Alternating current losses in Bi2Sr2Ca1Cu2O8+δ/Ag tapes at power frequenciesM. N. Pitsakis, T. Haugan, F. C. H. Wong, S. Patel, and D. T. Shaw Citation: Applied Physics Letters 67, 1772 (1995); doi: 10.1063/1.114378 View online: http://dx.doi.org/10.1063/1.114378 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/67/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Relationship between Critical Current Density and SelfField Losses of AgSheathed (Bi,Pb)2Sr2Ca2Cu3OxSuperconducting Tapes AIP Conf. Proc. 824, 696 (2006); 10.1063/1.2192412 Alternatingcurrent losses in silversheathed (Bi,Pb)2Sr2Ca2Cu3O10 tapes II: Role of interfilamentary coupling Appl. Phys. Lett. 67, 3180 (1995); 10.1063/1.115155 Alternatingcurrent losses in Agsheathed (Bi,Pb)2Sr2Ca2Cu3O x multifilamentary tapes Appl. Phys. Lett. 66, 1551 (1995); 10.1063/1.113643 Strain tolerance of doctorbladeprocessed Bi2Sr2Ca1Cu2O8−δ tapes J. Appl. Phys. 70, 6966 (1991); 10.1063/1.349824 50 Hz currentdependent losses of Bi2Sr2Ca1Cu2O8+x /Ag wires Appl. Phys. Lett. 57, 192 (1990); 10.1063/1.103955

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Alternating current losses in Bi 2Sr2Ca1Cu2O81d /Ag tapes at powerfrequencies

M. N. Pitsakis, T. Haugan, F. C. H. Wong, S. Patel, and D. T. ShawNew York State Institute on Superconductivity and State University of New York at Buffalo,Buffalo, New York 14260-1900

~Received 29 March 1995; accepted for publication 10 July 1995!

Measurements of transport alternating-current~ac! losses in Bi2Sr2CaCu2O81x powder-in-tubeAg-sheathed tapes at 4.2 and 65 K and at 20, 60, 200, and 400 Hz were carried out and comparisonsto the theoretically predicted hysteretic loss plus ohmic loss were made. The measured loss, albeitlarger than predicted, was found to agree with Bean’s critical state model. The loss, having a lineardependence on the frequency of the alternating transport current and increasing with decreasingcritical current density, confirms hysteresis as the dominant source of power dissipation at both 4.2and 65 K. However, at 4.2 K, the loss varies as the square of the amplitude of the transport current,which is not consistent with the model. ©1995 American Institute of Physics.

In high temperature superconductors, alternating current~ac! power loss is mainly hysteretic in nature and stems fromthe irreversibility of flux motion. It is foreseen that this losswill be the dominant heat load for the cooling system infuture applications where the high temperature supercon-ducting cable is subjected to varying magnetic field or tovarying transport current. The loss in W/cm2, based on theLondon–Bean approximation1 @assuming that critical currentdensity (Jc) is independent of the field#, for a tape of widthw and thicknesst, both in cm~w@t) exposed to a transversealternating magnetic field of amplitudeHm and frequencyf isgiven by

P/S51.33431022m0t fHm3 /wJc for Hm,Hp , ~1!

and

P/S5131022m0twJcfHm for Hm.Hp , ~2!

where

Hp512wJc ~3!

is the magnetic field that results in complete penetration.When an alternating transport current of amplitude,A2I rms, and frequencyf flows through the tape a transversemagnetic field is developed equal to

Hm5~2.828w2t !21/3I rms, ~4!

and the power loss in this case is given by

P/S50.471431022m0f I rms3 /w3Jc . ~5!

In practice, it is preferable to measure the losses since theyare influenced quite strongly by other factors such as inter-grain weak links2 and surface roughness,3 such as sausagingin the PIT tapes. Measurements of ac losses in different typesof high superconducting transition temperature (Tc) materi-als have been performed and published: in sinteredYBa2Cu3O71y ~YBCO! cylinders4 and bars,5 Bridgman-typeYBCO bars,5 YBCO round wire,6 YBCO/Ag tape wire,7 Ag-doped YBCO,8 ~Bi,Pb!2Sr2Ca2Cu3O101x ~Bi-2223!/Ag tapewire,5,9 Bi-2212 single crystals,10 and Bi-2212/Ag roundwire.11 However, to the best of our knowledge, ac loss mea-surements in Bi-2212/Ag tape wire have never been pub-

lished except for measurements in a magnet constructed outof Bi-2212/Ag tape wire12 investigating potential magnet acapplications for that material.

Ninty meter long Ag-sheathed Bi-2212 tapes were madeby the oxide PIT method and processed by a partial meltgrowth technique. Precursor powders were packed by me-chanical agitation into silver tubes~1/4 in38 ft! and werepreannealed with a very fast heating profile to control bubbleformation. Following preannealing, the tubes were coldrolled into tape form~;60 mm thick and;9 mm wide!using over 200 rolling steps. After the tapes were set in coilform by annealing in Teflon molds, they were processed free-standing by a partial melt, slow cooling profile. The detailsof the fabrication process are described elsewhere.13–15

Transport ac losses of short samples~3 cm long, 65 mmthick, 9.4 mm wide! cut from a 90 m long, PIT, Bi-2212/Ag-sheathed tape described above have been measured in ourlaboratory at zero applied field in liquid helium~4.2 K!, andin liquid nitrogen at reduced pressure~65 K! with a lock-inamplifier ~Princeton Applied Research M/N 5210! and a cur-rent source~California Instruments M/N 3213 K!. Details ofthe experimental setup and measurement method are de-scribed elsewhere.16 Two types of measurements were per-formed under computer control: amplitude sweep and fre-quency sweep. In the amplitude sweep case, the powerdissipation was measured as the amplitude of the transportcurrent was increased, while its frequency was held constant.In the frequency sweep case, the power dissipation was mea-sured as the frequency of the transport was increased, whileits amplitude was held constant. The total power dissipationmeasured indirectly by the lock-in amplifier and calculatedby the computer was divided by the surface area of the su-perconductor part of the tape~0.7 cm2), which was containedby the voltage taps. Frequency sweep data are useful in de-termining the nature of the power loss since ohmic loss,which occurs when the sample is in the normal state, is in-dependent of frequency. Hysteretic loss, on the other hand,which occurs in the material, varies by the first power offrequency and eddy current loss, which occurs in the silver

1772 Appl. Phys. Lett. 67 (12), 18 September 1995 0003-6951/95/67(12)/1772/3/$6.00 © 1995 American Institute of Physics

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cladding, varies by the second power of frequency.Data taken at 65 K in amplitude sweep mode are plotted

in Fig. 1 and in frequency sweep mode in Fig. 2. Data takenat 4.2 K in amplitude sweep mode are plotted in Fig. 3 and infrequency sweep mode in Fig. 4. The loss, shown in Fig. 1, ishysteretic below critical currentI c ~measured as 9.3 A rightbefore the ac loss measurement! and predominantly ohmicabove I c as all data regardless of frequency converge to-gether with the dc loss@calculated from the voltage–current~V–I! data#. Power curve fitting reveals loss dependence onthe third power of the transport current amplitude~n53! bothbelow and, surprisingly, aboveI c . The hysteretic nature ofthe loss is also evident in Fig. 2, where the power loss isplotted versus frequency at 9.8 A, which is slightly higherthan I c , and at 2.8 A, which is lower thanI c ,as there is alinear dependence on frequency. Notice that as expected,there is ohmic loss at 9.8 A in addition to the hysteretic loss.This is because at zero frequency the loss is not zero. At 4.2K the loss is predominantly hysteretic below or above theI c ~measured 27.3 A! as seen in Fig. 3; and the ohmic loss isquite smaller also as seen Fig. 4. However, according topower law curve fitting, the loss depends on the square of theamplitude of the current~n52!. This surprising result wasfirst observed by Zannelaet al.11 in PIT Bi-2212/Ag round

wires and has been confirmed by magnetic measurements ofsimilar samples produced in our facilities and measured atBrookhaven National Laboratory.17 This result was also ob-served, without explanation, in Nb3Sn cables measured atBrookhaven National Laboratories.18 The measured loss, inagreement with theoretical prediction, increases with increas-ing temperature and with increasing frequency. The lineardependence of Bi-2212/Ag power loss on frequency at 4.2 Khas been confirmed by magnetic measurements of similarsamples produced in our facilities and measured atBrookhaven National Laboratory17 and by Zannelaet al.11 inBi-2212/Ag round wires. This finding is in contrast to Bi-2223/Ag, which shows anf 2 dependence attributed to eddycurrent losses9 in the sheathing.

Calculation using Eq.~5! yields significantly smallervalues than measured. For a better estimation, the ohmicloss due to the silver cladding resistanceRag,

19 and dueto the superconductor dynamic resistance,dV/dI rms5(Vc /I c)I rms

n21, must be considered. The total loss is the sumof the I rms

2 R loss of the parallel combination of the aboveresistances plus the hysteretic loss given by Eq.~5!

FIG. 1. Measured ac loss vs amplitude of transport current at 20, 60, 200,and 400 Hz, at 65 K.

FIG. 2. Measured ac loss vs frequency of transport current at 65 K fortransport currents below critical current~top! and above it~bottom!.

FIG. 3. Measured ac loss vs amplitude of transport current at 20, 60, 200,and 400 Hz at 4.2 K.

FIG. 4. Measured ac loss vs frequency of transport current at 4.2 K fortransport currents below critical current~top! and above it~bottom!.

1773Appl. Phys. Lett., Vol. 67, No. 12, 18 September 1995 Pitsakis et al.

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P/S5~VcRagI rmsn11!/~VcI rms

n211RagI cn!10.4714

31022m0t f I rms3 /w2I c , ~6!

whereVc51 mV ~from 1mV/cm I c criterion!; andn is thenvalue of the dcV–I data as determined by power law curvefitting. Table I contains a summary of the sample parametersand values needed to evaluate Eq.~6!. The predicted lossesby Eq. ~5!, Eq. ~6!, the measured loss, and the ohmic~dc!loss at 65 K are plotted in Fig. 5 and at 4.2 K are plotted inFig. 6. The measured loss is still higher than predicted. Thismay be because while the intergranular loss plus the loss dueto the surface roughness are not accounted for in Eq.~6!,they are inherently included in the transport measured data.Losses varying by more than two orders of magnitude wereobserved in Nb3Sn rods and tapes, related to the surfaceroughness.3 Losses higher than expected were also observedpreviously in Nb3Sn cables.18 The difference in slope forpredicted (n53) and for measured (n52) is evident at4.2 K, while at 65 K the predicted loss data converges to thedc loss for currents higher than;2* I c in the same fashion asthe measured data.

In summary, at 65 K the loss is hysteretic belowI c andpredominantly ohmic greater than 2* I c . The loss is propor-tional to frequency andI 3 at all currents, in agreement withthe hysteretic loss model. At 4.2 K the loss is proportional tofrequency andI 2 above and belowI c , in agreement withprevious results for Bi-2212 wires, however in contrast to

Bi-2223/Ag wires ~loss proportional tof 2). At 4.2 K thefrequency dependence of loss is in agreement with the hys-teretic loss model, however the loss is proportional toI 2

which is not predicted by hysteresis~proportional to I 3),however has been observed previously in Nb3Sn cables. Themeasured loss at 4.2 and 65 K is greater than the theoreti-cally predicted hysteretic plus ohmic loss, similar to previousresults for Bi-2212 wires at 4.2 K and Nb3Sn cables or rodsand tapes. The greater than expected loss may be due tosurface roughness in the PIT tapes, possibly including sau-saging variations.

1W. J. Carr, Jr.,AC Loss and Macroscopic Theory of Superconductors~Gordon and Breach, New York, 1983!.

2K. H. Muller, IEEE Trans. Magn.MAG-27, 2174~1991!.3J. F. Bussiere, M. Garber, and M. Suenaga, IEEE Trans. Magn.MAG-11,324 ~1975!.

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12T. Hase, T. Egi, K. Shibutani, S. Hayashi, R. Ogawa and Y. Kawate,Cryogenics34, 307 ~1994!.

13T. Haugan, M. Pitsakis, J. Ye, F. Wong, S. Patel, and D. T. Shaw, Appl.Supercond.3, 85 ~1995!.

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15T. Haugan, S. Patel, M. Pitsakis, F. Wong, S. J. Chen, and D. T. Shaw, J.Electron. Mater.~to be published!.

16M. Pitsakis, F. Wong, and T. Haugan~unpublished!.17M. Suenaga~private communication!.18E. B. Forsyth and R. A. Thomas, Cryogenics26, 599 ~1986!.19Y. Iwasa, E. J. McNitt, R. H. Bellis, and K. Sato, Cryogenics33, 836

~1993!.

FIG. 6. Measured ac loss, compared to ohmic~dc! loss, predicted hystereticloss, and combined predicted hysteretic and ohmic losses at 4.2 K.

TABLE I. Parameters used for modeling of power loss.

At 4.2 K At 64 K

n 16.4 9.5I c ~A! 27.3 9.3Jc ~A/cm2! 21 550 7410w ~cm! 0.7 0.7t ~mm! 0.018 0.018RAg (mV) 0.252 18.9

FIG. 5. Measured ac loss, compared to ohmic~dc! loss, predicted hystereticloss, and combined predicted hysteretic and ohmic losses at 65 K.

1774 Appl. Phys. Lett., Vol. 67, No. 12, 18 September 1995 Pitsakis et al.

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