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Magnetization modeling and measurements

1st Workshop on Accelerator Magnets in HTS May 21 – 23, 2014 Hamburg, Germany (May 22, 2014). Magnetization modeling and measurements. N. Amemiya (Kyoto University ). Background …

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Magnetization modeling and measurements

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  1. 1st Workshop on Accelerator Magnets in HTS May 21 – 23, 2014 Hamburg, Germany (May 22, 2014) Magnetization modeling and measurements N. Amemiya (Kyoto University)

  2. Background … • When using a coated conductor with wide tape shape for an accelerator magnet, its large magnetization is apparently a big concern. • Electromagnetic field analyses, which can clarify the electromagnetic phenomena inside coated conductors, must be powerful tools to study the magnetizations of coated conductors, cables, and coils. Today’s presentation includes … • Modeling cables and coils as well as coated conductors for electromagnetic field analyses • Comparing numerical analyses with experiments N. Amemiya, WAMHTS-1, May 22, 2014

  3. Outline • Principle of modeling and formulation • Magnetization modeling and comparison with measurements in … • Roebel cable: ac losses • Striated coated conductor: ac losses • Dipole magnet comprising race-track coils: field quality (temporal evolution of magnetic field harmonics) • Recent challenge and future plan N. Amemiya, WAMHTS-1, May 22, 2014

  4. Principle of modeling and formulation M. Nii et al. SUST25(2013)095011 N. Amemiya, WAMHTS-1, May 22, 2014

  5. Key points when modeling and our approaches • Superconducting property • Use of the extended Ohm’s law using equivalent (nonlinear) conductivity or resistivity as the constitutive relation • Three-dimensional geometry and very thin superconductor layer of coated conductor • Use of the thin-strip approximation, where the thin strip of superconducting layer of a coated conductor follows a curved geometry of the coated conductor in a cable or in a coil N. Amemiya, WAMHTS-1, May 22, 2014

  6. Governing equation and constitutive equation Equivalent conductivity derived from E-J characteristic: Ex. 〔Definition of current vector potential〕 〔Faraday’s law〕 〔Extended Ohm’s law〕 〔Biot-Savart’s law〕 Thin strip approximation High cross-sectional aspect ratio of coated-conductor allows its use. Integrate along thickness of coated-conductor N. Amemiya, WAMHTS-1, May 22, 2014 Computational cost can be reduced drastically.

  7. Consideration of three-dimensionally-curved coated conductors This term representing B in Faraday’s law is calculated by Biot-Savart’s law based on currents on arbitrary 3D-shaped conductors N. Amemiya, WAMHTS-1, May 22, 2014

  8. Roebel cable N. Amemiya et al. SUST27(2014)035007 N. Amemiya, WAMHTS-1, May 22, 2014

  9. Electromagnetic field analysesand magnetization loss measurements Roebel cable as well as reference conductors N. Amemiya, WAMHTS-1, May 22, 2014

  10. Transverse magnetic field only He / (Ic1/ pw) = 0.5 He / (Ic1/ pw) = 3.2 He / (Ic1/ pw) = 7 N. Amemiya, WAMHTS-1, May 22, 2014

  11. Transverse magnetic field only He / (Ic1/ pw) = 3.2 • (Low field) Single CC >Roebel cable > 32-stack ~ 3-stack • (Mid field) Single CC > Roebel cable ~ 32-stack ~ 3-stack • (High field) Single CC ~ Roebel cable ~ 32-stack ~ 3-stack N. Amemiya, WAMHTS-1, May 22, 2014

  12. Transport current + transverse magnetic field It / Ic1 = 0.6, He / (Ic1/ pw) = 2 N. Amemiya, WAMHTS-1, May 22, 2014

  13. Striated coated conductor N. Amemiya et al. SUST17(2004)1464 N. Amemiya et al. IEEE-TAS15(2005)1637 N. Amemiya, WAMHTS-1, May 22, 2014

  14. Actual 2D analysis region untwisted on a flat plane Model of striated-and-twisted coated conductors N. Amemiya, WAMHTS-1, May 22, 2014

  15. Specifications of conductors for analysis Frequency of transport current and applied magnetic field is fixed at 50 Hz. N. Amemiya, WAMHTS-1, May 22, 2014

  16. Calculated current lines N. Amemiya, WAMHTS-1, May 22, 2014

  17. Multifilament Rg = 0.1 mW Multifilament Rg = 10 mW Monofilament Current distribution in monofilament conductor and multifilamentary conductors carrying no transport current N. Amemiya, WAMHTS-1, May 22, 2014

  18. Specification of measured multifilamentary sample Non twisted but finite length N. Amemiya, WAMHTS-1, May 22, 2014

  19. 1D model and 2D model One-dimensional FEM model Two-dimensional FEM model Enabling us to calculate the current distribution in a wide face of an finite-length conductor at partially decoupled state Enabling us to calculate the current distribution in a cross section of an infinitely-long completely decoupled conductor AC loss reduced to the ideal level in completely decoupled conductor can be calculated. Coupling loss can be studied. N. Amemiya, WAMHTS-1, May 22, 2014

  20. Measured losses in samples with various length ST40L (100 mm) ST40M (50 mm) ST40S (25 mm) Frequency dependence in measured loss disappears with decreasing sample length. N. Amemiya, WAMHTS-1, May 22, 2014

  21. (Qm,f-Qm,0)/(fL2) (Qm,f-Qm,11.3Hz)/(f-11.3) vs. m0Hm Qm,0: extrapolated loss at 0 Hz Coupling loss and hystresis loss components • collapse to one line • slope is 2. Hysteretic loss • Data for each samples collapse to one line. • Slope is 2: Proportional to (m0Hm)2 N. Amemiya, WAMHTS-1, May 22, 2014

  22. At 0.5 mT, 10-1k Hz, the measured loss and calculated loss is compared to determined the transverse resistance between filaments. Measured and calculated coupling loss Rt = 4.8 mW for 1 m • Using this Rt, numerical calculations were made for f = 11.3 Hz, 72.4 Hz & 171.0 Hz, and L = 50 mm & 100 mm. • Calculated coupling losses reasonably agree with experimental values. N. Amemiya, WAMHTS-1, May 22, 2014

  23. Dipole magnet N. Amemiya et al. to be submitted to SUST? N. Amemiya, WAMHTS-1, May 22, 2014

  24. Dipole magnet RTC4-F comprising race-track coils Ic ~ 110 A N. Amemiya, WAMHTS-1, May 22, 2014

  25. Temporal evolutions of current distribution (a) (d) (b) (e) (c) • ↓ • ↓ • ↓ • ↓ • ↓ • ↓ 50A (f) 0 1800 3600 5400 7200 Time (s) (a) (b) (c) (d) (e) (f) Shut down Excited N. Amemiya, WAMHTS-1, May 22, 2014

  26. Comparison between experiment and calculation Hysteresis loop Experiment Calculation Designed value without magnetization substituted N. Amemiya, WAMHTS-1, May 22, 2014

  27. Comparison between experiment and calculation Repeated (50 A, 1 h) – excitations Excited 2-pole 6-pole Experiment Calculation N. Amemiya, WAMHTS-1, May 22, 2014

  28. Comparison between experiment and calculation Influence of 50 A – excitation between 30 A - excitations 2-pole 6-pole Experiment Calculation N. Amemiya, WAMHTS-1, May 22, 2014

  29. Recent challenge and future plan N. Amemiya, WAMHTS-1, May 22, 2014

  30. 3D analyses of cosine-theta magnet Dipole magnet for rotary gantryfor carbon cancer therapy N. Amemiya, WAMHTS-1, May 22, 2014

  31. Coil wound with Roebel cable N. Amemiya, WAMHTS-1, May 22, 2014

  32. Summary • We have been developing models for numerical electromagnetic field analyses of cables and coils consisting of coated conductors. • They have been applied successfully to • HTS Roebelcables • Twisted striated coated conductors • Dipole magnets (2D) and compared with measurements. • Applications to CORC cables as well as twisted stacked-tape cables are possible in principle. • Recent challenge and future plan • 3D analyses of cosine-theta magnet • Coil wound with Roebel cable N. Amemiya, WAMHTS-1, May 22, 2014

  33. Overview of S-Innovation project N. Amemiya, WAMHTS-1, May 22, 2014

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