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Hysteresis of V–I curve of BSCCO-2223 tape
Physica C 350 (2001) 139±146
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Hysteresis of V±I curve of BSCCO-2223 tape P. Us ak *,1, L'. Jans ak, M. Pol ak Department of Electrodynamics of Superconductivity, Institute of Electrical Engineering, Slovak Academy of Sciences, Dubravska cesta 9, 842 39 Bratislava, Slovak Republic Received 29 June 2000; accepted 29 August 2000
Abstract On measurement of V±I curves of BSCCO-2223/Ag tapes, a hysteresis was observed during ramping the current up and down over Ic level. The hysteresis was not observed for mono®lamentary tapes, but it was frequently present in multi®lamentary tapes. Typical electric ®eld in our measurements was from 10ÿ5 to 10ÿ1 V/m. The larger the maximum of the voltage, the larger was the hysteresis eect. For a ®xed maximum voltage, the larger the ramping rate, the broader was the hysteresis loop. If the change in current was stopped over Ic , the relaxation of the voltage was observed. For ascending curve, the relaxation was negative and voltage decreased with time when current was held constant. For descending curve, it was positive and voltage increased when the current decrease was stopped. The eect was present both for short samples as well as for a tape wound in the form of a coil. The hysteresis of V±I curves measured on short samples is suppressed by an external perpendicular magnetic ®eld. The exact value of the ®eld was dependent on sample type and form. In our sample, this ®eld was 15 mT. A model of electromagnetic ®eld relaxation is used to explain qualitatively the eect of hysteresis and its suppression by the external magnetic ®eld. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.40.+k; 74.60.Ge; 74.60.Jg Keywords: HTC tape; BSCCO-2223/Ag; I±V curve; Hysteresis
1. Introduction Two important parameters of HTC tapes intended for power applications are obviously investigated: AC losses and current carrying capacity. For reference purposes, the latter is frequently reduced to measurement of critical current corresponding to electric ®eld E0 10ÿ4 V/m. The V±I curve is measured at a given temperature T
* Corresponding author. Tel.: +421-7-5477-5826, ext.: 2719; fax: +421-7-5477-5816. E-mail address: [email protected] (P. UsÏaÂk). 1 http://nic.savba.sk/sav/inst/elu/oes/usak.html.
and external magnetic ®eld B. The current value corresponding to E0 is determined as critical current Ic . All the measurements are referred to as DC measurements and the achieved V±I curve is mentioned as DC characteristic of the sample. Contrary to the resistivity measurement R T when temperature is changed under ®xed current through the sample and ®xed external magnetic ®eld around, the V±I measurements are made at non-zero sweeping rate dI=dt. Distribution of current within sample does not obey the critical state model as in steady R T measurement but re¯ects the non-linear dynamics of vortex motion and continually decreases inward the sample.
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 0 ) 0 1 5 7 5 - 6
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Corresponding electric ®eld E is produced by thermally activated drift of vortices driven by Lorentz force and resulting in E proportional to the mean drift velocity v of vortices. For R T measurement is this drift steady and velocity is about the same. But in V±I measurement, the current and electric ®eld diuses from surface toward the centre. The current density varies spatially, and the vortices are in unsteady motion, i.e. V±I curve measurement is unsteady. Following the idea mentioned, Zhang et al. [1] have found that V±I curves for Ag-Bi-2223 tapes are aected by the sweeping rate dI=dt. They found both experimentally for BSCCO-2223 tapes and using numerical model based on diusion equation for E in an in®nite slab that V±I curves move toward smaller current with increasing dI=dt. This means that when we compare V±I curves of two dierent samples, we should be careful to use the same sweeping speed dI=dt. This is often ignored in practice. Dependence of V±I curve on dI=dt implies that there exists electric ®eld relaxation. This relaxation was also calculated and proved experimentally [1]. The current I was ramped up with speed dI=dt until the level I0 was achieved. Then, the current was maintained constant and the ®eld E(t) decay was observed and calculated. The same decay of E, i.e. decrease of the measured voltage of V±I curve when current stopped was observed in our measurements on dierent BSCCO-2223 tapes. Contrary to Refs. [1,2] wherein measurements on multi®lament and also monocore samples are mentioned, we have observed the relaxation eect on multi®lament samples only but not on monocore.
measurement precision. Quite a dierent behaviour was found in the case of multi®lament tapes. The uprising part of the curve was shifted to higher voltage and smaller current with respect to the downrising one. Typical hysteresis loop is shown in Fig. 1. Ten consecutive measurements interrupted by repeated heating to room temperature and cooling to 77 K are shown in the ®gure. Except a small shift produced by thermal shocks, the hysteresis feature remains stable for this sample (N). The eect was observed when voltage V measured between voltage tapes distanced by 1 cm crossed the obvious critical current region in the vicinity of 1 lV, i.e. E 10ÿ4 V/m. The higher the maximum current level Imax and corresponding voltage Umax where the sweeping rate changed the sign, the larger was the dierence in up and down voltages Vup and Vdown corresponding to the same current I. The experimental demonstration of this eect is shown in Fig. 2 where Umax is a parameter (sample N). The hysteresis region was observed over Ic . When current decreased well below Ic the dierence between Vup and Vdown curves diminished. Surprisingly, we frequently observed a tiny shift of line Vdown over the line Vup at currents below Ic . Typical V±I curve hysteresis is also shown in Fig. 3 for BSCCO-2223 silver sheathed tape 3 mm in width, 0.2 mm in thickness and 36 mm in length (sample S). The sweeping rate was 0.1 A/s. The measurement was done at 77 K in liquid nitrogen
2. Hysteresis of V±I curve In Refs. [1,2] there is no remark about the in¯uence of dI=dt on V±I curve when sweeping rate is reversed and dI=dt changes the sign. We have experimentally observed this eect. We found that for monocore BSCCO-2223 samples immersed in LN2 at 77 K, the sweeping rate polarity has no in¯uence on V±I curve and ramping up and down parts of V±I curve are practically identical within
Fig. 1. Reproducibility of hysteresis loop.
P. U s ak et al. / Physica C 350 (2001) 139±146
Fig. 2. In¯uence of peak voltage.
Fig. 3. Interpretation of critical current.
bath. The sample was positioned horizontally with wetted surface down. The scale in Fig. 3 is selected in such a way as to enhance the present hysteresis eect. Dierent critical currents result in applying the standard criterion E 10ÿ4 V/m for uprising and downrising parts of hysteretic V±I curve. Uprising critical current Ic 54:1 A is 1.2 A smaller than the downrising one. This time the reproducibility of measurement is checked within the same cooldown. The larger the maximum voltage of ramping curve, the larger was the dierence between curves Vup and Vdown (Fig. 2). The larger the ramping rate, the larger is the hysteresis (Fig. 4). To observe relaxation eect mentioned in Section 1 and to reveal the role of polarity dI=dt, we decided to measure it not only for ascending curve Vup when the current was stopped during ramping up but
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Fig. 4. The role of the ramping rate.
also for descending curve Vdown where stop was applied during current ramping down. The results are shown in Fig. 5 for Vup and in Fig. 6 for decreasing part of hysteresis curve Vdown . The measurement was done on the short sample cut from the same long tape as was cut from the mentioned sample type N. In Fig. 5 we can see that the relaxation of voltage measured between voltage taps of the sample is negative. i.e. the voltage decreases after stopping the current during its ramping up. Contrarily, in Fig. 6, we can see that the relaxation is positive, i.e. voltage increases after current stops during ramping down. The sign of relaxation is dependent on sign of dI=dt. The relaxation for dI=dt P 0 is somewhat stronger than that for dI=dt 6 0. The maximum voltage measured on distance 1 cm was from tens of microvolts up to 3 mV. The ramping rate was 0.7 A/s. The eect is
Fig. 5. Relaxation after ramping up.
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Fig. 8. The role of parallel ®eld Bjj . Fig. 6. Relaxation after ramping down.
Fig. 7. Relaxation on long sample.
much more pronounced with respect to noise when measured on large length of the tape. In Fig. 7 relaxation is measured on 1.1 m long helically wound tape (sample type S) when stop was applied during ramping up. The distance between voltage taps was 75 cm and the maximum voltage measured on this distance was 2.5 mV
typically at 100 mT, there was no hysteresis at all (Fig. 8). Helically wound long tape (S) was inserted in external ®eld. Winding axis and B external were parallel. In perpendicular ®eld, the hysteresis measured on short samples was suppressed even at the level of 15 mT. The precise value depended on the sample type. The role of perpendicular magnetic ®eld component on width of hysteresis loop measured on short sample of multi®lament tape is demonstrated in Fig. 9 (sample N). A question arises about the nature of the mechanism of this hysteresis suppression. Is it some sort of switching o of weak links as it is observed in proximity eect? Surely it is the change in complex nature of eective barriers in electric ®eld diusion process.
3. Suppression of hysteresis by magnetic ®eld When we applied external magnetic ®eld perpendicular or parallel to the tape surface, the hysteresis eect was less pronounced and at some threshold level of magnetic ®eld it disappeared. Over this threshold level of Bt , the hysteresis of V± I curve was not observed. Even for parallel ®eld,
Fig. 9. The role of perpendicular ®eld Bÿ .
P. U s ak et al. / Physica C 350 (2001) 139±146 n
Zhang [1] showed that power n in E E0 I=Ic has an important in¯uence on the relaxation process. The increase in n decreases the relaxation rate. The reason is that n re¯ects the eective pinning strength governed by temperature, magnetic ®eld and quenched disorder. The electric ®eld diusion process is retarded at high energy barrier. It was shown in Ref. [1] that the higher the n of the sample, the broader scattered are the V±I curves for the same corresponding range of dI=dt values as parameters. As the presence of external magnetic ®eld results in decrease in n in the corresponding V±I curve, the eect of the same ramping dI=dt on V±I shift at higher ®eld is smaller than at zero external ®eld. The larger the ®eld, the smaller is the shift. This can explain qualitatively the suppressive eect of external magnetic ®eld on negative shift (with respect to current) of uprising part of V±I curve and positive shift (with respect to current) of downgoing part, i.e. suppressing the hysteresis. Nevertheless, why in our measurements the effect of hysteresis was not observed on monocore tape even at zero external ®eld is unclear for us at the moment. The eect disappeared even when the multi®lament tape was cut longitudinally into ®ve sub-tapes. No sub-tape revealed hysteresis. Eect of hysteresis was observed also on BSCCO-2223 multi®lament tape in the form of
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monolayer helical coil with a diameter of 28 mm. The measurements were done on individual turns as well as on all the coil covering several turns. The hysteresis was present in both cases and was preserved up to high currents reaching 9Ic of the weakest portion when peculiar instabilities appeared. The details will be published elsewhere [3]. 4. Test of the role of self-®eld We tried to look for an alternative explanation for the eect. To clear and check the possible in¯uence of self-®eld in the eect of hysteresis, we prepared the measurement based on the following idea: when the current is ramping in the tape during V±I measurements, the self-®eld of the tape results in inductive voltage loops between the central part and both edges of the tape. These are generated by time variance of perpendicular component of self-®eld (perpendicular to tape surface) leading to E in the direction of j at edges and E opposite to j at the tape centre during ramping up. During ramping down, when dI=dt is negative, the situation is reversed and E at edges is opposite to j and of the same orientation with j at the centre of the tape (Fig. 10). When current is ramping up, in central portion of taps, the inductive local voltage from
Fig. 10. Self ®eld in¯uence on local E.
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perpendicular component of self-®eld is oriented in the opposite direction and a higher input source voltage has to be applied to overcome this obstacle. When current ramps down, the inductive voltage component of self-®eld (B? ) is in common with source voltage and for the same current the applied voltage for central taps is lower. For edge parts of tape, the situation is reversed. For edge taps, the source and self-®eld inductive voltages are during ramping up of current in common, i.e. less source voltage is needed for the same current as during ramping down when self-®eld voltage component is opposite to source voltage and eective resistance is higher. If observed hysteresis eect is not explained by highly non-linear diusivity analysed in Ref. [1] but is the result of changing polarity of inductive E loops between central part of the tape and edges during ramping up and down, the hysteresis ought to be reversed when measured on voltage taps at edges with respect to mentioned hysteresis measured on voltage taps positioned at the centre of the tape. This means that during rising up of current, the V±I curve measured at edge portion ought to be shifted to higher currents and during declining of current, it ought to be shifted to lower currents, i.e. quite opposite to shifts measured at central portion. To check this expected hysteresis reversal, we prepared the special short sample Q (type S). We decided to measure V±I curves on four voltage taps located as strictly parallel pairs in the centre of the tape (C,D) and at one edge of the tape (A,B). The longitudinal positions (in the direction of current) of points A,C and also of points B,D were the same. The results of measurement are shown in Fig. 11. Contrary to our expectation, no reversal of hysteresis was observed. In both curves for edge A,B voltage taps as well as for central C,D taps the uprising part of V±I curve was shifted to higher voltages and smaller current with respect to downgoing part of the V±I curve and the hysteresis had the same character no matter whether it was measured at the edge or in central portion. This kind of shift and the corresponding hysteresis was even observed when orthogonal pair of voltage points A,C was used in
Fig. 11. Peculiar shift of all the edge curve.
measurements. A,C pair was oriented perpendicular to current direction. The V±I curve for A,C was not exponential but was not also zero as one may expect for two voltage taps on supposed equipotential line. The hysteresis of this curve was smaller but evident and with the same behaviour as for longitudinal portions A,B and C,D. Contrarily, measurement on voltage taps B,D with the same perpendicular orientation with respect to current direction con®rmed that both points lay approximately on equipotential line. The entire measurement was done at the same speed dI=dt 0:3 A/s. Surprisingly, as can be seen in Fig. 11, the entire V±I curve (including its hysteresis feature) measured at the centre of the tape (points C,D) is shifted to higher currents with respect to the entire V±I curve measured at edge (points A,B). We have no explanation for this phenomenon except much more complex nature of current distribution within the tape width than is obviously accepted. The dierence in V±I curves for perpendicular pairs of points A,C and B,D can be explained by the presence of local defect distorting partially the current path within the line A,C. To deny the possibility that this is not a special feature of this sample Q, we decided to repeat the measurement on sample W of the same type S. This time the central voltage tapes 3,4 were completed by pairs 1,2 and 5,6 positioned at edges of the tape (Fig. 12). The results of V±I measurements for pairs of voltage taps (1,2), (3,4) and (5,6)
P. U s ak et al. / Physica C 350 (2001) 139±146
Fig. 12. Tapes position independent hysteresis.
showed that the curves are practically identical, irrespective of their position selected : central, one edge or another edge. The hysteresis of V±I curve also does not change. The mutual shift of V±I curves for central and edge parts was not proved this time. This means that the observed shift is a special feature of the measured portion of sample Q. Finally, we can conclude that self-®eld generated changes in E are not the explanation for observed V±I hysteresis and non-linear diusivity model for E applied in Ref. [1] remains only a plausible explanation. Nevertheless, there is a mechanism and dynamics of self-®eld ¯ux trapping in the conductor volume re¯ecting ®nite time of ¯ux diusion and relaxation within tape volume. This was proved by measurement of current distribution dynamics in superconducting tape [4]. 5. Samples and experimentation The eect of hysteresis was observed on a broad range of multi®lament tapes from dierent producers. In this contribution, two kinds of samples were used for demonstration of the eect. The ®rst is multi®lament tape S with 55 ®laments in silver matrix. The second source of samples is silver sheathed multi®lament tape N with 37 ®laments. The potential taps were glued on silver surface or alternatively mechanically contacted by sharp hard rods in the form of a comb. The series of rods covered the sample on distance 10 mm. Mutual
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distance between individual rods was 1 mm. The reason was to reveal possible inhomogeneities in longitudinal direction along the tape. In hysteresis measurements, the largest distance, 10 mm, between rods was used. The glued taps were distanced 10 mm or, rarely, 20 mm. The way in which taps contacted had no in¯uence on the form of voltage hysteresis measured by standard fourprobe method. Measurements on mono®lament tapes as well as on series of sub-tapes longitudinally cut from the same initial multi®lament tape are not displayed for their triviality (no hysteresis). The external magnetic ®eld was produced by LN2 cooled copper split coil magnet. Limiting ®eld was 350 mT. The short sample was inserted in the direction with vector B perpendicular to broader surface of the tape. Helically wound long tape had winding axis in parallel with B, i.e. B was parallel to tape surface.
6. Conclusion 1. The hysteresis of V±I curve was observed at the vicinity and over Ic for multi®lament Ag-Bi2223 tapes measured at 77 K and zero external magnetic ®eld. 2. No such hysteresis was observed for monocore tapes within the precision of measurement. 3. The hysteresis of V±I curve could be suppressed by external magnetic ®eld of appropriate magnitude. The eect of suppression was observed both for parallel and perpendicular ®elds with respect to tape plane. 4. The qualitative explanation of hysteresis and its suppression by magnetic ®eld was applied based on the idea of highly non-linear diusivity of electric ®eld [1] and its dynamics in a superconductor with assumptions dierent from simple critical state model.
References [1] P. Zhang, C. Ren, S.Y. Ding, Q. Ding, F.Y. Lin, Y.H. Zhang, H. Luo, X.X. Yao, Eect of electrical ®eld
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relaxation on the V±I curve, Supercond. Sci. Technol. 12 (1999) 571. [2] S.Y. Ding, C. Rent, X.X. Yao, Y. Sun, H. Zhang, Eect of current sweep rate on critical current of superconducting Ag-Bi-2223 tapes, Cryogenics 38 (1998) 809.
[3] P. Usak, F. Chovanec, Stability of I±V curves of BSCCO2223/Ag multi®lamentary tapes, in preparation. [4] P. Us ak, Measurement of the transport current distribution in a superconducting tape, Physica C 316 (1999) 229.
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Hysteresis of V±I curve of BSCCO-2223 tape P. Us ak *,1, L'. Jans ak, M. Pol ak Department of Electrodynamics of Superconductivity, Institute of Electrical Engineering, Slovak Academy of Sciences, Dubravska cesta 9, 842 39 Bratislava, Slovak Republic Received 29 June 2000; accepted 29 August 2000
Abstract On measurement of V±I curves of BSCCO-2223/Ag tapes, a hysteresis was observed during ramping the current up and down over Ic level. The hysteresis was not observed for mono®lamentary tapes, but it was frequently present in multi®lamentary tapes. Typical electric ®eld in our measurements was from 10ÿ5 to 10ÿ1 V/m. The larger the maximum of the voltage, the larger was the hysteresis eect. For a ®xed maximum voltage, the larger the ramping rate, the broader was the hysteresis loop. If the change in current was stopped over Ic , the relaxation of the voltage was observed. For ascending curve, the relaxation was negative and voltage decreased with time when current was held constant. For descending curve, it was positive and voltage increased when the current decrease was stopped. The eect was present both for short samples as well as for a tape wound in the form of a coil. The hysteresis of V±I curves measured on short samples is suppressed by an external perpendicular magnetic ®eld. The exact value of the ®eld was dependent on sample type and form. In our sample, this ®eld was 15 mT. A model of electromagnetic ®eld relaxation is used to explain qualitatively the eect of hysteresis and its suppression by the external magnetic ®eld. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.40.+k; 74.60.Ge; 74.60.Jg Keywords: HTC tape; BSCCO-2223/Ag; I±V curve; Hysteresis
1. Introduction Two important parameters of HTC tapes intended for power applications are obviously investigated: AC losses and current carrying capacity. For reference purposes, the latter is frequently reduced to measurement of critical current corresponding to electric ®eld E0 10ÿ4 V/m. The V±I curve is measured at a given temperature T
* Corresponding author. Tel.: +421-7-5477-5826, ext.: 2719; fax: +421-7-5477-5816. E-mail address: [email protected] (P. UsÏaÂk). 1 http://nic.savba.sk/sav/inst/elu/oes/usak.html.
and external magnetic ®eld B. The current value corresponding to E0 is determined as critical current Ic . All the measurements are referred to as DC measurements and the achieved V±I curve is mentioned as DC characteristic of the sample. Contrary to the resistivity measurement R T when temperature is changed under ®xed current through the sample and ®xed external magnetic ®eld around, the V±I measurements are made at non-zero sweeping rate dI=dt. Distribution of current within sample does not obey the critical state model as in steady R T measurement but re¯ects the non-linear dynamics of vortex motion and continually decreases inward the sample.
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 0 ) 0 1 5 7 5 - 6
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Corresponding electric ®eld E is produced by thermally activated drift of vortices driven by Lorentz force and resulting in E proportional to the mean drift velocity v of vortices. For R T measurement is this drift steady and velocity is about the same. But in V±I measurement, the current and electric ®eld diuses from surface toward the centre. The current density varies spatially, and the vortices are in unsteady motion, i.e. V±I curve measurement is unsteady. Following the idea mentioned, Zhang et al. [1] have found that V±I curves for Ag-Bi-2223 tapes are aected by the sweeping rate dI=dt. They found both experimentally for BSCCO-2223 tapes and using numerical model based on diusion equation for E in an in®nite slab that V±I curves move toward smaller current with increasing dI=dt. This means that when we compare V±I curves of two dierent samples, we should be careful to use the same sweeping speed dI=dt. This is often ignored in practice. Dependence of V±I curve on dI=dt implies that there exists electric ®eld relaxation. This relaxation was also calculated and proved experimentally [1]. The current I was ramped up with speed dI=dt until the level I0 was achieved. Then, the current was maintained constant and the ®eld E(t) decay was observed and calculated. The same decay of E, i.e. decrease of the measured voltage of V±I curve when current stopped was observed in our measurements on dierent BSCCO-2223 tapes. Contrary to Refs. [1,2] wherein measurements on multi®lament and also monocore samples are mentioned, we have observed the relaxation eect on multi®lament samples only but not on monocore.
measurement precision. Quite a dierent behaviour was found in the case of multi®lament tapes. The uprising part of the curve was shifted to higher voltage and smaller current with respect to the downrising one. Typical hysteresis loop is shown in Fig. 1. Ten consecutive measurements interrupted by repeated heating to room temperature and cooling to 77 K are shown in the ®gure. Except a small shift produced by thermal shocks, the hysteresis feature remains stable for this sample (N). The eect was observed when voltage V measured between voltage tapes distanced by 1 cm crossed the obvious critical current region in the vicinity of 1 lV, i.e. E 10ÿ4 V/m. The higher the maximum current level Imax and corresponding voltage Umax where the sweeping rate changed the sign, the larger was the dierence in up and down voltages Vup and Vdown corresponding to the same current I. The experimental demonstration of this eect is shown in Fig. 2 where Umax is a parameter (sample N). The hysteresis region was observed over Ic . When current decreased well below Ic the dierence between Vup and Vdown curves diminished. Surprisingly, we frequently observed a tiny shift of line Vdown over the line Vup at currents below Ic . Typical V±I curve hysteresis is also shown in Fig. 3 for BSCCO-2223 silver sheathed tape 3 mm in width, 0.2 mm in thickness and 36 mm in length (sample S). The sweeping rate was 0.1 A/s. The measurement was done at 77 K in liquid nitrogen
2. Hysteresis of V±I curve In Refs. [1,2] there is no remark about the in¯uence of dI=dt on V±I curve when sweeping rate is reversed and dI=dt changes the sign. We have experimentally observed this eect. We found that for monocore BSCCO-2223 samples immersed in LN2 at 77 K, the sweeping rate polarity has no in¯uence on V±I curve and ramping up and down parts of V±I curve are practically identical within
Fig. 1. Reproducibility of hysteresis loop.
P. U s ak et al. / Physica C 350 (2001) 139±146
Fig. 2. In¯uence of peak voltage.
Fig. 3. Interpretation of critical current.
bath. The sample was positioned horizontally with wetted surface down. The scale in Fig. 3 is selected in such a way as to enhance the present hysteresis eect. Dierent critical currents result in applying the standard criterion E 10ÿ4 V/m for uprising and downrising parts of hysteretic V±I curve. Uprising critical current Ic 54:1 A is 1.2 A smaller than the downrising one. This time the reproducibility of measurement is checked within the same cooldown. The larger the maximum voltage of ramping curve, the larger was the dierence between curves Vup and Vdown (Fig. 2). The larger the ramping rate, the larger is the hysteresis (Fig. 4). To observe relaxation eect mentioned in Section 1 and to reveal the role of polarity dI=dt, we decided to measure it not only for ascending curve Vup when the current was stopped during ramping up but
141
Fig. 4. The role of the ramping rate.
also for descending curve Vdown where stop was applied during current ramping down. The results are shown in Fig. 5 for Vup and in Fig. 6 for decreasing part of hysteresis curve Vdown . The measurement was done on the short sample cut from the same long tape as was cut from the mentioned sample type N. In Fig. 5 we can see that the relaxation of voltage measured between voltage taps of the sample is negative. i.e. the voltage decreases after stopping the current during its ramping up. Contrarily, in Fig. 6, we can see that the relaxation is positive, i.e. voltage increases after current stops during ramping down. The sign of relaxation is dependent on sign of dI=dt. The relaxation for dI=dt P 0 is somewhat stronger than that for dI=dt 6 0. The maximum voltage measured on distance 1 cm was from tens of microvolts up to 3 mV. The ramping rate was 0.7 A/s. The eect is
Fig. 5. Relaxation after ramping up.
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Fig. 8. The role of parallel ®eld Bjj . Fig. 6. Relaxation after ramping down.
Fig. 7. Relaxation on long sample.
much more pronounced with respect to noise when measured on large length of the tape. In Fig. 7 relaxation is measured on 1.1 m long helically wound tape (sample type S) when stop was applied during ramping up. The distance between voltage taps was 75 cm and the maximum voltage measured on this distance was 2.5 mV
typically at 100 mT, there was no hysteresis at all (Fig. 8). Helically wound long tape (S) was inserted in external ®eld. Winding axis and B external were parallel. In perpendicular ®eld, the hysteresis measured on short samples was suppressed even at the level of 15 mT. The precise value depended on the sample type. The role of perpendicular magnetic ®eld component on width of hysteresis loop measured on short sample of multi®lament tape is demonstrated in Fig. 9 (sample N). A question arises about the nature of the mechanism of this hysteresis suppression. Is it some sort of switching o of weak links as it is observed in proximity eect? Surely it is the change in complex nature of eective barriers in electric ®eld diusion process.
3. Suppression of hysteresis by magnetic ®eld When we applied external magnetic ®eld perpendicular or parallel to the tape surface, the hysteresis eect was less pronounced and at some threshold level of magnetic ®eld it disappeared. Over this threshold level of Bt , the hysteresis of V± I curve was not observed. Even for parallel ®eld,
Fig. 9. The role of perpendicular ®eld Bÿ .
P. U s ak et al. / Physica C 350 (2001) 139±146 n
Zhang [1] showed that power n in E E0 I=Ic has an important in¯uence on the relaxation process. The increase in n decreases the relaxation rate. The reason is that n re¯ects the eective pinning strength governed by temperature, magnetic ®eld and quenched disorder. The electric ®eld diusion process is retarded at high energy barrier. It was shown in Ref. [1] that the higher the n of the sample, the broader scattered are the V±I curves for the same corresponding range of dI=dt values as parameters. As the presence of external magnetic ®eld results in decrease in n in the corresponding V±I curve, the eect of the same ramping dI=dt on V±I shift at higher ®eld is smaller than at zero external ®eld. The larger the ®eld, the smaller is the shift. This can explain qualitatively the suppressive eect of external magnetic ®eld on negative shift (with respect to current) of uprising part of V±I curve and positive shift (with respect to current) of downgoing part, i.e. suppressing the hysteresis. Nevertheless, why in our measurements the effect of hysteresis was not observed on monocore tape even at zero external ®eld is unclear for us at the moment. The eect disappeared even when the multi®lament tape was cut longitudinally into ®ve sub-tapes. No sub-tape revealed hysteresis. Eect of hysteresis was observed also on BSCCO-2223 multi®lament tape in the form of
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monolayer helical coil with a diameter of 28 mm. The measurements were done on individual turns as well as on all the coil covering several turns. The hysteresis was present in both cases and was preserved up to high currents reaching 9Ic of the weakest portion when peculiar instabilities appeared. The details will be published elsewhere [3]. 4. Test of the role of self-®eld We tried to look for an alternative explanation for the eect. To clear and check the possible in¯uence of self-®eld in the eect of hysteresis, we prepared the measurement based on the following idea: when the current is ramping in the tape during V±I measurements, the self-®eld of the tape results in inductive voltage loops between the central part and both edges of the tape. These are generated by time variance of perpendicular component of self-®eld (perpendicular to tape surface) leading to E in the direction of j at edges and E opposite to j at the tape centre during ramping up. During ramping down, when dI=dt is negative, the situation is reversed and E at edges is opposite to j and of the same orientation with j at the centre of the tape (Fig. 10). When current is ramping up, in central portion of taps, the inductive local voltage from
Fig. 10. Self ®eld in¯uence on local E.
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perpendicular component of self-®eld is oriented in the opposite direction and a higher input source voltage has to be applied to overcome this obstacle. When current ramps down, the inductive voltage component of self-®eld (B? ) is in common with source voltage and for the same current the applied voltage for central taps is lower. For edge parts of tape, the situation is reversed. For edge taps, the source and self-®eld inductive voltages are during ramping up of current in common, i.e. less source voltage is needed for the same current as during ramping down when self-®eld voltage component is opposite to source voltage and eective resistance is higher. If observed hysteresis eect is not explained by highly non-linear diusivity analysed in Ref. [1] but is the result of changing polarity of inductive E loops between central part of the tape and edges during ramping up and down, the hysteresis ought to be reversed when measured on voltage taps at edges with respect to mentioned hysteresis measured on voltage taps positioned at the centre of the tape. This means that during rising up of current, the V±I curve measured at edge portion ought to be shifted to higher currents and during declining of current, it ought to be shifted to lower currents, i.e. quite opposite to shifts measured at central portion. To check this expected hysteresis reversal, we prepared the special short sample Q (type S). We decided to measure V±I curves on four voltage taps located as strictly parallel pairs in the centre of the tape (C,D) and at one edge of the tape (A,B). The longitudinal positions (in the direction of current) of points A,C and also of points B,D were the same. The results of measurement are shown in Fig. 11. Contrary to our expectation, no reversal of hysteresis was observed. In both curves for edge A,B voltage taps as well as for central C,D taps the uprising part of V±I curve was shifted to higher voltages and smaller current with respect to downgoing part of the V±I curve and the hysteresis had the same character no matter whether it was measured at the edge or in central portion. This kind of shift and the corresponding hysteresis was even observed when orthogonal pair of voltage points A,C was used in
Fig. 11. Peculiar shift of all the edge curve.
measurements. A,C pair was oriented perpendicular to current direction. The V±I curve for A,C was not exponential but was not also zero as one may expect for two voltage taps on supposed equipotential line. The hysteresis of this curve was smaller but evident and with the same behaviour as for longitudinal portions A,B and C,D. Contrarily, measurement on voltage taps B,D with the same perpendicular orientation with respect to current direction con®rmed that both points lay approximately on equipotential line. The entire measurement was done at the same speed dI=dt 0:3 A/s. Surprisingly, as can be seen in Fig. 11, the entire V±I curve (including its hysteresis feature) measured at the centre of the tape (points C,D) is shifted to higher currents with respect to the entire V±I curve measured at edge (points A,B). We have no explanation for this phenomenon except much more complex nature of current distribution within the tape width than is obviously accepted. The dierence in V±I curves for perpendicular pairs of points A,C and B,D can be explained by the presence of local defect distorting partially the current path within the line A,C. To deny the possibility that this is not a special feature of this sample Q, we decided to repeat the measurement on sample W of the same type S. This time the central voltage tapes 3,4 were completed by pairs 1,2 and 5,6 positioned at edges of the tape (Fig. 12). The results of V±I measurements for pairs of voltage taps (1,2), (3,4) and (5,6)
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Fig. 12. Tapes position independent hysteresis.
showed that the curves are practically identical, irrespective of their position selected : central, one edge or another edge. The hysteresis of V±I curve also does not change. The mutual shift of V±I curves for central and edge parts was not proved this time. This means that the observed shift is a special feature of the measured portion of sample Q. Finally, we can conclude that self-®eld generated changes in E are not the explanation for observed V±I hysteresis and non-linear diusivity model for E applied in Ref. [1] remains only a plausible explanation. Nevertheless, there is a mechanism and dynamics of self-®eld ¯ux trapping in the conductor volume re¯ecting ®nite time of ¯ux diusion and relaxation within tape volume. This was proved by measurement of current distribution dynamics in superconducting tape [4]. 5. Samples and experimentation The eect of hysteresis was observed on a broad range of multi®lament tapes from dierent producers. In this contribution, two kinds of samples were used for demonstration of the eect. The ®rst is multi®lament tape S with 55 ®laments in silver matrix. The second source of samples is silver sheathed multi®lament tape N with 37 ®laments. The potential taps were glued on silver surface or alternatively mechanically contacted by sharp hard rods in the form of a comb. The series of rods covered the sample on distance 10 mm. Mutual
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distance between individual rods was 1 mm. The reason was to reveal possible inhomogeneities in longitudinal direction along the tape. In hysteresis measurements, the largest distance, 10 mm, between rods was used. The glued taps were distanced 10 mm or, rarely, 20 mm. The way in which taps contacted had no in¯uence on the form of voltage hysteresis measured by standard fourprobe method. Measurements on mono®lament tapes as well as on series of sub-tapes longitudinally cut from the same initial multi®lament tape are not displayed for their triviality (no hysteresis). The external magnetic ®eld was produced by LN2 cooled copper split coil magnet. Limiting ®eld was 350 mT. The short sample was inserted in the direction with vector B perpendicular to broader surface of the tape. Helically wound long tape had winding axis in parallel with B, i.e. B was parallel to tape surface.
6. Conclusion 1. The hysteresis of V±I curve was observed at the vicinity and over Ic for multi®lament Ag-Bi2223 tapes measured at 77 K and zero external magnetic ®eld. 2. No such hysteresis was observed for monocore tapes within the precision of measurement. 3. The hysteresis of V±I curve could be suppressed by external magnetic ®eld of appropriate magnitude. The eect of suppression was observed both for parallel and perpendicular ®elds with respect to tape plane. 4. The qualitative explanation of hysteresis and its suppression by magnetic ®eld was applied based on the idea of highly non-linear diusivity of electric ®eld [1] and its dynamics in a superconductor with assumptions dierent from simple critical state model.
References [1] P. Zhang, C. Ren, S.Y. Ding, Q. Ding, F.Y. Lin, Y.H. Zhang, H. Luo, X.X. Yao, Eect of electrical ®eld
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relaxation on the V±I curve, Supercond. Sci. Technol. 12 (1999) 571. [2] S.Y. Ding, C. Rent, X.X. Yao, Y. Sun, H. Zhang, Eect of current sweep rate on critical current of superconducting Ag-Bi-2223 tapes, Cryogenics 38 (1998) 809.
[3] P. Usak, F. Chovanec, Stability of I±V curves of BSCCO2223/Ag multi®lamentary tapes, in preparation. [4] P. Us ak, Measurement of the transport current distribution in a superconducting tape, Physica C 316 (1999) 229.