Occurrence of Flux Jumps in MgB2 Bulk Magnets during Pulse-Field Magnetization

The magnetic flux capturing of MgB2 bulk magnets made by spark plasma sintering process has been precisely investigated to clarify the mechanism of flux motions during the pulse-field magnetization processes. The field trapping ratio B T/B P was evaluated as a key parameter of field trapping ability which strongly relates to the heat generation due to the rapid flux motion in the samples. The time dependence of magnetic flux density revealed the actual flux motion which penetrated the samples. The trapped fields B T and field trapping ratios B T/B P of various samples were classified into three regions of ‘no flux flow’, ‘fast flux flow’ and ‘flux jump’ according to the generation of heat and its propagation. A flux jump was observed late at 280 ms from the beginning of PFM process, while the field penetration B P showed its peak at 10 ms. Considering the heat propagation speed, the long-delayed flux jump should be attributed to the macroscopic barriers against the heat propagation to the surface centre of bulk magnet.


Introduction
It is well known that the largely-grown high temperature superconducting (HTS) bulk materials are capable of capturing the magnetic flux under their superconducting state, and of acting as the trapped field magnets (TFM) or bulk magnets [1], [2]. Since the field-trapping ability is linearly improved with lowering temperature, it is quite important to cool the materials beneath 77 K. When we employ the cryo-coolers instead of liquid nitrogen, Tc values of HTS materials are not serious issues to worry about any more, because we can easily attain certain low temperature conditions merely by turning on the switches of cryo-coolers [3].
In addition to the RE-Ba-Cu-O (RE: rare earth elements) family, a simple metallic compound, MgB2, whose Tc = 39 K, is regarded as a promising candidate with various unique characteristics superior to other TFMs [4]. Sintered MgB2 bulk superconductor is a sort of very homogeneous metallic compounds, which may bring us more uniform magnetic field than RE-Ba-Cu-O bulk magnets. This advantage is attributed to longer coherence length than that of oxide superconductors. This would overcome the weak-link problem. Magnesium is one of the common metals, which suggests us low material cost [5], [6]. When considering the magnetic field intensity, the bulk magnets are feasible candidates as intense  [7], [8].
The low specific heat of MgB2 and the narrow temperature margin between Tc and operating temperature causes serious flux jumps, which dissipate the trapped flux in the pulsed field magnetization (PFM) processes [9], [10]. The authors have reported the experimental results on the magnetic flux capturing in the PFM process for the MgB2 bulk magnets made by hot-pressing. Miyazaki et al. reported that the flux invasion depends on the thickness of the piled-up MgB2 plates [11]. Next, the authors showed that the field trapping ratios systematically shift with increasing thickness of stacked samples due to the field-shielding effect [12]. Furthermore, the authors discussed the frequent flux jumps during PFM for the MgB2 samples made by hot-pressing and spark plasma sintering (SPS) [13]. In the paper, we focus on the samples made by SPS, and discuss the high field trapping ratio and its variations. In near future, we would analyze various flux jump phenomena and clarify the mechanism.

Preparation of MgB2 bulk samples
We employed MgB2 bulk magnets selected among the samples which were synthesized by SPS. Table  1 shows the sample specifications. These samples are all genuine MgB2 compounds without any additives. The precursors were sintered by SPS with applying pressure of 50-100 MPa and heat-treated at 900-1200 °C for 1-20 min. The fabrication conditions were different among sintering temperatures, holding time at the highest temperatures, sample thickness, resulted in different densities from 1.45 to 2.62 g/cm 3 . The sample density strongly depended on the sintering temperature, while the pressure does not affect the density of the materials. Among these five samples, the highest density reached 2.62 g/cm 3 . Some samples were not adopted to the experiments because of cracks. The parameter BT/BP was defined as shown in ref. [13]. BP means the highest penetration field measured by the Hall sensor at the center of the bulk surface during the PFM. BT means the final trapped field after PFM. The value of BA means the peak value of applied field, which were calculated from the voltage at the shunt resister. The ratio of BT/Bp indicates the field-trapping ability, and is strongly affected by the generation of heat and its propagation in the sample. The pulse-fields of 0.4 -2.2 T with a rise time of 10 ms were applied by feeding current from 60 mF condenser to the cryo-cooled bulk MgB2 samples with use of 112-turn copper coil. The coil is cooled in the liquid nitrogen vessel to reduce the resistance, as shown in Figure 1c. The coil constant is 1.26 mT/A.  Figure 2, the data shows the trapped fields BT after PFM which were measured at the centre of the bulk surface, as shown in Figure 1. One sees three levels in the data plots. The highest trappings were observed at about 0.7 T, while one sees insufficient field trappings of around 0.4 T for two samples and low field trapping of 0.15 T in wide field range from 0.4 to 2.0 T. We should discuss whether the flux has reached at the centre of the sample or not. Or, we may assume three kinds of Jc values in three levels of 0.7, 0.4, and 0.1 T class field capturing abilities. One may notice that the thickness of the sample would affect the shielding effect to prevent the flux to invade.

Trapped fields and field trapping ratios
These profiles clearly exhibited the flux jump regions where the applied fields exceeded 1.6 T. The low field capturing of I689 might be attributed to a couple of reasons. One might be the strong shielding effect which prevent the flux to invade, and the other might be attributed to low Jc values which could let the flux dissipate. We need further observation on the flux motion throughout the field applications at various locations on the sample surface.   Figure 3 shows the field trapping ratios derived from Figure 2. The data plots exhibit three categories, which reflects the field trapping performances. All the data tends to decrease with increasing applied field, following the shielding effect which was roughly attributed to the thickness of the samples. The highest value reached 95.6% and 88.4% at 1.0 T and 1.2 T for F526 and E116, respectively. As for I690, the value of BT/BP reached 84.1% at 0.8 T. This means that the flux penetration causes no serious heat generation in this excitation process, which we call as 'no flux flow (NFF)'. The NFF regions are observed in other samples and instances. On the contrary, low BT/BP ratios less than 20% were clearly attributed to low Jc value of I689. In Figure 3, I add the dashed circles showing three regions of NFF, FFF, and FJ regions. Figure 4 shows the typical flux trapping behaviours which reflect the flux motion and resultant heat generation. We classified the flux motion regions as NFF, "fast flux flow (FFF)", and "flux jump (FJ)". In Figure 4a, NFF means that the magnetic flux which invaded in the sample are kept as it was without any degradation and heat generation during PFM. As shown in Figure 4b, the drastic decreases of BT/BP with increasing applied field shown in Figure 3 are likely attributed to FFF which are responsible for heat generation. In the FFF region, flux jump would suddenly happen at long-delayed 280 ms at around 1.6 T. Although the mechanism is not precisely clear, yet, the lately-happening flux jump may likely be attributed to the long propagation time of heat, which is responsible for the macrostructure such as cracking, inclusions, dispersion of the second phases, and so on.

Conclusion
The authors have estimated the magnetic flux trapping property of MgB2 samples made by SPS in Caen University by analyzing the parameter of field trapping ratios BT/BP with various values in thickness and density. The field invasion was suppressed in thicker sample than those of thinner ones because of the shielding effects. The invading flux motion is classified to three patterns of NFF, FFF, and FJ regions. Although the applied fields were kept as same intensity as applied in NFF region, the flux trapping drastically decreased in the FFF region with sudden occurrences of FJs. To expand the NFF region to high applied fields, we need further works both in the microstructural material designing and macroscopic development of heat draining techniques in the future.

ACKNOWLEDGMENT
The study has been partially assisted by the overseas challenge program for young researcher project on JSPS. The authors thank Mr. Takeda as a former student in our laboratory for his great efforts.