CERN Accelerator School Superconductivity for Accelerators Case Study 5 – Case Study 6

CERN Accelerator School

Superconductivity for Accelerators

Case Study 5 – Case Study 6Case Study Summary

2

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!

Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF

3

Q5.1&5.2: f change with TLondon penetration depth: ,

; , so.

Why not 243mm?Because correspondsto , so the point has no absolute meaning. Only the slope has.Larger than bulk number (36 nm) since


𝑇→𝑇 𝑐

4

This is used in real life

Junginger et al.: “RF Characterization of Superconducting Samples”,https://cds.cern.ch/record/1233500


https://cds.cern.ch/record/1233500



5

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: ; assuming : 34 mJPower loss into the (small) defect: : 93 mWSize (assuming : .If observed at 7.3 cm, one would have deduced a slightly smaller size.


*

3 ∙1091 .5 ∙109

1.1 MVm

Characterizing cavities• Resonance frequency

• Transit time factorfield varies while particle is traversing the gap

• Shunt impedancegap voltage – power relation

• Q factor

• R/Qindependent of losses – only geometry!

• loss factorCAS Varna/Bulgaria 2010- RF Cavities 6

lossacc PRV 22

lossPQW 0

CL

WV

QR acc

0

2

2

CL

10

WV

QRk acc

loss 42

20

Linac definition

lossacc PRV 2

WV

QR acc

0

2

WV

QRk acc

loss 44

20

Circuit definition

zE

zeE

z

zc

z

d

dj

23-Sept-2010

7

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)..

After 40 µm etchingAfter 150 µm etching

MPBarrier

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…

The cavity is still tuned, i.e. SC

Q5.6 – Bulk Nb Cavity

8

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 () ?In this model, if the “hole” becomes too narrow, the field cannot enter it no field enhancement factor


9

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.


10

Q5.9: Thermal – Kapitza ResistanceComment 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


Incr

easi

ng K

apiz

a co

nduc

tanc

e

11

Q6.1, Q6.2&Q6.3 – cavity geometry

Total energy: , , ,

Cavity length: π-mode: particle travels in time :, : .

Parameters in the above table are purely geometric.


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Q6.4 – BCS resistance

It’s worth it to go to lower T. Cf. P. Lebrun’s lecture


1 2 3 4 51

10

100

1000

10000

Tc/T [1/K]

Rbcs

[nΩ

]

2K

4.3K

T [K] RBCS [nΩ]

4.3 362.1

4 266.2

3 61.0

2 3.2

f=704.4 MHzTc(Nb)=9.2 K

∆ 𝑓

T

dominating

13

Q6.5 – unloaded Q:

Given & geometry factor :

For real cavities, . includes effects fromTrapped magnetic fieldNormal conducting precipitatesGrain boundariesInterface lossesSubgap states... and some mysterious other things


14

Q6.6,Q6.7 & Q6.8 – gradient, wall loss, max. gradient

Accelerating gradient: , Dissipated power: , .190 mT equivalent max. gradient of : we’re OK. Magnetic quench most likely near the equator.Magnetic quench can be caused by thermal dissipation on defects, residual resistance, …


15

Q6.6,Q6.7 & Q6.8 – gradient, wall loss, max. gradient

Accelerating gradient: , Dissipated power: , .190 mT equivalent max. gradient of : we’re OK. Magnetic quench most likely near the equator.Magnetic quench can be caused by thermal dissipation on defects, residual resistance, …


16

Q6.9: Input power and external Q, bandwidth

- very strong coupling! ()

Bandwidth: from : 14 mHz!!!from : 245 Hz


0

111QQQ extL

0PPP externaltot

UP

UP

UP externaltot

0

100kW ≫5.7W

2.88 ∙106≪5 ∙1010

f

Inte

nsity

Q0

QL

17

Cavity equivalent circuit


R

Cavity

Generator

IG

ZP

C=Q/(R0)

Vacc

Beam

IB

L=R/(Q0)LC

: coupling factor

R: Shunt impedance : R-upon-Q

Simplification: single mode

R

CL

18

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

19

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 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…


20

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!


21

Annex – from the case study introduction: Cases 5 and 6


CASE STUDY 5Courtesies: M. Desmon, P. Bosland, J. Plouin, S. Calatroni

Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 22

Case study 5RF 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 = (1-(T/TC)4)-1/2


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 ?

*


local defect…


Bulk Niobium: local defects

Q6 : regarding the previous questions, and the field distribution in these cavities, how can you explain the multiple observed Q-switches ?

After 40 µm etching

After 150 µm etching


local defect…


Bulk Niobium: local defects: steps @ GB


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) ?


local defect…


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?

Steps @ GB w. realistic dimension

RF only


local defect…


Steps @ GB w. realistic dimension

RF + thermal


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 ?

CASE STUDY 6Courtesies: J. Plouin, D. Reschke


Case study 6

RF test and properties of a superconducting cavityBasic 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 βg, 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.Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May,

2013 Case study Summary -- Superconducting RF 32

Case study 6


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.


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 qualitativelyHow can you calculate the effects?Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May,

2013 Case study Summary -- Superconducting RF 35

Case study 6

Additional questionsEvaluate, 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


CERN Accelerator School Superconductivity for Accelerators Case Study 5 – Case Study 6

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