Ž. Physia C 310 1998 372 376 Heat propagation and stability in a small high T superondutor oil T. Kiss a,), V.S. Vysotsky a, H. Yuge a, H. Saho a, Yu.A. Ilyin a, M. Takeo a, K. Watanabe b, F. Irie a Graduate Shool of ISEE, Department of Eletrial and Eletroni Systems Engineering, Kyushu UniÕersity, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan b Institute for Material Researh, Tohoku UniÕersity, Sendai 980-77, Japan Kyushu Eletri Power, Fukuoka 815, Japan Abstrat Using a Bi-based small high T superondutor Ž HTSC. oil, we have studied its stability against a loal disturbane and urrent-indued quenh in the helium gas ooling ondition. While the stability margin of HTSC oil against a loal disturbane was very large, quenh urrent was limited by a atastrophi temperature rise whih originated from the nonlinear harateristi of the Joule heating. The ruial parameter for the quenh beomes the nonlinear resistane in HTSC as a funtion of temperature and transport urrent. It has been shown that the dynami harateristis of the quenh an be desribed quantitatively by the simplified one-dimensional heat balane equation. q 1998 Elsevier Siene B.V. All rights reserved. Keywords: Bi-2212 tape; Bi-2223 tape; Superonduting oil; Quenh; Heat propagation 1. Introdution Bi-based high T superondutor Ž HTSC. is one of the most promising materials beause of the steady progress in a fabriation proess for long size tapes and the possibility of high magneti field use. However, the method as how to haraterize the quenh properties in the HTSC oil is not well-established. In other words, the basi theory for a devie design is still laking. The ritial urrent density in HTSC determined by the onventional eletri field riterion, 1 mvrm, or resistivity riterion, 10 y13 V m, ) Corresponding author. Tel.: q81-92-6423910; Fax: q81-92- 6423963; E-mail: kiss@s.kyuhsu-u.a.jp does not have a signifiant meaning as a material parameter. For example, the flux flow state is very stable even though the applied urrent is onsiderably larger than the ritial urrent beause Ž. 1 gently rising eletri field Ž E. vs. urrent density Ž J. harateristis wx 1 makes the boundary between superonduting state and resistive state indistint and Ž. 2 the large value of speifi heat at the elevated temperature improves thermal stability very muh. Therefore, the oneption of the ritial urrent density and the stability in HTSC needs to be revised. In this paper, we present a basi study on the stability in a small Bi-based HTSC tape oil. The influene of a loal disturbane and the relationship between quenh and the nonlinear transport harateristis in the tape are disussed. 0921-4534r98r$ - see front matter q 1998 Elsevier Siene B.V. All rights reserved. Ž. PII: S0921-4534 98 00494-8
( ) T. Kiss et al.rphysia C 310 1998 372 376 373 2. Experiment The measurements were made using two different HTSC oils. One of them was for the test of loal heating. The details of the measurement were dewx 2. Six turns of sribed in the previous paper silver sheathed Bi-2212 multifilamentary tape were wound as a single layer solenoid on a opper former. The size of the former was 20 mm in outer diameter and 25 mm in height. The surfae of the former was overed by a thin teflon layer. We installed seven potential taps at approximately 7 m intervals. Several thermometers and miniature heaters were also installed. The voltage signals at the potential taps and the thermometers were measured simultaneously by a multi-hannel data aquisition system. The bias temperature was ontrolled by hanging the flow rate of helium gas. For the test of urrent-indued quenh, we made another oil. The basi struture of the oil was the same as mentioned above, however, we used Bi-2223 multifilamentary tape for this oil. The size of the opper former was also a little bit larger than the previous one, that is, 55 mm in outer diameter, 50 mm in inner diameter and 51 mm in height. The average distane between the potential taps was about 15 m. The details of the measurement will be wx published separately 3. 3. Influene of loal heating Fig. 1 indiates the voltage response for a loal pulse heating at the bias temperature of 20 K. The onstant urrent as high as 150 A was applied to the tape, then the pulse shape voltage was applied to the heater. The ritial urrent, I, determined by the 1 mvrm riterion, was 110 A at the heated setion. The amplitude of the heating power was 1.6 W and the duration was 1 s. As an be seen in Fig. 1, a synhronized response was observed at the heated setion, V V. However, in the next setion, V V, 3 4 4 5 and after the next setion, V V, no signifiant 6 7 voltage rise was observed. Therefore, the temperature rise was loalized. We tested up to 5 W heating power; however, no normal-zone propagation was wx observed for a time sale of 10 s 2. Fig. 1. Voltage response for a loal heating at heated setion, V 3 V 4, the next setion, V 4 V 5, and the after next setion, V 6 V 7. Pulse shape heating power with the amplitude of 1.6 W and 1 s duration was applied repeatedly. The voltage response was loalized at the heated setion, then as soon as the heater was swithed off, the voltage level was reovered. Next, we show the results for long heating with the same transport urrent. The temperature rise measured by a thermometer at the heated position for a step heating with the amplitude of 2.1 W is shown in Fig. 2. The solid line indiates the experimental result, whereas the dots indiate the alulation result by the three-dimensional heat balane equation as follows: E T CŽ T. s\ kž T.\T qqqq J Ž 1. E t where C is heat apaity, k is thermal ondutane, T is temperature and Q is heating power at the heater and Q J is the Joule heating power in the tape. We adopt the Neumann-type boundary onditions for the surfae. We assumed thermal properties of the tape as follows: the value of speifi heat was equal to 85% of that of silver entire tape wx 4, and only silver matrix was taken into aount for the alulation of thermal ondutane. The temperature dependene of C and k for silver, opper and teflon were taken from the literature wx 4. As shown in Fig. 2, the alulation results agree quantitatively with the measured ones.
374 ( ) T. Kiss et al.rphysia C 310 1998 372 376 Fig. 2. Temperature rise at the heated position for a step heating with the amplitude of 2.1 W. The dots indiate the alulation results by three-dimensional finite element method, while the line is measured result. as a funtion of time. We applied step urrent with the different amplitude at the bias temperature of 40 K. When the transport urrent, I, was 60 A and 80 T A, the eletri field was saturated at 2.5=10 y6 to 1.5=10 y5 Vrm and 5.3=10 y5 to 8=10 y5 Vrm, respetively. For 100 A, on the other hand, the eletri field diverged after almost 3 min as shown in Fig. 4a. Note that the initial eletri field rise was very slow, then followed by a sharp inrease. The variation of the temperature observed simultaneously at the same onditions is shown in Fig. 4b. When IT s 60 A and 80 A, the temperature was saturated at 40.3 to 40.4 K and 41.3 to 41.5 K, respetively. We an see that the quenh is very uniform in the tangential Ž longitudinal. diretion. The main reasons of this uniformity are likely Ž. 1 gentle inrease of E J urves and Ž. 2 large values of thermal ondutivities in the tape and the former. If we assume that the temperature is uniform also in Using the same equation, we estimated the stability margin for a loal disturbane as shown in Fig. 3. The harateristi time, t, was defined as the time when the initial temperature was inreased as high as a temperature riterion. In the present ase, the initial temperature was 20 K, while the temperature riterion was 60 K as an example. The harateristi time strongly depends on the input power wx 2. If the heating power is smaller than a limiting Ž ritial. power, the temperature will not inrease more than the temperature riterion even at the steady state Ž ts`.. At the present ondition, the limiting power an be estimated as about 1.3 W. From these estimations, we an obtain a riterion for the quenh protetion due to a loal disturbane. 4. Current-indued quenh While the influene of loal disturbane is rather small as mentioned in Setion 3, the important parameter from a pratial point of view is the heat quenh urrent, I q. When the transport urrent was inreased high enough, we observed sharp inrease of the eletri field as shown in Fig. 4a where the eletri field measured at different setions is plotted Fig. 3. Estimation of the stability margin against a loal heating obtained by the simulation, where the harateristi time, t, is defined as the time when the initial temperature, 20 K, is inreased to the temperature riterion of 60 K as an example. If the input power is smaller than the limiting power shown by the thik line, the saturated temperature in the steady state will be smaller than 60 K, i.e., t s`.
( ) T. Kiss et al.rphysia C 310 1998 372 376 375 also determine the ross-points between the Joule heating urve and the ooling line from the saturation temperatures for IT s 60 A and 80 A. The obtained ooling line is shown by the solid line in Fig. 5, where the ooling oeffiient G is obtained as about 0.34 WrK. Now we an see that the quenh point is a typial unstable point usually observed in a nonlinear system. The quenh limiting urrent in the steady state an be defined as the urrent at whih Q Ž I, T. J T urve touhes the ooling line. The quenh urrent, however, is inreased as the duration of the urrent pulse is redued. The dynami harateristis of the quenh an be desribed quantitatively by Eq. Ž. 2. Using the Q J T relationship shown in Fig. 5, we alulated time evolution of the temperature. As shown in Fig. 6, the results agree very well with the experiments. Note that the value of heat apaity was taken from the data sheet wx 4, so we did not use fitting parameter for the alulation. It is worthwhile to ompare the value of quenh urrent Iq and I. From the four-probe measurement, I was determined as 55 A by the 1 mvrm rite rion. Therefore, Iq was at least 45% larger than I in the present ase. In the ase of multi-layered tight winding, however, two-dimensional Žor three-dimen- Ž. Ž. Fig. 4. a Eletri field and b temperature response at different setions for the transport urrents 60 A, 80 A and 100 A. The eletri field and temperature were observed simultaneously, so E, E, E orrespond to T, T, T, respetively. 12 23 45 1 2 4 the radial diretion, the heat balane equation an be simplified as follows. E T CŽ T. sq JyGŽ TyT 0., Ž 2. E t where G is the ooling oeffiient desribing the heat transfer to the surroundings of the tape, and T 0 is the bias temperature. From the measurement shown in Fig. 4a and b, we an determine the average Joule heating in the total length of HTSC tape as a funtion of temperature. In Fig. 5, we show the Q J T urves for the three ases, i.e., IT s60 A, 80 A and 100 A. We an Fig. 5. The Joule heating and ooling urves determined from the measurements shown in Fig. 4. The quenh point is a atastrophi transition point originated from the nonlinear harateristis of the Joule heating.
376 ( ) T. Kiss et al.rphysia C 310 1998 372 376 Fig. 6. Time evolution of the temperature for three transport urrents, 60 A, 80 A and 100 A alulated from Eq. Ž. 2. The results show good agreement with the measurements shown in Fig. 4b. sional. analysis will be neessary to determine I q beause the assumption of uniform temperature distribution in the radial diretion will not be valid. The influene of the magneti indution on the E J urves, whih an be ignored in the present small oil, will be essential too. 5. Conlusion Bi-based HTSC oil shows good stability against a loal disturbane. As far as the loal heating power is worth a few watts, the influene on the stability is very small. On the other hand, the quenh urrent is mainly attributed to the nonlinear resistane of the HTSC tape. The quenh point is haraterized as the atastrophi transition point originated from the nonlinear Joule heating. The main feature of the quenh is that the transition ours uniformly, then the transition time is independent of the length of the oil. That is very different from the quenh in LTSC oil where normal-zone aused by a loal disturbane will propagate as a traveling wave. It has been shown that the dynami harateristis of the quenh in the well-ooled small HTSC oil an be desribed quantitatively by the simplified one-dimensional heat balane equation. For the design of large-sale devies, the haraterization of the nonlinear resistane of HTSC and the thermal design taking into aount a heat transfer will be the important issue. The study on the nonlinear transport harateristis in HTSC as a funtion of transport urrent, temperature and magwx 5 neti field will be presented elsewhere. Aknowledgements This study is partly supported by National Insti- Ž. tute for Fusion Siene NIFS in Japan. Referenes wx 1 T. Kiss, T. Nakamura, M. Takeo, K. Yamafuji, F. Irie, IEEE Trans. Appl. Sup. 7 Ž.Ž 2 1997. 1161. wx 2 V.S. Vysotsky, T. Kiss, M. Takeo, Yu. A. Ilyin, M. Matsuo, T. Nakamura, H. Saho, K. Watanabe, S. Awaji, Pro. of MT. 15 Ž. 2, Siene Press, 1998, 1056. wx 3 V.S. Vysotsky, T. Kiss, Yu. A. Ilyin, M. Takeo, H. Saho, K. Funaki, T. Hasegawa, Pro. of ICEC 17, Bournemouth, UK, 1998, to be published. wx 4 Y. Iwasa, Case Studies in Superonduting Magnets, Plenum, New York, 1994. wx 5 T. Kiss, T. Nakamura, K. Hasegawa, M. Inoue, H. Okamoto, K. Funaki, M. Takeo, K. Yamafuji, F. Irie, Pro. of ICEC 17, Bournemouth, UK, 1998, to be published.