CERN Accelerator School Superconductivity for Accelerators Erice April 25 th May 4 th 2013 LucaBottura cernch Plan of the lecture T raining and degradation P erturbation spectrum overview ID: 1022268
Download Presentation The PPT/PDF document "Superconductor Stability" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
1. Superconductor StabilityCERN Accelerator SchoolSuperconductivity for AcceleratorsErice, April 25th – May 4th, 2013Luca.Bottura@cern.ch
2. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topicsfocus on LTS magnetsadiabatic, or helium cooled
3. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topics
4. Training…Superconducting solenoids built from NbZr and Nb3Sn in the early 60’s quenched much below the rated current …… the quench current increased gradually quench after quench: trainingM.A.R. LeBlanc, Phys. Rev., 124, 1423, 1961. NbZr solenoidChester, 1967P.F. Chester, Rep. Prog. Phys., XXX, II, 561, 1967.
5. … and degradationNbZr solenoid vs. wireIc of NbZr wireImax reached in NbZr solenoid… but did not quite reach the expected maximum current for the superconducting wire !This was initially explained as a local damage of the wire: degradation, a very misleading name.All this had to do with stabilityP.F. Chester, Rep. Prog. Phys., XXX, II, 561, 1967. The prediction of the degraded current […] proved to be impossible and […] the development of coils passed through a very speculative and empirical phase
6. Training todayTraining of an model Nb3Sn 11 T dipole for the LHC upgrade in liquid and superfluid heliumStill, training may be necessary to reach nominal operating currentShort sample limit is not reached, even after a long training sequence stability is (still) important !11 T field in the dipole boreCourtesy of G. Chlachidze, Fermilab, April 2013, unpublished
7. Dealing with early instabilities“Those tiny, primitive magnets were, of course, terribly unstable […] One had to have faith to believe that these erratic toys of the low temperature physicist would ever be of any consequence as large engineered devices” (J. Hulm, ASC 1982)W.B. Sampson, Proc. Int. Symp. Mag. Tech., SLAC, 530-535, 1965
8. A Woodstock for SC accelerator magnetsA six weeks summer study organized and hosted by BNL in 1968The crème de la crème addressed material and engineering issues of superconducting accelerators, among them:Stability, training and degradationFlux-jumps in composite superconductorsTwisting of multi-filamentary wires and cablesJ. HaleY. IwasaW. SampsonP. SmithM. MorpurgoB. MontgomeryP. LazeyrasR. Wittgenstein
9. An event tree for stability (and quench)Stable operating conditionExternal perturbation: flux jump conductor motions insulation cracks AC loss heat leaks nuclear …Approach Jc(T, B, …)QuenchyesnoStable operating conditionTransition to normal state and Joule heat generation in current sharingheat generation > heat removalstability analysis and designHeat balancePerturbation spectrum
10. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topics
11. Perturbation spectrumMechanical eventsWire motion under Lorentz force, micro-slipsWinding deformationsFailures (at insulation bonding, material yeld)Electromagnetic eventsFlux-jumps (important for large filaments, old story ?)AC loss (most magnet types)Current sharing in cables through distribution/redistributionThermal eventsCurrent leads, instrumentation wiresHeat leaks through thermal insulation, degraded coolingNuclear eventsParticle showers in particle accelerator magnetsNeutron flux in fusion experiments
12. Perturbation scalesTransient (stability concern)point Q [Joules]distributed Q’’’ [Joules/m3] [mJ/cm3]Continuous (sizing of cooling system)point q [Watts]distributed q’’’ [Watts/m3]
13. Perturbation overview
14. Flux jump mechanismExternal field change induces screening persistent currents (JC) in the superconductorA drop in screening current causes the field profile to enter in the superconductorEnergy is dissipated (flux motion)Thermal diffusivity and heat capacity is small in the superconductor and the temperature increasesCritical current density decreases at increasing temperatureA small perturbation induces a temperature increaseAfter the work of M.N. Wilson, Superconducting Magnets, Plenum Press, 1983BJCBJC
15. Flux-jumps energyDuring a complete flux-jump the field profile in a superconducting filament becomes flat:e.g.: field profile in a fully penetrated superconducting slabenergy stored in the magnetic field profile:D = 50 mm, Jc = 10000 A/mm2Q’’’ 6 mJ/cm3area lost during flux jumpNOTE: to decrease Q’’’, one can decrease D
16. Flux jumps then and nowA.D. McInturrf, Composite Materials, Proceedings of the 1968 Summer School on Superconducting Devices and Accelerators, BNL 50155 (C-55)B. Bordini, et al., Magnetization Measurements of High-JC Nb3Sn Strands, CERN-ATS-2013-029Complete flux jumpPartial flux jumpFlux jumps is not an old story, we still suffer from magnetic instabilities when pushing for high conductor JC
17. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topics
18. Prototype heat balanceHeat sourceJoule heatConductionHeat transferHeat capacitycoolinggeneration
19. Temperature transientheat pulse Q’’’ext……effect of heat conduction and cooling…Q’’’ext = Q’’’+e generation > coolingQ’’’ext = Q’’’-e generation < cooling…decision time…
20. Energy margin…Q’’’, energy marginMinimum energy density that leads to a quenchMaximum energy density that can be tolerated by a superconductor, still resulting in recoverySimple and experimentally measurable quantity (…)Measured in [mJ/cm3] for convenience (values 1…1000)Also called stability marginCompared to the energy spectrum to achieve stable designQ, quench energy Better adapted for disturbances of limited space extensionMeasured in [mJ] to [mJ]
21. … and other useful marginsTJcB14.5 T9 Ktypical NbTi5 T4.2 K3000 A/mm2operating planeJBJopBopBcBmaxJcMargin in critical currentTcsJTJopTopTcMargin in temperatureMargin along the loadlineJop/JC ≈ 0.5Bop/Bmax ≈ 0.8 (Todesco’s 80 %)Tcs-Top ≈ 1…2 K
22. A measured stability transient (LHC dipole magnet training)Voltage increase generated by a sudden heat input…cooling……decision time……quench2 ms15 mVfast !!!What happens here ?
23. Current sharingTcsTIopTopTcIcTcs < T < TcT < TcsT > Tcquenchedcurent sharingstabilizersuperconductor
24. Joule heatingTTcsTopTcIopcurrent in stabilizercurrent in superconductor
25. Joule heating (cont’d)Linear approximation for Ic(T):Joule heatingTTcsTopTc
26. Cooling: many optionsIndirect: (adiabatic, no cooling)Contact to a heat sink through conduction (e.g. to a cryo-cooler)In practice, no cooling on the time scale of interest for stabilityDirect: (cooling by heat transfer at the surface)Bath cooling, to a pool of liquid helium at atmospheric pressure and saturation temperature (4.2 K)Force-flow cooling to a supercritical or two-phase flowSuperfluid cooling to a stagnant bath of He-II
27. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topics
28. Adiabatic stabilityAdiabatic conditions:No cooling (dry or impregnated windings)Energy perturbation over large volume (no conduction)Stable only if q’’’Joule=0 (TTcs) !energy marginvolumetric enthalpyTTcsTopTc
29. Specific enthalpy23023enthalpy reserve increases at increasing T (Note: HTS !) do not sub-cool !(if you can only avoid it…)
30. Adiabatic stability re-capApplies to:Adiabatic, compact, high current density windings (dry or indirectly cooled)Very fast heat perturbations (flux-jumps)The heat capacity of the conductor absorbs the external heat perturbation Stability (at equal temperature margin) improves as the temperature increases (HTS !) Choose materials with high heat capacity (e.g. loading of epoxy)Relatively small energy margin: 1…10 mJ/cm3
31. Cooling in a bath of pool boiling heliumIgnore conduction for large energy perturbations volumesRequest steady state stability in all conditionsCryostabilityworst possible casegeneration cooling A.R. Krantowitz, Z.J.J. Stekly, Appl. Phys. Lett., 6, 3, 56-57, 1965.Z.J.J. Stekly, J.L. Zar, IEEE Trans. Nucl. Sci., 12, 367-372, 1965.
32. Heat balance (ideal case)generation cooling stablecryostablenot cryostablenot cryostableconstant heat transfer to the helium
33. Stekly-aStekly cryostability condition:can be formulated as aStekly 1 :Improve coolingIncrease the cross section of stabilizerIncrease the temperature marginDecrease the operating current
34. Cryo-stability recapApplies to:Well-cooled, low current density windings (pool-boiling)Any type of heat perturbations, all time and space scalesThe coolant can take the Joule heating under all possible conditionsIdeally infinite energy margin
35. Assume that the normal zone is long and above cryostable operating conditionsThe temperature will reach an equilibrium temperatureCold-end effects – 1Teqcryostablenot cryostable
36. What happens if the ends are cold ? Request steady state stability in all conditionsCold-end effects – 2TxTcTcsTeqTopcold-end conduction lead to recoverytTxTcTcsTeqTopcold-end conduction not sufficient to prevent quencht
37. Cold-end effects – 3introduce a new variable S:B.J. Maddock, G.B. James, W.T. Norris, Cryogenics, 9, 261-273, 1969.Sop = 0 Seq = 0wh (T-Top)A/w q’’’JTxTcTcsTeqTopq’’x
38. An equal area theoremStable conditions are obtained when the net area between generation and cooling curves is zeroB.J. Maddock, G.B. James, W.T. Norris, Cryogenics, 9, 261-273, 1969.Values of a nearly twice as large as from the Stekly criterion are possible !Stekly: a ≤ 1Maddock: a ≤ 2-fop
39. Cold-end effects recapApplies to:Well-cooled, low current density windings (pool-boiling)Any type of heat perturbations, all time and space scalesThe coolant and the cold ends take the Joule heating under all possible conditionsIdeally infinite energy marginImproved stability with respect to the cryostability condition, allow operation at higher current
40. Meta-stable conductorsAdiabatically stabilized conductors:High Jop (good for cost)Small Q’’’ (bad for large magnets)Cryo-stabilized conductors (including cold-ends):Large Q’’’, ideally infinite (good for large magnets)Low Jop (bad for cost)Is there a compromise ?
41. Idea-1: helium !The helium heat capacity is orders of magnitude larger than for metals at low temperatureAdd helium in intimate contact with the cable
42. ICS’s and CICC’sM.O. Hoenig, Y. Iwasa, D.B. Montgomery,Proc. 5th Magn. Tech. Conf., Frascati, 519, (1975)
43. Conductor temperature:But the helium temperature evolves as well:Under which conditions the heat capacity is effectively used ?NOTE: at large enough h, TTheHeat balance for CICC’s
44. Stability of CICC’sDQ’’’Iopllimhelium + strand heat capacitystrand heat capacityJoule heat<coolingJoule heat>coolingwell-cooledill-cooledbalance of Joule heat and cooling at:equivalent to aStekly = 1 In this case however the CICC is meta-stable as a large enough energy input will cause a quench !J.W. Lue, J.R. Miller, L. Dresner, J. Appl. Phys., 51, 1, 772, (1980)J.H. Schultz, J.V. Minervini, Proc. 9th Magn. Tech. Conf., Zurich , 643, (1985)
45. Idea-2: heat conduction !xTTcTcsT’eqTopxq’’wh (T-Top)A/w q’’’JS=0 at the boundariesequal area still possiblebut implies lower T’eq < TeqShort normal zone
46. Normal zone temperatureThe temperature profile can be traced by numerical integration of the equal area balanceThis is an unstable equilibrium temperature profile, and defines the minimum length of superconductor that could grow and develop into a quench: Minimum Propagating Zone (MPZ)The energy required to form the MPZ is the Minimum Quench Energy (MQE)xTq’’’JM.N. Wilson, Y. Iwasa, Cryogenics, 18, 17-25, 1978
47. MPZ estimatesTo estimate the size of the MPZ we can solve the heat balance approximatelySteady state conditions and no coolingAfter the work of M.N. Wilson, Superconducting MagnetsPlenum Press, 1983Jop = 400 A/mm2k = 500 W/m Kh = 1 nW mTC-Top = 2 KMPZ ≈ 3.5 mmMQE ≈ 10 mJ
48. Plan of the lectureTraining and degradationPerturbation spectrum overviewHeat balanceStabilization strategies and criteriaA summary and more complex topics
49. SummarySuperconductor stability is the art of balancing large stored energies (and potential for energy release) with a little capital (aka: “leveraging” for our US colleagues)Extremely important in LTS-based magnet to reach the desired performance (10 MJ vs 10 mJ)Generally not an issue for HTS-based magnetsStability is not absolute, it implies comparing the perturbation spectrum to the available marginSeveral strategies can be applied to achieve stable operating conditions under the envelope of foreseeable perturbation spectrum
50. A summary of strategiesOperating current density (A/mm2)Energy margin (mJ/cm3)11010010001101001000CICCAdiabaticCryostableCold endMPZ/MQE
51. Advanced topicsCurrent distribution and RRLRamp-rate quenchesHolding quenchesMagneto-thermal instabilitiesDynamic stability Self-field instabilityThere are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.type Btype AA. Devred, T. Ogitsu, Frontiers of Accelerator Magnet Technology, World Scientific, 184, 1996 B. Bordini and L. Rossi, IEEE TAS, 19, 2470 (2009).
52. A zoo of configurations…CICC’sStrands and tapespower transmission cablesRutherfordinduced flow,transient heat transfer,AC operation,current distribution,HTS,coolants (N2, Ne, H2)…Internally cooled
53. … and modelsThings can get fairly complex
54. Ah, and… what if it falls ???Then, you need to protect !
55. Where to find out morePapers, reviews and proceedings:A.R. Krantowitz, Z.J.J. Stekly, A New Principle for the Construction of Stabilized Superconducting Coils, Applied Physics Letters, 6, 3, 56-57, 1965.P.F. Chester, Superconducting Magnets, Rep. Prog. Phys., XXX, Part II, 561-614, 1967. B.J. Maddock, G.B. James, W.T. Norris, Superconductive Composites: Heat Transfer and Steady State Stabilization, Cryogenics, 9, 261-273, 1969.M.N. Wilson, Y. Iwasa, Stability of Superconductors against Localized Disturbances of Limited Magnitude, Cryogenics, 18, 17-25, 1978. L. Dresner, Superconductor Stability 1983: a Review, Cryogenics, 24, 283, 1984.Books:M.N. Wilson, Superconducting Magnets, Plenum Press, 1983.L. Dresner, Stability of Superconductors, Plenum Press, 1995.P.J. Lee ed., Engineering Superconductivity, J. Wiley & Sons, 2001.B. Seeber ed., Handbook of Applied Superconductivity, IoP, 1998.Y. Iwasa, Case Studies in Superconducting Magnets, Plenum Press, 1994.