Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation

We have studied the instability of the current flow in a superconducting tape of the second generation and the transition of the tape into the resistive state. Contrary to usually studied quasisteady regimes of the instability development, we consider here the adiabatic case of fast sample heating....

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Date:	2011
Main Authors:	Degtyarenko, P.N., Dul'kin, I.N., Fisher, L.M., Kalinov, A.V., Voloshin, I.F., Yampol'skii, V.A.
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Language:	English
Published:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2011
Series:	Физика низких температур
Subjects:	Сверхпроводимость, в том числе высокотемпературная
Online Access:	http://dspace.nbuv.gov.ua/handle/123456789/118508
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Cite this:	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation / P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, V.A. Yampol'skii // Физика низких температур. — 2011. — Т. 37, № 2. — С. 127–133. — Бібліогр.: 19 назв. — англ.

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spelling	irk-123456789-1185082017-05-31T03:03:08Z Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation Degtyarenko, P.N. Dul'kin, I.N. Fisher, L.M. Kalinov, A.V. Voloshin, I.F. Yampol'skii, V.A. Сверхпроводимость, в том числе высокотемпературная We have studied the instability of the current flow in a superconducting tape of the second generation and the transition of the tape into the resistive state. Contrary to usually studied quasisteady regimes of the instability development, we consider here the adiabatic case of fast sample heating. Two kinds of measurements of the current-voltage characteristics (CVC) have been performed, specifically, using the tape excitation by a single sineshaped current pulse I(t)=I₀sin(ωt) with different amplitudes I₀ and by a continuous ac current flow. The main results were obtained for the current amplitudes I₀ exceeding the critical current value Ic . We have found that the dynamic CVC are practically reversible for low amplitudes, whereas they become irreversible and assume the N -shaped form for higher current amplitudes. The dynamic CVC are found to change radically if the dissipated energy attains some threshold value Wth which is equal to about 5 mJ/cm for our tapes. Once achieving this energy, the tape transits to the resistive state due to a normal domain formation. The development of instability for a continuous ac current flow was studied for a relatively small amplitude when the energy dissipated per one half-cycle is much lower than Wth. Even in this case, the tape transition to the resistive state occurs owing to an effect of energy accumulation (heat pumping). Due to this pumping, the transition takes place after a definite number of ac current periods when the total accumulated energy reaches the same threshold value Wth. The specific features of dynamic CVC are qualitatively interpreted within an approach where the appearance of the resistive domain is taken into account. Estimations performed on the basis of the CVC agree well with our experimental data. The results obtained can be useful for the design of superconducting fault current limiters. 2011 Article Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation / P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, V.A. Yampol'skii // Физика низких температур. — 2011. — Т. 37, № 2. — С. 127–133. — Бібліогр.: 19 назв. — англ. 0132-6414 PACS: 74.25.Sv, 74.25.–q, 74.78.–w, 84.71.Mn http://dspace.nbuv.gov.ua/handle/123456789/118508 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная
spellingShingle	Сверхпроводимость, в том числе высокотемпературная Сверхпроводимость, в том числе высокотемпературная Degtyarenko, P.N. Dul'kin, I.N. Fisher, L.M. Kalinov, A.V. Voloshin, I.F. Yampol'skii, V.A. Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation Физика низких температур
description	We have studied the instability of the current flow in a superconducting tape of the second generation and the transition of the tape into the resistive state. Contrary to usually studied quasisteady regimes of the instability development, we consider here the adiabatic case of fast sample heating. Two kinds of measurements of the current-voltage characteristics (CVC) have been performed, specifically, using the tape excitation by a single sineshaped current pulse I(t)=I₀sin(ωt) with different amplitudes I₀ and by a continuous ac current flow. The main results were obtained for the current amplitudes I₀ exceeding the critical current value Ic . We have found that the dynamic CVC are practically reversible for low amplitudes, whereas they become irreversible and assume the N -shaped form for higher current amplitudes. The dynamic CVC are found to change radically if the dissipated energy attains some threshold value Wth which is equal to about 5 mJ/cm for our tapes. Once achieving this energy, the tape transits to the resistive state due to a normal domain formation. The development of instability for a continuous ac current flow was studied for a relatively small amplitude when the energy dissipated per one half-cycle is much lower than Wth. Even in this case, the tape transition to the resistive state occurs owing to an effect of energy accumulation (heat pumping). Due to this pumping, the transition takes place after a definite number of ac current periods when the total accumulated energy reaches the same threshold value Wth. The specific features of dynamic CVC are qualitatively interpreted within an approach where the appearance of the resistive domain is taken into account. Estimations performed on the basis of the CVC agree well with our experimental data. The results obtained can be useful for the design of superconducting fault current limiters.
format	Article
author	Degtyarenko, P.N. Dul'kin, I.N. Fisher, L.M. Kalinov, A.V. Voloshin, I.F. Yampol'skii, V.A.
author_facet	Degtyarenko, P.N. Dul'kin, I.N. Fisher, L.M. Kalinov, A.V. Voloshin, I.F. Yampol'skii, V.A.
author_sort	Degtyarenko, P.N.
title	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
title_short	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
title_full	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
title_fullStr	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
title_full_unstemmed	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
title_sort	thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2011
topic_facet	Сверхпроводимость, в том числе высокотемпературная
url	http://dspace.nbuv.gov.ua/handle/123456789/118508
citation_txt	Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation / P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, V.A. Yampol'skii // Физика низких температур. — 2011. — Т. 37, № 2. — С. 127–133. — Бібліогр.: 19 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT degtyarenkopn thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration AT dulkinin thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration AT fisherlm thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration AT kalinovav thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration AT voloshinif thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration AT yampolskiiva thermoelectricinstabilityinducedbyasinglepulseandalternatingcurrentinsuperconductingtapesofsecondgeneration
first_indexed	2025-07-08T14:08:07Z
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fulltext	© P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, and V.A. Yampol'skii, 2011 Fizika Nizkikh Temperatur, 2011, v. 37, No. 2, p. 127–133 Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, and I.F. Voloshin All-Russian Electrical Engineering Institute, 12 Krasnokazarmennaya Str., Moscow 111250, Russia V.A. Yampol'skii A.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine 12 Proskura Str., Kharkov 61085, Ukraine E-mail: yam@ire.kharkov.ua Received April 2, 2010, revised July 1, 2010 We have studied the instability of the current flow in a superconducting tape of the second generation and the transition of the tape into the resistive state. Contrary to usually studied quasisteady regimes of the instability development, we consider here the adiabatic case of fast sample heating. Two kinds of measurements of the cur- rent-voltage characteristics (CVC) have been performed, specifically, using the tape excitation by a single sine- shaped current pulse 0( ) = sin ( )I t I tω with different amplitudes 0I and by a continuous ac current flow. The main results were obtained for the current amplitudes 0I exceeding the critical current value cI . We have found that the dynamic CVC are practically reversible for low amplitudes, whereas they become irreversible and assume the N -shaped form for higher current amplitudes. The dynamic CVC are found to change radically if the dissipated energy attains some threshold value thW which is equal to about 5 mJ/cm for our tapes. Once achieving this energy, the tape transits to the resistive state due to a normal domain formation. The development of instability for a continuous ac current flow was studied for a relatively small amplitude when the energy dissi- pated per one half-cycle is much lower than thW . Even in this case, the tape transition to the resistive state oc- curs owing to an effect of energy accumulation (heat pumping). Due to this pumping, the transition takes place after a definite number of ac current periods when the total accumulated energy reaches the same threshold value thW . The specific features of dynamic CVC are qualitatively interpreted within an approach where the appear- ance of the resistive domain is taken into account. Estimations performed on the basis of the CVC agree well with our experimental data. The results obtained can be useful for the design of superconducting fault current li- miters. PACS: 74.25.Sv Critical currents; 74.25.–q Properties of superconductors; 74.78.–w Superconducting films and low-dimensional structures; 84.71.Mn Superconducting wires, fibers, and tapes. Keywords: quench, normal domain, adiabatic regime, energy pumping. 1. Introduction The problem of the transition of hard superconductors carrying transport current I to the normal state (quench) have called considerable attention of researchers for many years, see, e.g., papers [1–3] and references therein. To solve this problem, it is necessary to consider jointly a complex equation system involving the Maxwell and time- dependent heat transfer equations, material equations for superconducting materials. We have to take into account the temperature dependence of all ingressed parameters. Usually, this problem is considered for quasisteady re- gimes of a current flow when the equality ( , ) = ( )P I T Q T (1) is satisfied. Here =P UI is the Joule heating, U is the voltage drop along a sample, Q is a heat transferring from a sample to cryogenic liquid, T is the sample temperature. P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, and V.A. Yampol'skii 128 Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 Very interesting phenomena occur when the thermal bal- ance Eq. (1) has three solutions, 1 2 3< <T T T . Two of them, 1=T T and 3= > cT T T , correspond to stable states of a system, whereas 2=T T is an unstable solution ( cT is the critical temperature). The development of instability can result in the resistive domain formation or in the pro- pagation of a thermal wave. The quench problem is important not only from the physical point of view, but for different applications also. One of the most promising applications are the fault cur- rent limiters (FCL) [4,5]. An operation of these devices, in their resistive version, is directly based on the transition to the dissipative state induced by current with density above the critical value cJ . The resistance that is introduced into an electrical cir- cuit by FCL is determined by the dynamic current-voltage characteristics (CVC) of the superconducting tapes. Specif- ically, these dynamic CVC determine the superconducting tape application in various electrical devices. The results of the dynamic CVC studies were published in a number of papers (see, for example, [2,6–8]). A physical nature of a superconductor response to a fast current increase within a millisecond range and the sample transition to the dissipa- tive state was discussed in literature [9,10]. In this paper, we study the dynamic transport properties of the SuperPower tapes designed especially for the FCL application. These tapes do not have a thick metal cover and are characterized by a relatively high electrical resis- tance in the normal state. The specific feature of FCL op- eration is very fast heating, and their dynamics cannot be described well by the stationary thermal balance Eq. (1). Moreover, the adiabatic approximation is much more ac- ceptable to describe the non-stationary processes in these composites. Indeed, the convective heat transfer process in liquid nitrogen is established several dozen milliseconds after a start of heating [11]. The more enhanced heat trans- fer process by nucleate boiling begins after the convection process is developed [12]. Thus, for short times the single mechanism which is responsible for the heat transfer from the tape to liquid nitrogen is the heat conduction. This process is characterized by a high thermal resistance. Therefore, the heating of a tape for times about 5 ms (spe- cifically, the time duration will be interesting for us below) can be considered as adiabatic one. This statement was confirmed by the direct measurements in Ref. 13. We show that the dynamic CVC is irreversible and N -shaped for high current amplitudes exceeding cI . The dynamic CVC become more cumbersome if the energy dissipated in a tape attains some threshold value thW which is about 5 mJ/cm. For the case of a continuous ac current with am- plitude 0I above the critical value cI , 0 ≥ cI I , we have observed an interesting feature of the tape transition to the resistive state. This transition occurs after a number of pe- riods of the ac current. We prove that the tape resistance appears due to formation of a stationary domain of the normal phase. A number of current pulses necessary for the tape transition to the state with normal domain increas- es significantly when 0 → cI I . Thus, a phenomenon of the energy pumping during each half-period is observed for the case of a continuous ac current flow. All results are discussed on the basis of the current-voltage characteristics of our tapes. 2. Experiment The dynamic current-voltage characteristics of tapes were measured using the scheme shown in Fig. 1. The short current pulse technique is widely used for studies of the critical current, nucleation and propagation of normal zones, etc. in various superconductors including coated conductors and devices based on them (see, for example, papers [1,2,6,7,14–19] and references therein). In our ex- periment, an alternating current ( )I t was excited due to a discharge of the capacitor C in the LC circuit with a re- sonance frequency close to 50 Hz. The coil = 270L μH was wound of a copper bus and cooled by liquid nitrogen 2(LN ) to increase its Q-quality. The current ( )I t in the circuit was triggered by the current feed to the gate cathode of the thyristor Th. The thyristor was turned off when the current changed its sign from positive to negative. Thus, the half-wave current was formed in the circuit. We have measured simultaneously an active part of the voltage drop on the potential probes of the sample and the voltage on the active standard resistor 0R with the sampling period (1/40000) s. To suppress the reactive emf in the sample pickup circuit we used the auxiliary coil auxL positioned near the «warm» current bus of the LC circuit. The coil auxL was connected to the input of AD converter in series with the spring-loaded point potential contacts on the tape. Our results of the voltage measurements did not depend on whether contacts were placed at the tape edges or across the tape width. According to data of Ref. 7, the dynamic current-voltage characteristics can depend on the arrange- ment of the taps and can significantly differ from the dc characteristics. However, these results were mainly ob- served for the case of relatively low current amplitudes 0 cI I whereas we made our measurements for > cI I . We have tested the linearity and synchronism of the mea- suring circuits for the current amplitudes up to 1600 A Fig. 1. Function circuit for measurement of a tape response to a single half-period current wave. I t( )L C ThZtape R = 0.25 m�0 U IR= tape Laux Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 129 with a copper tape as a sample. The method of the ac current excitation in HTS tapes is illustrated in Fig. 2. To measure the dynamic CVC in a regime of the conti- nuous ac current flow, we have used a soft excitation by means of an amplifier with a voltage feedback and a step- down transformer. All our measurements were performed on the tapes SF12050 and SF12100 produced by the SuperPower Co. The tape sizes are = 12w mm in width; superconducting and silver layers are 1 = 1δ μm and 2 = 2δ μm in thick- ness, respectively; hastelloy substrate 50 μm (for SF12050) and 100 μm (for SF12100) in thickness. They have no additional metal stabilizer layers. We used tapes of different lengths. The majority of results were obtained for long enough tapes SF12100 with distance = 23l cm be- tween the potential contacts. The tapes were immersed into liquid nitrogen at normal pressure. 3. Results and Discussions The current-voltage characteristics for the tape SF12100 in a quasisteady regime are shown in Fig. 3 by open circles in a double logarithmic scale. According to these data, the critical current for this tape (by criterion = 1 V/cmcE μ ) is about 420cI A at tem- perature = 77T K. This current-voltage characteristics can be described by a power function, = \| / \| , \| / \| 1.12α ≤c c cE E I I I I (2) with = 34α . Unfortunately, the CVC measurements can be performed for currents 1.12 470≤ ∼cI I A only. Cur- rents > 1.12 cI I deteriorate irreversibly the superconduct- ing properties of the tape. However, the voltage drop across a tape for high currents can be determined by anoth- er way, specifically, making measurement in the dynamic regime. We made these measurements using the sine- shaped current pulse during its first quarter-period. The results of dynamic CVC measurement performed at differ- ent amplitudes 0I are also displayed in Fig. 3. The dynam- ic CVC can be described by equation, 5.09 13= 10 \| ( ) / \| , \| ( ) / \|> 1.12.− c cE I t I I t I (3) In spite of high currents and, correspondingly, high power dissipation, the temperature rise is limited due to a short time of the dissipation. The dynamic CVC can be also described by a power function (see Eq. (3)) but the exponent = 13α is less than in the case of the static CVC. The main reason of a significant change in the ( )E I beha- vior is related to noticeable shunting a superconducting layer by a silver one at currents > cI I . We could not measure the dynamic CVC for currents less than 460 A because of lack of sensitivity. Note that the experiments have been performed (see, e.g., Ref. 17) where the static and dynamic CVC have been measured for the same current region. These CVC were close to each other. Contrary to such experiments, we stu- died the non-stabilized tapes of the second generation that are deteriorated at high currents. Accordingly, our static and dynamic CVC meet each other in a narrow region near 0 464≈I A. 3.1. Instability induced by a single current pulse It is of interest to consider the dynamic CVC during the first half-period since the irreversibility of CVC can be observed in this regime. The dynamic CVC for different pulse amplitudes 0I are shown in Fig. 4. These characte- ristics are almost reversible for amplitudes 0 660≤I A Fig. 2. Scheme of a soft ac current excitation of HTS tapes. U U t= sin ( )0 � R = 0.25 m� U IR= tape Laux Amplifier I t( ) + – Ztape Fig. 3. Current-voltage characteristics in dc (open circles) and dynamic (triangles and solid line) regimes for SF12100 tape. I, A 450 600 750 1000 100 10 1 0.1 0.01 E , 1 0 V /c m – 5 �� Fig. 4. Dynamic current-voltage characteristics of a sample 23 cm in length for different amplitudes 0I of current pulse. 0 200 400 600 0 5. 0.4 0 3. 0.2 0.1 I, A U , V I = 693 А0 I0 = 6 А61 I = 6 А700 P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, and V.A. Yampol'skii 130 Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 (see the red dashed line in this figure). Actually, a very weak irreversibility related to a small temperature rise due to the Joule heating is observed for such small currents. The curves ( )U I undergo a qualitative change for current amplitudes 0 > 680I A. They become irreversible and assume the N -shaped form with two peaks (see the solid curve in Fig. 4). For higher amplitudes, the dynamic CVC assume the strongly irreversible form with a single maximum whereas the first peak is transformed into the inflection point (see the blue dashed curve with symbols in Fig. 4). The analogous re- sults have been obtained for other tapes. The effective electrical resistance R can be calculated from dynamic CVC shown in Fig. 4. Using the temporal dependences ( )U t and ( )I t we plotted the resistance ( ) / ( ( ) )U t I t l per unit length versus time in Fig. 5. The resistance starts to increase at a time moment when the current I exceeds the critical value cI and is saturated for > 6t ms. Notice a remarkable feature of the curves in Fig. 5. Namely, the effective electrical resistance increases even after the current ( )I t has passed a maximum. The saturation values of the total resistance of the tape are 0.5R mΩ for current amplitude 0 = 693I A and 0.8R mΩ for 0 = 706I A. These results indicate that our tape is in the resistive state. However, the resistance values are much less than the total tape resistance in the normal state. Indeed, the normal resistance of the tape is about 1.4 mΩ /cm× 23 cm = 32.2 mΩ at 92 K that is much greater than 0.8 mΩ . There exist two ways to in- terpret this result. — First, following to commonly used consideration, we can suppose that a domain of the normal phase is formed in the tape [1]. A simple estimation gives a surprisingly short length of this domain (about 5 mm). Recall that the tape width is 12 mm. — Second, it is not necessary for the resistive domain to be in the normal state. It can be longer than 5 mm but in the superconducting resistive state. Anyway, a sharp change of the dynamic CVC near the minimum ( )U I (solid curve in Fig. 4) justifies the forma- tion of the resistive domain which structure and geometry are not important for further study. Below all results and estimations in the text and figures are presented for one of our samples of the tape SPC12100. To determine the conditions for the tape transition to the resistive state, we have estimated the accumulated energy in the tape before this transition. The temporal de- pendence of the dissipated power ( )P t is presented in Fig. 6 for the same current amplitudes as in Figs. 4 and 5. The solid curve in Fig. 6 corresponds to the case of almost reversible dynamic CVC while two other curves shown by symbols describe the irreversible transition to the resistive state. Integrating the function ( )P t over t we obtain the ac- cumulated energy ( )tW in the tape (upper curves in Fig. 6). The threshold value thW of the accumulated ener- gy that initializes the transition to the resistive state is re- vealed to be near 5 mJ/cm for all our samples. It is possible to estimate the temperature rise ΔT of the YBCO layer by a simple relation (4) if we assume that this threshold energy is accumulated in the YBCO and silver layers only: th 2 = . p T wa C Δ δ γ W (4) Here the parameter pC is the specific heat of silver, γ is the silver density, a is the tape length. We can neglect the specific heat of the YBCO layer in comparison with the specific heat of silver. Substituting the numerical values of Fig. 5. Effective electrical resistance per 1 cm of the tape length (left axis) and electrical current (right axis) vs time t . 800 600 400 200 0 2 4 6 8 10 50 40 30 20 10 0 t, ms I, A L in ea r re si st an ce , /c m � Fig. 6. Temporal dependence of the dissipated power (lower curves) and accumulated energy (upper curves) in the tape per 1 cm of its length. W , m J/ cm P , W /c m 10 10 8 8 6 6 4 4 2 2 0 0 12 t, ms 2 4 6 8 10 661 667 693 706 I0, A Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 131 these quantities ( th = 5W mJ/cm, 2 = 2δ μm, =w 1.2 cm, = 1.049γ g/cm3, = 0.15pC J/(g·K), = 1a cm) into Eq. (4), we obtain that the temperature increase of YBCO and silver layers is about 10 K approximately. It is important to note that all described experiments were performed so quickly (duration Δt was less than 10 ms) that heat has not time to be not transferred to the environment. This fact was confirmed by additional direct measurements of the temperature rise ( )T t of the tape which was heated by the single current pulses with differ- ent amplitudes and corresponding theoretical estimations within the adiabatic approximation. Thus, we consider that the instability develops as fol- lows. When increasing the current ( )I t , the dissipated energy is accumulated in the tape. At some moment inst=t t , ( )tW achieves the threshold value thW . Accor- dingly, the resistive domain is nucleated in the sample at inst=t t that is indicated by the kink in the temporal de- pendence of the tape resistance (see Fig. 4). Then the do- main develops during about two milliseconds, and the re- sistance increases despite the decrease of the transport current ( )I t . 3.2. Instability induced by a continuous ac current It is of interest to realize the described scenario of the instability development for a continuous ac current. Ob- viously, the instability can develop at lower ac current am- plitudes 0I than in the case of a single pulse (but still for 0 > cI I ). The threshold energy can be accumulated after several periods in this case. One can evaluate a necessary number of periods that depends on the current amplitude. The dissipated power P and accumulated energy W per one cycle and 1 cm of the tape length can be written as, 0( ) =\| ( ) sin ( ) \|,P t E t I tω (5) /2 0 = 4 ( )P t dt π ω ∫W (6) where ω is the current cyclic frequency; the value E in Eq. (5) is determined by Eq. (2) for 0\|( sin ( )/ )\| 1.12cI t Iω ≤ and by Eq. (3) for 0\|( sin ( )/ )\| >1.12cI t Iω . A number n of cycles and time τ necessary for the do- main nucleation are, th= / , = (2 / ) .n nτ π ωW W (7) This number can be large enough if the current amplitude 0I is close to cI . For example, our tapes should transit to the resistive state after = 100n periods of the current 480 A in amplitude. To check this prediction we have measured the tempor- al dependence of the voltage drop and current along the tape 43 cm in length. The ac current through the sample was supplied using the ac power amplifier with the voltage feedback and output step-down transformer (see Fig. 2). The superconducting tape was connected to the transfor- mer secondary winding. The computer records of the initial and final fragments of the ( )I t and ( )U t dependences are shown in Fig. 7 for the amplitude 0 = 475I A and fre- quency = 73f Hz. The curves in this figure demonstrate a nontrivial behavior of ( )I t and ( )U t . After switching on the ac current ( )I t at t = 0, it changes quasi-harmonically during 4.71 s and then decreases abruptly owing to the transition of the tape into the resistive state. The fragment of CVC shown in the insert demonstrates details of this transition. During the transition, the current is lowered dramatically by a factor about four. Such a behavior re- sembles a current limitation after the action of a fault cur- rent limiter. Simultaneously with a current change, the voltage drop increases considerably. A direct observation of the tape immersed into the liquid nitrogen shows an appearance of intensive boiling along a short part of the tape that corresponds to the occurrence of the resistive do- main. The length of this domain is about of 1 cm. The re- sistance dR of the domain can be evaluated using meas- ured I and U . We obtain 0.2 /100 = 2dR mΩ that is higher than the tape resistivity 1.4 mΩ per 1 cm at 92 K. This means that the domain is definitely in the normal state. All considerations performed above correspond to the adiabatic case. If this approach is correct, the tape transi- Fig. 7. Initial and final fragments of the computer records of ( )I t and ( )U t for 0 = 475I A, = 73f Hz. Insert shows a voltage drop across the tape in the vicinity of sharp transition to the resis- tive state. The vertical dashed line shows the time delayе τ. U , V U , V I, A t, s t, s t, s 400 200 0 –200 –400 0.2 0.1 0 –0.2 –0.1 –0.3 0.3 0 0 0.1 0.1 4.6 4.6 4.8 4.8 5.0 5.0 0.2 0.1 0 –0.1 –0.2 4.68 4.70 4.72 4.74 P.N. Degtyarenko, I.N. Dul'kin, L.M. Fisher, A.V. Kalinov, I.F. Voloshin, and V.A. Yampol'skii 132 Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 tion to the resistive state should be observed for any cur- rent amplitude 0 > cI I , owing to the heat pumping phe- nomenon. However, according to our experimental data, this transition takes place only for currents higher than some threshold value th = 468I A. As is found, the ac current with amplitude 0 th<I I can flow continuously through the tape without its transition to the non-uniform state. This means that the tape is in the thermal equilibri- um for 0 th<I I , i.e., the dissipated energy is transferred to LN 2 . It is possible to evaluate this amount of energy by means of Eqs. (2)–(6). We obtain = 0.03Q mJ/cm per a cycle. Accordingly, to take into account a heat transfer, Eq. (7) should be corrected by subtraction of Q from the denominator, th= / ( ).−n QW W (8) We have studied the time delay = /τ n f for the tape transition to the resistive state for different currents 0 th>I I . The results of measurement are presented by points in Fig. 8. The solid curve in this figure corresponds to the calcu- lation data obtained by means of Eq. (8) and Eqs. (3)–(6). The experimental and calculated results are in a good agreement. It should be noted, however, that such a corre- lation can be considered as a qualitative result only. The matter of fact is that the parameter Q in Eq. (8) is not measured but evaluated only. We can also evaluate the domain temperature. For the dissipated power 0 00.5 = 12P I U W (see Fig. 7) we have the heat flux about / = 10P w W/ 2cm . According to the steady-state boiling curve of 2LN , the temperature excess within the domain in this case is about 13 K. 4. Conclusion In this paper, we have studied experimentally the transi- tion of non-stabilized HTC tapes of the second generation to the resistive states under the action of single current pulses, or ac continuous current, with amplitudes higher than the critical one. It turned out that the quench in such a kind of tapes cannot be interpreted within the commonly accepted theory that is valid only for the stationary regimes of the current and heat flows. Moreover, due to the low heat capacity of examined tapes, the adiabatic regime is characteristic for our experiment. In addition, the existing theory (see reviews [1,2]) is constructed for spatially uni- form superconductors whereas the non-stabilized tapes of the second generation can be essentially non-uniform. The nucleation of the normal domain in the same point on the tape in our multiple experiments is a manifestation of the sample inhomogeneity. A key point for the physics of tape quenching in the adiabatic regime is the revealed fact of the existence of the threshold accumulated energy neces- sary for the appearance of the instability. On the basis of this approach, we have qualitatively interpreted our obser- vations of the domain nucleation induced by both a single current pulse and the continuous ac current flow. For quan- titative calculations, a new theory should be developed. This work is supported by RFBR grant 08-08-00453. 1. R.G. Mints and A.L. Rakhmanov, Rev. Mod. Phys. 53, 551 (1981). 2. V.S. Vysotsky, A.L. Rakhmanov, and Yu.A. Ilyin, Physica C401, 57 (2004). 3. A.L. Rakhmanov, V.S. Vysotsky, Yu.A. Ilyin, T. Kiss, and M. Takeo, Cryogenics 40, 9 (2000). 4. A.P. Malozemoff, S. Fleshler, M. Rupich, C. Thieme, X. Li, W. Zhang, A. Otto, J. Maguire, D. Folts, J. Yuan, H.-P. Kraemer, W. Schmidt, M. Wohlfart, and H.-W. Neumueller, Supercond. Sci. Technol. 21, 034005 (2008). 5. J.C.H. Llambes, C.S. Weber, and D.W. Hazelton, IEEE Trans. Appl. Supercond. 19, 1968 (2009). 6. T. Kiss, M. Inoue, K. Hasegawa, K. Ogata, V.S. Vysotsky, Yu.A. Ilyin, M. Takeo, H. Okamoto, and E. Irie, IEEE Trans. Appl. Supercond. 9, 1073 (1999). 7. V. Meerovich, V. Sokolovsky, L. Prigozhin, and D. Rozman, Supercond. Sci. Technol. 19, 267 (2006). 8. L. Frolek, J. Oravec, and J. Souc, J. Phys.: Conf. Ser. 97, 012085 (2008). 9. J. Viña, M.T. González, M. Ruibal, S.R. Currás, J.A. Veira, J. Maza, and F. Vidal, Phys. Rev. B68, 224506 (2003). 10. M. Ruibal, G. Ferro, M.R. Osorio, J. Maza, J.A. Veira, and F. Vidal, Phys. Rev. B75, 012504 (2007). 11. C.M. Vest and M.L. Lawson, Int. J. Heat Mass Transfer 15, 1281 (1972). 12. D.N. Singha, L.C. Brodie, and J.S. Semura, Phys. Rev. B36, 4082 (1987). 13. I.N. Dul'kin, D.V. Evsin, L.M. Fisher, V.P. Ivanov, A.V. Kalinov, and V.A. Sidorov, IEEE Trans. Appl. Supercond. 18, 7 (2008). 14. M. Dixit, T.H. Kim, H.M. Kim, K.J. Song, S.S. Oh, R.K. Ko, H.S. Kim, and K.B. Park, Physica C434, 199 (2006). Fig. 8. Time delay for the tape transition to the resistive state. 5 4 3 2 1 0 Experiment Our calculation 470 480 490 500 510 520 , s � I0, A Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation Fizika Nizkikh Temperatur, 2011, v. 37, No. 2 133 15. M.Ch. Ahn, S.E. Yang, D.K. Park, H. Kang, B.Ye. Seok, and K.T. Ko, Cryogenics 47, 425 (2007). 16. V.S. Vysotsky, Yu.A. Ilyin, T. Kiss, M. Inoue, M. Takeo, F. Irie, H. Okamoto, M. Kanazawa, K. Ohya, S. Hayashida, and A.L. Rakhmanov, Cryogenics 40, 19 (2000). 17. V. Meerovich, V. Sokolovsky, and I. Vajda, IEEE Trans. Appl. Supercond. 15, 2047 (2005). 18. Yu.A. Ilyin, V.S. Vysotsky, T. Kiss, M. Takeo, H. Okamoto, and F. Irie, Cryogenics 41, 665 (2001). 19. F. Sirois and A. Bernier, IEEE Trans. Appl. Supercond. 19, 3585 (2009).

Thermoelectric instability induced by a single pulse and alternating current in superconducting tapes of second generation

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