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

1. CERN Accelerator SchoolSuperconductivity for AcceleratorsCase Study 5 – Case Study 6 Case Study Summary

2. Q5.1&5.2: f change with T Case study Summary -- Superconducting RF 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!

3. Q5.1&5.2: f change with T Case study Summary -- Superconducting RF • London 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

4. This is used in real life Case study Summary -- Superconducting RF Junginger et al.: “RF Characterization of Superconducting Samples”,https://cds.cern.ch/record/1233500

5. Q5.3,5.4&5.5: Q-switch – hot spot * Case study Summary -- Superconducting RF 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 mJ Power loss into the (small) defect: : 93 mW Size (assuming : . If observed at 7.3 cm, one would have deduced a slightly smaller size.

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 Circuit definition Linac definition CAS Varna/Bulgaria 2010- RF Cavities

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

8. Q5.7 – Modelling grain boundary Case study Summary -- Superconducting RF 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 Case study Summary -- Superconducting RF 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 Resistance Increasing Kapiza conductance Case study Summary -- Superconducting RF 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 κand/or RS? ktends 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 Nballows 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

11. Q6.1, Q6.2&Q6.3 – cavity geometry Case study Summary -- Superconducting RF Total energy: , , , Cavity length: π-mode: particle travels in time : , : . Parameters in the above table are purely geometric.

12. Q6.4 – BCS resistance dominating f=704.4 MHz Tc(Nb)=9.2 K T Case study Summary -- Superconducting RF It’s worth it to go to lower T. Cf. P. Lebrun’s lecture

13. Q6.5 – unloaded Q: Case study Summary -- Superconducting RF • Given & geometry factor : • For real cavities, . includes effects from • Trapped magnetic field • Normal conducting precipitates • Grain boundaries • Interface losses • Subgapstates • ... and some mysterious other things

14. Q6.6,Q6.7 & Q6.8 – gradient, wall loss, max. gradient Case study Summary -- Superconducting RF 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 Case study Summary -- Superconducting RF 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 Q0 Intensity QL f Case study Summary -- Superconducting RF - very strong coupling! () Bandwidth: from : 14 mHz!!! from : 245 Hz

17. Cavity equivalent circuit IB Beam Simplification: single mode IG Vacc P Generator Z C L R L=R/(Qw0) : coupling factor C=Q/(Rw0) Cavity R: Shunt impedance : R-upon-Q Case study Summary -- Superconducting RF

18. Q6.10: Tuners Effects on cavity resonance requiring tuning: • Static detuning (mechanical perturbations) • Quasi-staticdetuning (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 Case study Summary -- Superconducting RF

19. Q6.11: NC defects Case study Summary -- Superconducting RF 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 Case study Summary -- Superconducting RF 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 Summary -- Superconducting RF

22. Case study Summary -- Superconducting RF CASE STUDY 5 Courtesies: M. Desmon, P. Bosland, J. Plouin, S. Calatroni

23. 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 Case study Summary -- Superconducting RF

24. Case study 5RF 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 ? Case study Summary -- Superconducting RF

25. Case study 5RF 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 ? Case study Summary -- Superconducting RF

26. Case study 5RF cavities: superconductivity and thin films, local defect… Bulk Niobium: local defects: steps @ GB Case study Summary -- Superconducting RF

27. Case study 5RF 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) ? Case study Summary -- Superconducting RF

28. Case study 5RF 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? Case study Summary -- Superconducting RF

29. Case study 5RF cavities: superconductivity and thin films, local defect… Steps @ GB w. realistic dimension RF + thermal Case study Summary -- Superconducting RF

30. Case study 5RF 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 ? Case study Summary -- Superconducting RF

31. Case study Summary -- Superconducting RF CASE STUDY 6 Courtesies: J. Plouin, D. Reschke

32. Case study 6 Case study Summary -- Superconducting RF • 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 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.

33. Case study 6 Case study Summary -- Superconducting RF

34. Case study 6 Case study Summary -- Superconducting RF • 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.

35. Case study 6 Case study Summary -- Superconducting RF • 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?

36. Case study 6 Case study Summary -- Superconducting RF • 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