Bi-2223 tapes in low external DC magnetic fields

PHYSICA ELSEVIER

Physica C 272 (1996) 319-325

Transport AC losses in multifilamentary Ag/Bi-2223 tapes in low external DC magnetic fields M. Ciszek a,,, S.P. Ashworth a, B.A. Glowacki a,1, A.M. Campbell a, P. Haldar b a IRC in Superconductivity, University of Cambridge, Cambridge CB30HE, UK b Intermagnetic General Corporation, Latham, New York 12110, USA

Received 22 August 1996

Abstract Experimental results of measurements of the AC transport current losses on silver sheathed ( B i , P b ) 2 S r 2 C a 2 C u 3 0 x multifilamentary tapes are presented. In the frequency range 33-180 Hz the self-field losses are hysteretic. Transport loss changes due to low DC, applied transverse magnetic fields are also studied. External transverse DC magnetic field causes an increase in the transport losses due to lowering of the critical current I e of the superconductor. Critical current dependence on the external magnetic field extracted from loss data is compared with that measured directly by standard DC four-probe measurements. PACS: 74.60.Jg; 74.72.Hs; 74.72.Fq; 85.25.Kx Keywords: High-Tc superconductors; AC losses; Critical current; Superconducting tapes

1. Introduction The widespread use o f high temperature oxide superconductors (HTS) in the electric p o w e r field would bring many advantages. Designs exist for highly efficient and compact transmission cables, motors, generators and transformers [1,2]. There are also applications utilizing superconductors which are really not possible with non-superconducting technology, for example magnetic energy storage. The technical and commercial success of many o f these

* Corresponding author. 1Also at the Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK.

applications depends on the availability of HTS wire or tape in long lengths and with adequate critical current densities at 77 K. The most highly developed HTS material for power applications is at present the (Bi,Pb)ESr2CaECU30]0 ( " B i - 2 2 2 3 " ) silver sheathed multifilamentary tapes of which are now produced in 100 m scale lengths with critical current densities over 2 0 0 0 0 A / c m 2 at 77 K [3-5]. The A C losses are due to the changing magnetic flux within the superconductor, this flux may be primarily due to an external applied changing field or due to the self field o f a transport current or, more likely, a combination o f both. The techniques for minimizing A C loss in the two cases differ, but it is obviously important to develop accurate techniques for measuring A C losses.

0921-4534/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0921-4534(96)00603-X

320

M. Ciszek et a l . / Physica C 272 (1996) 319-325

In this paper we report the losses due to a sinusoidal AC transport current in a Bi-2223 tape in liquid nitrogen as measured by an electrical technique. This technique uses a lock-in amplifier to sensitively measure the voltage generated in phase with the transport current along the sample. When using this technique it is important to realize that the measured loss voltage does not simply arise due to the flux within the superconductor at any instant, but also how the magnetic field around the sample has been changed by the presence of a superconductor. To obtain an accurate measure of the AC losses using this technique all this flux must be encompassed within the measuring circuit [6-8]. This is achieved by the counter-intuitive step of, instead of tightly twisted pairs of wire for voltage measurement (as would be more usual in good experimental technique), producing an open " l o o p " of wire, including the sample, which in effect acts as a pick-up coil to include the magnetic flux outside the sample in the measurement. In theory this loop should extend to infinity, in practice though extending the loop to three times the tape width includes more than 90% of the required flux [8-11]. We also report the effect of applied DC magnetic fields on the transport losses. Previously we have shown [12] that the application of a magnetic field to a monocore HTS tape, parallel to its surface, carrying an AC current increases the AC transport losses. One must be careful to distinguish here between total losses (arising from a simultaneous external field and flowing transport current) and transport losses, caused only by transport current. It is helpful to consider the experiment with AC transport current and externally AC applied magnetic field. There are in effect two power supplies in this system, one driving the current through the superconductor and one driving the coil producing the magnetic field. In our experiments we essentially only measure the load on the current supply, and how that load changes when external magnetic field is applied to the superconductor. In this paper we do not report on the magnetic losses as experienced by the coil supply. These can be obtained in experiments using pickup coils on the superconducting tapes. Previous measurements [12] indicate that for applied fields less than 100 mT and with peak power frequency AC transport currents in the range 30% to 70% of the DC critical current

(self-field only), AC and DC applied fields yield much the same increase in transport losses, indicating that the increase in transport losses is primarily due to the decreased critical current of the tape. In this low field regime, for transport currents greater than 50% of the zero field DC critical current, the transport losses dominate the magnetic losses. As a consequence of this a reasonable approximation to the total losses generated by AC applied fields and AC transport currents can be obtained by the much simpler measurement of transport losses due to AC transport currents with DC applied magnetic fields.

2. Results and discussion

The superconducting Ag/(Bi,Pb)2Sr2Ca2Cu30 x multifilamentary (37 filaments) tape was produced by a technique described previously [4]. The ratio of ceramic to silver in the cross-section of the final tapes estimated by optical microscopy and image analysis was about 1.85. The samples used for AC measurements were 60 m m long, with DC critical currents I c in zero magnetic field at 77 K of 24.5 A. These critical currents (defined at 1 ~ V / c m electric field criterion) correspond to critical current densities Jc of approximately 14500 A / c m 2. For the AC transport results, current leads were in the form of silver tapes of the same width as the sample and were directly soldered to the ends of the specimen. The configuration of the potential terminals is shown in the inset to Fig. 1. The sinusoidally varying transport current was supplied to the sample by means of a power amplifier. Measurements were carried out for frequencies from 33 to 180 Hz. The lossy component U~s, of the voltage signal at the fundamental frequency induced between the potential leads, was measured by using a dual phase lock-in amplifier. An external magnetic field, directed parallel to the faces of the tape, was generated by a race-track shaped copper solenoid. The inductive component of the voltage was reduced by a part of the pure inductive signal taken from a system of compensating coils. The apparent transport loss, per cycle, per unit length of the tape, was calculated using the formula Qt=(lu)-lU~slrms where u is the frequency, Irms is the transport current and U"s is the loss voltage measured between potential leads

M. Ciszek et aL /Physica C 272 (1996) 319-325

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Fig. 1. Transport current loss Qt versus current amplitude Io, measured with different voltage wire loops (inse0. Losses measured with leads arrangements TI or T2 (with distances " x " or " y " from the edge of the tape) do not differ considerably ("true

loss").

with separation l. All measurements were carried out at liquid nitrogen temperature. It has been demonstrated previously that the value of AC "loss voltage" obtained in transport current experiments strongly depends on the arrangement of the voltage " t a p s " and associated measuring circuit [8,13,14]. Consequently in reporting AC loss data it is important to demonstrate that the measurement " l o o p s " are in fact yielding reasonable results. We accomplish this by showing, in Fig; 1, the AC " l o s s " data resulting from three different sets of voltage taps on the same sample as a function of peak AC current at a frequency of 90 Hz. The losses are quoted as energy loss per unit length of tape per AC cycle and were all carried out in liquid nitrogen at 77 K. Taps T1 to T3 include increasingly large loops (T1 - on sample edge, no loop; T2 - position " x " , 4 mm from the tape loop, T3 - position " y " , 7 mm loop, as shown schematically in the inset to Fig. 1). According to the criteria published in Refs. [6,7] taps T1 are below the dimension expected to yield accurate AC loss voltages, whilst T2 and T3 should yield values within less than 10 percent of the tree loss. As can be seen from Fig. 1, T2 and T3 data are indistinguishable, whilst T1 yields apparent losses significantly higher. The T2 and T3 loops are obviously all sufficiently large so as to return the correct values of loss voltage. All data shown henceforth in

321

this paper is taken using loops similar in size to T3. Fig. 2 shows the effect of different AC frequencies (in the range 33 Hz to 180 Hz) on the loss voltage U " s. There is a spread of data for transport current amplitudes below critical current value I c, but all the data points converges to a common curve at and above I c. For peak currents I 0 greater than IcX/2 the voltage is due to flux flow in the superconductor, just as would be seen in the case of DC currents these are independent of frequency in this range, like in normal conductors. If a DC transport current, Idc, generates a voltage Vdc which is some function of Idc, V=f(Idc), then an AC current of amplitude I 0 will generate a voltage, as measured by a lock-in amplifier, of Vlos~= (f(10))rms in addition to any hysteretic " A C loss" voltage. Flux flow voltage is a very rapid function of current though and the " A C " loss generated in this way rapidly becomes negligible as peak AC current is reduced below Ic [15]. In Fig. 3, the loss voltage data of Fig. 2 is converted to losses per AC cycle per unit length of the tape, and plotted as a function of normalized transport current i defined as the ratio i = Io/I c In the region 0.08 < i < 1 the data for different frequencies fall on a common curve, confirming that the losses are purely hysteretic. Losses due to transport currents for i > 1 show some divergence, arising 10a

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Fig. 2. The dependence of the loss voltage U~s on the amplitude of the AC transport current Io as measured for different frequencies. The arrow shows the current amplitude 1o corresponding to DC critical current 1c ( = 24.5 A).

322

M. Ciszek et a l . / Physica C 272 (1996) 319-325

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from flux flow as described previously. There is also some possible spread in the data at i < 0.08 and at low frequency range, although this is at the noise limits of the apparatus. Also shown by lines on Fig. 3 are the theoretical losses predicted by Norris [16] for superconductors with elliptical (solid line, Eq. (1)) or strip (dashed line, Eq. (2)) cross section ~ 0 X c2

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where/*0 = 4~-× 10 -7 W b / A m is the vacuum permeability. In the derivation of these losses it is assumed that flux penetration follows a critical state model and that the superconductor is isotropic and homogeneous with critical current density independent of magnetic field. At the critical current the loss per cycle per unit length for an elliptical wire with a critical current Ic is about 0.16 /ZoI2 and that for a thin rectangular film is 0.12 /,01e2 so that the difference is not very significant. For small values of the transport current amplitudes I o, such that i << 1, Eq. (1) for round (elliptical) wire can be simplified to the form of

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By analogy, Eq. (2) for the strip takes similar form but with 14 proportionality. Fig. 3 shows that the AC losses are well described by Norris's equation for elliptical superconductors, Eq. (2), in which the only parameter describing the superconductor is the DC transport critical current I c. From Eq. (2), at a fixed fraction of DC critical current i, the loss of a tape is proportional to the square of the DC critical current I c. The experimental data follows rather closely the losses for the elliptical cross section for over nearly five orders of magnitude in losses. This implies that the magnetic field penetrates as concentric ellipses throughout this range, which is perhaps rather surprising given that the Bi-2223 within the tape is highly anisotropic and composed of filaments. There is also no sign of losses due to eddy currents in the silver cladding, these would manifest as a change in frequency dependence (eddy losses per cycle are proportional to frequency) and a reduced dependence on current (eddy losses are proportional to i 2, whereas hysteresis losses vary a s i 3 or higher). This is in agreement with loss measurements by magnetic methods reported in Refs. [ 17,18], where contributions from eddy currents were only observed at lower temperatures (4.2, 27 K) where silver resistivity drops considerably. As previously published [12] the transport losses in a superconducting single core tape carrying an AC transport current and exposed to an external AC applied magnetic field ("IAc/IAc" experiments) are similar to those in tapes with only a DC applied field, the "'IAc/Ioc" experiment (at least in the range of fields less than 100 mT applied parallel to the tape face and at power frequencies). The advantage is that the "IAc/IDc" experiment is much more straightforward to interpret. In an "IAc/IAc" experiment there will be another contribution to the total energy loss in the sample, namely due to the varying applied external AC field, which is not measured by our transport method. This component of loss can be obtained by methods utilizing a pick up coil. In Fig. 4 we show the losses due to an AC transport current in the presence of a constant magnetic field B applied parallel to the tape face. This shows an increase in transport losses throughout the range of fields, note though that for a tape operating at 50% of its zero field critical current I c, the

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Fig. 4. Transport loss Qt per unit length and per cycle as a function of the current amplitude 10 for various external magnetic fields B, applied parallel to the face of the tape. transport losses increase only by a factor o f 2; from 0.7 i x J / c m / c y c l e at B = 0 m T to about 1.5 i x J / c m / c y c l e in an applied field o f 70 mT. The A C magnetic loss due to an applied A C field only, for similar tapes, would be approximately 4 t x J / c m / c y c l e with a field amplitude o f 70 m T [18]. The change in DC transport critical current with applied DC magnetic field for these A g / B i - 2 2 2 3 tapes is shown in Fig. 5, where the field is applied 1.0 I~)

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Fig. 5. The dependencies of the critical current densities Jc on the external magnetic field directed parallel to the plane of the tape and perpendicular to the current. Arrows show the ascending and descending branches of the characteristics. Solid line in the inset is theoretical according to Kim model with fitting parameter BK = 118.5 mT.

Fig. 6. Loss factor, defined as the ratio of the transport loss Qt to the square of the critical current Ic, as a function of normalised transport current i b (= I o/le(B)). Solid line represents ellipse, and the dashed one-strip. Experimental data are taken from Fig. 4.

parallel to the tape face and arrows indicate the increasing and decreasing fields. The I t ( B ) dependence is typical o f this class o f superconducting materials, with characteristic hysteresis on changing the external magnetic field [19]. F o r the samples investigated here we do not observe any pronounced peak in the decreasing branch of the magnetic field (filled squares), characteristic o f more granular materials, like sintered Y B C O or T S C C O ceramics. In the inset to Fig. 5 the solid line is the fit to experimental data (only for descending field) according to the K i m relation o f the form l c ( B ) / I c ( O ) = 1 / ( 1 + B / B K ) , the fitting gives value o f B K parameter equal to about 120 roT. To show the effect o f DC applied field on A C transport losses, in Fig. 6 we plot A C loss per cycle divided b y I 2 ( B ) , against ib(B) for various applied fields. Here ib(B) is the ratio of the peak transport current I 0 to critical current I~(B) o f the tape at a given DC magnetic field (also defined using the 1 p N / c m criterion, see Fig. 5). All the data points follow the behaviour predicted by Eq. (2) in the range o f 1 > i b > 0.5, implying that the primary effect o f applied field on A C losses is simply to reduce the critical current density o f the superconductor and hence to increase ib(B) and thus to increase losses. A t lower values o f ib(B) the losses tend above the predicted value, the deviation above Eq. (2) with increasing field saturates at 30 mT,

M. Ciszek et al./Physica C 272 (1996) 319-325

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the changing local flux within the tape due to the transport self field (which generates the AC transport losses) is not reducing the amount of flux pinned within the grains due to the reduced applied field. This may be taken as evidence that whilst the self field is penetrating the tape (and causing losses) it is not actually penetrating the grains themselves but rather the inter-grain regions. In fact the critical current density is generally a certain function of magnetic induction, so traasport loss versus magnetic field should follow the critical current dependency on B, for a given constant 1o. If we assume that transport loss for a given current depends on the external field only through Ic(B) relation, the Eq. (3) can be displayed as Qt(B) a [Ic(B)]- 1. The reciprocal of this expression should follow the Ic(B) dependence for a given sample and we can write the simple expression (~(B) = Q t - ' [ Ic(B)] at Ic(0) f ( B ) ,

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Fig. 7. Transport loss Qt per unit length and per cycle as a function of the DC external field B for different transport peak currents i. Arrows show increasing and decreasing magnetic field.

which is approximately the applied field which penetrates to the center of the tape. In deriving Eq. (2) it is assumed that the self field due to a DC transport current penetrates the superconductor in elliptical contours, an increase in Q t / / 1 2 ( B ) a s shown in Fig, 6, indicates that the penetration is faster than expected, even taking into account the reduced I c due to the applied field. Fig. 5 (DC critical current versus applied magnetic field) shows hysteresis, the I c for increasing fields is lower than the I c for decreasing field which is common in HTS superconductors [19], this change in I c should also affect the tape AC transport losses. Fig. 7 a - 7 d shows the AC transport loss at fixed transport current amplitude as a function of applied DC magnetic fields, for increasing and decreasing field. Data are shown for i from 0.1 to 0.4 (referred to the zero field critical curren0, hysteresis in losses is clearly visible in all the curves. This implies that

(4)

where I~(0) is the value of the critical current in B = 0 and f ( B ) is a function describing its field dependence (e.g. Kim, exponential, power or others models). It is also possible to invert the analysis and extract Ic(B) from loss data - given the assumption that Eq. (3) holds. This is done by measuring loss at constant peak current as a function of applied magnetic field.

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M. Ciszek et al./Physica C 272 (1996) 319-325

In this way we obtain the " l o s s critical current". This is shown in Fig. 8 (normalized to the zero field value I ~ ( B --- 0)). Also shown in Fig. 8 is the " D C " critical current (direct measured with 1 I x V / c m criterion, see Fig. 5) and examples of the critical current variations with B predicted by the K i m model. Solid lines represent the fitting equations according to K i m model with parameters B K = 15 m T and B K -- 42 m T for i = 0.1 and i = 0.4, respectively. One can see that general tendency is that the data plots approach the " D C data c u r v e " when amplitude of the transport current I 0 rises towards I c. However, the drop of the " l o s s " I c versus B is faster than ones measured directly, which means that the transport loss increases faster with B than the DC critical current decreases. One can suppose that self-field loss in multifilamentary tapes, for low transport current amplitudes, depends on external magnetic field not only formally via Ic(B) relationship but also through other additional factors, among them, for example, flux creep or anisotropy, i.e. the resultant local magnetic field direction in the space between filaments does not necessarily correspond to the direction of that one externally applied. Moreover, the difference between " l o s s " critical current and " D C " critical current may arise due to the somewhat arbitrary choice of criteria for critical current determination (e.g. 1 i~V/cm).

3. Conclusions Experimental results of measurements of the AC transport c u r r e n t losses on silver sheathed (Bi,Pb)SrCaCuO-2223 multifilamentary tapes are presented. In the used frequency range 3 0 - 1 8 0 Hz the self-field losses are hysteretic in nature. Losses due to combined low DC external transverse magnetic fields directed parallel to the face of the tapes, are also reported. External transverse DC magnetic fields yields an increase in the transport losses primarily due to the decrease of the critical current density of the tape,

325

Acknowledgements The authors wish to thank E. Robinson for technical assistance. M.C. acknowledges support from the European Commission under contract number BRECT93-0531.

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