# Shielding Effect on Flux Trapping in Pulsed-Field Magnetizing for Mg-B Bulk Magnet

Tetsuo Oka, Kengo Yamanaka, Kimiaki Sudo, Longji Dadiel, Jun Ogawa, Kazuya Yokoyama, Walfgang Hässler, Jacques Noudem, Kévin Berger, Naomichi Sakai, et al.

► To cite this version:

Tetsuo Oka, Kengo Yamanaka, Kimiaki Sudo, Longji Dadiel, Jun Ogawa, et al. Shielding Effect on Flux Trapping in Pulsed-Field Magnetizing for Mg-B Bulk Magnet. Journal of Physics: Conference Series, 2021, 33rd International Symposium on Superconductivity (ISS2020) 1-3 December 2020, Tsukuba, Japan, 1975, pp.012019. 10.1088/1742-6596/1975/1/012019. hal-03361048

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# Shielding Effect on Flux Trapping in Pulsed-Field Magnetizing for Mg-B Bulk Magnet

To cite this article: T Oka et al 2021 J. Phys.: Conf. Ser. **1975** 012019

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# Shielding Effect on Flux Trapping in Pulsed-Field Magnetizing for Mg-B Bulk Magnet

T Oka¹, K Yamanaka¹, K Sudo¹, L Dadiel¹, J. Ogawa², K Yokoyama³, W Häßler⁴,
J Noudem⁵, K Berger⁶, N Sakai¹, M. Miryala¹ and M Murakami¹

¹ Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-Ward, Tokyo 135-8548, Japan

² Niigata University, 8050 Ikarashi-Ninocho, Nishi-Ward, Niigata 950-8151, Japan,

³ Ashikaga University, 268-1 Omae-cho, Ashikaga 326-8558, Japan

⁴ IFW Dresden, 20 Helmholtzstr., Dresden 01069, Germany

⁵ Caen University, rue Louis Aragon BP78 50130 Cherbourg-Octeville, France

⁶ Lorraine University, 54 506 Vandœuvre-lès-Nancy Cedex, France

**Abstract.** MgB₂ superconducting bulk materials are characterized as simple and uniform metallic compounds, and capable of trapping field of non-distorted conical shapes. Although pulsed-field magnetization technique (PFM) is expected to be a cheap and an easy way to activate them, the heat generation due to the magnetic flux motion causes serious degradation of captured fields. The authors precisely estimated the flux trapping property of the bulk samples, found that the flux-shielding effect closely attributed to the sample dimensions. The magnetic field capturing of Ti-5.0wt% sample reached the highest value of 0.76 T. The applied field which reached the centre of the sample surface shifted from 1.0 T to 1.2 T with increasing sample thickness from 3.67 mm to 5.80 mm. This means that the shielding effect was enhanced with increasing the sample thickness. Moreover, Ti-addition affected the frequency of flux jump happenings. The occurrence of flux jumps was suppressed in 5.0wt%Ti-added sample. This means that the heat capacity of the compounds was promoted by Ti addition.

## 1. Introduction

The field-trapping principle of high temperature superconducting bulk materials (hereafter abbreviated as HTS bulk magnets or bulk magnets) is different from that of conventional permanent magnets such as Nd-Fe-B or ferrite magnets [1], [2], [3]. Since the trapped field of bulk magnets are roughly simulated as what we call pancake coils, one can obtain extremely intense magnetic field by flowing the intense current to the coils composed of superconductors because the electrical resistivity is negligible. Melt-grown bulk materials are regarded as a sort of non-insulated coils. Both systems may be characterized by the rearrangement of superconducting current. Extraordinary intense magnets are realized when they capture the applied fields by field cooling method (FC) from superconducting solenoid magnets [4], [5] or the pulsed-field magnetizing (PFM) technique [6], [7].

Beside the rare earth-based compounds (REBa₂Cu₃O₇-γ system, RE means rare earth elements), MgB₂ bulk materials are characterized as its uniform crystal structure and resultant uniform field trapping [8]. Although the *T*<sub>c</sub> is low as 39 K, the field distribution with no distortion brings its advantageous applications which demand homogeneous field spaces [9], [10], [11].

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
<table><caption>**Table 1.** Specification of bulk samples</caption><thead><tr><td>Sample</td><td>Ti addition (wt%)</td><td>Thickness (mm)</td><td>Aspect ratio</td></tr></thead><tbody><tr><td>MH104b</td><td>2.5</td><td>3.30</td><td>6.06</td></tr><tr><td>MH104d</td><td>2.5</td><td>5.55</td><td>3.60</td></tr><tr><td>MH113a</td><td>5.0</td><td>3.23</td><td>6.19</td></tr></tbody></table>

20 mm in diameter, Hot-pressed, Single-layer

Dr. Häßler *et al.* in IFW Dresden

Although the world-highest record of 1.61 T has been reported [12], the thermal instability originated from the low specific heat and high thermal propagation coefficient due to “metallic” character has caused serious flux jump phenomena in PFM processes, as compared with FC-activated 5.4 T [13].

The authors have been attempting to overcome the crucial drawbacks to obtain high field trapping in $MgB_2$ bulk magnets. The experimental approaches were proposed as a couple of ways of material processing and application procedure of magnetic pulses. On the other, it was reported that the flux jumps assist the flux invasion at the very beginnings of field application against the critical state model [14], [15]. Thus, the flux jump is the essential property to be controlled. The authors analysed various flux jump matters which dissipated the trapped fields from the bulk magnets. Since the Ti-addition results in the enhancement of $J_c$ [16], in this paper, the authors preliminarily notice the flux shielding with sample thickness and effect of metallic Ti-addition to estimate the flux jump phenomena.

## 2. Experimental procedure

### 2.1 $MgB_2$ sample preparation

The samples were processed by in-situ mode with using hot-press in IFW Dresden. Since the Ti-addition was effective for enhancing $J_c$ and surface shielding of bulk magnet, the authors chose the 2.5 wt% and 5.0 wt%Ti-added samples. Table 1 shows the specifications of the samples with varying the thickness and Ti-content. The detailed were shown elsewhere [17], [18].

### 2.2 Pulsed field magnetization and magnetic flux motions

As shown by the illustration and photos in Figure 1, the authors conducted the PFM activation with use of a two-stage GM-cryocooler. The pulse-fields of 0.6 - 2.0 T with a rise time of 10 ms were fed from 60 mF condenser to the cryocooled bulk $MgB_2$ samples with use of 112-turn copper coil, which was cooled in liquid nitrogen vessel to reduce its resistance. The coil constant is 1.26 mT/A. The magnetic field data were measured at the centre of the bulk surface by a Hall sensor BHT921 (F. W. Bell). The

<figure><img src="image_5.png" /><figcaption>**Figure 1.** Illustration of equipment structure (a), views of experiment (b) and the bulk sample surface (c).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 2. Definition of parameters.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 3. Penetration field $B_p$.</figcaption></figure>

temperatures before starting PFM were settled at 14 K which was controlled at the cold stage behind the bulk sample.

As shown in Figure 2, the parameters were defined as the field penetration ratio $B_p/B_A$ and field trapping ratio $B_T/B_p$ to estimate the flux motion during the PFM processes, where $B_A$ and $B_p$ were the highest applied field calculated from the voltage of shunt resistor and the highest flux penetration measured by the Hall sensor, respectively [18], [19]. $B_T$ means the final trapped field at the end of time-changing profiles. The ratio of $B_p/B_A$ indicates the shielding effect against the flux invasion into the sample and introduction of fluxoid in the mixed state. The ratio of $B_T/B_p$ indicates the flux-trapping which reflects the heat generation and propagation in the sample.

### 3. Results and Discussion

#### 3.1 Penetration fields

Figure 3 shows the applied field dependence of the penetration fields $B_p$ with varying thickness and Ti-content. The lines deviated beneath the line of $B_p/B_A=1$, suggesting the shielding effects which were affected by the thickness and not by Ti-addition. In the low field region, the $B_p$ of thick sample clearly shifted to be small. And plotted lines aligned parallel to each other, which means that the shielding effect remains as it was to its high field region.

#### 3.2 Trapped field and field trapping ratio

Figure 4 and 5 show the applied field dependence of the trapped fields $B_T$ as functions of sample thickness (a) and Ti-content (b), respectively. The trapped flux reached the highest peak of 0.76 T at 1.3 T application to thick sample. In Figure 4, one sees apparent shift of data plots to high field region as

<figure><img src="image_8.png" /><figcaption>Figure 4. Effect of Sample Thickness on $B_T$.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 5. Effect of Ti-addition on $B_T$.</figcaption></figure>
increasing sample thickness. Although the shift of field invasion is natural in low field region before showing the peaks, remarkable is that the applied field which indicates drastic decrease due to flux jumps clearly shifted to high field region as well. This means that the flux jump might be suppressed in thick or well-shielded sample.

In Figure 5, the field trapping property is apparently different. One sees no significant changes in the data except for the resultant trapped field between different Ti-content samples in the higher field regions more than 1.0 - 1.1T. We observed the apparent improvement in field trapping in Ti-5.0wt% sample. This surely suggests the suppression of flux jump by Ti addition. The field-trapping $B_T$ strongly relates to the applied field $B_A$. On the other, the penetrated flux $B_P$ at the center should affect the local heating and resultant flux jumps. We need to estimate the effect between $B_P$ and $B_T$ soon after.

### 3.3 Flux motion during PFM

The time-varying profiles of PFM operations were shown in Figure 6, referring to $B_T$ data in g. The motions exhibit clear classifications to we call no-flux flow (NFF) behaviour and flux jump (FJ) regions at high and low trapping phenomena, respectively. NFF means the flux behaviour which shows no apparent decay in $B$ after showing $B_P$. FJ means the state which shows apparent sudden drops in $B$ on the profiles. NFF suggests us the most ideal flux trapping with less heat generation, showing no-significant differences between for the flux motion. This shows that the flux motions are all similar in

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Flux motion in NFF (a-c) and FJ (d-f) in field trapping profiles (g).</figcaption></figure>
low field application regions. However, flux jumps frequently happen to degrade $B_T$ values in high field region with crucial heat generation.

There are two things to note. The shielding effect by elevating sample thickness has shifted the FJ region to high field region. It would be understandable in the low field region at the very beginning of flux invasion. But, all the data including FJ region shifted to high field with sample thickness even in high field regions. This is consistent to the gaps between the paralleled lines in Figure 3. This may suggest that the shielding effect affects over the range of field application in the experiment. Since sufficient flux invasion causes the high $B_P$ and resultant high $B_T$, the shielding effect and diamagnetic effect should continue to the high field region until FJ appears. Furthermore, we may note that the FJs in Ti-5.0wt% sample exhibit a bit smaller drop than those of others in Figure 6. This may imply that Ti-addition might have suppressed the flux-jump occurrence. We should investigate the thermal properties like specific heat of Ti-added materials should be precisely studied in near future. In the present study, we inspected flux motion only at the centre point of the sample. As the heat generation affect FJ happening, we should detect the FJ on various points on the sample surface in the future.

## 4. Conclusion

Trapped field data during and after the PFM procedure were estimated on the sample thickness and metal Ti-added samples with 2.5 and 5.0wt% at cryocooled 14 K. The field invasion to the sample were influenced by the sample thickness by the shielding effect. The shielding effect remained to high field regions where FJ frequently happened. All the high field trappings in these data exhibited NFF region in all the samples regardless of sample thickness or Ti-content. Even in the FJ region of high field application, flux jumps happened with showing a bit difference between the sudden $B_T$ decreases by FJ.

## Acknowledgments

This work has been partially supported by the project named as Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation of JSPS.

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