W.M. de Rapper , S. Le Naour and H.H.J. ten Kate
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A novel model for Minimum Quench Energy calculation of impregnated Nb3Sn cables and verification on real conductors
W.M. de Rapper, S. Le Naour and H.H.J. ten Kate
CHATS on Appl. Supercond.12th October 2011
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Outline Introduction Thermal stability Conductor design
Model Geometry Thermal calculation Electrical calculation Solving algorithm
Validation on measurement Extrapolation Magnet X-section of measured conductor Outlook: Full scale conductor and magnet
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IntroductionThermal stability:A small perturbation (~1 mJ) results in a small normal zone(1-5 mm) in a conductor
This normal zone eithercollapses or results in athermal run-away (quench)
The goal of this model is to accurately predict the energy needed to initiate a thermal run away in high-Jc Nb3Sn cables and magnets
Boundary conditions: Needs to run on a desktop PC Being able to evaluate measurements directlyWhat is the bare minimum of factors that need to be taken into
account?
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Thermal stability
Initial perturbation
NZ > MPZ
No quench
Strand
NZ < MPZ
Cable
I re-distribution
NZ spreads to neighboring strands
Reduced Joule heating
NZ: Normal ZoneMPZ: Minimum Propagation Zone
Magnet
No recovery possibility Magnet Quench
Cable quench
Strand quench
Recovery by cable
Insufficient Current sharing
Recovery by wire
High energyBad cooling
Low energyGood cooling
Conclusion:There are only two recovery routes There is no need to take any magnet effects into account.
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Conductor: Wire
Made up from small Nb3Sn filaments imbedded in a pure copper matrix (RRP – PIT) with high RRR
Assumptions:Temperature is homogeneous over wire X-sectionNormal current instantly redistributes to Cu (ρNb3Sn>>ρCu)This allows to simulate the wire as a 1D object
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This consists of 14-40 Nb3Sn wires, twisted, rolled and impregnated to form a mechanically stable conductor
Assumptions:The cross contacts are negligibleThe cable geometry is negligibleFully adiabaticThis allows to simulate the cable as system of equidistantly coupled 1D wires
Conductor: Cable
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Conductor: CableThe assumption that there are no cross connections is mandatory:Cross contact resistances must be 100 time as small as adjacent contact resistances to keep AC-loss low.
Exception:Coated wires(Poor thermal stability)
Any useful conductor will have negligible Rc
AC-loss in a typical conductor
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Model: Geometry
The model consists of:1D wiresParallel wiresStraightEquidistantly coupledThis assumes that the cable geometry is irrelevant to model the thermal stability of a Rutherford cable and therefore a magnet.
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Model: Thermal calculation
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Model: Electrical calculation
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Model: Electrical calculation
1 2 3
Bz
y
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Model: Meshing
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Model: Solving algorithmThe model solves:1.Current2.Temperature3.Material properties
Adaptive time stepping to reduce calculation time Limited ΔI Limited ΔT
Model runs until all elements are SC or a length longer than preset value is normalThe initial perturbation is varied to find the Minimum Quench Energy (MQE)
I
T
Prop
+ Δt Δt/2
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Model: SimulationTransient thermal simulation of a perturbation
T (K) I (A) P (W)
t = 0.1 mst = 1.0 mst = 2.0 mst = 4.0 mst = 5.0 mst = 6.0 ms
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A measurement over a large field range, 2 currents and 2 temperatures can be fitted with a single parameter set
Validation
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ExtrapolationThe measured conductor was used in the Small Model Coil 3 (SMC3)
DipoleDouble pancake14 strands1.25 mm13T @ 14.3 kA
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Extrapolation
MeasuredExtrapolated
MQE(B) curve plotted to a field map of the SMC3:
Unmeasurable
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Future workFull-scale magnet with the full-scale conductor:
Assuming full-scale conductor has the same MQE(B) curve!
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Conclusions
To accurately model MQE in High-Jc Nb3Sn cables the following assumptions are appropriate: Fully adiabatic Cross contacts are negligible Cable geometry is negligible 1D wire approximation is correct
Extrapolations for magnet cross section: Total number of cables with weak spots (<10µJ) in
cos(Θ) design much higher as in block design