Bi Numerical Evaluation of AC Loss Property in Bi-2223 Tapes Affected by Multifilament Structure

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1 Bi-2223 Numerical Evaluation of AC Loss Property in Bi-2223 Tapes Affected by Multifilament Structure Research Institute of Superconductor Science and Systems Kazuhiro Kajikawa, Kazuo Funaki Department of Electrical and Electronic Systems Engineering Daisuke Nakamura, Toshihiro Hayashi Abstract This paper describes the numerical results of AC losses in various types of non-twisted multifilamentary tapes that actual Bi-2223 Ag-sheathed wires are idealized. The penetration process of magnetic flux into the superconductor filaments subject to Bean s critical state model is simulated for the application of an external transverse magnetic field perpendicular to the broadest face of tape wire by means of energy minimization. The AC losses under cyclic fields are calculated from the distribution of a vector potential in an initial state. The influences of arrangements and shapes of the filaments on the losses are investigated as compared with those for a wire that the entire filamentary region is regarded as a homogeneous superconductor.. km Bi-2223 Bi-2223 Bi-2223 Bi-2223, 2) ( ) He is now with Sumitomo Electric Industries, Ltd.

2 3 7) Bean 8) 9, 0) 2. Bi a w 4.0 mm 2b w mm N 2a f 3.6 mm 2b f 0.8 mm α (= a f /b f ) 20 S f πa f b f 4a f b f r Ag S s S s = 4a w b w /( + r Ag ) Table /4 Figs., 2 Table 2 Fig. Fig. 2 Figs. (a) (j) a f Table. Specifications of multifilamentary tapes for loss evaluation Width of tape 2a w 4.0 mm Thickness of tape 2b w mm Width of filamentary region 2a f 3.6 mm Thickness of filamentary region 2b f 0.8 mm Aspect ratio of filamentary region α 20

3 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Fig.. Cross-sectional view of wire models with elliptic filamentary region. All the wires are symmetric with respect to the principal axes, and only a quarter of the cross section is shown in each figure. The characteristic field h c for a homogeneous superconductor with elliptic cross section same as the entire filamentary region is estimated as (a) (b) (c) (d) (e) (f) Fig. 2. Cross-sectional view of wire models with rectangular filamentary region. All the wires are symmetric with respect to the principal axes, and only a quarter of the cross section is shown in each figure. The characteristic field h c for a homogeneous superconductor with rectangular cross section same as the entire filamentary region is estimated as 2.32.

4 Table 2. Characteristics of multifilamentary tapes Structure Filament number, N Silver ratio, r Ag Kink field, h k = H k /H 0 Kink field, h k /h c Fig.(a) Fig.(b) Fig.(c) Fig.(d) Fig.(e) Fig.(f) Fig.(g) Fig.(h) Fig.(i) Fig.(j) Fig.(k) Fig.(l) Fig.2(a) Fig.2(b) Fig.2(c) Fig.2(d) Fig.2(e) < < 0. Fig.2(f) /α (horizontal arrangement) (vertical arrangement) Figs. (b), (e) Figs. (k), (l) Fig. (i) Figs. 2(a) (c) (d) (f) (rectangular packing) (hexagonal packing) Figs. 2(c), (f) Figs., 2 ) z N x, y J c Bean 8) 9, 0) 7, 0)

5 4. H m 2) Γ = W/(2µ 0 H 2 m) W H 0 = J c S s /(2πa f ) h m = H m /H 0 Figs., 2 H c h c = H c /H Figs. 3, Figs. 3, 4 0% (kink field) H k Table 2 H k J c Figs. (b), (e) 55 Figs. 4(a), (b) Figs. 2(a) (c) Figs. 2(d) (f) Fig. 5 6 Fig. 5 Table 2 Fig Fig

6 (a) horizontal arrangement (b) vertical arrangement 0 elliptic superconductor Fig.(a), N = 6 Fig.(b), N = 55 Fig.(c), N = 37 0 elliptic superconductor Fig.(d), N = 6 Fig.(e), N = 55 Fig.(f), N = Fig. 3. Comparison between numerical results of AC losses in multifilamentary tapes with elliptic filamentary region and different filament arrangements. The dotted curve is for the case where the entire filamentary region is regarded as a homogeneous superconductor. (a) rectangular packing (b) hexagonal packing 0 rectangular superconductor Fig.2(a), 7 9 Fig.2(b), 9 7 Fig.2(c), rectangular superconductor Fig.2(d), 7 9 Fig.2(e), 9 7 Fig.2(f), Fig. 4. Comparison between numerical results of AC losses in multifilamentary tapes with rectangular filamentary region and different filament arrangements. The dotted curve is for the case where the entire filamentary region is regarded as a homogeneous superconductor. /3

7 0 elliptic superconductor Fig.(g), r Ag =.5 Fig.(h), r Ag = 2.0 Fig.(a), r Ag = 2.5 Fig.(i), r Ag = 3.0 Fig.(j), r Ag = Fig. 5. Comparison between numerical results of AC losses in multifilamentary tapes with elliptic filamentary region and different silver ratios. The dotted curve is for the case where the entire filamentary region is regarded as a homogeneous superconductor. 0 elliptic superconductor Fig.(i), elliptic filaments Fig.(k), rectangular filaments Fig.(l), rhomboid filaments 0. 0 Fig. 6. Comparison between numerical results of AC losses in multifilamentary tapes with elliptic filamentary region and different filament shapes. The dotted curve is for the case where the entire filamentary region is regarded as a homogeneous superconductor Applied Superconductivity Conference (ASC2006)

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