- Email: [email protected]
Ag tapes and pancake coils
Physica C 424 (2005) 138–144 www.elsevier.com/locate/physc
Comparison of self-field effects between Bi-2223/Ag tapes and pancake coils A.K.M. Alamgir *, C. Gu, Z. Han Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Building Li Zhai, Room 209, Beijing 100084, China Received 14 February 2005; received in revised form 18 April 2005; accepted 12 May 2005 Available online 28 June 2005
Abstract Knowledge on self-field behavior in HTS tape and coil becomes important for the design of HTS devices. We report on the comparative nature and influence of self-field in Bi-2223/Ag tape and pancake coils in terms of critical current and ac loss. Measured dc and ac properties of short tape and pancake coils are verified based on the self-field. It is proved that perpendicular component of self-field acting in opposite direction at the two halves of tape-width determines critical current in short tape and single-turn coil. On the other hand, perpendicular component of self-field pointed in the same direction at the two halves of tape-width determines critical current in multi-turn coils. Influence of magnitude and orientation of self-field on ac loss is also investigated for a series of pancake coils based on the measured self-field ac loss in short sample. Ó 2005 Elsevier B.V. All rights reserved. Keywords: AC loss; Bi-2223/Ag tapes; Critical current; Pancake coil; Self-field effect
1. Introduction Numerous R&D projects, so far on HTS devices like magnet, power cable, motor, transformer, fault-current limiter have been introduced worldwide but many of them are not satisfactory due to lack of design strategy as well as for anisotropic *
Corresponding author. Fax: +86 10 6278 5784. E-mail addresses: [email protected], alam643@hotmail. com (A.K.M. Alamgir).
behavior of superconductor itself [1]. In order to promote design strategy, role of self-field in HTS tape and coil must be reviewed and compared in terms of performance related parameters [2]. We have investigated self-fields in Bi-2223/Ag tape and a series of prototype pancake coils in order to realize the comparative influence of electromagnetic behavior. Tape in coil (or stacks) experiences both circulating self-field and randomly directed mutual field when carries transport current. In tape and single-turn coil, self-field is
0921-4534/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.05.009
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
exclusively circulating in nature. In multi-turn coil, on the other hand, self-field is dominated by mutual fields (arise from neighboring turns or other parts of the same turn) and becomes no longer circulating in individual tape. Due to circulating nature of self-field, tape and single-turn coil experience magnetic field varying from 0° to 360° orientation at the cross-section. For multi-turn coil, any turn experiences self-field varying between 0° and 180° orientation. Again, perpendicular component of self-field in single tape or single-turn coil rises exponentially from center and becomes sharp near the edges. The rising tendency of perpendicular component of self-field in multi-turn coil deviates more from exponential to linear with increasing number of turns. To evaluate the field dependence of critical current in short tape, we employed a pair of strip magnet that provides perpendicular field in opposite direction at the two halves of tape-width. In this case, the sample tape was attached with other tape face to face carrying opposite currents to diminish the self-field. In order to realize the basic nature of self-field, we investigated field profile of a series of prototype pancake coils with number of turns, n = 1, 2, 8, 16 and 32. We report influence of self-fields on the evaluation of critical current and ac loss in Bi-2223/Ag tape and pancake coils.
139
Fig. 1. Estimated perpendicular component of self-field in HTS tape and single-turn coil.
2. Investigation of self-fields 2.1. In case of short tape Epoxy resin impregnated and non-twisted Bi2223/Ag multifilamentary tape with 4 mm width and 0.25 mm thickness was employed to investigate the influence of self-field in short tape and pancake coils. Based on Biot–Savart law for strip with homogeneous current, magnetic flux density distribution of the tape and pancake coils was estimated by means of ANSYS program. Estimated perpendicular component of self-field at critical current of 51 A for tape and 44.2 A for single-turn coil is depicted in Fig. 1. Predicted isometric fluxlines of single-turn coil (50 mm inner diameter) are also displayed in Fig. 2. Spatial variation of selffield is estimated over tape cross-section where per-
Fig. 2. Estimated self-field distribution of single-turn coil.
pendicular component, Bper lies in y-direction and parallel component, Bpar lies in x-direction for a Cartesian coordinate system. It can be noted that the tendency of flux-lines in straight tape should be similar as that of single-turn coil. For the sake of simple realization, the self-field flux-lines and associated magnetic force in single tape are sketched in Fig. 3a and b respectively. It can be observed that perpendicular component (see Fig. 1) and orientation (see Fig. 2) of self-field increases toward the ends of tape. Zero orientation
140
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 3. Sketch of isometric self-field flux-lines showing (a) magnetic torque and (b) magnetic force.
means field points toward x-direction. Again, as the self-field flux-lines circulate in the cross-section of straight tape (also of single-turn coil), virtually the perpendicular component at the two haves of tape-width acts in opposite direction just like a torque (shown by arrows in Fig. 3a). As the thickness of tape is very small (0.2–0.3 mm) in principle, we consider the oppositely directed perpendicular component of self-field is mostly responsible for the determination of critical current in tape and single-turn coil. Accordingly, in order to evaluate critical current of tape, a setup of experiment was introduced where a pair of strip-magnet was employed to provide perpendicular field but directed oppositely at the two halves of tape-width. Strip magnets were placed head to head in such a way that bottom surface of upper magnet and top surface of lower magnet lie in same plane. As the field is opposite at the interface, virtually no field appears at the center of the tape-width. This is also consistent with real situation because perpendicular component of self-field becomes zero at the center of tape-width (see Fig. 1). Two tapes, however, attached face to face but with opposite current were placed in the magnet-pair to neutralize the selffield. A sketch and a photograph of sample arrangement are shown in Fig. 4(a) and (b) respectively. The experiment provides critical current, Ic0 of tape without self-field as a function of
Fig. 4. (a) Schematic and (b) photograph of sample arrangement, in which tape is held at oppositely directed perpendicular field provided by a pair of strip magnet.
Fig. 5. Measured critical current without self-field of HTS tape as a function of oppositely directed applied perpendicular field.
oppositely directed perpendicular magnetic field, Bper-op. The experimental result is presented in Fig. 5 and compared with the critical current, Ics estimated at self-field in straight tape, single-turn coil and double-turn coil. The measured critical current of the tape without self-field is 68 A.
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
141
Table 1 Specification of pancake coils Turns 0 (tape) 1 2 8 16 32
Inner diameter (mm)
Self-field Ic (A)
Ave. resultant field (mT)
Ave. resultant orientation (degree)
Ave. penetration field (mT)
50 50 50 50 50
51.0 44.2 40.7 33.8 32.6 29.2
4.5 7.5 8.3 21 31 37
29 30 37 41 42 43
18.33 16.04 16.04 14.08 13.79 12.55
2.2. In case of multi-turn coils In order to investigate the influence of self-field on critical current and ac loss, a series of prototype pancake coils with number of turns, n = 1, 2, 8, 16 and 32 were constructed. All the coils have same bore (50 mm diameter) and composed of the same roll of tapes. The self-field distributions of all the coils at own critical currents were estimated by ANSYS program. The detail specification of the tape and coils is listed in Table 1. As a representative of multi-turn coils, profile of magnetic fluxlines for 8-turn coil is presented in Fig. 6. It can be observed that coil self-field circulates through entire cross-section of the coil and individual turns experience field orientation between 0° and 180° throughout the tape-width. Again, although orientation increases toward the end of tape for any
Fig. 6. Estimated self-field distribution of 8-turn pancake coil.
turn, it decreases toward the outer turns. Virtually, tape of individual turns of a multi-turn coil experiences field orientation less than 90° at the two halves of the tape-width which is contrary to the case of straight tape or single-turn coil. This fact implies that effect of field orientation on critical current in multi-turn coil is less than tape or single-turn coil. The high degradation of critical current in multi-turn coil results mostly from the high magnitude of self-field. However, average perpendicular component, Bper-av of self-field pointed in the same direction throughout the tape-width is assumed to be effective for the determination of critical current in multi-turn coil. As the field varies non-linearly from center to edges, we assumed effective field as the mean of the linear value of average perpendicular field over all the turns. For example, mean of average of perpendicular field and resultant field in 8-turn coil is 13.4 mT and 21.5 mT respectively at critical current of 33.8 A as illustrated in Fig. 7. Resultant
Fig. 7. Spatial distribution of self-field for 8-turn pancake coil.
142
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 8. Measured self-field critical current of HTS tape as a function of perpendicular field applied in the same direction throughout the tape-width.
In order to investigate the influence of other relevant parameters on coil ac loss, only amplitude of average resultant field over all turns in pancake coils is taken into account and presented in Fig. 9. The average of resultant field orientation is also depicted in Fig. 10. As the field varies non-linearly across tape cross-section, a mean of linear value was assumed in the calculation of coil ac loss. AC loss of the pancake coils is estimated on the basis of measured self-field loss in short sample taking into account of only field amplitude. Therefore, this estimation of ac loss does not represent the real loss of coils but gives rise an idea of parameter influences. The estimated
field is the vector sum of normal and parallel components of self-field. In order to evaluate critical current of multi-turn coils, estimated I–Bper-av relations for various coils are extrapolated with measured Ics–Bper-sa curve of short tape as shown in Fig. 8. The symbol, Bper-sa stands for the perpendicular field applied in the same direction throughout the tape-width.
3. Investigation of ac losses Self-field ac loss in superconductors for elliptical and strip cross-section has been demonstrated by Norris in terms of only two parameters namely transport current and critical current [3]. Self-field loss in conventional Ag-sheath Bi-2223 tape satisfies the Norris formula well with cross-section in between of ellipse and strip. The evaluation of self-field ac loss, however, in superconducting coil is different to that of single tape in principle. The main contribution to coil ac loss is mutual field of neighboring turns (acting as applied fields) in addition with bending strain and magnetic force. In coil or stack, the mutual field dominates self-field of each tape and hence makes the resultant flux-lines locally unidirectional rather than circulating (see Fig. 6). In addition, amplitude and orientation of coil field in every turn is different and also varies throughout the tape crosssection.
Fig. 9. Spatial distribution of amplitude of self-field in tape and pancake coils.
Fig. 10. Spatial distribution of orientation of self-field in tape and pancake coils.
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 11. Comparison of measured and estimated self-field ac loss in pancake coils as a function of turn numbers.
coil ac loss is compared with measured one in Fig. 11. The ac losses (in tape and coils) were measured by electrical method at 30 Hz and 77 K with current ratio, Im/Ic = 1 for sinusoidal transport current.
4. Results and discussion 4.1. In case of critical currents The perpendicular component of self-field, Bper(mean of linear value) in Bi-2223/Ag tape is estiav mated to be 2 mT at self-field critical current (Ics) of 51 A. Fig. 5 shows that I–Bper-av curve for short tape crosses Ic0–Bper-op curve almost at 51 A. Similarly, I–Bper-av curve for single-turn coil intersects Ic0–Bper-op curve almost at 44.2 A being the critical current of single-turn coil with Bper-av = 3.2 mT. On the other hand, I Bper-av curve for double-turn coil does not support Ic0 Bper-op curve at critical current of 40.7 A with self-field, Bper-av = 5.4 mT. Because, magnitude of self and mutual field in individual turn of double-turn coil is comparable and field orientation is such that no field in any turn make perfect torque rather held at some angles smaller then 90°. Therefore, it can be concluded that when self-field dominates over mutual field and circulates through the cross-section of the HTS tape, then critical current is governed by perpendicular component of the self-field directed in opposite direction at the two halves of tape-width.
143
Fig. 3(b) shows that magnetic forces due to selffield in straight tape (or single-turn coil) point inward across cross-section of the tape. It is assumed qualitatively that this compressive force tends the superconducting core to separate from the outer Ag-sheath. Therefore, it is important to arrange the tapes in stack as tight as possible to avoid mechanical influences. The Ics–Bper-sa curve for Bi-2223/Ag tape is obtained experimentally and compared with I–Bper-av curve of a series of pancake coils as shown in Fig. 8. It can be observed that double-turn coil (Ic = 40.7 A) does not support the Ics–Bper-sa curve which exhibits 48 A corresponding to Bper-av = 5.4 mT. Whereas, I–Bper-av curve of coils with n = 16 and n = 32 coincides with Ics–Bper-sa curve well at critical currents of 32.6 A and 29.2 A corresponding to Bper-av = 19.5 mT and 23 mT respectively. This result can be explained as follows: mutual fields in coils with a little number of turns are not enough strong to change the flux-lines from circulating behavior. As the number of turns increases, mutual field dominates the self-field and governs the field orientation in each turn. Therefore, the idea of critical current governed by the perpendicular field acting in the same direction of entire tape-width is reasonable for the coil with many turns. The work done by Wolfus et al. [4] also supports this phenomenon. 4.2. In case of ac losses Estimated ac loss in multi-turn coils is found to be smaller than measured one in Fig. 11. Because, as superconducting coils are subjected to significant amount of self-field, several parameters including critical current density, field amplitude, field orientation and penetration field greatly influence the coil ac losses. For single turn coil, average field orientation (30°) and field ratio, Bm/Bp (<1) is almost similar to that of short sample (see Table 1) and hence, the estimated ac loss coincides well with the measured value (see Fig. 11). Double-turn coil also provides Bm/Bp <1 but field orientation (37°) is higher than that of short sample and hence, the measure loss is higher than predicted one. For coils with n = 8, 16 and 32, both field orientation (41°, 42° and 43° respectively) and field ratio,
144
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Bm/Bp (>1) differ from those of short sample. Naturally, variation of ac losses in estimation and measurement occurs. It should be noted that, although difference of field orientations in multiturn coils is very small (about 1°), the variation of measured and estimated loss increases with number of turns. This may be attributed to the mechanical loss component caused by magnetic force which increases with number of turns [5]. Therefore, to evaluate coil ac loss based on the short sample data, it is important to develop a loss relation in terms of both applied field and penetration field with orientations. Also, for accurate prediction of coil ac losses, local contribution of critical current density and field should be considered rather than global value.
5. Concluding remarks Nature and influence of self-field in Bi-2223/Ag tape and pancake coils in terms of critical current and ac loss have been studied. Average perpendicular component of self-field directed oppositely at the two halves of tape-width has been proved to be responsible for the determination of critical current in tape and single-turn coil. On the other
hand, average perpendicular component of selffield directed in one direction throughout the tape-width determines the critical current in multi-turn coil. Although self-field orientation increases significantly toward the end of the tape, resultant field amplitude remains almost unchanged throughout the tape width for tape and single-turn coil. Whereas, both of amplitude and orientation of self-field increases toward the end of the tape for multi-turn coil. Investigation shows that, evaluation of coil ac loss based on the short sample data requires applied field and penetration field with orientation to be accounted for. The comparative investigation of dc and ac behavior in HTS tape and coil would be useful for the development of HTS magnet design.
References [1] T. Matsushita, Supercond. Sci. Technol. 13 (2000) 51. [2] J.X. Jin, C. Grantham, Y.C. Guo, J.N. Li, R. Bhasale, H.K. Liu, S.X. Dou, Physica C 278 (1997) 85. [3] W.T. Norris, J. Phys. D 3 (1970) 489. [4] Y. Wolfus, Y. Fleger, A. Friedman, F. Kopansky, B. Kalisky, Y. Yeshurun, Z. Bar-Haim, Z. Ron, L. Ying, N. Pundak, Physica C 401 (2004) 222. [5] M. Furuse, H. Tanaka, J. Kondoh, M. Umeda, IEEE Trans. Appl. Supercond. 14 (2) (2004) 90.
Comparison of self-field effects between Bi-2223/Ag tapes and pancake coils A.K.M. Alamgir *, C. Gu, Z. Han Applied Superconductivity Research Center, Department of Physics, Tsinghua University, Building Li Zhai, Room 209, Beijing 100084, China Received 14 February 2005; received in revised form 18 April 2005; accepted 12 May 2005 Available online 28 June 2005
Abstract Knowledge on self-field behavior in HTS tape and coil becomes important for the design of HTS devices. We report on the comparative nature and influence of self-field in Bi-2223/Ag tape and pancake coils in terms of critical current and ac loss. Measured dc and ac properties of short tape and pancake coils are verified based on the self-field. It is proved that perpendicular component of self-field acting in opposite direction at the two halves of tape-width determines critical current in short tape and single-turn coil. On the other hand, perpendicular component of self-field pointed in the same direction at the two halves of tape-width determines critical current in multi-turn coils. Influence of magnitude and orientation of self-field on ac loss is also investigated for a series of pancake coils based on the measured self-field ac loss in short sample. Ó 2005 Elsevier B.V. All rights reserved. Keywords: AC loss; Bi-2223/Ag tapes; Critical current; Pancake coil; Self-field effect
1. Introduction Numerous R&D projects, so far on HTS devices like magnet, power cable, motor, transformer, fault-current limiter have been introduced worldwide but many of them are not satisfactory due to lack of design strategy as well as for anisotropic *
Corresponding author. Fax: +86 10 6278 5784. E-mail addresses: [email protected], alam643@hotmail. com (A.K.M. Alamgir).
behavior of superconductor itself [1]. In order to promote design strategy, role of self-field in HTS tape and coil must be reviewed and compared in terms of performance related parameters [2]. We have investigated self-fields in Bi-2223/Ag tape and a series of prototype pancake coils in order to realize the comparative influence of electromagnetic behavior. Tape in coil (or stacks) experiences both circulating self-field and randomly directed mutual field when carries transport current. In tape and single-turn coil, self-field is
0921-4534/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2005.05.009
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
exclusively circulating in nature. In multi-turn coil, on the other hand, self-field is dominated by mutual fields (arise from neighboring turns or other parts of the same turn) and becomes no longer circulating in individual tape. Due to circulating nature of self-field, tape and single-turn coil experience magnetic field varying from 0° to 360° orientation at the cross-section. For multi-turn coil, any turn experiences self-field varying between 0° and 180° orientation. Again, perpendicular component of self-field in single tape or single-turn coil rises exponentially from center and becomes sharp near the edges. The rising tendency of perpendicular component of self-field in multi-turn coil deviates more from exponential to linear with increasing number of turns. To evaluate the field dependence of critical current in short tape, we employed a pair of strip magnet that provides perpendicular field in opposite direction at the two halves of tape-width. In this case, the sample tape was attached with other tape face to face carrying opposite currents to diminish the self-field. In order to realize the basic nature of self-field, we investigated field profile of a series of prototype pancake coils with number of turns, n = 1, 2, 8, 16 and 32. We report influence of self-fields on the evaluation of critical current and ac loss in Bi-2223/Ag tape and pancake coils.
139
Fig. 1. Estimated perpendicular component of self-field in HTS tape and single-turn coil.
2. Investigation of self-fields 2.1. In case of short tape Epoxy resin impregnated and non-twisted Bi2223/Ag multifilamentary tape with 4 mm width and 0.25 mm thickness was employed to investigate the influence of self-field in short tape and pancake coils. Based on Biot–Savart law for strip with homogeneous current, magnetic flux density distribution of the tape and pancake coils was estimated by means of ANSYS program. Estimated perpendicular component of self-field at critical current of 51 A for tape and 44.2 A for single-turn coil is depicted in Fig. 1. Predicted isometric fluxlines of single-turn coil (50 mm inner diameter) are also displayed in Fig. 2. Spatial variation of selffield is estimated over tape cross-section where per-
Fig. 2. Estimated self-field distribution of single-turn coil.
pendicular component, Bper lies in y-direction and parallel component, Bpar lies in x-direction for a Cartesian coordinate system. It can be noted that the tendency of flux-lines in straight tape should be similar as that of single-turn coil. For the sake of simple realization, the self-field flux-lines and associated magnetic force in single tape are sketched in Fig. 3a and b respectively. It can be observed that perpendicular component (see Fig. 1) and orientation (see Fig. 2) of self-field increases toward the ends of tape. Zero orientation
140
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 3. Sketch of isometric self-field flux-lines showing (a) magnetic torque and (b) magnetic force.
means field points toward x-direction. Again, as the self-field flux-lines circulate in the cross-section of straight tape (also of single-turn coil), virtually the perpendicular component at the two haves of tape-width acts in opposite direction just like a torque (shown by arrows in Fig. 3a). As the thickness of tape is very small (0.2–0.3 mm) in principle, we consider the oppositely directed perpendicular component of self-field is mostly responsible for the determination of critical current in tape and single-turn coil. Accordingly, in order to evaluate critical current of tape, a setup of experiment was introduced where a pair of strip-magnet was employed to provide perpendicular field but directed oppositely at the two halves of tape-width. Strip magnets were placed head to head in such a way that bottom surface of upper magnet and top surface of lower magnet lie in same plane. As the field is opposite at the interface, virtually no field appears at the center of the tape-width. This is also consistent with real situation because perpendicular component of self-field becomes zero at the center of tape-width (see Fig. 1). Two tapes, however, attached face to face but with opposite current were placed in the magnet-pair to neutralize the selffield. A sketch and a photograph of sample arrangement are shown in Fig. 4(a) and (b) respectively. The experiment provides critical current, Ic0 of tape without self-field as a function of
Fig. 4. (a) Schematic and (b) photograph of sample arrangement, in which tape is held at oppositely directed perpendicular field provided by a pair of strip magnet.
Fig. 5. Measured critical current without self-field of HTS tape as a function of oppositely directed applied perpendicular field.
oppositely directed perpendicular magnetic field, Bper-op. The experimental result is presented in Fig. 5 and compared with the critical current, Ics estimated at self-field in straight tape, single-turn coil and double-turn coil. The measured critical current of the tape without self-field is 68 A.
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
141
Table 1 Specification of pancake coils Turns 0 (tape) 1 2 8 16 32
Inner diameter (mm)
Self-field Ic (A)
Ave. resultant field (mT)
Ave. resultant orientation (degree)
Ave. penetration field (mT)
50 50 50 50 50
51.0 44.2 40.7 33.8 32.6 29.2
4.5 7.5 8.3 21 31 37
29 30 37 41 42 43
18.33 16.04 16.04 14.08 13.79 12.55
2.2. In case of multi-turn coils In order to investigate the influence of self-field on critical current and ac loss, a series of prototype pancake coils with number of turns, n = 1, 2, 8, 16 and 32 were constructed. All the coils have same bore (50 mm diameter) and composed of the same roll of tapes. The self-field distributions of all the coils at own critical currents were estimated by ANSYS program. The detail specification of the tape and coils is listed in Table 1. As a representative of multi-turn coils, profile of magnetic fluxlines for 8-turn coil is presented in Fig. 6. It can be observed that coil self-field circulates through entire cross-section of the coil and individual turns experience field orientation between 0° and 180° throughout the tape-width. Again, although orientation increases toward the end of tape for any
Fig. 6. Estimated self-field distribution of 8-turn pancake coil.
turn, it decreases toward the outer turns. Virtually, tape of individual turns of a multi-turn coil experiences field orientation less than 90° at the two halves of the tape-width which is contrary to the case of straight tape or single-turn coil. This fact implies that effect of field orientation on critical current in multi-turn coil is less than tape or single-turn coil. The high degradation of critical current in multi-turn coil results mostly from the high magnitude of self-field. However, average perpendicular component, Bper-av of self-field pointed in the same direction throughout the tape-width is assumed to be effective for the determination of critical current in multi-turn coil. As the field varies non-linearly from center to edges, we assumed effective field as the mean of the linear value of average perpendicular field over all the turns. For example, mean of average of perpendicular field and resultant field in 8-turn coil is 13.4 mT and 21.5 mT respectively at critical current of 33.8 A as illustrated in Fig. 7. Resultant
Fig. 7. Spatial distribution of self-field for 8-turn pancake coil.
142
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 8. Measured self-field critical current of HTS tape as a function of perpendicular field applied in the same direction throughout the tape-width.
In order to investigate the influence of other relevant parameters on coil ac loss, only amplitude of average resultant field over all turns in pancake coils is taken into account and presented in Fig. 9. The average of resultant field orientation is also depicted in Fig. 10. As the field varies non-linearly across tape cross-section, a mean of linear value was assumed in the calculation of coil ac loss. AC loss of the pancake coils is estimated on the basis of measured self-field loss in short sample taking into account of only field amplitude. Therefore, this estimation of ac loss does not represent the real loss of coils but gives rise an idea of parameter influences. The estimated
field is the vector sum of normal and parallel components of self-field. In order to evaluate critical current of multi-turn coils, estimated I–Bper-av relations for various coils are extrapolated with measured Ics–Bper-sa curve of short tape as shown in Fig. 8. The symbol, Bper-sa stands for the perpendicular field applied in the same direction throughout the tape-width.
3. Investigation of ac losses Self-field ac loss in superconductors for elliptical and strip cross-section has been demonstrated by Norris in terms of only two parameters namely transport current and critical current [3]. Self-field loss in conventional Ag-sheath Bi-2223 tape satisfies the Norris formula well with cross-section in between of ellipse and strip. The evaluation of self-field ac loss, however, in superconducting coil is different to that of single tape in principle. The main contribution to coil ac loss is mutual field of neighboring turns (acting as applied fields) in addition with bending strain and magnetic force. In coil or stack, the mutual field dominates self-field of each tape and hence makes the resultant flux-lines locally unidirectional rather than circulating (see Fig. 6). In addition, amplitude and orientation of coil field in every turn is different and also varies throughout the tape crosssection.
Fig. 9. Spatial distribution of amplitude of self-field in tape and pancake coils.
Fig. 10. Spatial distribution of orientation of self-field in tape and pancake coils.
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Fig. 11. Comparison of measured and estimated self-field ac loss in pancake coils as a function of turn numbers.
coil ac loss is compared with measured one in Fig. 11. The ac losses (in tape and coils) were measured by electrical method at 30 Hz and 77 K with current ratio, Im/Ic = 1 for sinusoidal transport current.
4. Results and discussion 4.1. In case of critical currents The perpendicular component of self-field, Bper(mean of linear value) in Bi-2223/Ag tape is estiav mated to be 2 mT at self-field critical current (Ics) of 51 A. Fig. 5 shows that I–Bper-av curve for short tape crosses Ic0–Bper-op curve almost at 51 A. Similarly, I–Bper-av curve for single-turn coil intersects Ic0–Bper-op curve almost at 44.2 A being the critical current of single-turn coil with Bper-av = 3.2 mT. On the other hand, I Bper-av curve for double-turn coil does not support Ic0 Bper-op curve at critical current of 40.7 A with self-field, Bper-av = 5.4 mT. Because, magnitude of self and mutual field in individual turn of double-turn coil is comparable and field orientation is such that no field in any turn make perfect torque rather held at some angles smaller then 90°. Therefore, it can be concluded that when self-field dominates over mutual field and circulates through the cross-section of the HTS tape, then critical current is governed by perpendicular component of the self-field directed in opposite direction at the two halves of tape-width.
143
Fig. 3(b) shows that magnetic forces due to selffield in straight tape (or single-turn coil) point inward across cross-section of the tape. It is assumed qualitatively that this compressive force tends the superconducting core to separate from the outer Ag-sheath. Therefore, it is important to arrange the tapes in stack as tight as possible to avoid mechanical influences. The Ics–Bper-sa curve for Bi-2223/Ag tape is obtained experimentally and compared with I–Bper-av curve of a series of pancake coils as shown in Fig. 8. It can be observed that double-turn coil (Ic = 40.7 A) does not support the Ics–Bper-sa curve which exhibits 48 A corresponding to Bper-av = 5.4 mT. Whereas, I–Bper-av curve of coils with n = 16 and n = 32 coincides with Ics–Bper-sa curve well at critical currents of 32.6 A and 29.2 A corresponding to Bper-av = 19.5 mT and 23 mT respectively. This result can be explained as follows: mutual fields in coils with a little number of turns are not enough strong to change the flux-lines from circulating behavior. As the number of turns increases, mutual field dominates the self-field and governs the field orientation in each turn. Therefore, the idea of critical current governed by the perpendicular field acting in the same direction of entire tape-width is reasonable for the coil with many turns. The work done by Wolfus et al. [4] also supports this phenomenon. 4.2. In case of ac losses Estimated ac loss in multi-turn coils is found to be smaller than measured one in Fig. 11. Because, as superconducting coils are subjected to significant amount of self-field, several parameters including critical current density, field amplitude, field orientation and penetration field greatly influence the coil ac losses. For single turn coil, average field orientation (30°) and field ratio, Bm/Bp (<1) is almost similar to that of short sample (see Table 1) and hence, the estimated ac loss coincides well with the measured value (see Fig. 11). Double-turn coil also provides Bm/Bp <1 but field orientation (37°) is higher than that of short sample and hence, the measure loss is higher than predicted one. For coils with n = 8, 16 and 32, both field orientation (41°, 42° and 43° respectively) and field ratio,
144
A.K.M. Alamgir et al. / Physica C 424 (2005) 138–144
Bm/Bp (>1) differ from those of short sample. Naturally, variation of ac losses in estimation and measurement occurs. It should be noted that, although difference of field orientations in multiturn coils is very small (about 1°), the variation of measured and estimated loss increases with number of turns. This may be attributed to the mechanical loss component caused by magnetic force which increases with number of turns [5]. Therefore, to evaluate coil ac loss based on the short sample data, it is important to develop a loss relation in terms of both applied field and penetration field with orientations. Also, for accurate prediction of coil ac losses, local contribution of critical current density and field should be considered rather than global value.
5. Concluding remarks Nature and influence of self-field in Bi-2223/Ag tape and pancake coils in terms of critical current and ac loss have been studied. Average perpendicular component of self-field directed oppositely at the two halves of tape-width has been proved to be responsible for the determination of critical current in tape and single-turn coil. On the other
hand, average perpendicular component of selffield directed in one direction throughout the tape-width determines the critical current in multi-turn coil. Although self-field orientation increases significantly toward the end of the tape, resultant field amplitude remains almost unchanged throughout the tape width for tape and single-turn coil. Whereas, both of amplitude and orientation of self-field increases toward the end of the tape for multi-turn coil. Investigation shows that, evaluation of coil ac loss based on the short sample data requires applied field and penetration field with orientation to be accounted for. The comparative investigation of dc and ac behavior in HTS tape and coil would be useful for the development of HTS magnet design.
References [1] T. Matsushita, Supercond. Sci. Technol. 13 (2000) 51. [2] J.X. Jin, C. Grantham, Y.C. Guo, J.N. Li, R. Bhasale, H.K. Liu, S.X. Dou, Physica C 278 (1997) 85. [3] W.T. Norris, J. Phys. D 3 (1970) 489. [4] Y. Wolfus, Y. Fleger, A. Friedman, F. Kopansky, B. Kalisky, Y. Yeshurun, Z. Bar-Haim, Z. Ron, L. Ying, N. Pundak, Physica C 401 (2004) 222. [5] M. Furuse, H. Tanaka, J. Kondoh, M. Umeda, IEEE Trans. Appl. Supercond. 14 (2) (2004) 90.