- Email: [email protected]
Thermal stability of reinforced Nb3Sn composite superconductor under cryocooled conditions
Cryogenics 44 (2004) 687–693 www.elsevier.com/locate/cryogenics
Thermal stability of reinforced Nb3Sn composite superconductor under cryocooled conditions q Tsuyoshi Yamamoto a, Kenji Watanabe a, Satoru Murase Kazuo Watanabe b, Akio Kimura c a
a,*
, Gen Nishijima b,
Department of Electrical and Electronic Engineering, Okayama University, 3-1-1, Tsushimanaka, Okayama 700-8530, Japan b HFLSM, Institute for Materials Research, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai 980-8577, Japan c The Furukawa Electric Co., Ltd., 2-6-1 Marunouchi, Chiyoda-ku, Tokyo 100-8322, Japan Received 18 August 2003; accepted 5 March 2004
Abstract Several types of reinforced Nb3 Sn wires have been developed to prevent reduction of superconducting properties by applying a strong electromagnetic force. To fabricate a cryocooled magnet using those reinforced wires, we experimentally measured the minimum quench energy (MQE) under cryocooled conditions of some reinforced Nb3 Sn wires. As a result, it became clear that thermal stability expressed as MQE was controlled by the temperature margin between the temperature of the operating condition and the transition temperature from superconductivity to normal. Using the FEM analysis, it was realized that the cause of the decline in thermal stability for the reinforced wires was the low thermal conductivity of the reinforced materials. 2004 Elsevier Ltd. All rights reserved. Keywords: Reinforced Nb3 Sn wire; MQE; Cryocooling
1. Introduction The superconducting coils that generate high magnetic-fields are subjected to a large electromagnetic force, which applies the stress and the strain to the wound superconducting wires. Because cryocooled superconducting magnets that generate more than 12 T require compaction, enormous stresses are induced due to the increase in the current density. Furthermore, because compound superconductors such as Nb3 Sn are generally sensitive to stress and strain, superconducting properties such as critical current density decrease as force increases. To prevent the reduction of the superconducting properties, several types of reinforced Nb3 Sn wires have been developed using internally reinforced materials such as Cu–Nb [1], Ta [2,3], alumina-Cu [4] q Translation of article originally published in Cryogenic Engineering (Journal of Cryogenic Association of Japan) vol. 38 (2003) pp. 262–269. * Corresponding author. Tel.: +81-86-251-8117; fax: +81-86-2518259. E-mail address: [email protected] (S. Murase).
0011-2275/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.03.017
and Nb–Ti–Cu [5] for the cryocooled 20-T class superconducting magnets being planned [6]. However, it is difficult to maintain the superconducting state against thermal disturbance because the Cu volume fraction of these internally reinforced wires is lower than that of conventional Cu-stabilized Nb3 Sn wires. There are some reports on thermal stability for Cu– Nb-reinforced wires [7,8], but there have been no reports published on Nb–Ti–Cu-reinforced ones yet. In the present paper, we investigated the minimum quench energy (MQE) under the cryocooled condition of Nb– Ti–Cu-reinforced Nb3 Sn wire. In superconducting coils that are generating a magnetic field, quenching by some sort of disturbance quite frequently occurs, even if the transport current is less than the critical current. There are two types of disturbances resulting in instability: a continuous phenomenon such as AC losses, and a pulsed one [9]. This study has been designed to investigate pulsed disturbances caused by wire-movement and cracks in epoxy in the coil. If a disturbance energy is inputted to the sample wire, there would exist an energy threshold that leads to quenching of the wire. We then measure the minimum energy value required to quench
688
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
the wire, the minimum quench energy (MQE), and evaluate it as the thermal stability of the superconducting wire. There is now a critical current-margin (CCM) design criterion for high-performance magnet stability under conventional bath-cooled conditions [9]. According to the CCM design criterion, if the disturbance energy level does not transform nuclear boiling to film boiling, quenching would not occur, regardless of the magnetÕs operating current. However, this criterion cannot be applied to the magnet under cryocooled conditions. Therefore, we have conducted research to design the criterion for the magnet stability under cryocooled conditions, focusing on the temperature margin, which is the difference between the operating temperature and the superconducting-to-normal transition temperature under various loaded conditions of the applied magnetic-field, temperature, and the transport current. In present paper, we report obtained MQE results focusing on the temperature margin. Furthermore, using the FEM analysis for thermal conduction, we discuss why the thermal stability decreases when internal reinforcement is added to the wire.
Table 1 Specifications of Nb–Ti–Cu-reinforced Nb3 Sn sample wire Nb–Ti–Cu-reinforced Nb3 Sn wire Wire diameter (mm) Filament diameter (lm) Number of filament
1.013 3.5 (nominal) 7638(19 · 402)
Material Diffusion barrier Reinforcement
Nb Cu–30wt.%Ni/Nb–46.5wt.%Ti
Volume fraction (%) Cu stabilizer Bronze/Nb3 Sn with diffusion Reinforcement
22.4 53.2 24.4
Heat treatment
675 C_40 h
Current contact
Sample wire FRP bobbin
2. Measurement of MQE 2.1. Experimental procedure A cross-sectional view of Nb–Ti–Cu-reinforced Nb3 Sn wire used as a sample is shown in Fig. 1 and Table 1. The Nb–Ti–Cu is arranged at the center of the composite wire 1 mm in diameter and with a Nb barrier. After heat treatment to form the Nb3 Sn layer, Nb–Ti– Cu transforms into Cu2 Ti, which plays a role in the reinforcement. In this experiment, the sample wire was wound around a 36-mm diameter FRP bobbin, as shown in Fig. 2. The sample bobbin was installed on the second stage of a GM (Gifford–McMahon) cryocooler. A thin strain gauge 1.5 by 1.5-mm square with 120-X resistance used for generating the heat disturbance was attached to the sample. Voltage taps, V1–V5, and temperature sensors (Cernox), T1–T4, were set on the
Fig. 1. Cross-sectional view of Nb–Ti–Cu-reinforced Nb3 Sn wire. The reinforcement composite is placed in the center of the wire (/ 1 mm).
36 mm φ
Fig. 2. Schematic view of the sample coil. An FRP bobbin is used to simulate a potted condition.
4 mm heater
T2
T1
T3
T4
29 mm
20
15.5
32.5
29
V1
V2
V3
V4
V5
Fig. 3. The locations of voltage taps, temperature sensors and heater for disturbance. As the sample is wound like a coil, V5 is located just above V1.
sample as shown in Fig. 3. Signals obtained from these sensors were recorded by a personal computer and a digital oscilloscope. Disturbance energy increasing by 0.06-mJ steps was inputted to the sample under the transport current of 80–90% of the critical current. The minimum energy for quenching of the sample wire is defined as the MQE. The MQE was measured at temperatures of 4.5, 6, and 7 K, and at applied magneticfields of up to 14.5 T on the cryocooled superconducting magnet, 15T-CSM, at the Institute for Materials Research, Tohoku University.
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
2.2. Experimental result and discussion
689
200
10 T
180
11 T
160
12 T
Ic (A)
140 120
13 T
100
14 T
80 60 40 20 0
4
5
6 7 Temperature (K)
8
9
Fig. 5. Critical current, Ic , as a function of temperature and magneticfield strength for Nb–Ti–Cu-reinforced Nb3 Sn wire.
1.4 1.2 1
MQE (mJ)
Results in Fig. 4 show that voltage–time characteristics of normal state propagation for Nb–Ti–Cu-reinforced Nb3 Sn wire observed in the digital oscilloscope did not show a recovery from the normal state to the superconducting state with a Cu stabilizer for any of these experimental conditions. This result indicates that the occurrence of only a small part of the normal state leads to immediate quenching. It was realized that controlling of the transfer to quenching after the current sharing was not expected because the suppression of joule-heat generation by the stabilization material was insufficient under these cryocooled conditions. This means that the stabilizer has no function as a current bypass under cryocooled conditions. These experimental results suggest that MQE for Nb–Ti–Cu-reinforced Nb3 Sn wire under cryocooled conditions was controlled through the temperature margin for each loaded condition; we defined the temperature margin as a difference, Tc Top , between the operating temperature, Top , and the superconducting-to-normal transition temperature, Tc , under each condition. Thus, Tc depends on loading conditions of the applied magnetic-field and the transport current of the conductor. To confirm these results, we measured the temperature dependency of the critical current on the Nb–Ti–Cu-reinforced wire as a function of magnetic-field strength, as shown in Fig. 5, and investigated Tc under each MQE measurement condition. Fig. 6 shows the temperature margin dependencies of the MQE as a function of the magnetic-field strength of Nb–Ti–Cu-reinforced Nb3 Sn wire at 7 K. It was found that the MQE and temperature margin positively correlated, i.e. MQE-temperature margin characteristics could be described as a straight line even if applied magnetic-field strength and transport current varied. The same relationship was obtained at sample temperatures of 4.5 and 6 K. Furthermore, Fig. 7 shows
0.8 0.6 Nb-Ti-Cu-reinforced wire (10 T 7 K) Nb-Ti-Cu-reinforced wire (11 T 7 K) Nb-Ti-Cu-reinforced wire (12 T 7 K)
0.4 0.2 0
0
0.5 1 Temperature margin (K)
1.5
Fig. 6. Temperature margin dependencies of the minimum quench energy, MQE, as a parameter of magnetic-field strength for Nb–Ti– Cu-reinforced Nb3 Sn wire at 7 K.
Fig. 7. Temperature margin dependencies of the MQE for non-reinforced and Cu–Nb-reinforced wires.
Fig. 4. Oscillograms showing voltage response traces (at V1, V2, V3, V4, and V5) of the sample wire at 7 K and 11 T.
the reploted result of the temperature margin dependencies of Cu–Nb-reinforced and Cu-stabilized wire that we have studied previously [1]. We obtained different straight lines for the MQE vs. temperature margin for Cu–Nb-reinforced and Cu-stabilized wires, respectively. In addition, Fig. 7 infers that their MQE values were also controlled by the temperature margin.
690
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
Therefore it was realized that MQE of superconducting wires under cryocooled conditions is dominated by the temperature margin, regardless of whether reinforcement is provided. Fig. 8 shows the temperature margin dependencies of the MQE as a function of temperature for Nb–Ti–Cureinforced Nb3 Sn wire. As the specific heat increases with temperature increase, the higher the temperature, the higher the obtained MQE at the same temperature margin. This indicates that the higher specific heat of the wire produces higher thermal stability. Furthermore, the scaling curve of the measured value for Nb–Ti–Cureinforced Nb3 Sn wire at 4.5 K corresponds to that for Cu–Nb-reinforced wireÕs (Fig. 7). As a result, we confirmed that thermal stability expressed as MQE is obviously controlled by the temperature margin estimated by the applied field, temperature and transport current, and that controlling the transfer-to-quenching effect was not expected in the Cu stabilizer after current sharing, even if the normal zone was only small. Similar results were obtained using conventional Custabilized wire with a Cu volume fraction of over 50%. In such a case, reduction of heat generation by high electrical conductivity of the stabilizer does not contribute to the superconductorÕs thermal stability. Therefore, the superconducting wire for use under cryocooled conditions must be designed, based on a theory different from the bath-cooled condition formerly used. However, Fig. 7 shows that the MQE for reinforced wires is lower than that for conventional Cu-stabilized wire with the same temperature margin. Because the specific heat of 1070 J/m3 K for Cu–Nb is higher than that for Cu (390 J/m3 K at 4.2 K) [10], the cause of the decline in thermal stability by reinforcement is not the specific heat. Consequently, using only our experimental results, we could not identify the reason for decrease of the MQE by adding the internal reinforcement to the wire.
3. FEM analysis of heat transfer To investigate the cause of decline of the thermal stability in the reinforced wire, we conducted an FEM analysis of heat transfer along both the longitudinal direction and in the cross-sectional plane of the wire. Fig. 9 shows the cross-sectional view of an analyzed Nb– Ti–Cu-reinforced wire model. Similarly, Figs. 10 and 11 show models of Cu–Nb-reinforced and Cu-stabilized with ten filamentary composite wires, respectively, and the same composite material ratios as that of the wires used in the experiment. The densities of 8040, 8640, 8930 and 8798 kg/m3 were used for the constituent materials, Nb3 Sn, Cu–Nb, Cu and CuSn, respectively [10]. The specific heat and thermal conductivity values were regarded as functions of the temperature, shown in Figs. 12 and 13, respectively [10], and property values of Cu– Nb were used instead of Nb–Ti–Cu because the volume ratio and property values of Cu2 Ti in Nb–Ti–Cu after heat treatment are still unknown. The length of each analyzed model was set to 30 mm, while the width, height, and longitudinal length of the heat source was 0.1, 0.02, and 2 mm, respectively, as shown in Fig. 14. This heat source contacted the surface
Fig. 9. Cross-sectional view of analyzed Nb–Ti–Cu-reinforced wire model with 1-mm diameter and 22% Cu volume fraction.
Fig. 8. Temperature margin dependencies of the MQE as a function of temperature for Nb–Ti–Cu-reinforced Nb3 Sn wire.
Fig. 10. Cross-sectional view of analyzed Cu–Nb-reinforced wire model with 1-mm diameter and 17% Cu volume fraction.
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
Fig. 11. Cross-sectional view of analyzed Cu-stabilized wire model with 1-mm diameter and 55% Cu volume fraction.
691
cryocooled condition. The boundary conditions were that the wire surfaces were thermally insulated and the temperatures of both ends of the wire were kept to the initial wire temperatures. Figs. 15–17 show the temperature distributions of each model at 25 ls after inputting the initial temperature above 4.2 K from heat source to the wire model at the initial temperature of 4.2 K. Figs. 15–17 show not only temperature distribution in the longitudinal direction, but also in the transverse direction resulting from thermal diffusion. In Fig. 17, the Cu-stabilized model shows faster diffusion of heat than do the other reinforced models. Most of the inputted heat spread around the surface of the wire first, then
4 Nb3Sn
Specific heat (J/kgK)
3.5
Cu Cu-Nb CuSn
3 2.5 2 1.5 1
Fig. 14. Overall view of analyzed model and the contact heat source.
0.5 0
3
5
7 Temperature (K)
9
11
Fig. 12. Temperature dependencies of specific heat for each material (Nb3 Sn, Cu, Cu–Nb and Cu–Sn).
Nb3Sn Cu-Nb
Thermal Conductivity (W/mK)
10000
Cu CuSn
1000 100 10
Fig. 15. Temperature distribution of the Nb–Ti–Cu-reinforced model at 25 ls after heat generation.
1 0.1 3
5
7 Temperature (K)
9
11
Fig. 13. Temperature dependencies of thermal conductivity for each material (Nb3 Sn, Cu, Cu–Nb and Cu–Sn).
of the center for the analyzed wire model. The initial temperature of the heat source was given in the model as a disturbance because we intended to focus this study on pulsed disturbances. The input energy was subsequently estimated from the heat sourceÕs heat capacity and the difference between the initial temperatures of the heat source and the model. It was assumed that transient heat transferred only in the longitudinal direction of the wire to simulate a
Fig. 16. Temperature distribution of the Cu–Nb-reinforced model at 25 ls after heat generation.
692
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693 2.0 1.8
4.2 K 6.0 K 7.0 K
Temperature rise (K)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Fig. 17. Temperature distribution of the Cu-stabilized model at 25 ls after heat generation.
6.2 Nb-Ti-Cu-reinforced model Cu-Nb-reinforced model Cu-stabilized model
Temperature (K)
6.0 5.8 5.6 5.4 5.2 5.0
0
0.1
0.2 Time (ms)
0.3
0.4
Fig. 18. Time dependencies for the filament temperature after heat generation at the initial temperature of 4.2 K for each model.
longitudinally propagated mainly by Cu. Therefore, it was found that slower thermal diffusion for reinforced models was caused by a low volume fraction of Cu, which has high thermal conductivity. Temperature change in the Nb3 Sn filament at the nearest heat source by this thermal diffusion using FEM was calculated and plotted in Fig. 18, where time dependencies for filament temperature after heat generation at the initial temperature of 4.2 K for each model are shown. It is hereby realized that both reinforced models in which slow diffusion occurs raise the filament temperature more easily than the Cu-stabilized model. Furthermore, even though the filament of the Nb–Ti–Cu-reinforced model was closer to the heater than that of the Cu–Nb-reinforced one, the maximum temperature of the Nb–Ti–Cu-reinforced model was lower than that of the Cu–Nb-reinforced one at the same input energy. This result may be due to the higher volume fraction of Cu for the Nb–Ti–Cu-reinforced model. The results also indicate that high thermal diffusion is effective against controlling the temperature rise. From calculated results shown in Fig. 18 and experimental results shown in Fig. 7, we realized that it is difficult to increase the filament temperature in a wire
0
0.1
0.2 Time (ms)
0.3
0.4
Fig. 19. Time dependencies of the Nb–Ti–Cu-reinforced modelÕs filament at elevated temperatures 4.2, 6 and 7 K after heat generation.
with a higher MQE value. This means that the superconducting wires were stabilized by the high thermal conductivity of the Cu stabilizer. Consequently, the reinforced wireÕs MQE, which has a low Cu volume fraction, was smaller in this study. Fig. 19 shows time dependencies of the Nb–Ti–Cureinforced modelÕs filament at elevated temperatures from the initial temperatures 4.2, 6 and 7 K after heat generation. It showed that the higher the initial temperature, the smaller the obtained temperature rise. Thus Fig. 19 corresponds to the experimental result shown in Fig. 8. Consequently, the experimental result wherein the higher MQE for the higher temperature was obtained at the same temperature margin as shown in Fig. 8, can be explained by an increase in the specific heat with an increase in temperature. From the aforementioned calculations, it was observed that thermal diffusion in reinforced wire models was slower than that in non-reinforced, Cu-stabilized, model. Furthermore, it was realized that reinforced models in which slow diffusion occurs easily increases the filament temperature in comparison with the non-reinforced model. We successfully obtained computed results that can explain the experimental results in this paper.
4. Conclusion We experimentally measured the MQE for the Nb– Ti–Cu-reinforced Nb3 Sn wire, one of the candidates for the 20-T class cryocooled superconducting magnet being planned under various load conditions as a parameter of the applied magnetic-field, temperature, and the transport current under cryocooled conditions. As a result, we confirmed that quenching occurred under the cryocooled condition after current sharing, even if only a small part of the normal zone was generated. It also became clear that thermal stability expressed as MQE was controlled by the temperature margin between the temperature of the operating condition and the super-
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
conductivity-to-normal transition temperature. Similar results were obtained with the other reinforced wires and conventional Cu-stabilized wire. It was realized via FEM analysis that the higher thermal conductivity and specific heat brought about higher thermal stability of the superconducting wires. In the case where recovery from the normal state to the superconducting state after current sharing is not expected, high electrical conductivity of the stabilizer does not contribute to thermal stability of the superconductor. In such a case, the thermal conductivity, which contributes to thermal stability, is more important than the electrical conductivity. Therefore, if a reinforcement material with high thermal conductivity and a suitable cross-sectional arrangement that makes it difficult to raise temperature of Nb3 Sn against outer disturbances is chosen, it would contribute to the wireÕs thermal stability. The findings shown in this paper can be applied not only to cryocooled magnets, but also the potted ones where no recovery is expected from the normal state to superconducting state after current sharing. If a superconducting wire and its coil under the cryocooled condition, which is different to the bath-cooled condition, using electrical conductivity of a stabilizer are designed
693
with consideration to thermal diffusion and specific heat, wires and coils could be fabricated with sufficient thermal stability.
Acknowledgements This work was performed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Watanabe K et al. IEEE Trans Appl Supercond 1993;5:1905. Miyazaki T et al. Adv Cryog Eng 1998;44:935. Iwaki G et al. IEEE Trans Appl Supercond 2002;12:1045. Murase S et al. IEEE Trans Magn 1996;32:2937. Sakamoto H et al. IEEE Trans Appl Supercond 2000;10:1008. Watanabe K. Private communication. Kaneko T et al. IEEE Trans Appl Supercond 2000;10:1235. Murase S et al. IEEE Trans Appl Supercond 2001;11:3627. Iwasa Y. Cryogenics 1979;19:705. Onodera T, et al. In: Proc ICEC 16, Kitakyushu, 1997. p. 1841.
Thermal stability of reinforced Nb3Sn composite superconductor under cryocooled conditions q Tsuyoshi Yamamoto a, Kenji Watanabe a, Satoru Murase Kazuo Watanabe b, Akio Kimura c a
a,*
, Gen Nishijima b,
Department of Electrical and Electronic Engineering, Okayama University, 3-1-1, Tsushimanaka, Okayama 700-8530, Japan b HFLSM, Institute for Materials Research, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai 980-8577, Japan c The Furukawa Electric Co., Ltd., 2-6-1 Marunouchi, Chiyoda-ku, Tokyo 100-8322, Japan Received 18 August 2003; accepted 5 March 2004
Abstract Several types of reinforced Nb3 Sn wires have been developed to prevent reduction of superconducting properties by applying a strong electromagnetic force. To fabricate a cryocooled magnet using those reinforced wires, we experimentally measured the minimum quench energy (MQE) under cryocooled conditions of some reinforced Nb3 Sn wires. As a result, it became clear that thermal stability expressed as MQE was controlled by the temperature margin between the temperature of the operating condition and the transition temperature from superconductivity to normal. Using the FEM analysis, it was realized that the cause of the decline in thermal stability for the reinforced wires was the low thermal conductivity of the reinforced materials. 2004 Elsevier Ltd. All rights reserved. Keywords: Reinforced Nb3 Sn wire; MQE; Cryocooling
1. Introduction The superconducting coils that generate high magnetic-fields are subjected to a large electromagnetic force, which applies the stress and the strain to the wound superconducting wires. Because cryocooled superconducting magnets that generate more than 12 T require compaction, enormous stresses are induced due to the increase in the current density. Furthermore, because compound superconductors such as Nb3 Sn are generally sensitive to stress and strain, superconducting properties such as critical current density decrease as force increases. To prevent the reduction of the superconducting properties, several types of reinforced Nb3 Sn wires have been developed using internally reinforced materials such as Cu–Nb [1], Ta [2,3], alumina-Cu [4] q Translation of article originally published in Cryogenic Engineering (Journal of Cryogenic Association of Japan) vol. 38 (2003) pp. 262–269. * Corresponding author. Tel.: +81-86-251-8117; fax: +81-86-2518259. E-mail address: [email protected] (S. Murase).
0011-2275/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.03.017
and Nb–Ti–Cu [5] for the cryocooled 20-T class superconducting magnets being planned [6]. However, it is difficult to maintain the superconducting state against thermal disturbance because the Cu volume fraction of these internally reinforced wires is lower than that of conventional Cu-stabilized Nb3 Sn wires. There are some reports on thermal stability for Cu– Nb-reinforced wires [7,8], but there have been no reports published on Nb–Ti–Cu-reinforced ones yet. In the present paper, we investigated the minimum quench energy (MQE) under the cryocooled condition of Nb– Ti–Cu-reinforced Nb3 Sn wire. In superconducting coils that are generating a magnetic field, quenching by some sort of disturbance quite frequently occurs, even if the transport current is less than the critical current. There are two types of disturbances resulting in instability: a continuous phenomenon such as AC losses, and a pulsed one [9]. This study has been designed to investigate pulsed disturbances caused by wire-movement and cracks in epoxy in the coil. If a disturbance energy is inputted to the sample wire, there would exist an energy threshold that leads to quenching of the wire. We then measure the minimum energy value required to quench
688
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
the wire, the minimum quench energy (MQE), and evaluate it as the thermal stability of the superconducting wire. There is now a critical current-margin (CCM) design criterion for high-performance magnet stability under conventional bath-cooled conditions [9]. According to the CCM design criterion, if the disturbance energy level does not transform nuclear boiling to film boiling, quenching would not occur, regardless of the magnetÕs operating current. However, this criterion cannot be applied to the magnet under cryocooled conditions. Therefore, we have conducted research to design the criterion for the magnet stability under cryocooled conditions, focusing on the temperature margin, which is the difference between the operating temperature and the superconducting-to-normal transition temperature under various loaded conditions of the applied magnetic-field, temperature, and the transport current. In present paper, we report obtained MQE results focusing on the temperature margin. Furthermore, using the FEM analysis for thermal conduction, we discuss why the thermal stability decreases when internal reinforcement is added to the wire.
Table 1 Specifications of Nb–Ti–Cu-reinforced Nb3 Sn sample wire Nb–Ti–Cu-reinforced Nb3 Sn wire Wire diameter (mm) Filament diameter (lm) Number of filament
1.013 3.5 (nominal) 7638(19 · 402)
Material Diffusion barrier Reinforcement
Nb Cu–30wt.%Ni/Nb–46.5wt.%Ti
Volume fraction (%) Cu stabilizer Bronze/Nb3 Sn with diffusion Reinforcement
22.4 53.2 24.4
Heat treatment
675 C_40 h
Current contact
Sample wire FRP bobbin
2. Measurement of MQE 2.1. Experimental procedure A cross-sectional view of Nb–Ti–Cu-reinforced Nb3 Sn wire used as a sample is shown in Fig. 1 and Table 1. The Nb–Ti–Cu is arranged at the center of the composite wire 1 mm in diameter and with a Nb barrier. After heat treatment to form the Nb3 Sn layer, Nb–Ti– Cu transforms into Cu2 Ti, which plays a role in the reinforcement. In this experiment, the sample wire was wound around a 36-mm diameter FRP bobbin, as shown in Fig. 2. The sample bobbin was installed on the second stage of a GM (Gifford–McMahon) cryocooler. A thin strain gauge 1.5 by 1.5-mm square with 120-X resistance used for generating the heat disturbance was attached to the sample. Voltage taps, V1–V5, and temperature sensors (Cernox), T1–T4, were set on the
Fig. 1. Cross-sectional view of Nb–Ti–Cu-reinforced Nb3 Sn wire. The reinforcement composite is placed in the center of the wire (/ 1 mm).
36 mm φ
Fig. 2. Schematic view of the sample coil. An FRP bobbin is used to simulate a potted condition.
4 mm heater
T2
T1
T3
T4
29 mm
20
15.5
32.5
29
V1
V2
V3
V4
V5
Fig. 3. The locations of voltage taps, temperature sensors and heater for disturbance. As the sample is wound like a coil, V5 is located just above V1.
sample as shown in Fig. 3. Signals obtained from these sensors were recorded by a personal computer and a digital oscilloscope. Disturbance energy increasing by 0.06-mJ steps was inputted to the sample under the transport current of 80–90% of the critical current. The minimum energy for quenching of the sample wire is defined as the MQE. The MQE was measured at temperatures of 4.5, 6, and 7 K, and at applied magneticfields of up to 14.5 T on the cryocooled superconducting magnet, 15T-CSM, at the Institute for Materials Research, Tohoku University.
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
2.2. Experimental result and discussion
689
200
10 T
180
11 T
160
12 T
Ic (A)
140 120
13 T
100
14 T
80 60 40 20 0
4
5
6 7 Temperature (K)
8
9
Fig. 5. Critical current, Ic , as a function of temperature and magneticfield strength for Nb–Ti–Cu-reinforced Nb3 Sn wire.
1.4 1.2 1
MQE (mJ)
Results in Fig. 4 show that voltage–time characteristics of normal state propagation for Nb–Ti–Cu-reinforced Nb3 Sn wire observed in the digital oscilloscope did not show a recovery from the normal state to the superconducting state with a Cu stabilizer for any of these experimental conditions. This result indicates that the occurrence of only a small part of the normal state leads to immediate quenching. It was realized that controlling of the transfer to quenching after the current sharing was not expected because the suppression of joule-heat generation by the stabilization material was insufficient under these cryocooled conditions. This means that the stabilizer has no function as a current bypass under cryocooled conditions. These experimental results suggest that MQE for Nb–Ti–Cu-reinforced Nb3 Sn wire under cryocooled conditions was controlled through the temperature margin for each loaded condition; we defined the temperature margin as a difference, Tc Top , between the operating temperature, Top , and the superconducting-to-normal transition temperature, Tc , under each condition. Thus, Tc depends on loading conditions of the applied magnetic-field and the transport current of the conductor. To confirm these results, we measured the temperature dependency of the critical current on the Nb–Ti–Cu-reinforced wire as a function of magnetic-field strength, as shown in Fig. 5, and investigated Tc under each MQE measurement condition. Fig. 6 shows the temperature margin dependencies of the MQE as a function of the magnetic-field strength of Nb–Ti–Cu-reinforced Nb3 Sn wire at 7 K. It was found that the MQE and temperature margin positively correlated, i.e. MQE-temperature margin characteristics could be described as a straight line even if applied magnetic-field strength and transport current varied. The same relationship was obtained at sample temperatures of 4.5 and 6 K. Furthermore, Fig. 7 shows
0.8 0.6 Nb-Ti-Cu-reinforced wire (10 T 7 K) Nb-Ti-Cu-reinforced wire (11 T 7 K) Nb-Ti-Cu-reinforced wire (12 T 7 K)
0.4 0.2 0
0
0.5 1 Temperature margin (K)
1.5
Fig. 6. Temperature margin dependencies of the minimum quench energy, MQE, as a parameter of magnetic-field strength for Nb–Ti– Cu-reinforced Nb3 Sn wire at 7 K.
Fig. 7. Temperature margin dependencies of the MQE for non-reinforced and Cu–Nb-reinforced wires.
Fig. 4. Oscillograms showing voltage response traces (at V1, V2, V3, V4, and V5) of the sample wire at 7 K and 11 T.
the reploted result of the temperature margin dependencies of Cu–Nb-reinforced and Cu-stabilized wire that we have studied previously [1]. We obtained different straight lines for the MQE vs. temperature margin for Cu–Nb-reinforced and Cu-stabilized wires, respectively. In addition, Fig. 7 infers that their MQE values were also controlled by the temperature margin.
690
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
Therefore it was realized that MQE of superconducting wires under cryocooled conditions is dominated by the temperature margin, regardless of whether reinforcement is provided. Fig. 8 shows the temperature margin dependencies of the MQE as a function of temperature for Nb–Ti–Cureinforced Nb3 Sn wire. As the specific heat increases with temperature increase, the higher the temperature, the higher the obtained MQE at the same temperature margin. This indicates that the higher specific heat of the wire produces higher thermal stability. Furthermore, the scaling curve of the measured value for Nb–Ti–Cureinforced Nb3 Sn wire at 4.5 K corresponds to that for Cu–Nb-reinforced wireÕs (Fig. 7). As a result, we confirmed that thermal stability expressed as MQE is obviously controlled by the temperature margin estimated by the applied field, temperature and transport current, and that controlling the transfer-to-quenching effect was not expected in the Cu stabilizer after current sharing, even if the normal zone was only small. Similar results were obtained using conventional Custabilized wire with a Cu volume fraction of over 50%. In such a case, reduction of heat generation by high electrical conductivity of the stabilizer does not contribute to the superconductorÕs thermal stability. Therefore, the superconducting wire for use under cryocooled conditions must be designed, based on a theory different from the bath-cooled condition formerly used. However, Fig. 7 shows that the MQE for reinforced wires is lower than that for conventional Cu-stabilized wire with the same temperature margin. Because the specific heat of 1070 J/m3 K for Cu–Nb is higher than that for Cu (390 J/m3 K at 4.2 K) [10], the cause of the decline in thermal stability by reinforcement is not the specific heat. Consequently, using only our experimental results, we could not identify the reason for decrease of the MQE by adding the internal reinforcement to the wire.
3. FEM analysis of heat transfer To investigate the cause of decline of the thermal stability in the reinforced wire, we conducted an FEM analysis of heat transfer along both the longitudinal direction and in the cross-sectional plane of the wire. Fig. 9 shows the cross-sectional view of an analyzed Nb– Ti–Cu-reinforced wire model. Similarly, Figs. 10 and 11 show models of Cu–Nb-reinforced and Cu-stabilized with ten filamentary composite wires, respectively, and the same composite material ratios as that of the wires used in the experiment. The densities of 8040, 8640, 8930 and 8798 kg/m3 were used for the constituent materials, Nb3 Sn, Cu–Nb, Cu and CuSn, respectively [10]. The specific heat and thermal conductivity values were regarded as functions of the temperature, shown in Figs. 12 and 13, respectively [10], and property values of Cu– Nb were used instead of Nb–Ti–Cu because the volume ratio and property values of Cu2 Ti in Nb–Ti–Cu after heat treatment are still unknown. The length of each analyzed model was set to 30 mm, while the width, height, and longitudinal length of the heat source was 0.1, 0.02, and 2 mm, respectively, as shown in Fig. 14. This heat source contacted the surface
Fig. 9. Cross-sectional view of analyzed Nb–Ti–Cu-reinforced wire model with 1-mm diameter and 22% Cu volume fraction.
Fig. 8. Temperature margin dependencies of the MQE as a function of temperature for Nb–Ti–Cu-reinforced Nb3 Sn wire.
Fig. 10. Cross-sectional view of analyzed Cu–Nb-reinforced wire model with 1-mm diameter and 17% Cu volume fraction.
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
Fig. 11. Cross-sectional view of analyzed Cu-stabilized wire model with 1-mm diameter and 55% Cu volume fraction.
691
cryocooled condition. The boundary conditions were that the wire surfaces were thermally insulated and the temperatures of both ends of the wire were kept to the initial wire temperatures. Figs. 15–17 show the temperature distributions of each model at 25 ls after inputting the initial temperature above 4.2 K from heat source to the wire model at the initial temperature of 4.2 K. Figs. 15–17 show not only temperature distribution in the longitudinal direction, but also in the transverse direction resulting from thermal diffusion. In Fig. 17, the Cu-stabilized model shows faster diffusion of heat than do the other reinforced models. Most of the inputted heat spread around the surface of the wire first, then
4 Nb3Sn
Specific heat (J/kgK)
3.5
Cu Cu-Nb CuSn
3 2.5 2 1.5 1
Fig. 14. Overall view of analyzed model and the contact heat source.
0.5 0
3
5
7 Temperature (K)
9
11
Fig. 12. Temperature dependencies of specific heat for each material (Nb3 Sn, Cu, Cu–Nb and Cu–Sn).
Nb3Sn Cu-Nb
Thermal Conductivity (W/mK)
10000
Cu CuSn
1000 100 10
Fig. 15. Temperature distribution of the Nb–Ti–Cu-reinforced model at 25 ls after heat generation.
1 0.1 3
5
7 Temperature (K)
9
11
Fig. 13. Temperature dependencies of thermal conductivity for each material (Nb3 Sn, Cu, Cu–Nb and Cu–Sn).
of the center for the analyzed wire model. The initial temperature of the heat source was given in the model as a disturbance because we intended to focus this study on pulsed disturbances. The input energy was subsequently estimated from the heat sourceÕs heat capacity and the difference between the initial temperatures of the heat source and the model. It was assumed that transient heat transferred only in the longitudinal direction of the wire to simulate a
Fig. 16. Temperature distribution of the Cu–Nb-reinforced model at 25 ls after heat generation.
692
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693 2.0 1.8
4.2 K 6.0 K 7.0 K
Temperature rise (K)
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Fig. 17. Temperature distribution of the Cu-stabilized model at 25 ls after heat generation.
6.2 Nb-Ti-Cu-reinforced model Cu-Nb-reinforced model Cu-stabilized model
Temperature (K)
6.0 5.8 5.6 5.4 5.2 5.0
0
0.1
0.2 Time (ms)
0.3
0.4
Fig. 18. Time dependencies for the filament temperature after heat generation at the initial temperature of 4.2 K for each model.
longitudinally propagated mainly by Cu. Therefore, it was found that slower thermal diffusion for reinforced models was caused by a low volume fraction of Cu, which has high thermal conductivity. Temperature change in the Nb3 Sn filament at the nearest heat source by this thermal diffusion using FEM was calculated and plotted in Fig. 18, where time dependencies for filament temperature after heat generation at the initial temperature of 4.2 K for each model are shown. It is hereby realized that both reinforced models in which slow diffusion occurs raise the filament temperature more easily than the Cu-stabilized model. Furthermore, even though the filament of the Nb–Ti–Cu-reinforced model was closer to the heater than that of the Cu–Nb-reinforced one, the maximum temperature of the Nb–Ti–Cu-reinforced model was lower than that of the Cu–Nb-reinforced one at the same input energy. This result may be due to the higher volume fraction of Cu for the Nb–Ti–Cu-reinforced model. The results also indicate that high thermal diffusion is effective against controlling the temperature rise. From calculated results shown in Fig. 18 and experimental results shown in Fig. 7, we realized that it is difficult to increase the filament temperature in a wire
0
0.1
0.2 Time (ms)
0.3
0.4
Fig. 19. Time dependencies of the Nb–Ti–Cu-reinforced modelÕs filament at elevated temperatures 4.2, 6 and 7 K after heat generation.
with a higher MQE value. This means that the superconducting wires were stabilized by the high thermal conductivity of the Cu stabilizer. Consequently, the reinforced wireÕs MQE, which has a low Cu volume fraction, was smaller in this study. Fig. 19 shows time dependencies of the Nb–Ti–Cureinforced modelÕs filament at elevated temperatures from the initial temperatures 4.2, 6 and 7 K after heat generation. It showed that the higher the initial temperature, the smaller the obtained temperature rise. Thus Fig. 19 corresponds to the experimental result shown in Fig. 8. Consequently, the experimental result wherein the higher MQE for the higher temperature was obtained at the same temperature margin as shown in Fig. 8, can be explained by an increase in the specific heat with an increase in temperature. From the aforementioned calculations, it was observed that thermal diffusion in reinforced wire models was slower than that in non-reinforced, Cu-stabilized, model. Furthermore, it was realized that reinforced models in which slow diffusion occurs easily increases the filament temperature in comparison with the non-reinforced model. We successfully obtained computed results that can explain the experimental results in this paper.
4. Conclusion We experimentally measured the MQE for the Nb– Ti–Cu-reinforced Nb3 Sn wire, one of the candidates for the 20-T class cryocooled superconducting magnet being planned under various load conditions as a parameter of the applied magnetic-field, temperature, and the transport current under cryocooled conditions. As a result, we confirmed that quenching occurred under the cryocooled condition after current sharing, even if only a small part of the normal zone was generated. It also became clear that thermal stability expressed as MQE was controlled by the temperature margin between the temperature of the operating condition and the super-
T. Yamamoto et al. / Cryogenics 44 (2004) 687–693
conductivity-to-normal transition temperature. Similar results were obtained with the other reinforced wires and conventional Cu-stabilized wire. It was realized via FEM analysis that the higher thermal conductivity and specific heat brought about higher thermal stability of the superconducting wires. In the case where recovery from the normal state to the superconducting state after current sharing is not expected, high electrical conductivity of the stabilizer does not contribute to thermal stability of the superconductor. In such a case, the thermal conductivity, which contributes to thermal stability, is more important than the electrical conductivity. Therefore, if a reinforcement material with high thermal conductivity and a suitable cross-sectional arrangement that makes it difficult to raise temperature of Nb3 Sn against outer disturbances is chosen, it would contribute to the wireÕs thermal stability. The findings shown in this paper can be applied not only to cryocooled magnets, but also the potted ones where no recovery is expected from the normal state to superconducting state after current sharing. If a superconducting wire and its coil under the cryocooled condition, which is different to the bath-cooled condition, using electrical conductivity of a stabilizer are designed
693
with consideration to thermal diffusion and specific heat, wires and coils could be fabricated with sufficient thermal stability.
Acknowledgements This work was performed at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Watanabe K et al. IEEE Trans Appl Supercond 1993;5:1905. Miyazaki T et al. Adv Cryog Eng 1998;44:935. Iwaki G et al. IEEE Trans Appl Supercond 2002;12:1045. Murase S et al. IEEE Trans Magn 1996;32:2937. Sakamoto H et al. IEEE Trans Appl Supercond 2000;10:1008. Watanabe K. Private communication. Kaneko T et al. IEEE Trans Appl Supercond 2000;10:1235. Murase S et al. IEEE Trans Appl Supercond 2001;11:3627. Iwasa Y. Cryogenics 1979;19:705. Onodera T, et al. In: Proc ICEC 16, Kitakyushu, 1997. p. 1841.