E-J Characteristics in a Wide Range of Electric Field for a Bi-2223 Silver-Sheathed Tape Wire Takeshi Kodama, Mitsuhiro Fukuda, Kazuo Shiraishi, Shoichi Nishimura, Edmund * *Soji Otabe, Masaru Kiuchi, Takanobu Kiss, Teruo Matsushita, Kikuo Itoh Abstract_ The E-J characteristics are measuredtforhaeBi-tape were 3.7 mm and 2* *70 ~m, respectively. The av- 2223 silver-sheathed tape wire using the foureprobermethodage width, w, and thi* *ckness, d, of superconducting fila- and a relaxation method of DC magnetization in the high and low electric field regions, respectively.meThenobtainedts were about 320 ~m* * and 11 ~m, respectively. The results in the two regions are approximatelytexplainedabype was cut in a length* * of l = 4:2 mm for the magne- a theoretical analysis based on the flux creep-flowtmodelization measurement. T* *he critical temperature, Tc, was in which the distribution of flux pinning strength1is1taken0 K. into account. It was found that the value of the pinning force density and its peak magnetic field areTlargelyhdifferente magnetic relax* *ation was measured in a magnetic between the two measurements. field parallel to the c-axis in a t* *emperature range of 40 Keywords_ E-J characteristics, Bi-2223, fluxtcreep-flowo 83 K using a SQUID ma* *gnetometer (MPMS-7). The model, wide range of electric field magnetic field of sufficient streng* *th was first applied to the PACS 74.25.Fy, 74.60.Ge, 74.60.Jg, 74.72.Hs,s85.25.Dqpecimen, and then reduced * *to a certain value, and the relaxation of the magnetic moment, * *m, was measured. The I.Introduction current density, J, and the electri* *c field, E, are estimated Electromagnetic properties of high-temperaturebsuper-y the following equations: conducting instruments are strongly influenced by the elec- 12m tric field (E) vs current density (J) characteristics of theJ = __________2; * * (1) superconductors. Therefore, it is necessary to estimate the w df(3l - w) E-J characteristics in a wide range of electric field. How- ~ dm ever, the characteristics have not yet been sufficientlyEclar-= -____0___. ___;* * (2) ified. This is ascribed to the lack of a detailed knowledge 2df(l + w) dt on the generation mechanism of electric fieldwandhonethere f = 59 is the number* * of filaments. influence of the distribution of flux pinningAstrength.four probe method was al* *so used to measure the E-J On the other hand, the E-J characteristics incthehrangearacteristics in a temp* *erature range of 40 to 77.3 K. The of resistive measurements have been successfullydexplainedistance between the v* *oltage terminals is about 10 mm. by the flux creep-flow model with a distribution of the flux pinning strength [1] and by the percolation flow modelI[2].II.Results and Discu* *ssion In the latter model the flux motion under a significantTther-he E-J curves eval* *uated from the both methods at 70 K mal activation is approximated by an equivalentafluxrflowe shown in Fig. 1. The* * range of the electric field by the by making the pinning potentials shallow. ThemE-Jacharac-gnetization measuremen* *t is of the order of 10-10V/m teristics are determined by the percolation propertyawhichnd 6 to 7 orders of m* *agnitude lower than that by the four is strongly influenced by the distribution ofptherfluxopin-be method. ning strength. Hence, the two models are essentiallyTbasedhese observed E-J cur* *ves are compared with the theo- on the same mechanism. retical analysis using the flux cre* *ep-flow model [1]. Accord- In this paper the E-J characteristics are measurediusingng to this model, the * *E-J characteristics can be calculated the four probe method and a relaxation methodwofhDCen the pinning potential is * *given: magnetization in high and low ranges of the electric field, respectively, for a Bi-2223 tape. The obtained result is 0:835g2kBJ1=2c0 compared with the result of the theoretical analysis basedU0= ___________(2ss)3* *=2B1=4;(3) on the flux creep-flow model in which the distribution of the flux pinning strength is taken into account.where Jc0is the virtual critica* *l current density in the creep- 2 is the number of f* *lux lines in the flux II.Experimental freebcaseuandngdle. The magnetic fi* *eld and temperature dependencies Specimen was a superconducting multifilamentaryoBi-f Jc0at low fields are assu* *med as 2223 silver sheathed tape with 59 filaments prepared by " ` ' #m the powder-in-tube method. The width and thickness of T 2 fl-1 Jc0= A 1 - __ B ; * * (4) T. Kodama, M. Fukuda, E. S. Otabe and T. Matsushita Tc are with Kyushu Institute of Technology, 680-4, Kawazu, Iizuka 820-8502 Japan (Telephone: +81-948-29-7683,whe-mail:ere A, m and fl are* * pinning parameters. It is assumed kodama@aquarius10.cse.kyutech.ac.jp) K. Shiraishi, S. Nishimura, M. Kiuchi and T.tKisshisawithtKyushuA is distribut* *ed as University, Fukuoka, Japan ~ * * ~ 2 K. Itoh is with National Research Institute for Metals,fTsukuba,(A) = Kexp -(l* *ogA_-_logAm)_;(5) Japan * * 2oe2 Fig. 1. Comparison of E-J curves between experiment (symbols) and theory (lines) at 70 K. Experimental results are obtained by four probe method (top) and the magnetization method (bottom). where Am is the most probable value, oe2 is a constant representing the degree of deviation and K is a constant. The value of g2 is assumed to be determined so that the critical current density under the flux creep might take on a maximum value [3], and is given by ~ ` '~4=3 g2= g2e5kBT_2UlnBaf_0 ; (6) e E where geis the value where flux lines form a perfect trian- gular lattice, and Ueis the value of U0when g = ge. Strictly speaking, g2depend on E as well as on B and T.FHowever,ig.e2.lPinningeforcecden* *sitytatr70iKcdefinedfati(a)ehighlandd(b)slow. Symbols and lines show experime* *n@ the value of g2 at E = 10-10V/m is approximatelyrusedespectively. as a typical value in the present calculation. For example, we used g2= 1:39 at B = 0:3 T and T = 70 K. The details of the calculation are described in [1]. The parameters Am, m and fl used in the numericalTcal-hus, it can be said that* * the flux creep-flow model can culation in the whole ranges of temperature andamagneticpproximately describe t* *he E-J characteristics in wide field are listed in Table 1. On the other hand,roe2,awhichnisges of temperature* *, magnetic field and electric field. used as a fitting parameter at each temperature.This shows that the thermal dep* *inning is the basic mech- The calculated results are compared with theaexperimen-nism which determines t* *he E-J characteristics in a wide tal results in Fig. 1. The theoretical resultsrexplainaap-nge of the electric * *field. proximately the experimental results except inFtheiregiong. 2 shows the pinnin* *g force-densities,4Fp, at 70 K of low current density. It is seen that the criticaldcurrentefined-at1(a)0E = 1* *:0 x 10 V=m and (b) E = 1:0 x density is different between the resistive and1magnetiza-0 V=m in the resist* *ive and magnetic measurements, tion methods because of the filament sausaging.rThateis,spectively. The value o* *f Fp and the peak magnetic field the magnetic Jcshows an average value and isalargerrthane largely different bet* *ween the two cases, suggesting a the resistive Jc which is determined by narrowlareaaofrfil-ge effect of flux cr* *eep. aments. The theoretical results show the higherFelectricig. 3 shows the distri* *bution width of Jc increases fields than observed in very high range of thewelectricifield.th temperature. * *This tendency is consistent with the This deviation comes from the sharing flow ofuthescurrentual temperature depend* *ence of n-value, since n becomes to the silver sheath in the experiment. smaller due to the increase of the * *distribution width of Jc according to increasing temperature. Although, the present theoretical * *model approximately explains the observed E-J character* *istics, the details can- TABLE I not be explained. That is, the dev* *iation becomes large Parameters used in the numerical calculation.at low current densities. The * *reason for this deviation is considered to be attributed to the * *expression of g2 at low ___Am_____m____fl_ current densities. That is, the de* *pendence of g2 on the 9:0 x 1082.0 0.51 electric field was disregarded. In * *addition, Eq.(6) was de- rived for the region far from the T* *AFF(thermally activated IV.Summary The E-J characteristics are approx* *imately explained by the flux creep-flow model over wide* * ranges of temperature, magnetic field and electric field. * *This shows that the ther- mal depinning is the basic mechanis* *m which determines the E-J characteristics.However, the de* *viation becomes large at low current densities. The reaso* *n for this deviation is considered to be attributed to the * *expression of g2 at low current densities. V. Acknowledgments The authors would like to acknowle* *dge Dr. H. Okamoto of Research Laboratory, Kyushu Elec* *tric Power Co. for providing the experimental data of * *E-J characteristics measured using a four probe method. References Fig. 3. Temperature dependence of oe2.[1]T. Matsushita, T. Tohdoh and * *N. Ihara, Physica C 259(1996) 321. [2]K. Yamafuji and T. Kiss, Physica* * C 258 (1996) 197. flux flow) state, while the theoretical prediction[shows3the]T. Matsushita, Phy* *sica C 217 (1993) 461. typical behavior in the TAFF state as can be seen from Fig. 1. Thus, the theoretical expression of g2 should be obtained in a self-consistent manner.