm2 .
If observed at 7.3 cm, one would have deduced a slightly smaller size.
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Characterizing cavities
•
Resonance frequency
•
Transit time factor
field varies while particle is traversing the gap
Circuit definition
•
Linac definition
Shunt impedance
gap voltage – power relation
•
Q factor
•
R/Q
independent of losses – only geometry!
•
loss factor
23-Sept-2010
CAS Varna/Bulgaria 2010- RF Cavities
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Q5.6 – Bulk Nb Cavity
After 40 µm etching
The cavity is still
tuned, i.e. SC
After 150 µm etching
MP
Barrier
Typical behaviour of quench : when
cavity becomes norm. cond. The
frequency changes and the power
cannot go in any more => the cavity
cools down and becomes SC again,
powers go in, etc…
Regarding the previous questions, and the field distribution in these cavities, how can
you explain the multiple observed Q-switches ?
Because of the size of the cavity there is a large variation of the magnetic field on the surface from the top to the bottom of the
cavity. If the surface is not well etched and present a distribution of poor superconducting small areas, the defect situated close
to the high magnetic field area will transit first, then the location of the “hot spot” will progressively get closer to the high
electrical field part.
Note : first curve (red dots) was better until the first Q-Switch @ ~ 4 MV/m. We do not know why. It can be due to a slight
difference in the He temp., or the ignition of a field emitter (if X-rays a measured simultaneously)..
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Q5.7 – Modelling grain boundary
The influence of the lateral dimensions of the defect? Its height ?
A step induces an increase of the local field. When H increases (shape
factor ↑) one reaches a “saturation”. The lateral dimension plays a minor
role.
The influence of the curvature radius?
The smaller the radius of curvature, the higher the field enhancement
factor.
The behavior at high field?
In the saturation region, at high field, the field enhancement factor is still
increases, but not so rapidly. It depends only on the shape factor H/R.
What happens if the defect is a hole instead of bump (𝐹 ≪ 𝐿) ?
In this model, if the “hole” becomes too narrow, the field cannot enter it
⇒ no field enhancement factor
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Q5.8 – more realistic dimensions, 2D model
Do these calculation change the conclusion from the
precedent simplified model?
The curvature radius indeed plays a major role. The lateral
dimension plays a minor role in the field enhancement factor,
but impacts the dissipation.
What prediction can be done about the thermal
breakdown of the cavity?
The breakdown is solely due to the dramatic heating of the
defect that suddenly exceeds the overall dissipation.
Why is this model underestimating the field
enhancement factor and overestimating the thermal
dissipations?
Because it is a 2D model: the defect is treated like if it was an
infinite wall. In case of finite dimension the shape factor gets
higher, inversely the dissipation would be reduced if coming
only from a finite obstacle.
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Comment these figures:
If the dissipation is correctly evacuated to the helium bath, it
is possible to maintain SC state up to a certain field, but a
slight increase of field (0.1 mT induces thermal runaway);
The amount of power that can be transferred to the bath is
limited by interface transfer;
A higher field can be reached with a good thermal transfer.
What will happen if we introduce thermal variation of κ
and/or RS?
k tends to increase with T, but this effect will be compensated
by the increase of RS with T.
What happens if we increase the purity of Nb? Why?
Increase of the purity of Nb allows to reduce the interstitial
content which acts as scattering centers for (thermal)
conduction electrons. It increases the thermal conductivity
and allows to better transfer the dissipated power, hence to get
higher field for an “equivalent” defect.
Comment: the quench happens on the defect edge both because
of morphologic field enhancement and temperature
enhancement: thermomagnetic quench at H<HC and T<TC
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Increasing Kapiza conductance
Q5.9: Thermal – Kapitza Resistance
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Q6.1, Q6.2&Q6.3 – cavity geometry
2
Total energy: 𝐸 = 𝑚𝑐 𝛾 = 𝑚𝑐
2
1
1−𝛽2
= 𝑚𝑐 2 + 𝐸𝑘𝑖𝑛
𝛽 = .47, 𝑚𝑐 2 = 938.272 MeV, ⇒ 𝐸 = 1.063 GeV, 𝐸𝑘𝑖𝑛 = 124.7 MeV
Cavity length: π-mode: particle travels 2𝐿 in time 1 𝑓:
𝛽𝑐 = 2𝐿𝑓, 𝜆𝑓 = 𝑐:
⇒𝐿=
𝛽𝜆
2
= 100 mm, 𝐿𝑎𝑐𝑐 = 0.5 m.
Parameters in the above table are purely geometric.
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Q6.4 – BCS resistance
𝑅𝐵𝐶𝑆 = 2 ∙ 10−4 Ω
K
𝑇
17.67 K
2
𝑓
− 𝑇
𝒆
1.5 GHz
dominating
f=704.4 MHz
Tc(Nb)=9.2 K
Rbcs [nΩ]
10000
∆𝑓
T [K]
RBCS [nΩ]
1000
4.3
362.1
100
4
266.2
3
61.0
2
3.2
4.3K
10
∆T
1
1
2
3
Tc/T [1/K]
𝑅𝐵𝐶𝑆 (4.3 K)
𝑅𝐵𝐶𝑆 (2 K)
4
2K
5
> 50! It’s worth
it to go to lower T.
Cf. P. Lebrun’s lecture
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Q6.5 – unloaded Q: 𝑄0
Given 𝑅𝐵𝐶𝑆 = 3.2 nΩ & geometry factor 𝐺 = 161 Ω:
𝑄0 =
𝐺
𝑅𝐵𝐶𝑆
= 5 ∙ 1010
For real cavities, 𝑅 = 𝑅𝐵𝐶𝑆 + 𝑅𝑟𝑒𝑠 . 𝑅𝑟𝑒𝑠 includes effects from
Trapped magnetic field
Normal conducting precipitates
Grain boundaries
Interface losses
Subgap states
... and some mysterious other things
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Q6.6,Q6.7 & Q6.8 – gradient, wall loss,
max. gradient
Accelerating gradient:
𝑅
𝑄
=
𝑉𝑎𝑐𝑐 2
𝜔𝑈
=
𝐸𝑎𝑐𝑐 𝐿𝑎𝑐𝑐 2
,
𝜔𝑈
⇒ 𝐸𝑎𝑐𝑐 = 14.1
Dissipated power: 𝑄0 =
𝜔𝑈
,
𝑃
MV
m
⇒ 𝑃 = 5.7 W.
190 mT ⇒ equivalent max. gradient of 𝐸𝑎𝑐𝑐,𝑚𝑎𝑥 ~34
14.1
MV
m
< 34
MV
m
MV
m
: we’re OK.
Magnetic quench most likely near the equator.
Magnetic quench can be caused by thermal dissipation on
defects, residual resistance, …
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Q6.6,Q6.7 & Q6.8 – gradient, wall loss,
max. gradient
Accelerating gradient:
𝑅
𝑄
=
𝑉𝑎𝑐𝑐 2
2𝜔𝑈
=
𝐸𝑎𝑐𝑐 𝐿𝑎𝑐𝑐 2
,
2𝜔𝑈
⇒ 𝐸𝑎𝑐𝑐 = 20
Dissipated power: 𝑄0 =
𝜔𝑈
,
𝑃
MV
m
⇒ 𝑃 = 5.7 W.
190 mT ⇒ equivalent max. gradient of 𝐸𝑎𝑐𝑐,𝑚𝑎𝑥 ~34
20
MV
m
< 34
MV
m
MV
m
: we’re OK.
Magnetic quench most likely near the equator.
Magnetic quench can be caused by thermal dissipation on
defects, residual resistance, …
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Q6.9: Input power and external Q,
bandwidth
𝑃𝑒𝑥𝑡 ≫ 𝑃0 - very strong coupling! (
𝑃𝑒𝑥𝑡
𝑃0
=
Ptot  Pexternal  P0
100 kW ≫ 5.7 W
𝑄0
𝑄𝑒𝑥𝑡
= 𝛽)
Ptot Pexternal
P

 0
U
U
U
1
1

QL Qext

1
Q0
Bandwidth: ∆𝑓 =
𝑓
𝑄
from 𝑄0 : 14 mHz!!!
from 𝑄𝑒𝑥𝑡 : 245 Hz
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Intensity
2.88 ∙ 106 ≪ 5 ∙ 1010
Q0
QL
f
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Cavity equivalent circuit
Simplification: single mode
IG
IB
Vacc
P
Z
Generator
R
:
C

L
coupling factor
Cavity
R: Shunt impedance
L
C
R
Beam
L=R/(Q0)
C=Q/(R0)
: R-upon-Q
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Q6.10: Tuners
Effects on cavity resonance requiring tuning:

Static detuning (mechanical perturbations)

Quasi-static detuning (He bath pressure / temperature drift)

Dynamic detuning (microphonics, Lorentz force detuning)
Tuning Mechanism

Electro-magnetic coupling

Mechanical action on the cavity
Types of Tuners

Slow tuner (mechanical, motor driven)

Fast Tuner (mechanical, PTZ or magnetostrictive)
Examples

INFN/DESY blade tuner with piezoactuators

CEBAF Renascence tuner

KEK slide jack tuner

KEK coaxial ball screw tuner
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Q6.11: NC defects
Assume that some normal conducting material is inside the
cavity;
i) what are the effects on gradient and Q?
Joule heating will enhance locally the surface temperature, which in turn
can enhance the 𝑅𝑠 of the neighboring Nb and lead to a thermal
breakdown (transition of the SC). If the defect is small and the thermal
conductivity of the Nb is good, it can be stabilized.
ii) How can you calculate the effects?
Forget about it: not enough data…
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Thanks
There was not one single right answer – the approach and the
thoughts were the goal.
Claire put in some inconsistencies and ambiguities in there
on purpose – you spotted them all!
There are a lot mysterious things happening with SC RF –
stay curious and try things out. This should lead the way to
“better” cavities & systems.
Thanks! (Also in the name of Claire) You did very well!
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Annex – from the case study introduction: Cases 5 and 6
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CASE STUDY 5
Courtesies: M. Desmon, P. Bosland, J. Plouin, S. Calatroni
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Thin Film Niobium: penetration depth
Frequency shift during cooldown. Linear representation is given in function of Y, where Y
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= (1-(T/TC)4)-1/2
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Thin Film Niobium: local defect
*
Q3 : explain qualitatively the experimental observations.
Q4 : deduce the surface of the defect. (For simplicity, one will take the field repartition and dimension from
the cavity shown on the right. Note the actual field Bpeak is proportional to Eacc (Bpeak/Eacc~2))
Q5: If the hot spot had been observed 7.3 cm from the equator, what conclusion could you draw from the
experimental data ?
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Bulk Niobium: local defects
After 40 µm etching
After 150 µm etching
Q6 : regarding the previous questions, and the field distribution in these
cavities, how can you explain the multiple observed Q-switches ?
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Bulk Niobium: local defects: steps @ GB
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Bulk Niobium: steps @ GB
2D RF model
Q7. What conclusion can we draw about:
•The influence of the lateral dimensions of the defect?
Its height ?
•The influence of the curvature radius?
•The behavior at high field?
•What happens if the defect is a hole instead of bump
(F<<L) ?
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Steps @ GB w. realistic
dimension
RF only
Q8.- do these calculation change the conclusion from the precedent simplified model ?
- what prediction can be done about the thermal breakdown of the cavity?
- why is this model underestimating the field enhancement factor and overestimating the thermal dissipations?
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Steps @ GB w. realistic
dimension
RF + thermal
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Case study 5
RF cavities: superconductivity and thin films, local
defect…
Q9 Comment these figures.
• What will happen if we introduce
thermal variation of k.
• What happen if we increase the
purity of Nb ?, why ?
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CASE STUDY 6
Courtesies: J. Plouin, D. Reschke
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Case study 6
RF test and properties of a superconducting cavity
Basic parameters of a superconducting accelerator cavity for
proton acceleration
The cavity is operated in its π-mode and has 5 cells.
What is the necessary energy of the protons for β = 0,47?
Please give the relation between β , λ and L. L is the distance between
two neighboring cells (see sketch above)
Calculate the value of L and Lacc.
Is it necessary to know the material of the cavity in order to calculate
the parameters given in the table? Please briefly explain your answer.
g
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Case study 6
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Case study 6
In operation a stored energy of 65 J was measured inside the
cavity.
What is the corresponding accelerating gradient Eacc?
What is the dissipated power in the cavity walls (in cw operation)?
If we take 190mT as the critical magnetic RF surface field at
2K, what is the maximum gradient, which can be achieved in
this cavity?
At which surface area inside the cavity do you expect the magnetic
quench (qualitatively)?
Verify that the calculated gradient in question 6 is lower than
in question 7.
Please explain qualitatively which phenomena can limit the
experimental achieved gradient.
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Case study 6
Please remember that the loaded quality factor QL is related to Q0
by:
Qext describes the effect of the power coupler attached to the cavity
Qext = ω∙W/Pext. W is the stored energy in the cavity; Pext is the
power exchanged with the coupler. In the cavity test the stored
energy was 65J, the power exchanged with coupler was 100kW.
Calculate the loaded quality factor QL and the frequency
bandwidth of the cavity.
Please explain which technique is used to keep the frequency of the
cavity on its nominal value.
Assume that some normal conducting material (e.g some piece of
copper) is inside of the cavity.
What are the effects on gradient and Q-value? Please explain qualitatively
How can you calculate the effects?
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Case study 6
Additional questions
Evaluate, compare, discuss, take a stand (… and justify it …)
regarding the following issues
High temperature superconductor: YBCO vs. Bi2212
Superconducting coil design: block vs. cos
Support structures: collar-based vs. shell-based
Assembly procedure: high pre-stress vs. low pre-stress
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