Lecture 2: Training, fine filaments & cables

Transcription

1 resistance Lecture : Training, fine filaments & cables 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 time quench initiation in LHC dipole Martin Wilson Lecture slide1

2 Engineering Current Critical surface and 7 magnet load lines 8 Engineering current density Amm superconducting magnet aperture field * resistive * density Amm magnet peak field Field T load line relates magnet field to current peak field > aperture (useful) field 16 we expect the magnet to go resistive 'quench' where the peak field load line crosses the critical current line * Martin Wilson Lecture slide

3 quench curren Degraded performance and training of magnets field 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 quench time quench number 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 well made magnets poorly made are better than Martin Wilson Lecture slide3

4 field acheived. 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 operating field stainless steel collars stainless steel collars aluminium collars quench number Training of LHC short prototype dipoles (from A. Siemko) Martin Wilson Lecture slide4

5 Specific Heat Joules / kg / K 10 Causes of training: (1) low specific heat the specific heat of all substances falls with temperature at 4.K, it is ~,000 times less than at room temperature 1 300K a given release of energy within the winding thus produce a temperature rise,000 times greater than at room temperature K temperature K the smallest energy release can therefore produce catastrophic effects Martin Wilson Lecture slide5

6 Causes of training: () J c decreases with temperature engineering current density Amm T 4T 6T 8T J c * * at any field, J c of NbTi falls ~ linearly with temperature - so any temperature rise drives the conductor towards the resistive state temperature K Martin Wilson Lecture slide6

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 F work done per unit length of conductor if it is pushed a distance dz W = F.d z = B.I.d z frictional heating per unit volume Q = B.J.d z B J typical numbers for NbTi: B = 5T J eng = 5 x 10 8 A.m - so if d = 10 mm then Q =.5 x 10 4 J.m -3 Starting from 4.K q final = 7.5K can you engineer a winding to better than 10 mm? Martin Wilson Lecture slide7

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 10 9 Pa n = 1 / 3 uniaxial strain Q 1 s Ye Y Q 1 =.5 x 10 5 J.m -3 q final = 16K triaxial strain Q 3 3s (1 n ) Y 3Ye (1 n ) Q 3 =.3 x 10 6 J.m -3 q final = 8K 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 Martin Wilson Lecture slide8

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 Martin Wilson Lecture slide9

10 How to reduce training? ) Make the conductor able to withstand disturbances without quenching increase the temperature margin operate at lower current engineering current density Amm T 4T 6T 8T but need more winding to make same field 600 * * 00 Engineering current density Amm * temperature K Field T harder at high fields than at low fields higher critical temperature - HTS? Martin Wilson Lecture slide10

11 energy release How to reduce training? ) 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 Gd O S HoCu 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. MQE 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 field Martin Wilson Lecture slide11

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 Martin Wilson Lecture slide1

13 I heater 15 mj carbon paste heater too big! 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 Energy MQE 10 mj too small! Martin Wilson Lecture slide13

14 MQE mj similar cables with different cooling better cooling gives higher MQE high MQE is best because it is harder to quench the magnet open insulation Porous metal ALS 83 bare bare wire 1000 experimental cable with porous metal heat exchanger 100 excellent heat transfer to the liquid helium coolant I / Ic 40mJ is a pin dropping 40mm Martin Wilson Lecture slide14

15 Factors affecting the Minimum Quench Energy h think of a conductor where a short section has been heated, so that it is resistive q c q o A J P l 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: k( qc qo ) ka( qc qo ) l hpl( qc qo ) Jc ral hp J ( ) l c r qc qo A 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 Energy to set up MPZ is the Minimum Quench Energy 1 long MPZ large MQE Martin Wilson Lecture slide15

16 How to make a long MPZ large MQE thermal conductivity W.m-1.K-1 l J c k( qc qo ) hp r ( qc qo ) A 1 make thermal conductivity k large make resistivity r small make heat transfer hp/a large (but low J eng ) 1.E+05 1.E+04 1.E+03 1.E+0 1.E+01 1.E+00 1.E-01 hi purity Cu OFHC copper epoxy resin NbTi 1.E temperature K Martin Wilson Lecture slide16

17 Large MPZ large MQE less training l J c k( qc qo ) hp r ( qc qo ) A 1 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) Martin Wilson Lecture slide17

18 Another cause of training: flux jumping 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 B y assume it's infinitely long in the z and y directions - simplifies to a 1 dim problem db/dt induces an electric field E which causes screening currents to flow at critical current density J c known as the critical state model or Bean model J in the 1 dim infinite slab geometry, Maxwell's equation says J B x B y x m J m J so uniform J c means a constant field gradient inside the superconductor o z o c Martin Wilson Lecture slide18

19 The flux penetration process plot field profile across the slab B field increasing from zero fully penetrated Bean critical state model current density everywhere is J c or zero change comes in from the outer surface field decreasing through zero Martin Wilson Lecture slide19

20 Flux Jumping a magnetic thermal feedback instability J J screening currents temperature rise reduced critical current density D q B flux motion energy dissipation temperature rise D Q D f -D Jc cure flux jumping by weakening a link in the feedback loop fine filaments reduce D f for a given -D Jc for NbTi the stable diameter is ~ 50mm Martin Wilson Lecture slide0

21 Flux jumping: the numbers for NbTi criterion for stability against flux jumping a = half width of filament so a 1 J c 3g C c mo 1 q q a = 33mm, ie 66mm diameter filaments o typical figures for NbTi at 4.K and 1T J c critical current density = 7.5 x 10 9 Am - g density = 6. x 10 3 kg.m 3 C specific heat = 0.89 J.kg -1 K -1 q c critical temperature = 9.0K Notes: least stable at low field because J c is highest instability gets worse with decreasing temperature because J c 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 Flux jumping is a solved problem Martin Wilson Lecture slide1

22 Magnetization persistent screening currents make the superconductor look like a magnetic material B J magnetization = magnetic moment per unit volume for round wire M Σ I A M 3π J c d A loop area = ac loss / cycle M B ext M magnetic material spoils field quality Hysteresis like iron, but diamagnetic iron H Martin Wilson Lecture slide

23 (Irreversible) magnetization of NbTi M B ext Hysteresis like iron, but diamagnetic M iron H Magnetization is important because it produces field errors and ac losses Martin Wilson Lecture slide3

24 Magnetization M A/m Magnetization M (A/m) Magnetization measurements flux jumping at low field caused by large filaments and high Jc RRP Nb 3 Sn wire with 50mm filaments NbTi wire for RHIC with 6mm filaments total magnetization 0 0 reversible magnetization field B Tesla Field B (T) Martin Wilson Lecture slide4

25 Fine filaments for low magnetization Accelerator magnets need the finest filaments - to minimize field errors and ac losses single stack double stack 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. Martin Wilson Lecture slide5

26 recap M s 3π reduce M by making fine filaments for ease of handling, filaments are embedded in a copper matrix Coupling between filaments J c d f 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 but in changing fields, the filaments are magnetically coupled screening currents go up the left filaments and return down the right Martin Wilson Lecture slide6 M e db dt 1 ρ t pw π per unit volume of wire where r t = resistivity across the matrix and p w = wire twist pitch

27 Magnetization Two components of magnetization 1) persistent current within the filaments M f depends on B M e External field M s λ su 3π J c (B) d where l su = fraction of superconductor in the unit cell f M s ) eddy current coupling between the filaments M e l wu db dt 1 ρ t pw π M e depends on db/dt or M e l wu μ o db dt τ where τ μo ρ t pw π where l wu = fraction of wire in the section Martin Wilson Lecture slide7

28 Accelerator magnets need cables for good tracking connect synchrotron magnets in series to reduce charging voltage must reduce inductance high operating current many wires in parallel 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 J c while inner are still empty rope Rutherford braid wires must be transposed, ie every wire must change places with every other wire inner wires outside outer wires inside Martin Wilson Lecture slide8

29 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 R c additional magnetization and loss Ḃ R c Martin Wilson Lecture slide9

30 Magnetization Coupling and ac losses between filaments in wire J within filaments between filaments in wire within filaments External field between wires in cable Martin Wilson Lecture slide30

31 skew quadrupole erro 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 mt/sec 13 mt/seec 19 mt/sec Field B (T) skew quadrupole error in Nb 3 Sn dipole which has exceptionally large coupling magnetization (University of Twente) Martin Wilson Lecture slide31

32 Concluding remarks 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 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 fine filaments are a good thing Martin Wilson Lecture slide3