Before conducting the PFM experiments, the three bulks had been magnetized by FC, while being cooled using liquid nitrogen. In both cases, the ramping rate was 27 mT/min and the maximum applied magnetic field was 3.1 T. After magnetization, a linear stage was used to measure the magnetic flux density, 1 mm above the top of the samples. The Hall sensor used for this measure was a F. W. Bell BHT-921.

The experimental setup is shown in Fig. 1. Three GdBa₂Cu₃O_7-δ (GdBCO) bulks made by a quench melt-growth process by Nippon Steel have been arranged side by side, similarly to the bulk arrangement in the 30 kW HTS rotating machine developed in TUMSAT [21]. It has been chosen to use a 3-bulk array in this experiment, rather than the full array of 3 by 5 bulks from the HTS rotating machine. Reducing the scale of the array simplifies conditions making the experimental work easier while allowing us to understand if a PFM technique could be used on multiple bulks. The bulks used were 50 mm by 50 mm squares and have a thickness of 15 mm for bulks no. 1 and no. 3 and 20 mm for bulk no. 2. The HTS bulks were separated by 1 mm, as shown in Fig. 1 (a). The z-axis shown in Fig. 1 (a) is collinear to the c-axis of the bulks.

To apply the magnetic field, three vortex-type copper coils had been placed 5 mm above each bulk. Having three coils for three bulks allowed us to magnetize all the bulks at once or individually and therefore potentially highlighting improper magnetization by PFM due to the proximity of each bulk. Moreover, vortex-type coils had been shown to apply a magnetic field with a conical distribution, which results in high trapped fields by PFM while requiring less energy than solenoid-type coils [23]. By placing one coil over each bulk, and trying different types of magnetization sequences, we aimed to obtain a conical distribution of the trapped magnetic flux density in each bulk despite the potential influence of neighboring bulks. The coils had a thickness of 30 mm, an outer diameter of 50 mm, and an inner diameter of 6 mm. Each coil had 145 turns of 2 mm in diameter wire, and a self-inductance of about 150 μH. The coils and the bulk were cooled to 77 K by being submersed in liquid nitrogen. Hall sensors (Asahi Kasei Microdevices HG-116A) were placed 1 mm from the top surface of the bulks and are visible in Fig. 1 (a) and (b). Hall sensors were placed at 13 locations across the three bulks on the x-axis, including the center of the bulks, and at 0 mm on the y-axis. These Hall sensors allowed us to show the trapped magnetic flux density distribution on a center line over the three bulks, measured after the flux creep caused by each pulse magnetization has settled down. Interesting sectors such as the center and growth sector (GS) of each bulk and the growth sector were covered by these sensors. Another 9 Hall sensors were placed on other interesting sectors of each bulk, such as the growth sector boundary (GSB), growth sector edge (GSe), and growth sector boundary edge (GSBe). These Hall sensors were used to measure a combination of the applied magnetic flux density and the dynamic variation of the magnetic flux density in real-time during the PFM and were then used to measure the trapped magnetic flux density.

To magnetize the bulks using the copper vortex-type coils, we used our pulse field magnetization power supply, presented in [24]. This magnetizing power supply allowed us to perform passive PFM in this study. A passive PFM relies on the exponential LCR response of the electrical circuit of the pulse magnetizer coupled with the coils. By changing the charge voltage of the capacitor bank from the pulse field magnetization power supply, we were able to change the magnetizing energy, thus changing the maximum pulsed current flowing through the coils and the maximum applied magnetic flux density.

The three copper coils were all used at once at first, by connecting them in series. The results obtained using this configuration are shown in section 3.2. We also experimented with the use of each individual coil separately, to improve the trapped field distribution of the three bulk, and to study the potential demagnetization occurring during a magnetization sequence. For the sequential magnetization, each bulk was magnetized separately.

An example of a pulsed current during a magnetization sequence is given in Fig. 2. First, the coil placed above bulk no. 1, coil no. 1, was connected to the pulse magnetizing power supply, and a first PFM is performed. After a 10 min interval, during which coil no. 2 is connected to the magnetizing power supply, replacing the first coil. A second PFM was performed, on bulk no. 2 using coil no. 2 this time. Finally, this process is repeated, and bulk no. 3 was magnetized with coil no. 3, 10 min after the bulk no. 2. The 10-minute interval was chosen in order to remove the heat generation when magnetizing the adjacent bulk and to change the connection and perform the next measurement.

Fig. 3 shows the trapped magnetic flux density distribution using FC magnetization, in the three GdBCO bulks, measured 1 mm from the top surface of the bulks. The maximum trapped magnetic flux density is 1.14 T in the center of bulk no. 2, which is 0.35 T higher than that of bulk no. 1 and 0.26 T higher than that of bulk no. 3. This difference may be explained by the increased thickness of bulk no. 2 over the other two bulks. The distribution is conical in each bulk, with each peak placed in the center of each bulk. The single-centered peak and absence of a valley indicate that the bulks don’t have cracks that could influence the trapping of the magnetic field.

The dynamic variation of magnetic flux density in five sectors of the three bulks during a passive PFM is shown in Fig. 4 (a), (b) and (c). The associated pulsed current is shown in Fig. 4 (d). The energy used for this magnetization was 7.6 kJ, where we observed the highest trapped magnetic flux density in the center of bulk no.2, using the three coils connected in series, at 0.68 T, as shown in Fig. 5 (a). The symmetrical characteristic of the experimental configuration can be confirmed by the variation of magnetic flux density in the bulks during the magnetization. The maximum values of magnetic flux density penetration in the no. 1 and no. 3 were within a margin of error of 5%, with a maximum of 4.08 T in the center, 3.03 T in the GS, and 2.38 T in the GSB. Bulk no. 2 on the other end, showed a reduction of the maximum penetration magnetic flux density in the center, GS, and GSB. The Hall sensor measuring the magnetic flux density over the GS was placed on the sector near the edge, share with bulk no. 3 (with a 1 mm gap between the bulks). Thus, it seems that the proximity of the other bulks was responsible for the decrease in the maximum penetration magnetic field in the GS. The diminution of the maximum penetration in the GSB was only 0.26 T compared to bulks no. 1 and no. 3, suggesting that the flux lines penetrating through the GSB were less impacted by the closeness to the other bulks. Finally, it can be noted the maximum penetration in the center is lowered by 0.96 T, which could be the direct consequence of the lower penetration in the GS, and GSB. The trapped magnetic flux density was still higher in bulk no. 2, despite the lower maximum penetration field, possibly due to the increased thickness over the side bulks. For the three bulks, the perpendicular component of the magnetic flux density measured in the GSB and GSBe is much lower than in the GS, GSB, and center. This can be explained, at least partially by the conical shape of the applied field distribution, due to the use of vortex-type magnetizing coils [25]. Another explanation is that the peak of measured applied magnetic flux density on the edges occurs a few milliseconds before the peak in the center. This suggests that the magnetic fields migrate from the edge to the center, reducing the measured magnetic flux density on the edges. In addition, in this experiment, only the perpendicular component is measured and there may be a non-negligible parallel component of the applied magnetic field at the edge of the bulks.

Fig. 5 (a) shows the trapped magnetic flux density on a center line over the three bulk samples, for various magnetizing energies. The associated pulsed current for each energy is shown in Fig. 5 (b). Fig. 5 (c) shows the trapped magnetic flux density in the center of each bulk, as a function of the magnetizing energy. From 0.5 kJ and upward, the trapped magnetic flux density distribution was conical in each bulk sample, as seen in Fig. 5 (a). However, from 1.5 kJ, the trapped magnetic flux density at x = −38.5 mm and x = 38.5 mm was higher than that at x = −63.5 mm and x = 63.5 mm. This is especially noticeable at high magnetizing energy from 3 kJ. The small gap of 1 mm between the bulk, combined with the use of the three vortex-type copper coils forces a high concentration of magnetic flux density, which seems to increase the trapped magnetic flux density in the bulk sector next to the gap. The slightly asymmetrical distribution of the trapped magnetic flux density was not observed when magnetizing the bulk using FC in Fig. 3. Moreover, it was also less apparent when using a magnetization sequence, as shown in section 3.3. The trapped magnetic flux density in the center of the three bulks, visible in Fig. 5 (c), increased almost linearly with the rise of the magnetizing energy until 2 kJ. Between 73 J and 1 kJ of magnetizing energy, the trapped magnetic flux density was lower in the center of bulk no. 2 than in bulks no. 1 and no. 3, where the value is similar. From 3 kJ, the trapped magnetic flux density in bulk no. 2 continued to increase while bulks no. 1 and no. 3 reach saturation. Thus, with sufficient magnetizing energy, the PFM technique allows for obtaining a comparable distribution of trapped magnetic flux density over the array of bulks to the distribution obtained by the quasi-static magnetization technique.

The key potential issues for the magnetization sequence are the possible demagnetization of an already magnetized neighboring bulk, in the second or third stage of the magnetization sequence and the trapping of a magnetic field of opposite polarity in a not yet magnetized bulk close to the bulk being magnetized. First, bulk no. 1 was magnetized, followed by bulk no. 2, and then bulk no. 3, by using the copper coils no. 1, no. 2, and no. 3 respectively. Fig. 6 shows the trapped magnetic flux density after each of the three pulses. Fig. 6 (a) shows the results for a magnetizing energy of E = 0.26 kJ, Fig. 6 (b) for E = 0.5 kJ, Fig. 6 (c) for E = 1 kJ, and Fig. 6 (d) for E = 1.5 kJ. For each magnetizing energy, the behavior of the trapped magnetic flux density is comparable. After the first pulse, using coil no. 1 for the magnetization, bulk no. 1 was magnetized, with full penetration of the magnetic flux density and with a conical distribution of the trapped magnetic field. Bulk no. 2 was affected by this first pulse because the Hall sensor placed at x = −12.5 mm showed a trapped magnetic flux density of −0.05 T for magnetizing energy of E = 1.5 kJ. At lower magnetizing energy the trapped magnetic flux density was lower, down to −0.01 T for E = 0.26 kJ. However, the penetration in bulk no. 2 was incomplete, and the trapped magnetic flux density at x = 0 and x = 12.5 mm was negligible. Therefore, the potentially negative impact of the unwanted magnetization in the inverse polarity of the neighboring bulk was limited. The second pulse was done using coil no. 2. Bulk no. 2 was fully magnetized, meaning that the penetration of the magnetic field during the pulse reached the center of the bulk and resulted in a conical-shaped distribution of the trapped magnetic flux density. However, we can see the effect of this second pulse on bulk no. 1, with a decrease from 0.58 T of trapped magnetic flux density after the first pulse to 0.53 T after the second pulse, for an energy of 1.5 kJ. At this stage, the trapped magnetic flux density in bulk no. 3 was low and comparable to the magnetization of bulk no. 2 with the 1st pulse. The 3rd and final passive PFM of the sequence resulted in a partial demagnetization of bulk no. 2, while bulk no. 3 was fully magnetized.

The values of trapped magnetic flux density measured after each pulse of the magnetization sequence are shown in Fig. 6, for various magnetizing energies. According to this data, the percentage of demagnetization of previously magnetized bulks seemed to be stable for the various energy, with a total maximum decrease of about 12%. In the case of bulk no. 1, the drop was about 10% or less in the 2nd pulse, while the 3rd pulse resulted in a decrease little. The magnetization in a sequence had therefore a negative impact on the trapped field of a magnetized on the bulk directly next to the one being magnetized while having little to no impact on bulks not placed further away.

To understand if changing the order of magnetization could help reduce the demagnetization effect and to try to maximize the trapped magnetic flux density in bulk no. 2, we experimented with different magnetizing sequences at the same energy. The goal is to obtain a field distribution desirable for the use of the array of GdBCO samples as a pole field of an HTS rotating machine.

Fig. 7 shows the trapped magnetic flux density distribution after each pulse of three magnetization sequences, at 1 mm above the samples and for y = 0, as a function of x. The field distribution shown in Fig. 7 (a) was obtained by magnetizing bulk no. 1, then bulk no. 3 and finally bulk no. 2. By using this magnetization sequence, we managed to avoid the partial demagnetization of bulk no. 2, and it resulted in the highest trapped magnetic flux in the center. While the 3rd magnetization affected the trapped magnetic field of the bulks no.1 and no. 3, the 2nd PFM did not affect the already magnetized bulk no. 1. This magnetizing sequence seems to be the most suitable for the use of the bulk array in a field pole, as it maximizes the peak of trapped magnetic flux density in the center bulk while reducing slightly the demagnetization effect of the magnetization.

The magnetization sequence used to trap the magnetic field distribution shown in Fig. 7 (b), started by magnetizing bulk no. 2, by using the vortex-type coil no. 2. Bulk no. 1 was then magnetized followed by bulk no. 3. Compared to the two previous magnetization sequences at the same energy, this sequence order seems to be less desirable because the partial demagnetization of bulk no. 2 happens twice. This different sequence also confirms that the demagnetization only affects the bulk directly next to the bulk being magnetized. This is important because it could allow a large array of bulks to be magnetized sequentially, without complete destruction of the magnetization in the bulks magnetized at the beginning of the sequence.