Pulse Field Magnetization of GdBCO Without Rapid Decrease in Magnetic Flux Density

Pulse field magnetization (PFM) method for high-temperature superconducting (HTS) bulks is attractive for promoting the use of HTS technology in various applications. Waveform control pulse field magnetization (WCPM) method is new techniques which has shown promising results so far in trapping strong magnetic fields by a single pulsed magnetic field. The cause of most of the magnetic field penetrating in the bulk by the application of a pulsed magnetic field not to be trapped is thought to be the local heat generated by the steep flux motion caused by the increase and decrease of that pulsed magnetic field. In this presentation, we show the results of magnetization under controlled conditions so that the magnetic flux that once entered the HTS bulk does not abruptly decrease. The penetration flux density measured on the surface of the GdBCO bulk was used as input to control the negative feedback as in previous studies. The bulk was placed between two vortex-type coils that replicated the internal structure of our previously developed axial-gap superconducting rotating2. At 40 K, by generating a pulsed magnetic field by negative-feedback-WCPM (NFB-WCPM) with a slight decrease in flux density, we applied almost constant magnitude magnetic flux density to the bulk sample for more than 1 s, and obtained a flux density nearly three times higher than the maximum flux density obtained with conventional PFM. NFB-WCPM worked effectively to obtain high trapped flux density even at 40 K. The bulk sample successfully trapped a flux density of nearly 4 T for less than two seconds by a single NFB-WCPM by adjusting the control conditions.

SECTION I. Introduction

As a result of recent developments in power electronics technology, permanent magnet synchronous rotating machines are often employed in applications requiring high power [1]. They are characterized by a very high efficiency of 95-97% and high power density. Such high performance is very attractive compared to other rotating machines, but it is technically difficult to increase the efficiency and power density further than now. However, when the permanent magnets used for the field pole magnet are replaced with high-temperature superconducting (HTS) bulks, it is possible to significantly increase the power density of the rotating machine. We have developed HTS rotating machines from this perspective and have achieved several good results [2], [3], [4], [5].

Since HTS bulk inside the rotating machine behaves as a quasi-permanent magnet, we need to magnetize HTS bulk before we can use it. Since the field pole magnet of a rotating machine has multiple HTS bulks, it is again technically difficult to install pre-magnetized bulk inside the rotating machine using a superconducting magnet. As one solution, we have established a technique to pulse field magnetize a HTS bulk using a dual armature coil of our rotating machines [2], [6]. The vortex-type copper coil was developed as the armature of a 30 kW class HTS rotating machine, and can carry an armature current of less than 100 A. By the way, the magnetic flux density required to magnetize the HTS bulk is generally generated by passing a current of several kA through the magnetizing coil, which greatly exceeds the armature current carrying capacity of the vortex-type copper coil. However, in pulse field magnetization (PFM), the HTS bulk is magnetized by passing a large current through the copper coil for a short period of time, so that can serve as the magnetizing coil as well as the armature.

By applying the charge stored in a large capacitor bank through copper coil with low DC resistance, we obtain the high current required for PFM for a short period of time. That is, the magnetizing circuit consists of a capacitor, an inductor, and the DC resistance of the circuit components and wiring, and the LCR transient response when a switch inserted in the circuit is turned on generates the pulse current. A schematic diagram of the magnetizing circuit is shown in Fig. 1(a). The current $i(t)$ flowing through this circuit when the switch is turned on is expressed by the following equation: $$\begin{equation*} \begin{array}{c} {i\ \left(t \right) = \frac{{{{V}_{charge}}}}{{\sqrt {\frac{1}{{LC}} - {{{\left({\frac{R}{{2L}}} \right)}}^2}} }}\ {{e}^{ - \frac{R}{{2L}}t}}\sin \sqrt {\frac{1}{{LC}} - {{{\left({\frac{R}{{2L}}} \right)}}^2}} t} \end{array} \tag{1} \end{equation*}$$ where $t$ is the elapsed time, $C$ is the capacitance of the capacitor, ${{V}_{charge}}$ is the voltage at both ends of the capacitor just before turn-on, $L$ is the self-inductance of a dual coils, and $R$ is the DC resistance of the circuit. Since the self-inductance of the magnetizing coil is generally large, the following equation holds in many cases: $$\begin{equation*} \begin{array}{c} {R\ < 2\sqrt {\frac{L}{C}} } \end{array} \tag{2} \end{equation*}$$

Fig. 1.

Basic magnetization circuit (a) without freewheeling diode (b) with freewheeling diode.

In this case, since the transient current is damped and oscillates as shown in Fig. 2, a magnetic field that reverses its polarity significantly is generated in a short time by passing the transient current to the magnetizing coil, and a HTS bulk is hardly magnetized. Therefore, as shown in Fig. 1(b), a freewheeling diode must be inserted into the magnetizing circuit to return the reverse polarity current to provide a unipolar magnetic field to the HTS bulk.

Fig. 2.

LCR transient in a magnetized circuit without freewheeling diode.

The magnetizing current thus generated rises for a short time and then converges, so that the magnetizing coil does not consume excessive power. Such a steep change in flux density is caused by the magnetizing circuit, and the HTS bulk is prone to flux jumps caused by the flux penetration the bulk when given a strong magnetic field [7]. At that time, the trapped flux density of the HTS bulk decreases significantly, and its trapped flux density distribution deviates from the ideal conical shape. As shown in (1), the magnetizing current depends on the values of $L$, $C$, and $R$ of the magnetizing circuit. Nevertheless, it is difficult to improve the trapped magnetic flux density distribution of the HTS bulk in response to the application of a pulse magnetic field because the transient current changes exponentially steeply even when the circuit constant is varied in the same way. In order to use PFM in rotating machines, improvement of the trapped magnetic field characteristics is an important issue. To solve this problem, we have developed a magnetization technique using a pulse magnetic field that the HTS bulk easily traps, rather than a pulse magnetic field that depends on the magnetization circuit. This is the waveform control pulse field magnetization (WCPM) method [8], [9], [10], [11], [12]. In particular, the negative-feedback-WCPM (NFB-WCPM) method, in which the magnitude of the pulse field is negatively feedback controlled based on the magnetic flux that enters the HTS bulk while it is being magnetized, significantly improves the trapped flux density of the HTS bulk [12]. In this paper, we show the experimental results of the trapped magnetic flux density by single PFM at 40 K.

SECTION II. Experimental Condtions

A. Sample Setup

The experimental setup is the same as Fig. 1 in [11]. The sample is a GdBCO bulk (GdBa₂Cu₃O_6.9 70.9 wt%, Gd₂BaCuO₅ 19.2 wt%, Ag 9.4 wt%, Pt 0.5 wt%, Nippon Steel) of 45 mm in diameter and 19 mm thickness, encased in a reinforcing stainless-steel ring and placed between a dual vortex-type copper coil. Each coil is 84 mm in diameter and 20 mm thickness and made of 10 turns and 19 layers of 2 mm copper wire. The self-inductance of the dual coils in series was L = 1.28 mH. This arrangement has been made to reproduce the internal layout of an axial-type HTS motor [2].

Regarding the cooling system, a GM cryocooler (Cryomech AL330) was used to cool down the bulk sample to 40 K from the side, using thermal conductors shown by Fig. 1 in [11]. We decided five characteristic regions of the bulk: the growth sector (GS), the growth sector boundary (GSB), the growth sector edge (GSe), the growth sector boundary edge (GSBe), and the center of the bulk, and fixed a Hall element (Toshiba THS118) at each position on the top surface of the bulk to measure the penetrating flux density (Fig. 3). Another Hall element was placed in the center of the bulk bottom surface so as not to interfere with the intrusion flux density measurement and was used for negative feedback control. The center of each Hall element was placed 2 mm away from the surface of the bulk sample in the c-axis direction. The temperature of the bulk during PFM was measured by a Cernox sensor placed at the GSB of the bulk bottom surface.

B. Waveform Control Pulse Field Magnetization Technique With Negative Feedback

As with conventional PFM power supply, it for realizing WCPM consists of a large capacitor, the magnetizing coils, and a small resistance. The major difference between the two is the replacement of the mechanical switch shown in Fig. 1 with a semiconductor switch for energizing and interrupting the pulse current [12]. Mainly because of the need for higher withstand voltages than the high voltages required for the HTS bulk magnetization to protect it against voltage surges, we employed IGBT (insulated gate bipolar transistors) for the semiconductor switches, which are opened and closed many times via gate drivers during PFM to shape the pulse magnetic field waveforms. Due to the large self-inductance of the magnetizing circuit, surge voltage due to counter electro-motive force is generated when the pulse current is applied or interrupted which may destroy the semiconductor switch. The solution to this problem is a key technology for the practical use of WCPM for the HTS bulk. In general, the magnitude of the surge voltage increases as the pulse current is applied or interrupted for shorter durations, so we decided waveform control with a period of 1 ms, which was sufficiently short for the duration of single PFM. Despite more than 1000 experiments under those experimental conditions, our PFM power supply has never broken down since it was completed and has been working properly.

When the IGBT interrupts the pulse current, the current supply from the capacitor bank to the magnetizing coils is also interrupted. However, the magnetizing circuit exhibits an LCR transient response, and the current through the magnetizing coils does not decrease significantly during the maximum 1 ms when the IGBT interrupts the current because the reverse current is returned to it by the freewheel diode. Adjusting the duty ratio involved in opening and closing the IGBT can change the shape of the pulse magnetic field. Although it depends on the values of $L$, $C$, and $R$ of the magnetizing circuit, it allows some freedom in shaping the pulse waveform by arbitrarily changing the duty ratio of the IGBT control signal during magnetization. This is thanks to the freewheel diode shown earlier, which allows the counter electro-motive force of the magnetizing coils to be effectively used for PFM.

The magnetic state of the bulk is difficult to estimate because it changes dramatically when flux jumps occur. We have shown in previous experiments that the HTS bulk can achieve high trapped magnetic flux density by controlling flux jumps with WCPM [9]. By the way, the magnetic state of the bulk changes drastically before and after flux jumps, and especially the unstable state during flux jumps requires dynamic control of the intrusion field by WCPM in order to obtain high trapped flux density. We have performed PID-controlled WCPM using the intrusion magnetic flux density read from a Hall element fixed on the surface of the HTS bulk as a negative feedback input, and have shown that it can obtain a high trapped magnetic flux density, comparable to that obtained by magnetization in a static magnetic field, by appropriately controlling the intrusion magnetic flux density. Our pulse field magnetizing power supply has the PID control circuit shown in Fig. 4, which redetermines the duty ratio of the control signal $u(t)$ of the IGBT that determines the pulse field waveform every 1 ms, using the pre-defined target flux density ${{B}_{target}}$ as $e(t)$ and the flux density from the magnetic field currently penetration the bulk as $y(t)$. However, because the waveform control time is relatively short, the integral term is not used in practice, and PD control is used.

Fig. 3.

Schematic diagram of the sensor arrangement on the bulk surface.

Fig. 4.

PID block diagram for negative feedback control in a WCPM power supply.

SECTION III. Results and Discussions

A. Pulse Field Magnetization Without Rapid Decrease in Magnetic Flux Density

Fig. 5 shows the magnetic flux density trapped by the GdBCO bulk when it was cooled to 40 K and magnetized once by a single NFB-WCPM with 13.1 kJ of magnetizing energy. The pulse current reached a maximum 8.7 ms after the start of magnetization and then decreased. However, the intrusion magnetic flux density measured at the center of the bulk surface reaches about 3.95 T 11 ms after the start of magnetization, showing a time lag between the pulse current change and the time. The magnetic flux density once slightly decreased and then slightly increased again, reaching a maximum magnetic flux density of 4.05 T approximately 87 ms after the start of magnetization. Thereafter, the magnetic flux density decreased slowly to about 3.79 T after 250 ms, a decrease of only 5.4%. The reason why the change in pulse current does not coincide with the change in magnetic flux density penetration the bulk sample is not only the diffusion rate of the magnetic flux penetrating, but also the magnetic field produced by the reverse current through the freewheeling diode that is flow. In addition, the behavior of the magnetic field filling the space around the HTS bulk sandwiched between the dual vortex-type copper coils should also be considered as a factor.

Fig. 5.

Penetrating magnetic flux density without rapid decrease by the single NFB-WCPM on the GdBCO bulk between (a) 0 and 250 ms, (b) 0.25 and 5 sec.

In Fig. 5(a), the fact that the magnetic flux density measured at the center of the bulk sample surface and in the GS and GSB regions is almost constant may give the illusion that flux creep is not occurring. However, flux creep is occurring because the pulse current continues to be supplied from the capacitor bank to the magnetizing coils, keeping the magnetic flux density constant. The pulse field magnetizing power supply is allowing almost as much magnetic flux to enter the bulk from the magnetizing coils as is lost thereby. In other words, the PID parameters appropriately set for dynamic control in NFB-WCPM realized a constant magnetic flux density at the center of the HTS bulk surface, as if a static magnetic field were applied by a superconducting magnet. In this experiment, the magnetic flux density penetration the HTS bulk decreased as the charge stored in the capacitor bank was used up. The magnetic flux density measured at the pulse current and at the center continued to decrease slowly until about 2 seconds after the start of magnetization, and the decrease in magnetic flux density continued after the current supply was cut off, but the change remained gradual. Finally, with only one pulse field of magnetization, we measured a trapped magnetic flux density of 3.23 T at the center of the bulk surface. That is, 81.8% of the maximum magnetic flux density of the magnetic field penetrating the HTS bulk was trapped. The fact that the decrease in the magnetic flux density was suppressed to 18.2% is since excessive magnetic flux density was not applied during the PFM, it can be said that the PFM was performed with less burden on the HTS bulk. In this experiment, the trapped magnetic flux density in the GS and GSB regions was 2.12 T and 2.11 T, respectively, which is almost the same value, suggesting that good magnetization of the conical shape magnetic flux density distribution was achieved. In contrast, in the conventional PFM at 40 K, the bulk sample never trapped the magnetic field in a conical shape, and the maximum trapped magnetic flux density in the center was 1.17 T when trapped in a conical trapezoidal shape, while the GS and GSB regions were 1.18 T and 1.12 T, respectively. Therefore, the maximum trapped magnetic flux density of 3.23 T obtained by the NFB-WCPM is 2.76 times larger than the best result by conventional PFM and is very large for this bulk sample, and together with the conical shape of the flux density distribution, the good trapped magnetic field is obtained.

B. Maximum Trapped Flux Density of 4 T by a Single NFB-WCPM

Fig. 6 shows the results of a single NFB-WCPM with a magnetization energy of 17 kJ. In this experiment, we achieved a central trapped magnetic flux density of 3.88 T with a maximum applied magnetic flux density of 5.44 T. The GS region was 2.41 T, 4.6% higher than the GSB region, which was 2.3 T. However, the two regions were roughly equal, and the magnetic flux density distribution can be regarded as a slightly bulging cone. This maximum magnetic flux density of close to 4 T after only 2 seconds of magnetization brings the HTS bulk one step closer to practical application and demonstrates once again the usefulness of the NFB-WCPM. The major difference between the results of this experiment and those of Fig. 5 and the conventional PFM experiment is that the magnetic flux density at the center of the HTS bulk increased slowly after the pulse current to the magnetizing coils began to decrease from its maximum peak, and reached its maximum magnetic flux density after a sufficient time had elapsed. This behavior is not possible with conventional PFM. The pulse current showed sometimes steep and small increases with time, thereby increasing the penetration magnetic flux produced by the magnetization energy supplied by the capacitor bank. In addition, as explained in the previous section, the reverse current through the freewheel diode created a new intruding magnetic flux, as well as the possible effect of the magnetic field already existing around the magnetizing coils and the HTS bulk. In this experiment, even though the magnetization energy is larger than in Fig. 5 and the maximum current is not much different, the total flux applied to the bulk is expected to be higher because the current itself flowing through the magnetizing coils during magnetization is larger.

Fig. 6.

Experimental result by the single NFB-WCPM with a maximum trapped magnetic flux density of 3.88 T.

C. Comparison of Pulse Field Magnetization Methods for Magnetization Energy

In contrast to conventional PFM, which determines the pulse field waveform depending on the physical quantities of the components in the magnetization circuit and whose waveforms all show exponentially steep changes, WCPM has the advantage that the HTS bulk generates a pulse field waveform that easily traps the penetration magnetic flux. We performed a number of PFM experiments at 40 K and examined the magnetization properties versus magnetization energy for each PFM method. Fig. 7(a) and (b) show plots of the trapped magnetic flux density measured at the center of the GdBCO bulk sample surface magnetized by conventional PFM, WCPM, and NFB-WCPM methods at 60 K and 40 K, respectively. Significant trapped magnetic flux densities were obtained for the bulk sample at both temperatures due to magnetization energies above 3.5 kJ. At 60 K, the bulk sample obtained a maximum trapped magnetic flux density at 3.5 – 4 kJ by conventional PFM, but the trapped magnetic flux density decreased with increasing magnetization energy. This indicates that although conventional PFM requires about 4 kJ of magnetizing energy to achieve a significant trapped magnetic flux density, the energy cannot be effectively retained in the HTS bulk, and the energy applied is wasted. In contrast, WCPM shows that the bulk sample can obtain several times higher trapped magnetic flux density than conventional PFM. For the range of magnetizing energies shown in Fig. 7, WCPM trapped magnetic flux density increases with increasing the energy, indicating WCPM, unlike conventional PFM, allows the HTS bulk to retain higher energy and still have room to spare. NFB-WCPM not only showed the same trend as WCPM, but also tended to obtain higher trapped magnetic flux density than WCPM.

Fig. 7.

Trapped magnetic flux density at the center of the bulk surface by each PFM method at (a) 60 K and (b) 40 K.

On the other hand, at 40 K, conventional PFM showed the same trend as at 60 K, and both the magnitude and the reduction rate of the trapped magnetic flux density became larger. WCPM trapped magnetic flux density, which showed a positive trend at 60 K, showed the same trend as that of conventional PFM, indicating that WCPM lost its superiority. In contrast, NFB-WCPM clearly showed higher trapped magnetic flux density than conventional PFM and WCPM, and the trapped magnetic flux density increased significantly with increasing magnetizing energy. NFB-WCPM differs from WCPM in that it uses the penetration magnetic flux density as a negative feedback control input to sequentially respond to the magnetic state during magnetization, but both use the same method for shaping the magnetic field waveform itself. This suggests that during conventional PFM, probably when flux jumps occur, the magnetic state in the HTS bulk changes more significantly at lower temperatures, which has a greater effect on the trapped magnetic field properties. And it is clear that NFB-WCPM is necessary to trap a strong magnetic field in the HTS bulk by a single pulsed magnetic field below 40 K.

Fig. 8(a) and (b) show plots of the temperature rise observed during magnetization at 60 K and 40 K, respectively. The temperature rise is due to local heating from flux motion in the HTS bulk, but because flux diffusion is faster than thermal diffusion in the type-II superconductors, the temperature rise is not necessarily proportional to the trapped magnetic flux density [13]. The overall trend is that as the magnetizing energy increases, the temperature rise also increases. This can be understood as an increase in the penetration flux the HTS bulk due to the higher magnetizing energy, resulting in greater local heating. Another trend is that the temperature rise increases with a threshold of 4 kJ. When considered in conjunction with the increase in trapped magnetic flux density near 4 kJ shown in Fig. 7, this could be due to an increase in the frequency of flux motion due to increased flux penetration into the HTS bulk or due to flux creep. Fig. 8(a) shows that at 60 K, conventional PFM shows a larger temperature increase than the other methods, with unclear difference between WCPM and NFB-WCPM. Taken together with the results shown in Fig. 7(a), the results with conventional PFM can be understood to indicate that the flux jumps cause a large amount of flux to intrude and leave the HTS bulk, resulting in a large flux diffusion and adiabatic temperature increase. In contrast, the flux jumps in WCPM and NFB-WCPM are controlled to some extent, and the adiabatic temperature rise is suppressed due to slower flux motion compared to conventional PFM.

Fig. 8.

Temperature rise of the bulk by each PFM method at (a) 60 K and (b) 40 K.

In contrast to 60 K, the results at 40 K shown in Fig. 8(b) clearly show that the temperature rise is suppressed in NFB-WCPM, while conventional PFM and WCPM show a similar large temperature rise. The increase in temperature rise and decrease in trapped flux density due to WCPM is due to the fact that the number of magnetic fluxes penetrating the HTS bulk due to flux jumps at 40 K is several times larger than that at 60 K. WCPM, which cannot respond immediately to changes in the magnetic state in the HTS bulk, may not be able to control flux jumps and suppress local heating. NFB-WCPM is expected to be able to control flux jumps when the magnetic flux density in the HTS bulk changes significantly due to flux jumps, because the magnitude of the applied flux density is reduced in as little as 1 ms.

Comparing Figs. 7 and 8, we notice that the increase in trapped magnetic flux density and temperature raise for each magnetization method do not correspond sequentially. At 60 K, there is a difference in the magnitude of the trapped flux density by conventional PFM, WCPM and NFB-WCPM, but the temperature raise due to magnetization is clearly suppressed by waveform control. At 40 K, the temperature rise was somewhat suppressed by the NFB-WCPM, but the trapped flux density increased significantly. The cause of this lack of correspondence between the result of the temperature raise and the increase in the trapped flux density is not clear. However, while the temperature rise in HTS bulk is clearly affected by flux, it does not accurately reflect it. Even if the application of different magnetization methods results in similar temperature raises, there are differences in the way magnetic flux penetrates between PFM and WCPM, or between WCPM and NFB-WCPM, which affect the magnetic field trapping characteristics.

SECTION V. Conclusion

We have performed WCPM on a disk-shaped GdBCO bulk which is 45 mm in diameter and 19 mm thickness at 40 K and clarified its magnetic field capturing characteristics. NFB-WCPM applied a short but constant magnetic field to the HTS bulk and achieved more than around 3 times the trapped magnetic flux density and better field distribution than conventional PFM. The HTS bulk obtained a maximum trapped magnetic flux density of about 4 T and a nearly conical magnetic flux density distribution with a magnetization energy of 17 kJ. While it was difficult to improve the trapped magnetic flux density with WCPM at 40 K, NFB-WCPM achieved a higher trapped magnetic flux density than the conventional PFM by a factor of several, and the temperature rise was suppressed. In order to realize high power and power density in the HTS bulk synchronous rotating machines and other quasi-permanent magnet type industrial devices, it is necessary to achieve high field trapping by applying a pulsed magnetic field at 30-40 K. This experimental result is valuable in that it proves HTS bulk is fully feasible for practical use and that the necessary magnetization technology has been developed for this purpose.

ACKNOWLEDGMENT

The authors thank A. A. Caunes, Ph.D. for his help with a part of the experiments at 60 K and for improving how to place thermal sensors.