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Twist effect on hysteresis loss in Bi2223 multifilamentary wires exposed to an AC magnetic field
Physica C 310 Ž1998. 154–158
Twist effect on hysteresis loss in Bi2223 multifilamentary wires exposed to an AC magnetic field M. Iwakuma a
a,)
, Y. Tajika a , K. Kajikawa a , K. Funaki a , T. Matsushita b, E.S. Otabe b, N. Ayai c , K. Hayashi c , K. Sato c
Research Institute of SuperconductiÕity, Kyushu UniÕersity, 6-10-1 Hakozaki, Higashi-Ku, Fukuoka 812-8581, Japan b Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan c Sumitomo Electric Industries, 1-1-3 Shimaya, Konohana-Ku, Osaka 554-0024, Japan
Abstract We fabricated Bi2223 multifilamentary sample wires with various twist pitches and investigated the electromagnetic properties experimentally. They showed monofilamentlike electromagnetic properties regardless of twisting due to the contacts among filaments andror proximity effect. The observed AC losses in the non-twisted sample wire agreed roughly with the theoretical prediction for a homogeneous superconducting slab with the same thickness of the filamentary region on the basis of Irie–Yamafuji model. However the AC losses in the twisted wires deviated from the theoretical ones, especially for the amplitude around the theoretically predicted penetration field of the slab. We showed that the observed AC loss properties can be explained by both the twist effect for the macroscopic shielding current and the contribution of the local shielding current. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Magnetic AC loss; Bi-2223 tape; Twist; Magnetization
1. Introduction For the application of oxide superconducting wires to the power machines and devices operating at LN2 temperature, we first evaluated the allowable wire parameters, e.g., a filament diameter and so on, assuming that the efficiency of the refrigerator is improved to 1r10 from 1r500 at LHe temperature, and showed that they are going to be realized in the near future w1x. We also proposed the introduction of a parallel conductor to enlarge the current capacity of the currently developed Bi2223 superconducting )
Corresponding author. Fax: q81-92-632-2438; E-mail: [email protected]
wires with a rectangular cross-section w2x. We adopted it for the fabrication of 800 kVA oxide superconducting transformer operating at subcooled LN2 temperature w3x. The AC loss induced in the superconducting windings of the transformer was one of dominant components in the total loss though the efficiency was as high as 99.3% w3x. To further improve the efficiency, we have been investigating the nonuniform current distribution and the additional AC losses due to the deviation of transposing points from the optimum ones in parallel conductors w4–7x. We also have been trying to reduce the AC losses in the strand itself. We showed that the electromagnetic properties of the Bi2223 non-twisted multifilamentary wires which were adopted for the
0921-4534r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 4 5 2 - 3
M. Iwakuma et al.r Physica C 310 (1998) 154–158
155
fabrication of the transformer were monofilamentlike and the AC losses agreed with the theoretical prediction based on the Irie–Yamafuji model w8x for a homogeneous bulk superconductor with the same thickness of the filamentary region w9x. Therefore, we fabricated the Bi2223 multifilamentary wires with various twist pitches and investigated the electromagnetic properties. In this paper, we discuss the observed results, especially a reduction of AC losses for the amplitude around the theoretically predicted penetration field of the slab by twisting. 2. Experiment We fabricated Bi2223 multifilamentary sample wires with various twist pitches. The characteristics of sample wires are listed in Table 1. We first measured the Ic y B characteristics at 77 K in a transverse magnetic field by the 4-probe method. An external magnetic field was applied in the parallel direction with the wide surface. The observed Ic y B characteristics are shown in Fig. 1. Though they are lower than those of previous sample wires w9x, they do not decrease so much as the twist pitches become shorter. We represented the observed Jc y B characteristics by use of Irie–Yamafuji model expressed as Jc s a B gy1 where a and g are pin parameters. Here the value of Jc was evaluated as the average critical current density over the filamentary region. The fitted pin parameters are also shown in Table 1. For the AC loss measurement by the pick-up coil method, sample wires with a length of about 1 m were wound into a one-layer solenoidal coil with a height of 50 mm and an inner diameter of 42 mm. An external magnetic field was applied in the parallel direction with the coil axis at the frequency of 1
Fig. 1. Ic y B characteristics at 77 K.
to 60 Hz. The amplitude dependencies of AC losses observed at 77 K are shown in Fig. 2. The theoretically predicted hysteresis losses on the basis of the Irie–Yamafuji model w8x are also plotted in Fig. 2 compared with the experimental results. The theoretical expressions are described in Ref. w9x. Here we supposed both cases where the electromagnetic properties of sample wires are equivalent to those of the ideal multifilamentary superconducting wires and those of the homogeneous superconducting slab with the same thickness of the filamentary region. The broken and solid lines in Fig. 2 correspond to the former and the latter cases, respectively. The observed AC losses in the non-twisted, a1, sample wire agreed comparatively well with the theoretical prediction in a superconducting slab for any amplitude. The observed results in the other sample wires also appear to agree with theoretical ones in the superconducting slab for the large amplitude though
Table 1 Characteristics of Bi2223 sample wires Sample number Silver matrixrBi2223 Number of filament Filament thickness Sizes Sizes of filamentary region Twist pitch wmmx Pin parameters, a Pin parameters, g
a1
a2
a3
` 6.51 = 10 6 0.704
2.3r1 61 ; 20 mm 0.22 mm = 3.3 mm 0.154 mm = 3.2 mm 32.3 6.17 = 10 6 0.703
9.6 4.18 = 10 6 0.686
156
M. Iwakuma et al.r Physica C 310 (1998) 154–158
for the amplitude around the theoretically predicted penetration field, Bp s Ž2 y g . m 0 a d fr 41rŽ2y g . as shown in Fig. 2. Here d fr is the thickness of the filamentary region. Correspondingly the AC loss curves of the twisted wires shown in Fig. 2Žb. and Žc. have double breaking points. The AC losses for the smaller amplitude than the lower breaking point became larger with the decrease of twist pitch. We also observed the magnetization curves. The observed results in the non-twisted, a1, sample wire and the most tightly twisted, a3, wire are shown in Figs. 3 and 4, respectively. Fig. 3Žb. and Fig. 4Žb. are only expanded in the horizontal direction. As evident from Figs. 3 and 4, the magnetization curves are tilting at a low magnetic field and the slopes of tilting vary gently. The apparent Bp in Fig. 4Žb. corresponds to the lower breaking point in the AC loss curve shown in Fig. 2Žc.. Comparing Fig. 3Žb. with Fig. 4Žb., we can see that the magnetization curves in the twisted wire are constricted in the vertical direction beyond the contribution of the decrease of Ic in the magnetic field around the theoretical Bp in the slab. Such a reduction of magnetization was enhanced with the decrease of twist pitch.
Fig. 2. AC loss vs. magnetic field amplitude in Ža. a1, Žb. a2 and Žc. a3 sample wires. T s 77 K. The solid and broken lines represent the theoretical prediction of hysteresis losses on the basis of Irie–Yamafuji model for the respective case of monofilamentary and multifilamentary wires.
a little frequency dependence is observed. However, as the twist pitch became shorter, the observed AC losses became smaller than the monofilamentary level
Fig. 3. Observed magnetization curves in a1 sample wire for the various amplitudes. Žb. Shows the enlarged magnetization curves for the small amplitude. T s 77 K.
M. Iwakuma et al.r Physica C 310 (1998) 154–158
157
3. Discussion
in the bent wires at 1 Hz are shown in Fig. 2 in comparison to the results in the non-bent wires. The AC losses induced in the local loops were considerably large contrary to our expectation. Here, assuming that the observed AC losses in the bent wires are caused only by the local shielding current, we estimated the AC losses due to the macroscopic shielding current by subtracting AC losses in the bent wire from those in the non-bent wires. The results at 1 Hz are shown in Fig. 5. The AC losses due to the macroscopic shielding current decrease as the twist pitch becomes shorter for the larger amplitude than Bp . On the other hand, for the smaller amplitude than Bp , the AC losses increase by twisting. Such AC loss properties due to the macroscopic shielding current are similar to those caused by the twist effect, which was observed in in-situ and powder metallurgy processed Nb 3 Sn wires w11,12x. These types of wires have many fine filaments and show the monofilamentlike electromagnetic properties due to the contact among filaments andror the proximity effect. The effective Jc in the direction perpendicular to the filaments should be much lower than Jc along the filaments which is equal to the transport Jc evaluated from the measurement of critical current by the 4-probe method. The twist effect is originated from the anisotropy of Jc . By twisting the wires, the shielding current density in the direction of wire axis
It seems that the double breaking points in the AC loss curves shown in Fig. 2 and the tilting magnetization curves shown in Figs. 3 and 4 suggest the presence of the local shielding current in addition to the macroscopic shielding current which corresponds to the transport current w10x. Therefore, in order to investigate the contribution of the local shielding current, we bent the sample wires repeatedly all over the length to diminish the macroscopic shielding current, and measured the magnetization curves and the AC losses in the same way as above-mentioned. As a result, though the magnetization curves were constricted in the vertical direction compared with those of the non-bent wires, the magnitude of the tilting of magnetization curves was not changed. Therefore the tilting of magnetization curve seems to be originated from HC1 in the grains. The gentle variations of the tilting slopes suggest that the grain sizes are widely distributed. The AC losses observed
Fig. 5. Estimated AC losses due to the macroscopic shielding current vs. magnetic field amplitude at 1 Hz.
Fig. 4. Observed magnetization curves in a3 sample wire for the various amplitudes. Žb. Shows the enlarged magnetization curves for the small amplitude. T s 77 K.
This corresponds to the reduction of AC losses for the amplitude around the theoretical Bp .
158
M. Iwakuma et al.r Physica C 310 (1998) 154–158
induced by the external transverse magnetic field is reduced compared with Jc along the filaments. It exactly corresponds to the decrease of Bp on the AC loss properties. That is, the AC losses in the twisted wires are smaller and larger than those of non-twisted wires for the respective amplitude larger and smaller than the effective Bp . The deviations of AC losses from those in non-twisted wires become larger with the decrease of the twist pitch. These facts are similar to those in the present sample wires. Hence, we concluded that the sample wires have monofilament-like electromagnetic properties and the observed AC loss properties result from the facts that the AC losses due to the macroscopic shielding current are reduced by the well-known twist effect while the AC losses induced in the local shielding loops do not change by twisting.
4. Summary We fabricated Bi2223 multifilamentary sample wires with various twist pitches and investigated the electromagnetic properties experimentally. The sample wires showed the monofilament-like electromagnetic properties due to the contact among filaments andror the proximity effect. The AC losses in the non-twisted wire roughly agreed with the theoretical prediction for a superconducting slab with the same thickness of the filamentary region. However the AC losses in the twisted wires were reduced by twisting only for the amplitude around the theoretical Bp in the slab. We showed that the phenomena can be explained by both the twist effect for the macroscopic shielding current and the contribution of the local shielding current which does not change by twisting. To develop a ideal Bi2223 multifilamentary
wire, we have to reduce the coupling among filaments. References w1x M. Iwakuma, K. Funaki, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, T. Haruyama, et al. ŽEds.., Proc. of ICEC16rICMC, Elsevier, Oxford, 1997, 1325. w2x M. Iwakuma, K. Funaki, K. Kanegae, H. Shinohara, T. Wakuda, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, T. Haruyama, et al. ŽEds.., Proc. of ICEC16rICMC, Elsevier, Oxford, 1997, 1329. w3x K. Funaki, M. Iwakuma, M. Takeo, K. Yamafuji, J. Suehiro, M. Hara, M. Konno, Y. Kasagawa, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, IEEE Trans. Appl. Supercond. 7 Ž1997. 824. w4x M. Iwakuma, K. Funaki, K. Kanegae, H. Shinohara, T. Wakuda, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, IEEE Trans. Appl. Supercond. 7 Ž1997. 298. w5x M. Iwakuma, K. Funaki, H. Shinohara, T. Sadohara, M. Takeo, K. Yamafuji, M. Konnno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, Advances in Superconductivity IX Ž1996. 831. w6x M. Iwakuma, T. Sadohara, H. Tanaka, K. Kajikawa, T. Matsushita, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, to be published in Proc. of MT-15, PD-48. w7x M. Iwakuma, H. Mori, A. Yoshimura, K. Kajikawa, T. Matsushita, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, to be published in Proc. of MT-15, PB-19. w8x F. Irie, Y. Yamafuji, J. Phys. Soc. Jpn. 23 Ž1967. 255. w9x M. Iwakuma, M. Okabe, K. Kajikawa, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, Advances in Superconductivity X Ž1997. 833. w10x K.-H. Muller, C. Andrikidis, K. Tachikawa, et al. ŽEds.., ¨ Critical State in Superconductors, World Scientific, Singapore, 1995, 36. w11x W.J. Carr Jr., J. Appl. Phys. 54 Ž1983. 6549. w12x M. Iwakuma, Y. Tomita, K. Yamafuji, F. Sumiyoshi, T. Miyatake, R. Ogawa, K. Matsumoto, Cryogenic Engineering 22 Ž1987. 186, in Japanese.
Twist effect on hysteresis loss in Bi2223 multifilamentary wires exposed to an AC magnetic field M. Iwakuma a
a,)
, Y. Tajika a , K. Kajikawa a , K. Funaki a , T. Matsushita b, E.S. Otabe b, N. Ayai c , K. Hayashi c , K. Sato c
Research Institute of SuperconductiÕity, Kyushu UniÕersity, 6-10-1 Hakozaki, Higashi-Ku, Fukuoka 812-8581, Japan b Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan c Sumitomo Electric Industries, 1-1-3 Shimaya, Konohana-Ku, Osaka 554-0024, Japan
Abstract We fabricated Bi2223 multifilamentary sample wires with various twist pitches and investigated the electromagnetic properties experimentally. They showed monofilamentlike electromagnetic properties regardless of twisting due to the contacts among filaments andror proximity effect. The observed AC losses in the non-twisted sample wire agreed roughly with the theoretical prediction for a homogeneous superconducting slab with the same thickness of the filamentary region on the basis of Irie–Yamafuji model. However the AC losses in the twisted wires deviated from the theoretical ones, especially for the amplitude around the theoretically predicted penetration field of the slab. We showed that the observed AC loss properties can be explained by both the twist effect for the macroscopic shielding current and the contribution of the local shielding current. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Magnetic AC loss; Bi-2223 tape; Twist; Magnetization
1. Introduction For the application of oxide superconducting wires to the power machines and devices operating at LN2 temperature, we first evaluated the allowable wire parameters, e.g., a filament diameter and so on, assuming that the efficiency of the refrigerator is improved to 1r10 from 1r500 at LHe temperature, and showed that they are going to be realized in the near future w1x. We also proposed the introduction of a parallel conductor to enlarge the current capacity of the currently developed Bi2223 superconducting )
Corresponding author. Fax: q81-92-632-2438; E-mail: [email protected]
wires with a rectangular cross-section w2x. We adopted it for the fabrication of 800 kVA oxide superconducting transformer operating at subcooled LN2 temperature w3x. The AC loss induced in the superconducting windings of the transformer was one of dominant components in the total loss though the efficiency was as high as 99.3% w3x. To further improve the efficiency, we have been investigating the nonuniform current distribution and the additional AC losses due to the deviation of transposing points from the optimum ones in parallel conductors w4–7x. We also have been trying to reduce the AC losses in the strand itself. We showed that the electromagnetic properties of the Bi2223 non-twisted multifilamentary wires which were adopted for the
0921-4534r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 4 5 2 - 3
M. Iwakuma et al.r Physica C 310 (1998) 154–158
155
fabrication of the transformer were monofilamentlike and the AC losses agreed with the theoretical prediction based on the Irie–Yamafuji model w8x for a homogeneous bulk superconductor with the same thickness of the filamentary region w9x. Therefore, we fabricated the Bi2223 multifilamentary wires with various twist pitches and investigated the electromagnetic properties. In this paper, we discuss the observed results, especially a reduction of AC losses for the amplitude around the theoretically predicted penetration field of the slab by twisting. 2. Experiment We fabricated Bi2223 multifilamentary sample wires with various twist pitches. The characteristics of sample wires are listed in Table 1. We first measured the Ic y B characteristics at 77 K in a transverse magnetic field by the 4-probe method. An external magnetic field was applied in the parallel direction with the wide surface. The observed Ic y B characteristics are shown in Fig. 1. Though they are lower than those of previous sample wires w9x, they do not decrease so much as the twist pitches become shorter. We represented the observed Jc y B characteristics by use of Irie–Yamafuji model expressed as Jc s a B gy1 where a and g are pin parameters. Here the value of Jc was evaluated as the average critical current density over the filamentary region. The fitted pin parameters are also shown in Table 1. For the AC loss measurement by the pick-up coil method, sample wires with a length of about 1 m were wound into a one-layer solenoidal coil with a height of 50 mm and an inner diameter of 42 mm. An external magnetic field was applied in the parallel direction with the coil axis at the frequency of 1
Fig. 1. Ic y B characteristics at 77 K.
to 60 Hz. The amplitude dependencies of AC losses observed at 77 K are shown in Fig. 2. The theoretically predicted hysteresis losses on the basis of the Irie–Yamafuji model w8x are also plotted in Fig. 2 compared with the experimental results. The theoretical expressions are described in Ref. w9x. Here we supposed both cases where the electromagnetic properties of sample wires are equivalent to those of the ideal multifilamentary superconducting wires and those of the homogeneous superconducting slab with the same thickness of the filamentary region. The broken and solid lines in Fig. 2 correspond to the former and the latter cases, respectively. The observed AC losses in the non-twisted, a1, sample wire agreed comparatively well with the theoretical prediction in a superconducting slab for any amplitude. The observed results in the other sample wires also appear to agree with theoretical ones in the superconducting slab for the large amplitude though
Table 1 Characteristics of Bi2223 sample wires Sample number Silver matrixrBi2223 Number of filament Filament thickness Sizes Sizes of filamentary region Twist pitch wmmx Pin parameters, a Pin parameters, g
a1
a2
a3
` 6.51 = 10 6 0.704
2.3r1 61 ; 20 mm 0.22 mm = 3.3 mm 0.154 mm = 3.2 mm 32.3 6.17 = 10 6 0.703
9.6 4.18 = 10 6 0.686
156
M. Iwakuma et al.r Physica C 310 (1998) 154–158
for the amplitude around the theoretically predicted penetration field, Bp s Ž2 y g . m 0 a d fr 41rŽ2y g . as shown in Fig. 2. Here d fr is the thickness of the filamentary region. Correspondingly the AC loss curves of the twisted wires shown in Fig. 2Žb. and Žc. have double breaking points. The AC losses for the smaller amplitude than the lower breaking point became larger with the decrease of twist pitch. We also observed the magnetization curves. The observed results in the non-twisted, a1, sample wire and the most tightly twisted, a3, wire are shown in Figs. 3 and 4, respectively. Fig. 3Žb. and Fig. 4Žb. are only expanded in the horizontal direction. As evident from Figs. 3 and 4, the magnetization curves are tilting at a low magnetic field and the slopes of tilting vary gently. The apparent Bp in Fig. 4Žb. corresponds to the lower breaking point in the AC loss curve shown in Fig. 2Žc.. Comparing Fig. 3Žb. with Fig. 4Žb., we can see that the magnetization curves in the twisted wire are constricted in the vertical direction beyond the contribution of the decrease of Ic in the magnetic field around the theoretical Bp in the slab. Such a reduction of magnetization was enhanced with the decrease of twist pitch.
Fig. 2. AC loss vs. magnetic field amplitude in Ža. a1, Žb. a2 and Žc. a3 sample wires. T s 77 K. The solid and broken lines represent the theoretical prediction of hysteresis losses on the basis of Irie–Yamafuji model for the respective case of monofilamentary and multifilamentary wires.
a little frequency dependence is observed. However, as the twist pitch became shorter, the observed AC losses became smaller than the monofilamentary level
Fig. 3. Observed magnetization curves in a1 sample wire for the various amplitudes. Žb. Shows the enlarged magnetization curves for the small amplitude. T s 77 K.
M. Iwakuma et al.r Physica C 310 (1998) 154–158
157
3. Discussion
in the bent wires at 1 Hz are shown in Fig. 2 in comparison to the results in the non-bent wires. The AC losses induced in the local loops were considerably large contrary to our expectation. Here, assuming that the observed AC losses in the bent wires are caused only by the local shielding current, we estimated the AC losses due to the macroscopic shielding current by subtracting AC losses in the bent wire from those in the non-bent wires. The results at 1 Hz are shown in Fig. 5. The AC losses due to the macroscopic shielding current decrease as the twist pitch becomes shorter for the larger amplitude than Bp . On the other hand, for the smaller amplitude than Bp , the AC losses increase by twisting. Such AC loss properties due to the macroscopic shielding current are similar to those caused by the twist effect, which was observed in in-situ and powder metallurgy processed Nb 3 Sn wires w11,12x. These types of wires have many fine filaments and show the monofilamentlike electromagnetic properties due to the contact among filaments andror the proximity effect. The effective Jc in the direction perpendicular to the filaments should be much lower than Jc along the filaments which is equal to the transport Jc evaluated from the measurement of critical current by the 4-probe method. The twist effect is originated from the anisotropy of Jc . By twisting the wires, the shielding current density in the direction of wire axis
It seems that the double breaking points in the AC loss curves shown in Fig. 2 and the tilting magnetization curves shown in Figs. 3 and 4 suggest the presence of the local shielding current in addition to the macroscopic shielding current which corresponds to the transport current w10x. Therefore, in order to investigate the contribution of the local shielding current, we bent the sample wires repeatedly all over the length to diminish the macroscopic shielding current, and measured the magnetization curves and the AC losses in the same way as above-mentioned. As a result, though the magnetization curves were constricted in the vertical direction compared with those of the non-bent wires, the magnitude of the tilting of magnetization curves was not changed. Therefore the tilting of magnetization curve seems to be originated from HC1 in the grains. The gentle variations of the tilting slopes suggest that the grain sizes are widely distributed. The AC losses observed
Fig. 5. Estimated AC losses due to the macroscopic shielding current vs. magnetic field amplitude at 1 Hz.
Fig. 4. Observed magnetization curves in a3 sample wire for the various amplitudes. Žb. Shows the enlarged magnetization curves for the small amplitude. T s 77 K.
This corresponds to the reduction of AC losses for the amplitude around the theoretical Bp .
158
M. Iwakuma et al.r Physica C 310 (1998) 154–158
induced by the external transverse magnetic field is reduced compared with Jc along the filaments. It exactly corresponds to the decrease of Bp on the AC loss properties. That is, the AC losses in the twisted wires are smaller and larger than those of non-twisted wires for the respective amplitude larger and smaller than the effective Bp . The deviations of AC losses from those in non-twisted wires become larger with the decrease of the twist pitch. These facts are similar to those in the present sample wires. Hence, we concluded that the sample wires have monofilament-like electromagnetic properties and the observed AC loss properties result from the facts that the AC losses due to the macroscopic shielding current are reduced by the well-known twist effect while the AC losses induced in the local shielding loops do not change by twisting.
4. Summary We fabricated Bi2223 multifilamentary sample wires with various twist pitches and investigated the electromagnetic properties experimentally. The sample wires showed the monofilament-like electromagnetic properties due to the contact among filaments andror the proximity effect. The AC losses in the non-twisted wire roughly agreed with the theoretical prediction for a superconducting slab with the same thickness of the filamentary region. However the AC losses in the twisted wires were reduced by twisting only for the amplitude around the theoretical Bp in the slab. We showed that the phenomena can be explained by both the twist effect for the macroscopic shielding current and the contribution of the local shielding current which does not change by twisting. To develop a ideal Bi2223 multifilamentary
wire, we have to reduce the coupling among filaments. References w1x M. Iwakuma, K. Funaki, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, T. Haruyama, et al. ŽEds.., Proc. of ICEC16rICMC, Elsevier, Oxford, 1997, 1325. w2x M. Iwakuma, K. Funaki, K. Kanegae, H. Shinohara, T. Wakuda, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, T. Haruyama, et al. ŽEds.., Proc. of ICEC16rICMC, Elsevier, Oxford, 1997, 1329. w3x K. Funaki, M. Iwakuma, M. Takeo, K. Yamafuji, J. Suehiro, M. Hara, M. Konno, Y. Kasagawa, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, IEEE Trans. Appl. Supercond. 7 Ž1997. 824. w4x M. Iwakuma, K. Funaki, K. Kanegae, H. Shinohara, T. Wakuda, M. Takeo, K. Yamafuji, M. Konno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, IEEE Trans. Appl. Supercond. 7 Ž1997. 298. w5x M. Iwakuma, K. Funaki, H. Shinohara, T. Sadohara, M. Takeo, K. Yamafuji, M. Konnno, Y. Kasagawa, K. Okubo, I. Itoh, S. Nose, M. Ueyama, K. Hayashi, K. Sato, Advances in Superconductivity IX Ž1996. 831. w6x M. Iwakuma, T. Sadohara, H. Tanaka, K. Kajikawa, T. Matsushita, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, to be published in Proc. of MT-15, PD-48. w7x M. Iwakuma, H. Mori, A. Yoshimura, K. Kajikawa, T. Matsushita, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, to be published in Proc. of MT-15, PB-19. w8x F. Irie, Y. Yamafuji, J. Phys. Soc. Jpn. 23 Ž1967. 255. w9x M. Iwakuma, M. Okabe, K. Kajikawa, K. Funaki, M. Konno, S. Nose, M. Ueyama, K. Hayashi, K. Sato, Advances in Superconductivity X Ž1997. 833. w10x K.-H. Muller, C. Andrikidis, K. Tachikawa, et al. ŽEds.., ¨ Critical State in Superconductors, World Scientific, Singapore, 1995, 36. w11x W.J. Carr Jr., J. Appl. Phys. 54 Ž1983. 6549. w12x M. Iwakuma, Y. Tomita, K. Yamafuji, F. Sumiyoshi, T. Miyatake, R. Ogawa, K. Matsumoto, Cryogenic Engineering 22 Ž1987. 186, in Japanese.