Force measurements for levitated bulk superconductors in electromaglev system

Transcription

1 International Journal of Applied Electromagnetics and Mechanics 14 (2001/2002) IOS Press Force measurements for levitated bulk superconductors in electromaglev system Yasuharu Tachi a, Tsuyoshi Nishikawa a, Koichiro Sawa a,, Masato Murakami b and Yukikazu Iwasa c a Department of System Design Engineering, Keio University, , Hiyoshi, Kohoku-ku, Yokohama, Japan b ISTEC, Superconductivity Research Laboratory, , Shibaura, Minato-ku, Tokyo, Japan c Francis Bitter Magnet Laboratory,Massachusetts Institute of Technology, Cambridge, MA, USA Abstract. We have directly measured the levitation force of levitated bulk superconductors in an electromaglev system. The levitation force had a hysteresis loop during increasing and decreasing field processes. Such a hysteretic behavior can be explained in terms of hysteretic penetration of external field to the superconductor. Based on such magnetization, we performed numerical simulations of the levitation forces, which were in fairly good agreement with experimental data. 1. Introduction Bulk superconductors have potential for various applications such as magnetic bearing and non-contact transport, since superconductors can levitate over permanent magnets or vice versa. However, so long as permanent magnets are used as the magnetic source, the levitation force and the levitation height cannot be varied. Iwasa et al. [1]. proposed the so-called electromaglev system in which an electromagnetic coil is used as the magnetic source. The system is attractive for practical applications, since the levitation force and levitation height can be controlled by simply changing the coil current. We constructed the levitation system for bulk YBCO superconductors using Bi-Sr-Ca-Cu-O superconducting coil for achieving large levitation force without heat generation [2]. In this levitation system, we have succeeded in controlling the electromagnetic force and the levitation height by changing the coil current. We further developed the force measurement system in which we can directly measure the force acting on the levitated bulk superconductors [3]. From these measurements, we confirmed that the properties of hysteresis influence the levitation forces. We also derived a theoretical model to simulate the levitation behavior for a levitated bulk superconductor. In this study, we measured the levitation force and compared it with the model which we derived. Corresponding author: Fax: ; sawa@sd.keio.ac.jp /01/02/$ /2002 IOS Press. All rights reserved

2 108 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system Fig. 1. Experimental apparatus. Fig. 2. Coil current changing process. 2. Experimental procedure For the force measurements, we used Y-Ba-Cu-O bulk superconductors grown by top-seeded meltgrowth process, the details of which are described elsewhere [4]. The samples were single grains of 45 mm diameter and 15 mm and 7 mm in thickness. The levitation coil is composed of a Bi2223 double pancake coil that operates below 30 K and is cooled by a cryocooler. The force measurement system consists of a balance and a load cell (see Fig. 1). In the force measurements, we employed the following procedure. The electric currents were passed through a levitation coil that generated the field B fc. The superconductor was placed at the center of the coil and cooled with liquid nitrogen in B fc. A previous experiment [5] demonstrated the importance of field-cooling for stable levitation of large bulk superconductors. Thereafter we further increased the coil current to levitate the YBCO sample, as shown in Fig. 2. We then measured the levitation force with a load cell. We repeated such increasing and decreasing field processes three times.

3 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system 109 Fig. 3. Experimental results of levitation force. Fig. 4. Three hysteretic behaviors of levitation force. 3. Results and discussions We directly measured the levitation force of bulk superconductors, and noticed the hysteretic behavior of the levitation force. The same hysteretic behavior was obserbed in both samples. Figure 3 shows the hysteretic behavior. In order to explain the hysteretic behavior, first we will derive the levitation force based on the zerothorder theory proposed by Iwasa et al. [6,7]. In the process of increasing the applied field, taking account

4 110 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system Fig. 5. Comparison of calculated and experimental levitation force (sample1). of the penetration of shielding current, the levitation force is given by Rd J c h F = R d δ c λ B r2πrdr, (1) where R d is the bulk radius, B r is r axis components of the magnetic field, J c is the critical current density, h is the thickness of the sample, λ is the Nagaoka coefficient, and δ a is the penetration depth derived from Maxwell s equations and Bean s model. Similarly, taking account of the hysteretic behavior of shielding current, the equations were derived in the first decreasing and second increasing field processes. In the calculation of two samples, the levitation force of bulk superconductor was calculated in each process in three areas. In first process, external magnetic field was increasing after field-cooling. In next process, external magnetic field was decreasing. In such situation, the levitation force F becomes as follows. R R δb F = J c hb r 2πrdr + J c hb r 2πrdr. (2) R δ b R δ m In the last process, external magnetic field was increasing again after external magnetic field had decreased to the minimum. Figure 4 shows these three hysteretic behaviors. The levitation force in this situation is represented as follows. F = R R δ c J c hb r 2πrdr R δc R δ min J c hb r 2πrdr + R δmin R δ n J c hb r 2πrdr. (3) Figures 5 and 6 respectively present the levitation forces calculated from Eq. (1) along with empirical results for two samples with different thickness of 15 and 7 mm. One can see that the levitation force has a hysteresis loop reflecting a hysteresis in field penetration. In Figs 5 and 6, solid line and dotted line represent calculated and experiment levitation force, respectively. In this study, we considered the values of J c constant by using Bean s model. Here we employed J c values of [A/m 2 ] for the sample 15 mm in thickness and [A/m 2 ] for the sample of 7 mm thick. These J c values were selected based on the best fitting. A difference in best-fitted J c values

5 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system 111 Fig. 6. Comparison of calculated and experimental levitation force (sample2). Fig. 7. Trapped field of sample1. is presumably ascribed to the geometrical effect, which we did not take into consideration for numerical simulation. It is evident that simulated levitation forces are in good agreement with experimental results. From Figs 5 and 6, calculated levitation forces have good agreement with experimental data. There were hysteretic behaviors of levitation force in both samples. The value of a deteriorated YBCO bulk was also estimated from the levitation force to be [A/m 2 ]. The value is two-thirds of that of

6 112 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system Fig. 8. Trapped field of deteriorated bulk. the sample 1. The deteriorated bulk superconductor is the same size as sample1. Figures 7 and 8 show the trapped field of the sample 1 and the deteriorated bulk superconductor, respectively. The value of J c in deteriorated one was estimated at. It can be said that the value of J c has the influence of deterioration from Figs 7 and Conclusion The levitation force of bulk superconductors had a hysteresis loop during increasing and decreasing field processes, which can be explained in terms of hysteretic penetration of external field to the superconductor. Based on such magnetization, we performed numerical simulations of the levitation forces, which was fairly in good agreement with experimental data. Here J c values were used as a fitting parameter. Almost identical Jc values were obtained for the sample with different thicknesses. A difference in best-fitted J c values is presumably ascribed to the geometrical effect. References [1] Y. Iwasa, paper presented at ISS 96, Sapporo, Japan, 1996.

7 Y. Tachi et al. / Force measurements for levitated bulk superconductors in electromaglev system 113 [2] K. Sawa, H. Horiuchi, K. Nishi, Y. Iwasa, H. Tsuda, Haigun Lee, K. Nagashima, T. Miyamoto, M. Murakami and H. Fujimoto, paper presented at 4th International Symposium on Magnetic Suspension, Gifu, Japan, [3] Y. Tachi, N. Uemura, K. Sawa, Y. Iwasa, K. Nagashima, T. Otani, T. Miyamoto, M. Tomita and M. Murakami, Supercond. Sci. Techno. 13 (2000), 850. [4] M. Murakami, Mod.phys.Lett. 4 (2000), 163. [5] K. Nishi, Y. Tachi, K. Sawa, Y. Iwasa, K. Nagashima, T. Miyamoto, M. Tomita and M. Murakami, paper presented at ISS 98, Fukuoka, Japan, [6] Y. Iwasa and Haigun Lee, Cryogenics 37 (1997), 807. [7] M. Tsuda, Haigun Lee and Y. Iwasa, Cryogenics 38 (1998), 743.