1. CERN Accelerator School Superconductivity for Accelerators Case Study 5 – Case Study 6 Case 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 2

3. Q5.1&5.2: f change with T Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 3

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

5. Q5.3,5.4&5.5: Q-switch – hot spot Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 5 *

6. Characterizing cavities Resonance frequency Transit time factor field varies while particle is traversing the gap Shunt impedance gap voltage – power relation Q factor R/Q independent of losses – only geometry! loss factor CAS Varna/Bulgaria 2010- RF Cavities6 Linac definition Circuit definition 23-Sept-2010

7. 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 etching 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… The cavity is still tuned, i.e. SC Q5.6 – Bulk Nb Cavity

8. Q5.7 – Modelling grain boundary Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 8

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. Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 9

10. Q5.9: Thermal – Kapitza Resistance 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 R S ?  tends to increase with T, but this effect will be compensated by the increase of R S 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<H C and T<T C Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 10 Increasing Kapiza conductance

11. Q6.1, Q6.2&Q6.3 – cavity geometry Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 11

12. Q6.4 – BCS resistance Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 12 T [K]R BCS [nΩ] 4.3362.1 4266.2 361.0 23.2 f=704.4 MHz T c (Nb)=9.2 K dominating

13. Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 13

14. Q6.6,Q6.7 & Q6.8 – gradient, wall loss, max. gradient Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 14

15. Q6.6,Q6.7 & Q6.8 – gradient, wall loss, max. gradient Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 15

16. Q6.9: Input power and external Q, bandwidth Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 16 f Intensity Q0Q0 QLQL

17. Cavity equivalent circuit Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 17 R Cavity Generator IGIG  P C=Q/(R  0 ) V acc Beam IBIB L=R/(Q  0 ) LC : coupling factor R : Shunt impedance : R-upon-Q Simplification: single mode

18. Q6.10: Tuners Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 18 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 19

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! Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 20

21. Annex – from the case study introduction: Cases 5 and 6 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 21

22. CASE STUDY 5 Courtesies: M. Desmon, P. Bosland, J. Plouin, S. Calatroni Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 22

23. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 23 Thin Film Niobium: penetration depth Frequency shift during cooldown. Linear representation is given in function of Y, where Y = (1-(T/T C ) 4 ) -1/2

24. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 24 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 B peak is proportional to Eacc (B peak /E acc ~2)) Q5: If the hot spot had been observed 7.3 cm from the equator, what conclusion could you draw from the experimental data ? *

25. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 25 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

26. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 26 Bulk Niobium: local defects: steps @ GB

27. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 27 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) ?

28. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 28 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

29. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 29 Steps @ GB w. realistic dimension RF + thermal

30. Case study 5 RF cavities: superconductivity and thin films, local defect… Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 30 Q9 Comment these figures. What will happen if we introduce thermal variation of  What happen if we increase the purity of Nb ?, why ?

31. CASE STUDY 6 Courtesies: J. Plouin, D. Reschke Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 31

32. 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 g, λ and L. L is the distance between two neighboring cells (see sketch above) Calculate the value of L and L acc. 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

33. Case study 6 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 33

34. Case study 6 In operation a stored energy of 65 J was measured inside the cavity. What is the corresponding accelerating gradient E acc ? 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. Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 34

35. Case study 6 Please remember that the loaded quality factor Q L is related to Q 0 by: Q ext describes the effect of the power coupler attached to the cavity Q ext = ω∙W/P ext. W is the stored energy in the cavity; P ext 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 Q L 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? Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 35

36. 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 Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013 Case study Summary -- Superconducting RF 36