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W.M. de Rapper , S. Le Naour and H.H.J. ten Kate

A novel model for Minimum Quench Energy calculation of impregnated Nb 3 Sn cables and verification on real conductors. W.M. de Rapper , S. Le Naour and H.H.J. ten Kate. CHATS on Appl. Supercond . 12 th October 2011. Outline. Introduction Thermal stability Conductor design Model

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W.M. de Rapper , S. Le Naour and H.H.J. ten Kate

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  1. 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

  2. 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

  3. Introduction Thermal stability: A small perturbation (~1 mJ) results in a small normal zone (1-5 mm) in a conductor This normal zone either collapses or results in a thermal 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 directly • What is the bare minimum of factors that need to be taken into account?

  4. Thermalstability Strand NZ: Normal Zone MPZ: Minimum Propagation Zone Low energy Goodcooling High energy Bad cooling Initialperturbation NZ > MPZ NZ < MPZ Recovery bywire No quench Strand quench Cable I re-distribution Reduced Joule heating Recovery bycable Currentsharing Insufficient NZ spreads toneighboring strands Magnet Cable quench MagnetQuench No recovery possibility Conclusion: There are onlytwo recovery routes There is no needto take anymagnet effects into account.

  5. Conductor: Wire Made up from small Nb3Sn filaments imbedded in a pure coppermatrix (RRP – PIT) with high RRR Assumptions: Temperature is homogeneous over wire X-section Normalcurrentinstantlyredistributesto Cu (ρNb3Sn>>ρCu) Thisallowstosimulate the wire as a 1D object

  6. Conductor: Cable This consists of 14-40 Nb3Sn wires, twisted, rolled and impregnated to form a mechanically stable conductor Assumptions: The cross contacts are negligible The cable geometry is negligible Fully adiabatic This allows to simulate the cable as system of equidistantlycoupled1D wires

  7. Conductor: Cable AC-loss in a typical conductor The 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

  8. Model: Geometry The model consists of: 1D wires Parallel wires Straight Equidistantly coupled This assumes that the cable geometry is irrelevant to model the thermal stability of a Rutherford cable and therefore a magnet.

  9. Model: Thermal calculation

  10. Model: Electrical calculation

  11. Model: Electrical calculation 1 2 3 Bz y

  12. Model: Meshing

  13. Model: Solving algorithm I Δt/2 + Δt T Prop The model solves: • Current • Temperature • 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 normal • The initial perturbation is varied to find the Minimum Quench Energy (MQE)

  14. Model: Simulation t = 5.0 ms t = 4.0 ms t = 6.0 ms t = 2.0 ms t = 1.0 ms t = 0.1 ms T (K) I (A) P (W) QUENCH Transient thermal simulation of a perturbation

  15. Validation A measurement over a large field range, 2 currents and 2 temperatures can be fitted with a single parameter set

  16. Extrapolation The measured conductor was used in the Small Model Coil 3 (SMC3) Dipole Double pancake 14 strands 1.25 mm 13T @ 14.3 kA

  17. Extrapolation Unmeasurable Measured Extrapolated MQE(B) curve plotted to a field map of the SMC3:

  18. Future work Assuming full-scale conductor has the same MQE(B) curve! Full-scale magnet with the full-scale conductor:

  19. 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 cableswith weak spots (<10µJ) in cos(Θ) design much higher as in block design

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