4.3. Experimental results
4.3.1. Critical currents at different temperatures and 8 T field
The results of the calculations and measurements agree well and then it was decided to apply the same heating method to real HTS conductors.
rise in the voltage. The temperature rise was due to the appearance of flux-flow resistance in the HTS conductor. By the time, the electric field was 1 μV/cm, the temperature of the conductor was about 5.5 K. For evaluating the critical current of the HTS conductor, the experimental data were fitted with a non-linear power law, E/Ec = (I/Ic)n, with Ec = 1 μV/cm criterion. The experimental data were fitted up to 5 μV/cm so that the error due to the temperature change of the conductor was not significant. The evaluated critical current and n-value of the HTS conductor at 8 T and 5.5 K is 14.2 kA and 30 respectively.
The measured V-I curve of the HTS conductor at 10 K in 8T bias field is shown in Fig. 4.17. Before supplying the current into the conductor, the conductor temperature at TS1, TS2, TS3, and TS4 locations was 10.4 K, 12.2 K, 9.9 K, and 9.8 K respectively. At the V6 voltage tap location, the temperature difference across the conductor cross-section was about 0.5K. The similar temperature conditions were established in the conductor for the measurements at 20 K and 30 K. As shown in Fig. 4.17, the conductor temperature kept increasing slowly due to the SS heater power during critical current measurements.
Once there was a non-linear rise in the voltage due to the appearance of the flux-flow resistance, the temperature also increased non-linearly. The conductor temperature was about 11 K by the time the electric field was 1 μV/cm. The critical current was evaluated by fitting the experimental data up to about 5 μV/cm with a non-linear power law, E/Ec = (I/Ic)n, with Ec = 1 μV/cm criterion. The evaluated critical current and n-value of the HTS conductor at 8 T and 11 K are 12.9 kA and 19.5, respectively. Similarly, the critical current measurements were done at 20 K, and 30 K in a bias magnetic field of 8T. The critical current and n-values at 22 K and 32 K are 10.5 kA, 17.2 and 8.23 kA, 17 respectively. The measured critical currents show linear dependence on temperature as shown in Fig. 4.18. The simple sum of the critical currents of all the tapes in HTS conductor (without self-field effects) and the calculated critical currents of the HTS conductor using load-line analysis (with self-field effects) [4.11] are also shown in Fig.
4.18.
The calculated critical currents of the HTS conductors agree well with the experimentally observed critical currents.
Fig. 4.16: V-I curve of the HTS conductor at 8 T bias field (// to ab-plane) and 4.2 K. The experimental data is fitted with a non-linear power law, E/Ec = (I/Ic)n, with 1 μV/cm criterion. The temperature evolution observed by a CERNOX temperature sensor, TS1, is also shown. The evaluated critical and n-value are 14.2 kA and 30 (at 5.5 K, 8 T) respectively.
Fig. 4.17: V-I curve of the HTS conductor at 8 T bias field (// to ab-plane) and 10K. The experimental data are fitted with a non-linear power law, E/Ec = (I/Ic)n, with 1 μV/cm criterion. The temperature evolution observed by CERNOX temperature sensor, TS1, is also shown. The evaluated critical and n-value are 12.9 kA and 19.5 (at 11 K, 8 T) respectively.
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HP1 HP2
HP3 HP1
HP2
HP3
(b)
Fig. 4.18: (a) temperature dependence of the measured critical currents of the HTS conductor. The simple sum of the critical currents of all the HTS tapes in HTS conductor (without self-field effects) and calculated critical currents of the HTS conductor with a load-line analysis (with self-field effects) are also shown; (b) calculated field distribution on the HTS tapes inside the conductors. Each tape is carrying 100 A current.
YBCO HTS conductor
Similar to Bi-2223/Ag HTS conductor, the YBCO conductor was tested by preparing a sample in hairpin configuration. The YBCO conductor was thermally insulated by epoxy and GFRP exactly in the same way as the Bi-2223/Ag conductor sample as discussed before. The other leg of the YBCO conductor sample was actually the Bi-2223/Ag conductor having 34 numbers of Bi-2223/Ag tapes inside the copper sheath. This leg was directly immersed in liquid helium. The joint between YBCO and Bi-2223/Ag conductors at the bottom of the sample was prepared by soldering the NbTi/Cu Rutherford cables between and outside the conductors to reduce the joint resistance as shown in Fig. 4.19.
The similar technique was used for Bi-2223/Ag conductor sample as well. The measured joint resistance was less than 2 nano-ohms at 15 kA and 8 T.
The critical currents of the YBCO conductor were measured using one pair of voltage taps attached at the center of the GFRP-insulated conductor. At the center, two CERNOX temperature sensors (designated as TS1 and TS3) were also attached on two opposite surfaces of the conductor to observe the temperature evolution. The bias magnetic field, parallel to ab-plane of the HTS tapes, was applied using an 8 T split coil.
The measured V-I curve of the HTS conductor at ~20 K and 8 T bias field is shown in Fig. 4.20. The raw data as well as the smoothed data are shown in Fig. 4.20. The measured temperature at the center of the conductor is also shown in Fig. 4.20. Similar to Bi-2223/Ag conductor, a non-linear rise in YBCO conductor temperature was observed, which exactly follows the non-linear rise in the electric field. The temperature rise was due to the appearance of flux-flow resistance in the conductor. By the time, the electric field was 1 μV/cm, the temperature of the conductor was about 24 K. For evaluating the critical current of the HTS conductor, the experimental data were fitted with a non-linear power law, E/Ec = (I/Ic)n, with Ec = 1 μV/cm criterion. The experimental data were fitted up to 5 μV/cm so that the error due to the temperature change of the conductor was not significant. The evaluated critical current and n-value of the YBCO conductor at 8 T and 24 K is 14.2 kA and 30 respectively.
The measured V-I curve of the HTS conductor at ~10 K in 8T bias field is shown in Fig. 4.21. Once there was a non-linear rise in the electric field due to the appearance of the flux-flow resistance, the temperature also increased non-linearly. The conductor
temperature was about 15.5 K by the time the electric field was 1 μV/cm. The critical current was evaluated by fitting the experimental data up to about 5 μV/cm with a non-linear power law, E/Ec = (I/Ic)n, with Ec = 1 μV/cm criterion. The evaluated critical current and n-value of the HTS conductor at 8 T and 15.5 K are 16.8 kA and 30, respectively. Similarly, the critical current measurements were done at ~25 K in a bias magnetic field of 8T. The evaluated critical current and n-values at 27 K are 12.5 kA and 30 respectively. The conductor temperature could not be raised beyond 25 K due to the current limitation in the S.S. heater power supplies and therefore measurements were restricted to only ~25 K. The critical current measurement at 4.2 K, 8 T was also tried but the other conductor leg of the sample, which was Bi-2223/Ag conductor, showed electric field rise rather than the YBCO conductor. This clearly means the critical current of the YBCO conductor was much higher than the Bi-2223/Ag conductor and therefore the critical current of the YBCO conductor could not be measured at 4.2 K, 8T.
The measured critical currents show linear dependence on temperature as shown in Fig. 4.22. The simple sum of the critical currents of all the tapes in HTS conductor (without self-field effects) and the calculated critical currents of the HTS conductor using load-line analysis (with self-field effects) [4.11] are also shown in Fig. 4.22. The experimental Ic-B-T characteristics of the YBCO and GdBCO tapes are not available and therefore, the percolation model [4.12] has been used to derive these characteristics. Due to the lack of real Ic-B-T characteristics of used YBCO and GdBCO tapes, the agreement between calculated and measured critical currents is not good. To improve the agreement between calculated and experimental results of critical currents, the experiments on the YBCO and GdBCO tapes are planned to be a future task. The derived Ic-B-T characteristics of the YBCO tape (using percolation model), required for our YBCO conductor calculations, are shown in Fig. 4.23. Even though the magnetic field dependence of the critical currents of GdBCO and YBCO tapes might be different from each other, in the present calculations, for simplicity, the Ic-B-T characteristics have been derived by considering the average critical current of 200 A of the YBCO (210 A) and GdBCO (190 A) at self-field and 77 K and therefore, both the tapes have been considered to be equivalent with each other for load line analysis.
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(b)
Fig. 4.19: (a) photo of joint between Bi-2223/Ag and YBCO conductor at the bottom of the sample. The NbTi/Cu cables are used in between and outside the conductors to reduce the joint resistance; (b) joint with clamps and heater attached just before starting the soldering of the joint.
Fig. 4.20: V-I curve of the YBCO conductor at 8 T bias field (// to ab-plane) and ~20 K.
The experimental data is fitted with a non-linear power law, E/Ec = (I/Ic)n, with 1 μV/cm criterion. The temperature evolution observed by a CERNOX temperature sensor, TS3, is also shown. The evaluated critical and n-value are 14.2 kA and 30 (at 24 K, 8 T) respectively.
Fig. 4.21: V-I curve of the YBCO conductor at 8 T bias field (// to ab-plane) and ~10 K.
The experimental data is fitted with a non-linear power law, E/Ec = (I/Ic)n, with 1 μV/cm criterion. The temperature evolution observed by a CERNOX temperature sensor, TS3, is also shown. The evaluated critical and n-value are 16.8 kA and 30 (at 15.5 K, 8 T) respectively.
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(b)
Fig. 4.22: (a) temperature dependence of the measured critical currents of the YBCO conductor. The simple sum of the critical currents of all the HTS tapes in the conductor (without self-field effects) and calculated critical currents of the YBCO conductor with a load-line analysis (with self-field effects) are also shown; (b) calculated field distribution on the HTS tapes inside the conductors. Each tape is carrying 100 A current.
Fig. 4.23: Calculated Ic-B-T characteristics of the YBCO tape using percolation model [4.12].