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

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

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?

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.

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

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

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

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.

Model: Thermal calculation

Model: Electrical calculation

Model: Electrical calculation

1 2 3

Bz

y

Model: Meshing

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

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

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

Validation

ExtrapolationThe measured conductor was used in the Small Model Coil 3 (SMC3)

DipoleDouble pancake14 strands1.25 mm13T @ 14.3 kA

Extrapolation

MeasuredExtrapolated

MQE(B) curve plotted to a field map of the SMC3:

Unmeasurable

Future workFull-scale magnet with the full-scale conductor:

Assuming full-scale conductor has the same MQE(B) curve!

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