Lecture 2: Training, fine filaments & cables

1. Degraded performance & Training load lines and expected quench current of a magnet causes of training - release of energy within the magnet minimum propagating zones MPZ and minimum quench energy MQE Magnetization of the Superconductor screening currents & the critical state model magnetization & field errors magnetization & ac loss fine filaments, coupling in wires & cables Lecture 2: Training, fine filaments & cables resistance time quench initiation in LHC dipole Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

2. resistive superconducting * magnet aperture field temperature K Engineering Current density Amm-2 magnet peak field 2 2 * 4 4 6 6 8 8 Field T • load line relates magnet field to current • peak field > aperture (useful) field • we expect the magnet to go resistive 'quench' where the peak field load line crosses the critical current line 10 12 14 16 * Critical surface and magnet load lines 7 Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

3. Degraded performance and ‘training’ of magnets quench field time • well made magnets are better than poorly made • an early disappointment for magnet makers came when the current (and field) of a magnet was ramped up for the first time • instead of going up to the critical line, it ‘quenched’ (went resistive) at less than the expected current • at the next try it did better • known as training • after a quench, the stored energy of the magnet is dissipated in the magnet, raising its temperature way above critical • you must wait for it to cool down and then try again Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

4. ‘Training’ of magnets • it's better than the old days, but training is still with us • it seems to be affected by the construction technique of the magnet • it can be wiped out if the magnet is warmed to room temperature • 'de-training is the most worrysome feature Training of LHC short prototype dipoles (from A. Siemko) Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

5. 102 102 10 Specific Heat Joules / kg / K 1 300K 10-1 4.2K 10-2 10 100 1000 1 temperature K Causes of training: (1) low specific heat • the specific heat of all substances falls with temperature • at 4.2K, it is ~2,000 times less than at room temperature • a given release of energy within the winding thus produce a temperature rise 2,000 times greater than at room temperature • the smallest energy release can therefore produce catastrophic effects Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

6. Causes of training: (2) Jc decreases with temperature temperature K Jc 2 2 2 2 4 4 4 4 * 6 6 6 6 * Field T 8 8 8 8 10 10 10 10 12 12 14 14 16 16 at any field, Jc of NbTi falls ~ linearly with temperature - so any temperature rise drives the conductor towards the resistive state Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

7. Causes of training: (3) conductor motion • Conductors in a magnet are pushed by the electromagnetic forces. Sometimes they move suddenly under this force - the magnet 'creaks' as the stress comes on. A large fraction of the work done by the magnetic field in pushing the conductor is released as frictional heating work done per unit length of conductor if it is pushed a distance dz W = F.dz = B.I.dz frictional heating per unit volume Q = B.J.dz typical numbers for NbTi: B = 5T Jeng = 5 x 108 A.m-2 so if d = 10 mm then Q = 2.5 x 104 J.m-3 Starting from 4.2Kqfinal= 7.5K canyouengineer a winding to better than 10 mm? Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

8. Causes of training: (4) resin cracking We try to stop wire movement by impregnating the winding with epoxy resin. Unfortunately the resin contracts much more than the metal, so it goes into tension. Furthermore, almost all organic materials become brittle at low temperature. brittleness + tension  cracking  energy release Calculate the stain energy induced in resin by differential thermal contraction let: s = tensile stress Y = Young’s modulus e = differential strain n = Poisson’s ratio typically: e = (11.5 – 3) x 10-3 Y = 7 x 109 Pa n = 1/3 uniaxial strain Q1= 2.5 x 105 J.m-3qfinal = 16K triaxial strain Q3= 2.3 x 106 J.m-3 qfinal = 28K an unknown, but large, fraction of this stored energy will be released as heat during a crack Interesting fact: magnets impregnated with paraffin wax show almost no training although the wax is full of cracks after cooldown. Presumably the wax breaks at low s before it has had chance to store up any strain energy Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

9. How to reduce training? 1) Reduce the disturbances occurring in the magnet winding • make the winding fit together exactly to reduce movement of conductors under field forces • pre-compress the winding to reduce movement under field forces • if using resin, minimize the volume and choose a crack resistant type • match thermal contractions, eg fill epoxy with mineral or glass fibre • impregnate with wax - but poor mechanical properties • most accelerator magnets are insulated using a Kapton film with a very thin adhesive coating on the outer face - away from the superconductor • allows liquid helium to penetrate the cable Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

10. How to reduce training? * * * 2) Make the conductor able to withstand disturbances without quenching • increase the temperature margin • operate at lower current • but need more winding to make same field • harder at high fields than at low fields • higher critical temperature - HTS? Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

11. How to reduce training? MQE energy release field 2) Make the conductor able to withstand disturbances without quenching • increase the temperature margin • increase the cooling - more cooled surface - better heat transfer - superfluid helium • increase the specific heat - experiments with Gd2O2S HoCu2 etc • most of this may be characterized by a single number Minimum Quench Energy MQE • defined as the energy input at a point in very short time which is just enough to trigger a quench. • energy input > MQE  quench • energy input < MQE  recovery • energy disturbances occur at random as a magnet is ramped up to field • for good magnet performance we want a high MQE Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

12. Quench initiation by a disturbance • CERN picture of the internal voltage in an LHC dipole just before a quench • note the initiating spike - conductor motion? • after the spike, conductor goes resistive, then it almost recovers • but then goes on to a full quench • this disturbance was more than the MQE Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

13. Iheater carbon paste heater Measuring the MQE for a cable 125 mJ too big! 120 mJ • pass a small pulse of current from the copper foil to the superconducting wire • generates heat in the carbon paste contact • how much to quench the cable? • find the Minimum Quench EnergyMQE too small! Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

14. Different cables have different MQEs • similar cables with different cooling • better cooling gives higher MQE • high MQE is best because it is harder to quench the magnet • experimental cable with porous metal heat exchanger • excellent heat transfer to the liquid helium coolant 40mJ is a pin dropping 40mm Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

15. h J P A l qc qo Factors affecting the Minimum Quench Energy • think of a conductor where a short section has been heated, so that it is resistive • if heat is conducted out of the resistive zone faster than it is generated, the zone will shrink - vice versa it will grow. • the boundary between these two conditions is called the minimum propagating zone MPZ • for best stability make MPZ as large as possible the balance point may be found by equating heat generation to heat removed. Very approximately, we have: where: k = thermal conductivity r = resistivity A = cross sectional area of conductor h = heat transfer coefficient to coolant – if there is any in contact P = cooled perimeter of conductor long MPZ  large MQE Energy to set up MPZ is the Minimum Quench Energy Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

16. How to make a long MPZ  large MQE • make thermal conductivity k large • make resistivity rsmall • make heat transfer hP/A large (but  low Jeng ) Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

17. Large MPZ  large MQE  less training • make thermal conductivity k large • make resistivity r small • make heat transfer term hP/A large • NbTi has high r and low k • copper has low r and high k • mix copper and NbTi in a filamentary composite wire • make NbTi in fine filaments for intimate mixing • maximum diameter of filaments ~ 50mm • make the windings porous to liquid helium - superfluid is best • fine filaments also eliminate flux jumping (solved problem) Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

18. Another cause of training: flux jumping J J B x • changing magnetic fields induce screening currents in superconductors • screening currents are in addition to transport currents, which come from the power supply • like eddy currents but don't decay because no resistance, • usual model is a superconducting slab in a changing magnetic field By • assume it's infinitely long in the zand y directions - simplifies to a 1 dim problem • dB/dtinduces an electric field E which causes screening currents to flow at critical current density Jc • known as the critical state model orBean model • in the 1 dim infinite slab geometry, Maxwell's equation says • so uniform Jc means a constant field gradient inside the superconductor Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

19. The flux penetration process B fully penetrated plot field profile across the slab field increasing from zero • Bean critical state model • current density everywhere is Jc or zero • change comes in from the outer surface field decreasing through zero Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

20. Flux Jumping J J • temperature rise Dq B • reduced critical current density • flux motion DQ -DJc • energy dissipation • temperature rise Df • cure flux jumping by weakening a link in the feedback loop • fine filaments reduce Df for a given -DJc • for NbTi the stable diameter is ~ 50mm a magnetic thermal feedback instability • screening currents Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

21. Flux jumping: the numbers for NbTi Flux jumping is a solved problem criterion for stability against flux jumping a = half width of filament typical figures for NbTi at 4.2K and 1T Jc critical current density = 7.5 x 10 9 Am-2 g density = 6.2 x 10 3 kg.m3 C specific heat = 0.89 J.kg-1K-1 qc critical temperature = 9.0K so a = 33mm, ie 66mm diameter filaments • Notes: • least stable at low field because Jc is highest • instability gets worse with decreasing temperature because Jc increases and C decreases • criterion gives the size at which filament is just stable against infinitely small disturbances - still sensitive to moderate disturbances, eg mechanical movement • better to go somewhat smaller than the limiting size • in practice 50mm diameter seems to work OK Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

22. Magnetization J loop area = ac loss / cycle M Hysteresis like iron, but diamagnetic H iron • magnetization = magnetic moment per unit volume • persistent screening currents make the superconductor look like a magnetic material B A for round wire M Bext magnetic material spoils field quality Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

23. (Irreversible) magnetization of NbTi M H iron M Bext Hysteresis like iron, but diamagnetic Magnetization is important because it produces field errors and ac losses Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

24. Magnetization measurements 5105 -5105 NbTi wire for RHIC with 6mm filaments RRP Nb3Sn wire with 50mm filaments flux jumping at low field caused by large filaments and high Jc total magnetization reversible magnetization Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

25. Fine filaments for low magnetization single stack double stack Accelerator magnets need the finest filaments - to minimize field errors and ac losses Typical diameters are in the range 5 - 10mm. Even smaller diameters would give lower magnetization, but at the cost of lower Jc and more difficult production. Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

26. Coupling between filaments recap • reduce M by making fine filaments • for ease of handling, filaments are embedded in a copper matrix • coupling currents flow along the filaments and across the matrix • fortunately they may be reduced by twisting the wire • they behave like eddy currents and produce an additional magnetization per unit volume of wire • but in changing fields, the filaments are magnetically coupled • screening currents go up the left filaments and return down the right where rt = resistivity across the matrix and pw = wire twist pitch Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

27. Two components of magnetization 1) persistent current within the filaments where lsu= fraction of superconductor in the unit cell Me 2) eddy current coupling between the filaments Ms or where where lwu = fraction of wire in the section Mf depends on B Magnetization External field Me depends on dB/dt Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

28. for good tracking connect synchrotron magnets in series to reduce charging voltage must reduce inductance  high operating current many wires in parallel Accelerator magnets need cables Rutherford rope braid • wires in parallel - zero resistance - current divides according to inductance • simple twisted cable - central wires in centre have a higher inductance than outer wires • current takes low inductance path and stays on the outside • outer wires reach Jc while inner are still empty • wires must be transposed, ie every wire must change places with every other wire • inner wires  outside outer wires  inside Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

29. Ḃ Coupling in Rutherford cables • for good current sharing need some electrical contact between strands of a cable • changing fields can induce circulating currents • worst case is transverse field • coupling via crossover resistance Rc  additional magnetization and loss Rc Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

30. Coupling and ac losses within filaments between filaments in wire J between wires in cable between filaments in wire Magnetization within filaments External field Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

31. Magnetization and field errors - extreme case Magnetization is important in accelerators because it produces field error. The effect is worst at injection because - DB/B is greatest - magnetization, ie DB is greatest at low field skew quadrupole error in Nb3Sn dipole which has exceptionally large coupling magnetization (University of Twente) Superconducting Accelerator Magnets: Cockroft Institute Jan 2013

32. Concluding remarks fine filaments are a good thing a) training • expected performance of magnet is where the load line hits the critical surface • degraded performance and ‘training’ are caused by sudden releases of energy within the winding • mechanical energy is released by conductor motion or by cracking of resin • minimum quench energy MQE is the energy needed to create a minimum propagating zone MPZ - large MPZ  large MQE  harder to quench the conductor • make large MQE by making superconductor as fine filaments embedded in a matrix of copper b) magnetization: • magnetic fields induce persistent screening currents  magnetization  field errors & ac loss - ac loss per cycle = area of hysteresis loop • filaments are coupled in changing fields  increased magnetization - reduce by twisting • accelerator magnets need cables  increased magnetization  more field errors & ac loss • for storage rings, field errors are main problem, for fixed target synchrotrons, ac loss dominates Superconducting Accelerator Magnets: Cockroft Institute Jan 2013