Magnetization loop modelling for a superconductor/ferromagnetic composite

Transcription

1 Magnetization loop modelling for a superconductor/ferromagnetic composite F. Gömöry, M. Solovyov, J. Šouc Institute of Electrical Engineering, Slovak Academy of Sciences, Bratislava, Slovakia

2 Magnetization loop modelling for a superconductor/ferromagnetic composite of a magnetic cloak (composite = 1SC/1FM) F. Gömöry, M. Solovyov, J. Šouc Institute of Electrical Engineering, Slovak Academy of Sciences, Bratislava, Slovakia

3 Outline 1) Introduction ) Numerical model ) Experimental verification 4) Conclusions

4 Introduction magnetic invisibility cloak: our ultimate goal no distortion of the applied field outside the shielded space

5 Introduction magnetic cloak: more than a simple shield combination of diamagnetic and ferromagnetic material m r m r > 1 m r = 7 m r = 1 m r = 15 no distortion of the applied field outside the cloak μ r R R Fo Fo R R Fi Fi C. Navau, D.-X. Chen, A. Sanchez, N. Del-Valle, Appl. Phys. Lett. 94, 451 (9)

6 magnetic field [mt] magnetic field [mt] DC Cloak (#1) SC tape (Superpower 1 mm wide, turns) Fe9Ni18Cr sheet (.1 mm thick, 5 turns) 1.5 mm mapping of magnetic field (Hall probe) 5 calculation 5 experiment 4 4 B FM only FM only 1 SC/FM cloak 1 SC/FM cloak SC only SC only horizontal coordinate [mm] horizontal coordinate [mm] cloaking properties confirmed F Gömöry, M. Solovyov, J. Šouc, C. Navau, J. Camps, A. Sanchez: Science 5 (1)

7 Finite element calculations in D superconductor: J(A,) formulation E y z z x A t z SC FM single element (tube) smoothed critical state model J = J c tanh(e/e c ) j/j c E/E c zero net transport current achieved through electrostatic charges: in the neutral zone Ez A z t parallel elements (tapes) i J( x, y) i J c tanh 1 E c A( x, y) t A, i

8 Finite element calculations in D ferromagnetic material: magnetic permeability µ r H

9 B Q Finite element calculations in D ferromagnetic material: magnetic permeability µ r AC regime: AC loss because of magnetic hysteresis H FM loss (per unit length) H Q FM FM Q( B ( x, y))dxdy BH D N Nguyen, S P Ashworth, J O Willis, F Sirois, F Grilli, Supercond Sci Technol (1) 51 F Gömöry, M Vojenčiak, E Pardo, M Solovyov, J Šouc, Supercond Sci Technol (1) 41. FM loss is added to the SC loss to obtain the total loss

10 c', c" Cloaking of AC fields new phenomenon: irreversibility of m(b) dependence on history phase shift of induced magnetic field AC loss M = m/v cloak (c = m M/B) c = m m / (V cloak B ) c = m m / (V cloak B ) Q Vcloak c " B m AC susceptibility chi" chi' B [T].1

11 Cloaking of AC fields SC tape (Superpower 1 mm wide, 4 strips) 1 mm Cloak A: Fe9Ni18Cr sheet (.1 mm thick, 5 layers) Cloak B: Fe-Si-B-Cu-Nb metallic glass (.5 mm thick, 4 strips) A B 6 mm

12 Q [J/m ] µr µr Properties of FM materials Fe9Ni18Cr sheet Fe-Si-B-Cu-Nb ribbon Fe-18%Cr-9%Ni sheet Fe-Si-B-Cu-Nb ribbon H [A/m] Fe-Si-B-Cu-Nb Fe-19%Cr-9%Ni H [A/m] mm P. Duhaj, P. Švec, D. Janickovic, I.Matko, M. Hlasnik, Mat. Sci. Eng. B14, 57 (199) H [A/m]

13 Q [J] Cloak A in AC field f = 6 Hz 1.E+ 1.E-1 1.E- SC inner shell FM outer shell SC/FM cloak Calculation separately 1.E- 1.E-4 1.E-5 1.E-6 1.E B [T].1

14 Q Estimation of FM hysteresis loop basic idea: Rayleigh s approach Q B S Chikazumi and C D Graham, Physics of Ferromagnetism, Oxford: Oxford University Press (1997) BH m FM m rev magnetic moment (per unit length) of FM: m FM m rev m hys B ac m hys

15 Q Estimation of FM hysteresis loop basic idea: Rayleigh s approach Q B S Chikazumi and C D Graham, Physics of Ferromagnetism, Oxford: Oxford University Press (1997) BH m FM m rev magnetic moment (per unit length) of FM: m FM m rev m hys B ac m hys ( B ac B ) m hys Q FM m FM db ac B B 8 ( B B db B ac ac Q FM 8 B 1 J Souc, M Solovyov, F Gömöry, J Prat-Camps, C Navau, A Sanchez New J. Phys (1).

16 Q Estimation of FM hysteresis loop basic idea: Rayleigh s approach Q B S Chikazumi and C D Graham, Physics of Ferromagnetism, Oxford: Oxford University Press (1997) BH m FM m rev magnetic moment (per unit length) of FM: m FM m rev m hys m m hys, hys, Q Q FM FM 8 8 B ac m hys ( B ( B B ac B B ac B ) ) Q FM m FM db ac B B m hys ( B 8 ( B B db B ac ac B ac Q FM J Souc, M Solovyov, F Gömöry, J Prat-Camps, C Navau, A Sanchez New J. Phys (1). ) 8 B 1

17 m [Am] m [Am] m [Am] Q [J] c', c" Cloak A in AC field 1.E+ 1.E-1 1.E- f = 6 Hz SC inner shell FM outer shell SC/FM cloak Calculation separately Cloak A assembled chi" calculation chi" experiment chi' calculation chi' experiment 1.E- 1.E-4 1.E-5 1.E E B [T] B [T].1.4 m_fm m_sc m_cloak 1 m_fm m_sc m_cloak 4 m_fm m_sc..5 m_cloak 1 B [T] B [T] B ac [T] FM hysteresis dominates

18 c', c" Cloak B in AC fields chi" calculation chi" experiment chi' calculation chi' experiment B [T].1

19 m [Am] m [Am] m [Am] Cloak B in AC fields.15.1 m_fm m_sc m_cloak m_cloak_exp B [T] m_fm m_sc m_cloak m_cloak_exp.8.4 m_fm m_sc m_cloak m_cloak_exp B [T] B [T].1

20 Cloak C = Cloak B + additional SC layer SC tape (Superpower 1 mm wide, 4 strips) Fe-Si-B-Cu-Nb ribbon (.5 mm thick, 4 strips) SC tape (Superpower 4 mm wide, 9 strips) 1 mm 1 mt

21 c', c" m [Am] Cloak C = Cloak B + additional SC layer 1 mm m_fm m_cloak m_sc m_cloak_exp -..5 chi" c calculation -. chi" c experiment chi' c calculation -.4 chi' c experiment B [T] -.1 very good performance at B < 1 mt B ac [T]

22 Conclusions Numerical modeling for magnetic properties of SC/FM composites in D provides reasonable predictions Adding the approximation of FM hysteresis to the calculated loops allows to understand better the magnetic behavior Design of cloaks reducing the AC magnetic signal x is possible

23 c', c" m [Am] AC field cloaking Experimental apparatus magnetic hysteresis loop 1 B ac = B cos(t) = f, f (6 88 Hz).5 AC susceptibility B ac [T] chi" chi' 1 WAVEFORM RECORDER + VOLTAGE INTEGRATOR B [T].1

24 Properties of FM material(s) ~ 1 meter of tape wound in toroidal sample