Improving the properties of GdBCO magnetic lenses by adopting a new design and resin impregnation

Bulk high-temperature superconductors (HTSs) have the potential to generate considerably higher magnetic fields than conventional permanent magnets. Recent improvements to the performance of HTS bulk materials have enabled their size and critical current density to be greatly enhanced by processing [1, 2]. Their mechanical strength and thermal conductivity can also be improved by external reinforcement. HTS bulk magnets can trap magnetic fields of over 17 T at 29 K, demonstrating their potential for use in high-field applications [3].

A magnetic lens is a device made from superconducting bulk material that causes an external magnetic field to converge. When a hollow magnetic lens with a tapered inner diameter is cooled in zero magnetic field, and then a background field is applied, the flux distribution is altered due to the high diamagnetism of the superconductor and the magnetic flux is focused at the center of the lens by the shape of the lens. This enables a static magnetic field to be concentrated by the magnetic lens. Flux concentration has been achieved by employing hollow cylinders made of Nb₃Sn and YBCO superconductors by using the induced current inside the superconductors [4–7]. Magnetic lenses requiring a large scale and current-carrying capacity have been developed that employ a hollow cylinder made from a bulk superconductor for use with a compact high-field magnet for laboratory use. A magnetic lens functions as an insert coil to increase the magnetic field. However, unlike insert coils, magnetic lenses can be easily assembled and can operate without power. A high field gradient forms inside a magnetic lens due to the modified flux distribution. Compact magnet systems with lenses are expected to be utilized in magnetic levitation experiments.

Several studies have investigated the magnetic properties of magnetic lenses. Magnetic lenses made from three different superconductors have been tested. GdBCO and MgB₂ bulks have been machined into magnetic lenses [8–11] and NbTi sheets have been stacked to make laminate lenses [12, 13]. Among these superconductors, GdBCO, with a high upper critical field (B_c2) exceeding 30 T, is the most promising material for magnetic lenses since it exhibits superior current-carrying capacity at high fields.

In a previous study, we designed a large magnetic lens made of GdBCO bulk and performed measurements on it for use in a compact high-field magnet that generates fields of over 10 T [14]. This magnetic lens concentrated the magnetic field to 11 T at 4.2 K. However, the lens was severely damaged by a strong flux jump at high fields. While it still functioned after being damaged, its performance was slightly degraded. In the present study, a new magnetic lens was fabricated with almost the same dimensions so that it could be compared with the previous one. This new lens was impregnated with epoxy resin prior to measurements to prevent it from being damaged.

Figure 1 shows schematic diagrams of machined GdBCO bulks and a photograph of lens 1 (the new lens) and lens 2 (the previous one). Single GdBCO domains were provided and machined by Nippon Steel Co. Ltd. REBCO bulks developed by Nippon Steel are commercialized nowadays [15]. The results in MgB₂ magnetic lenses demonstrate that the critical current densities (J_c) play an important role on the concentrated field [11]. The J_cs of bulk GdBCO exceed 3500 A mm⁻² (30 K/5 T), 5000 A mm⁻² (20 K/5 T) and 8000 A mm⁻² (4.2 K/5 T) [16]. These values are much higher than those of the minimum useful overall current density of 100 A mm⁻² in standard coils, suggesting that REBCO bulk can be used in magnetic lenses that require high J_c at high field. After being enclosed in a copper holder with insulation, lens 1 was impregnated with epoxy resin (Genus, GM-9050). It has almost identical dimensions to lens 2. The main difference between the two lenses is that they contain different numbers of GdBCO bulks. It is difficult to form a magnetic lens from only one bulk due to the size limitation of a single GdBCO domain. Lens 2 was constructed by stacking three thin bulks (figure 1), whereas lens 1 consisted of two thick bulks to prevent stress concentrating at sharp regions on the interface of lens 2. The two magnetic lenses have the same inner and outer diameters. Table 1 lists their dimensions.

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Measurements were performed on the two magnetic lenses using a 12 T superconducting magnet. We used a fiber-reinforced-plastic cryostat to measure the sample in liquid helium (LHe) and a cryostat with a single-stage Gifford–McMahon cryocooler to measure the sample at temperatures of 20 and 30 K. Remanent magnetization was removed by increasing the temperature above 100 K after each magnetization. The magnetic flux density at the center of the magnetic lens, B_center, was measured by a Hall sensor. The background field, B_bg, at the center of the coil was calculated from the magnet current. The concentration ratio, r_con, of the magnetic lens was defined as ΔB_center/ΔB_bg.

Commercial software (OPERA-3D) was used for finite element method simulations. The relative permeability was taken to be very small (μ_r = 10⁻¹⁰) to describe the perfect diamagnetism of superconducting materials. The r_cons calculated by OPERA are listed in table 1; the lower concentration ratio of lens 2 is due to its slightly higher IH.

The key characteristics of a magnetic lens are its magnetic properties, mechanical, thermal and temporal stabilities, concentration ratio and reproducibility. The degradation of lenses 1 and 2 in LHe was first investigated. Figures 2(a) and (b) show r_con and B_center as functions of B_bg in the first and second excitation processes for lenses 1 and 2, respectively. The lenses were charged to 5 T at the same field sweep rate (0.061 T min⁻¹) by zero-field cooling (ZFC). The dash-dotted lines in figure 2 indicate the calculated B_centers of the magnetic lenses. During charging, the calculated B_center varies linearly with B_bg because the relative permeability is assumed to be constant. The measured B_center deviates gradually from the calculated value with increasing B_bg, suggesting that the diamagnetism decreases due to flux penetrating the lens with increasing magnetic field.

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The large change in the r_con at around 0 T may be due to the relation between the magnet current and the magnetic field becoming nonlinear at very low fields due to magnetization. Figure 2(a) shows that the new epoxy resin-impregnated lens exhibited little degradation (0.28%) after the first excitation; it became stable in subsequent measurements (data not shown). In contrast, the r_con of lens 2 dropped by 8.6% at B_bg = 3 T after the first measurement. Some small flux jumps occurred in B_center before B_bg reached 5 T in the first and second excitations. Flux jump is an instability phenomenon in superconductors caused by disturbances. Impregnated lens 1 could be sufficiently cooled when magnetothermal instability occurred. The large magnetic force at high fields may be caused by small movements of various parts of the lens, inducing mechanical instability in the lens. Epoxy resin impregnation is thus an effective method for suppressing the mechanical and thermal disturbances that occurred in lens 2.

HTS bulk material has a low specific heat and a low thermal conductivity at low temperatures, making it easy to induce magnetothermal instability. Partial quenching caused by flux avalanche at high fields is inevitable, especially in LHe. Thus, the concentrated field at the flux jump point is a critical factor in determining the limitations of a magnetic lens. It is necessary to investigate the flux jump field of lenses. Figure 3 shows a plot of B_center as a function of B_bg for lenses 1 and 2. Both lenses were excited by ZFC until flux avalanche occurred and B_bg was then reduced to zero. This result shows that both lenses had flux jumps at B_center ≈ 11 T, even though they had different concentration ratios. Lens 1 had a higher r_con at the flux jump field than lens 2 because lens 2 was cracked prior to this measurement. The results suggest that lens 1 had better magnetic performance even though GdBCO lenses finally tend to be partially quenched at fields above 11 T at 4.2 K.

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Figure 4 shows the B_center of lens 1 as a function of time at 20 and 30 K. The magnet was excited to 7 T with a field sweep rate of 0.244 T min⁻¹ by ZFC. In contrast to the results at 4.2 K shown in figure 3, the concentrated field exceeded 11 T with no flux jumps. Flux jumps were suppressed because the heat capacity and the conductivity of the HTS bulk increased with increasing temperature. The highest concentrated field of 13 T was achieved with no flux jumps by ZFC at 20 K. Even at 30 K, B_center still reached 12.1 T. These results demonstrate that GdBCO lenses can be used in high fields above 10 T. The lower B_center at 30 K is due to the J_c behavior of superconductors. The r_con is influenced by the J_c of the bulk material. In contrast to the value of r_con of lens 2 at 20 K (1.55), the improved lens 1 had a higher value of 1.86 due to less flux leak than that from the cracks in lens 2.

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The magnetic relaxation in HTS materials due to flux creep usually exhibits an approximately logarithmic time dependence. Figure 5 shows the decay of the normalized B_center of lens 1 at three different temperatures. B_bg increased to 5 T with ZFC and then remained constant for some time in each measurement. The time at which B_bg reached the set value was taken to be t = 0. B_center decayed faster at higher temperatures. Figure 5 also shows fitted curves for the magnetization decay at different temperatures. The Kim–Anderson approach was applied to calculate the pinning energies as a function of the relaxation rate S =− kT/U₀ [17, 18]. U₀ was about 18, 32 and 35 meV at 4.2, 20 and 30 K, respectively. The results agreed well with the pinning energies reported in other REBCO bulk superconductors [19]. Extrapolation to 4.2 K indicated that the B_center of the lens dropped by only about 0.1% per hour after 5500 s. This suggests that this magnetic lens has the potential to be used in some applications, such as neutron scattering and a pulsed field, but not those (e.g., nuclear magnetic resonance and magnetic resonance imaging) that require a very high temporal stability with the drift <10⁻⁸ h⁻¹.

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In this study, a new GdBCO lens was fabricated for a compact high-field magnet. It exhibited stable performance at high magnetic fields. This GdBCO lens was optimized and impregnated with epoxy resin and it was compared with a previously fabricated lens. Its magnetic performance (i.e., concentration ratio, stability and reproducibility) was measured. Epoxy resin impregnation suppressed flux jumps caused by mechanical and thermal disturbances and prevented degradation in the first excitation. However, flux avalanches occurred in both GdBCO lenses at B_center > 11 T at 4.2 K. Flux jumps were suppressed at higher temperatures; the maximum concentrated field of 13 T was achieved with no flux jumps by ZFC at 20 K. The concentrated field at a B_bg of 5 T dropped by only about 0.1% per hour after 5500 s at 4.2 K. These results demonstrate that the performance of the impregnated GdBCO lens is sufficiently stable for it to be used in a compact high-field superconducting magnet.

This work was supported in part by Kakenhi (Grant No. 20656015).