Cu composite conductors

Physica C 354 (2001) 256±259

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Critical current density and magnetization of proximity-e€ect-induced superconducting Cu in multi®lamentary NbTi/Cu composite conductors Y. Kubota a,*, T. Moriya b, K. Yasohama a b

a College of Science and Technology, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101 8308, Japan Powertrain Manufacturing Engineering Department No. 2, Isuzu Motors Ltd., Tono-machi, Kawasaki-ku, Kawasaki-shi, Kanagawa 210 8524, Japan

Abstract The magnetization Mp of proximity-e€ect-induced superconducting Cu (PEISC) in multi®lamentary NbTi/Cu composite conductors has been measured in transverse ®elds Be smaller than Bc1 of the NbTi ®lament at 4.2 K. The conductors were designed speci®cally to subtract out the magnetization of the NbTi ®laments from magnetization of the conductors. The ®lament spacing is 1.38 lm and the width of the regular hexagonal ®lament is 7.60 lm. Twist pitches are 6.9, 13, 20, 94 and 189 mm. Mp was investigated as a function of the twist pitch lp and the ®eld amplitude Bm . The ®rst penetration ®eld Bc1p of the magnetic ¯ux, the decoupling ®eld Bdp of the ®lament coupling, and the width of the Mp at a given ®eld are directly proportional to the twist pitch. Mp magnetization loops intersect each other for Bc1p 6 Bm 6 Bdp and decrease suddenly at Bdp . The critical current density Jcp of PEISC is proportional to Be 2 and its value is 10 kA/m2 at 7 mT. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Proximity e€ect; Magnetization; Critical current density; Multi®lamentary NbTi/Cu

1. Introduction Considerable progress in the manufacturing techniques for multi®lamentary composite conductors has opened new prospects. Unfortunately, it was also found that ac losses in the conductor increased remarkably with decreasing ®lament spacing. This e€ect results from ®lament coupling due to proximity-e€ect-induced superconductivity in the normal matrix of the conductor. Therefore, the

amount of excess magnetization in the multi®lamentary composite conductor is greater than that estimated from BeanÕs critical state model [1,2]. The purpose of this paper is to measure the magnetization Mp of proximity-e€ect-induced superconductivity in Cu (PEISC) in multi®lamentary NbTi/Cu composite conductors and also to investigate the critical current density, their characteristic ®elds and Mp dependence on the twist pitch lp . 2. Experimental details

*

Corresponding author. Fax: +81-3-3293-8269. E-mail address: [email protected] (Y. Kubota).

The samples of the conductors used to measure the magnetization Mp of PEISC in multi®lamentary NbTi/Cu composite conductors have the

0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 0 7 4 - 0

Y. Kubota et al. / Physica C 354 (2001) 256±259

following speci®cations: 0.337 mm ®lament diameter, 7.60 lm width of the regular hexagonal ®lament, 1.38 lm ®lament spacing, and 931 ®laments number. They have twist pitches lp of 6.9, 13, 20, 94 and 189 mm. For the isothermal magnetization measurements, sample conductors of 12 cm in length were wound onto a FRP bobbin in the form of a bi®lar noninductive coil of three layers. A magnetic ®eld Be ˆ Bm sin xt was generated by a copper coil. The frequency of the ®eld is 0.1 Hz. Mp was measured by standard electric methods. The signal from two concentric pickup coils, one inside the sample, one outside, was fed through a ¯ux meter to a signal analyzer. Then, by adjusting the two coils, it was possible to subtract the diamagnetic signal of the NbTi ®laments from the signals balanced in the normal state. The resulting signal of the ¯ux meter, therefore, is just equal to Mp . 3. Results and discussion Consider a multi®lamentary composite conductor in a low transverse ®eld Be . A shielding current Jsz will ¯ow along the outermost surface of PEISC parallel to the z-axis (see Fig. 1). When tan h ˆ 2pRp =lp  1, we may calculate Jp ˆ Jsz  …2pRp =lp † and Jtf ˆ Jsz ‰1 ‡ 1=2…2pRp =lp †2 Š where Jp and Jtf are the two components of Josephson current ¯owing in the orthogonal and parallel directions to the ®lament, and Rp is the radius of PEISC region. Note that Jp is much smaller than Jtf and that they increase with Be up to Bpp which

Fig. 1. Schematic illustration of a multi®lamentary composite, where Be is the external ®eld. Jsz (Jp , Jtf ) is the shielding current density along the z-axis. Jp and Jtf are the components of the Josephson current ¯owing in the orthogonal and parallel directions to the ®lament.

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is the penetration ®eld of PEISC corresponding to Bp of a superconductor. Bc1p and Bdp in PEISC are determined by Jcp only. Combining MaxwellÕs equation of rot B ˆ l0 J and Jp , the two characteristics ®elds can be written within the BeanÕs critical state model as Bc1p ˆ D1 Jcp …lp =2pRp †;

…1†

Bdp ˆ D2 Jcp …lp =2pRp †;

…2†

where D1 and D2 are constants depending on the properties of matrix and ®lament spacing, Jcp is the critical current density in PEISC, Bc1p is the ®rst penetration ®eld in PEISC and Bdp is the ®eld at which the ®lament coupling due to the proximity-e€ect vanishes. We will call this the decoupling ®eld. For Bm 6 Bc1p , Mp exhibits the perfect diamagnetism of a magnetization of a type I superconductor, it forms a reversible straight line. The gradients are independent of lp . That implies that the region of PEISC does not vary with lp . For Bc1p < Bm < Bdp , spaces between the outermost adjacent ®laments are not saturated with the critical current of PEISC. Fig. 2 shows two Mp loops of PEISC in the lp ˆ 20 mm sample for Bm ˆ 0:36 and 0.53 mT, both near Bdp … ˆ 0:46 mT†. The Mp loop for Bm ˆ 0:36 mT has very little irreversibility and is nearly a straight line. In this case Mp approaches that of a bulk superconductor with the same diameter as PEISC.

Fig. 2. Low ®eld Mp loops for the sample with lp ˆ 20 mm.

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Y. Kubota et al. / Physica C 354 (2001) 256±259

For Bdp 6 Bm 6 Bpp , the Mp loops display an anomalous behavior. For Bm ˆ 0:53 mT, slightly greater than Bdp , there is a sharp break in Mp at Bdp and the Mp loop shows a hysteretic behavior. There are signi®cant di€erences between PEISC and a superconductor. Mp is not restricted to the width of the loops at larger ®elds and thus a series of intersecting Mp loops arises. The shape of the Mp loop changes from a parallelogram in low ®elds to an extremely asymmetric shape with respect to Mp ˆ 0 in high ®elds. The loops have approximately the same width DM at Be ˆ 0. For Be ˆ Bdp , the central parts of PEISC between the outermost adjacent ®laments saturate and then the coupling between outermost ®laments is broken. There also is the critical current density Jcp ¯owing through PEISC. This current is simply equal to that which produced the Bdp , and therefore the shielding current ¯ow suddenly changes its direction from a ¯ow parallel to the z-axis to one parallel to the ®laments. As the shielding currents increase with Be up to Bpp , the outermost regions of PEISC tend to saturate and, in turn, the shielding currents ¯ow into the interior of the PEISC. Therefore, all ®laments will be decoupled at Be ˆ Bpp . Mp behaves as a collection of individual ®laments yielding a hysteretic magnetization. For Bm > Bpp , Fig. 3 shows Mp for the lp ˆ 20 mm sample for Bm ˆ 3 and 9 mT. Mp behavior vs. Be is roughly accordant with the critical state model and similar to those of high Tc superconductors. The high-®eld Mp is roughly symmetric with respect to the M ˆ 0 axis and the width DM of Mp at a given ®eld always decreases with increasing jBm j. The ®gure shows that the Mp loops behave just like those of type II superconductors and can be approximated rather well by exp Be . Also DMp is proportional to lp as estimated by Harada et al. [3] but DM…0† is independent of lp . Fig. 4 shows the lower critical ®eld Bc1p of PEISC as a function of lp . Bc1p is determined as that ®eld at which the di€erential magnetization dMp =dBe vs. Be curves at a constant sweep rate of the ®eld depart from a constant value due to the Meissner e€ect. Bc1p is proportional to lp . Fig. 5 shows Bdp as a function of the twist pitch lp . The twist pitch dependence of Bdp approxi-

Fig. 3. High ®eld Mp loops for the sample with lp ˆ 20 mm.

Fig. 4. Bc1p as a function of lp .

mately follows the model. The values of Bdp were directly derived from experiment. Fig. 6 shows Jcp as a function of Be . Jcp as estimated from the twist pitch dependence of Mp is proportional to Be 2 . The discrepancy between this result and the theoretical results for SNS junctions may depend on the network of a large number of SNS junctions. Jcp is lower by six and seven orders of magnitude than the critical current density in NbTi ®laments.

Y. Kubota et al. / Physica C 354 (2001) 256±259

Fig. 6. Jcp as a function of Be .

Fig. 5. Bdp as a function of lp .

4. Conclusion The present paper clari®es the magnetizations of the PEISC in multi®lamentary NbTi/Cu composite conductors. Mp of PEISC changes from the magnetization of coupled ®lament to that of decoupled ®laments at Bdp and is proportional to exp Be for Bdp < Bm . The ®rst penetration ®eld Bc1p and the decoupling ®eld Bdp are directly proportional to the twist pitch. The transition from the bulk superconductor to individual ®lament be-

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havior at Bdp can be adjusted by changing the matrix conductivity, ®lament spacing, twist pitch and critical current density. References [1] A.K. Ghosh, W.B. Sampson, E. Gregory, T.S. Kleilick, IEEE Trans. Magn. MAG-23 (1988) 1145. [2] M.D. Sumption, E.W. Collings, Cryogenics 34 (1994) 491. [3] N. Harada, Y. Mawatari, O. Miura, Y. Tanaka, K. Yamafuji, Cryogenics 31 (1991) 183.