1. Heat management issues A perspective view centered on the design of superconducting devices Opinions of L. Bottura At the mWorkshop on Thermal Modeling and Thermal Experiments for Accelerator Magnets Sept. 30th, Oct. 1st, 2009

2. Outline Matters of steady state heat removal from coils, magnets and other superconducting systems Stability of superconductors Magnet quenches, and not only

3. Outline Matters of steady state heat removal from coils, magnets and other superconducting systems Stability of superconductors Magnet quenches, and not only

4. Cooling in steady operation - 1 Coil heat transfer What is the maximum power that can be removed from a coil ? Focus on strand-to-helium heat transfer, through the insulation Mainly motivated by LHC operation, NIT, HFM on the longer term Magnet heat transfer Same motivation as above, extend the analysis to the proximity cryogenics We will hear extensively on both

5. Cooling in steady operation - 2 Force-flow cooling Pressure drop, flow and heat transfer in supercritical helium flow Relevant for the SC link foreseen for the Phase I upgrade (and FCM ?) For SC link, two options being designed and prototyped NbTi (T max < 5.5 K !) through APUL at FNAL MgB 2 (T max < 10…15 K) at CERN A long SC link, possibly vertical geometry, is being designed within the scope of WP 7.5 of EuCARD program

6. NIT - SC link 8 x 0.6 kA 3 kA 14 kA 7 x 14 kA + 7 x 3 kA + 8 x 0.6 kA Cable R&D by courtesy of A. Ballarino, CERN-TE-MSC

7. Aha ! FCM Internally cooled cable prototype CERN/BNG D strand : 0.6 mm J c (4.2 K, 5 T) > 2500 A/mm 2 Cu:CuMn:NbTi = 2.4 D eff < 3  m  < 1 ms Number of strands = 32 Cable twist pitch < 80 mm B nom = 2 T T nom = 4.5 K I nom = 5800 A I c = 11500 A T cs > 6.5 K I op /I c = 50 % T margin > 2.0 K ID pipe = 4.5 mm OD conductor = 7.6 mm R a > 100  Massflow = 5 g/s Pressure drop (60 m) < 0.1 bar

8. Present state-of-the-art in pressure drop The customary approach to friction data modeling is to plot in dimensionless form f(Re), fit a model, and compare results Data for small-size CICC’s D cable = 12 mm D strand = 0.81 mm Cable: 3 x 3 x 4 x 4 Katheder

9. Alternative approach based on porous media Straight correlation plot to check accuracy: Average relative error  f ≈ 20 %

10. A tortuous matter - 1 Tortuosity is the ratio of the length l of a flow streamline between two points x 1 and x 2, and the distance of the two points d = | x 2 - x 1 | Larger tortuosity implies larger pressure drop Length effect Flow effect d l

11. A tortuous matter - 2 Tortuosity in porous media depends on void fraction (porosity) - we already take into account this effect In addition tortuosity in CICC’s depends on the cabling pattern - we do not take into account this effect ! Cable tomography by courtesy of ENEA and PSI

12. Scales and issues Small temperature increase, up to the temperature margin (< 1 K) The heat transfer process affects coil, magnet and proximity cryogenics (1 mm …100 m) Slow time scales, comparable to operation (1 s … 1 h) He-I and He-II are both of relevance Today, much of the experimental focus is on cable/coil in He II, but very little data in all other areas (magnet, powering cables) Modeling work is lagging behind experimental results, which is normal, but there may be a lack of basic understanding of the dominating physical mechanisms (micro/macro porosity in cables and insulations)

13. Outline Matters of steady state heat removal from coils, magnets and other superconducting systems Stability of superconductors Magnet quenches, and not only

14. Superconductors stability Measurements by M. de Rapper, CERN-TE-MSC Figure 3 Figure 2

15. Scales and issues Small temperature increase up to the decision recovery/quench (≈ 1 K) The heat transfer process is local to the strand in the cable (1 mm …1 cm) Fast time scales for the decision between recovery/quench (10  s … 10 ms) He-I and He-II are both of relevance We do not have a complete, consistent and validated model of heat transfer for these processes

16. Outline Matters of steady state heat removal from coils, magnets and other superconducting systems Stability of superconductors Magnet quenches, and not only

17. Quench propagation Single components (e.g. magnet, bus- bars (!?!)) require knowledge of heat transfer at the level of the cable Systems (e.g. strings of magnets) require knowledge of heat and mass transfer at the level of the proximity cryogenics

18. Clean gap ≈ 45 mm Quench in an LHC bus-bar Mock-up of defects in the LHC interconnects are tested to find the boundary between stable quenches (can be protected by a current dump) and thermal runaways (can lead to over-temperatures) Sample manufactured by C. Urpin, H. Prin, CERN-TE-MSC

19. Run 090813.15 Stable quench: a normal zone is established and reaches approximate steady-state conditions (T ≈ 30…40 K) stable Measurements by G. Willering, G. Peiro, A. Verweij, CERN-TE

20. Run 090813.20 Runaway quench: the temperature in the normal zone increases over a time scale of the order of few s to R.T. runaway t runaway Measurements by G. Willering, G. Peiro, A. Verweij, CERN-TE

21. Effect of heat transfer @ 1.8 K Adiabatic interconnect Wet interconnect Measurements by G. Willering, G. Peiro, A. Verweij, CERN-TE

22. Effect of heat transfer @ 4.3 K Wet interconnect Adiabatic interconnect Measurements by G. Willering, G. Peiro, A. Verweij, CERN-TE

23. Heat transfer coefficient Measurements by D. Richter, CERN-TE-MSC Analysis by P. Granieri and M. Casali, CERN-TE-MSC ?

24. A string of LHC magnets model of the regular LHC cell: D quadrupole and lattice correctors 3 dipoles F quadrupole and lattice correctors 3 dipoles QV9202SI QV920

25. Pressure evolution computed pressure

26. Quench propagation reasonable match of quench propagation MB3-MB2-MB1 quench propagation MB3-MB4 too fast

27. Scales and issues Large temperature increase, potentially up to room- temperature (≈ 100 K) The heat transfer process is local to the cable in the magnet (1 cm …1 m) Moderate time scales for the evolution of the temperature profile during quench (0.1 s … 100 s) He-I (including pressure waves and mass transport) is of most relevance The process spans several orders of magnitude, and involves transport phenomena, with uncertainties at each level of the multiple scales

28. Summary space time temperature 10 -3 10 -2 10 -1 1 10 100 1000 10 -3 10 -2 10 -1 1 10 100 0.1 1 10 100 Quench of magnet and busses Magnet cooling, Flow issues Stability Cable/Coil cooling