Experimental realization of a hybrid trapped field magnet lens using a GdBaCuO magnetic lens and MgB2 bulk cylinder

A hybrid trapped field magnet lens (HTFML) is a promising device that is able to concentrate a magnetic field higher than the applied field continuously, even after removing an external field, which was conceptually proposed by the authors in 2018. This paper presents, for the first time, the experimental realization of the HTFML using a GdBaCuO magnetic lens and MgB2 trapped field magnet cylinder. A maximum concentrated magnetic field of Bc = 3.55 T was achieved at the central bore of the HTFML after removing an applied field of Bapp = 2.0 T at T = 20 K. For higher Bapp, the Bc value was not enhanced because of a weakened lens effect due to magnetic flux penetration into the bulk GdBaCuO material comprising the lens. The enhancement of the trapped field using such an HTFML for the present experimental setup is discussed in detail.


Introduction
Trapped field magnets (TFMs) using superconducting bulks such as REBaCuO (RE: a rare earth element or Y) and MgB 2 have been vigorously investigated for various practical applications; for example, rotating machines, magnetic separation, flywheel energy storage systems and so on [1][2][3]. Superconducting bulk TFMs, in which magnetic flux is trapped by the strong 'vortex pinning effect', are usually magnetized by field-cooled magnetization (FCM) using a high, stationary magnetic field, for which a magnetic field nearly the same or slightly lower than the applied field can be trapped. The trapped field capability of such bulks, as estimated from state-of-the-art J c (B, T) characteristics could exceed 20 T at 20 K in a disk bulk pair [4]. However, the trapped field is limited experimentally by the poor mechanical strength of the brittle ceramic material [5]. A large Lorentz force is developed in the bulk during the magnetization process, which sometimes results in crack formation and propagation, leading to eventual mechanical failure [6,7]. To date, REBaCuO disk bulks have trapped magnetic fields over 17 T by mechanical reinforcement using glass fiber reinforced epoxy resin or shrink-fit stainless steel to reduce the electromagnetic hoop stress [4,8]. A ring-shaped bulk superconductor that can produce uniform, high magnetic fields within the central bore is a strong candidate for compact cryogen-free nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) systems [9][10][11]. The 1 H spectra of toluene with a full width at half maximum of 0.4 ppm (80 Hz) was achieved in the 10 mm room temperature bore in the bulk NMR [10]. The first MRIs using annular EuBaCuO bulks were also reported with a magnetic homogeneity of 37 ppm (peak-to-peak) achieved in a Φ 6.2 mm×9.1 mm cylindrical space with first order shimming [11]. Using this system, a clear 3D image of a chemically-fixed mouse fetus was acquired.
On the other hand, a 'magnetic lens' using cone-shaped superconducting bulks has been investigated, in which a magnetic field is concentrated in the bore of the lens using the 'diamagnetic shielding effect' of superconducting materials and the available magnetic field in the lens is higher than the applied field generated by an external magnetizing coil [12][13][14][15][16][17][18]. For example, a concentrated field of B c =12.42 T has been achieved at 20 K for a background field of B app =8 T using a bulk GdBaCuO magnetic lens [12]. Since the magnetic lens effect vanishes after the applied field decreased to zero, the external magnet must be operated continuously, which consumes energy and is not environmentally friendly.
We recently proposed a new concept of a hybrid trapped field magnet lens (HTFML) [19], consisting of a cylindrical bulk TFM exploiting the 'vortex pinning effect', combined with a bulk magnetic lens exploiting the 'diamagnetic shielding effect'. Using numerical simulations, the HTFML was shown to be able to reliably generate a magnetic field in the central bore of the magnetic lens that is higher than both the trapped field in the single cylindrical bulk TFM and the external magnetizing field, even after the externally applied field decreases to zero. For a REBaCuO magnetic lens and MgB 2 TFM cylinder, the HTFML could reliably generate a concentrated magnetic field of B c =4.73 T with an external magnetizing field B app =3 T. For an HTFML comprised of REBaCuO bulks for both magnetic lens and TFM cylinder, a concentrated magnetic field of B c =13.49 T could be generated with an external magnetizing field B app =10 T, where the temperature of both parts is controlled independently [19]. In addition, the shape of the magnetic lens in the HTFML has been optimized, and the mechanical stress in the cylinder and lens parts has also been estimated during the magnetizing process [20].
In this paper, we present, for the first time, the experimental realization of the HTFML using a GdBaCuO magnetic lens and MgB 2 TFM cylinder, based on the same magnetizing procedure proposed in [19]. The experimental results are compared with the simulated ones and enhancement of the B c value in HTFML is discussed in detail.  , and 60 mm in height (H)) was fabricated using the infiltration method by Experiments Projects Constructions S. R. I., Italy [21,22]. Figure 1(b) shows the cross-section and top view of the GdBaCuO magnetic lens. The GdBaCuO magnetic lens was prepared by the following process: stacked GdBaCuO cylindrical bulks (OD=36 mm, ID=10 mm, H=30 mm), fabricated using the QMG ™ method by Nippon Steel Corporation, Japan [23,24], were machined into a cone-shape of OD=30 mm, ID=10 mm, ID2=26 mm, outer height (OH)=30 mm and inner height (IH)=8.0 mm, as shown in figure 1(b). The dimensions of the bulk magnetic lens were (b) Cross-sectional and top views of the GdBaCuO magnetic lens with slits. When a magnetic field is applied along the +z-axis direction to the GdBaCuO magnetic lens, the magnetic field penetrates from the slits and the shielding current flows as shown by the red arrows. As a result, the magnetic field increases along the +z-direction due to the shielding current.

Experimental procedure
optimized using numerical simulations [20]. Thin slits of width 200 μm was made to disrupt the circumferential flow of the shielding current during the zero-field-cooling (ZFC) process, which plays an important role in magnetic flux concentration for the magnetic lens [19]. When an external magnetic field is applied along the +z-axis direction to the GdBaCuO magnetic lens, the same magnetic field penetrates into the central bore from the slits. The shielding current flows as shown by the red arrows in figure 1(b) and an additional magnetic field exists along the +z-axis direction, mainly due to the counterclockwise shielding current nearest to the central bore. As a result, the magnetic field is enhanced along the +z-axis direction, which is then higher than the applied field.
The GdBaCuO magnetic lens was encapsulated in a stainless steel (SS) holder to prevent fracture of the bulk due to the large Lorentz force during the magnetization process, and was connected thermally to the cold stage of the refrigerator. The MgB 2 cylindrical bulk was reinforced by a SS cylinder (ID=60 mm, OD=66 mm and H=60 mm) and the top SS plate (ID=36 mm, OD=66 mm and H=3 mm), which were effective in preventing mechanical fracture [25,26]. These SS holders apply a compressive stress to the bulk cylinder and bulk lens during the cooling process from room temperature to the operating temperature (e.g. 20 K) due to the difference in the coefficient of thermal expansion between SS and the bulk superconducting materials. Two CERNOX ™ thermometers were attached for monitoring the temperature of the HTFML; one was mounted directly on the top surface of the MgB 2 cylinder, and the other was placed on the top surface of the SS holder of the GdBaCuO lens. Thin indium sheets were inserted between the bulks and the cold stage of the refrigerator (or SS holder) to obtain good thermal contact. The temperature of the cold stage was controlled using a Pt-Co thermometer and a resistive heater, attached to bottom surface of the cold stage. The concentrated field, B c , was measured in the central bore of the HTFML by an axial-type Hall sensor (F W Bell, BHA-921). The HTFML device was placed in a vacuum chamber and then evacuated by a vacuum pump system. Figure 2 shows the time sequence of the external field (left vertical axis), B ex , at the center of the HTFML and the operating temperature (right vertical axis), T, during the magnetizing process of the HTFML. The magnetizing external field, B app , corresponds to the maximum value of B ex . The HTFML device set in the vacuum chamber was inserted into a cryocooled 10 T superconducting solenoid magnet (JASTEC JMTD-10T100). First, the MgB 2 bulk cylinder and GdBaCuO bulk lens were cooled to T=40 K. In this stage, the MgB 2 cylinder is in the normal state and the GdBaCuO lens is in the superconducting state, where the time step (TS) is defined as TS=0. The proof-of-concept experiments of the HTFML were performed according to the following magnetizing process.

Magnetization procedure
(1) The external magnetic field, B ex , was ramped up linearly at +0.222 T min −1 to B app =1−3 T over five steps, where TS of the ascending stage is defined as TS=1-5. This process corresponds to ZFC magnetization of the GdBaCuO lens, in which the magnetic field at the center is essentially higher than B app because of the shielding effect by the magnetic lens.
(2) The temperatures of both the MgB 2 cylinder and GdBaCuO lens were decreased to T=20 K under the applied field B app , with both materials now in the superconducting state. (3) B ex was decreased linearly at −0.011 T min −1 over five steps (TS=6-10) down to zero. During this process, the MgB 2 cylinder was magnetized by FCM and magnetic flux was trapped in the cylinder. A magnetic field at the center of the magnetic lens still remains due to the existence of the trapped field in the MgB 2 cylinder. As a result, the HTFML can reliably generate a magnetic field higher than the trapped field in the single MgB 2 TFM cylinder and B app , even after B ex =0.
Prior to the HTFML experiments, the trapped field properties of the MgB 2 cylinder and the magnetic concentration capability of the GdBaCuO lens were investigated independently using the same time sequence as shown in figure 2 under the external magnetic field of B app =1−3 T, in which either the MgB 2 cylinder or GdBaCuO lens was set on the cold stage.

Trapped field capability of the single MgB 2 cylinder
To confirm the trapped field capability of MgB 2 cylinder, the trapped field properties of the single MgB 2 cylinder was measured. Figure 3(a) shows the time evolution of the external field, B ex , and trapped field, B c , at the center of the single MgB 2 cylinder during the same time sequence shown in figure 2 under an external magnetic field of B app =2.0 T. Figure 3(b) shows the time evolution of the temperatures of the cold stage and the MgB 2 cylinder for the same process. In the ascending stage, the magnetic field, B c , increased linearly with increasing B ex and the magnitude of B c was the same as the external field (B c =B ex =2.0 T) because the MgB 2 cylinder was in normal state (T=40 K). In the descending stage, after cooling to 20 K, the B ex was slowly decreased at a constant rate of −0.011 T min −1 and the FCM process was performed for the MgB 2 cylinder. As a result, a trapped field remained of B c =2.0 T after B ex was decreased to zero due to the conventional vortex pinning effect. In figure 3(b), the temperature of the MgB 2 cylinder was nearly the same as that of the cold stage because of the good thermal contact. Figure 4 shows the TS dependence of the trapped field, B c , at the center of the single MgB 2 cylinder under external magnetic fields of B app =1−3 T. In the ascending stage from TS=0 to 5, the magnetic field increases linearly with increasing TS and the magnitude is the same as the external field because the MgB 2 cylinder is in normal state. In the descending stage of the FCM process, for the applied fields of B app =1.0 and 2.0 T, trapped fields of 1.00 T and 1.98 T, respectively, were achieved at TS=10 without flux creep. On the other hand, for higher applied fields of 2.5 and 3.0 T, the TS dependence of B c after TS=5 gradually decreased and the final trapped field was 2.18 T, which suggests the maximum trapped field capability of the MgB 2 cylinder at T=20 K. The trapped field cannot increase over 2.18 T, even if applied field is higher than 3.0 T. In the conceptual paper [19], B c =2.85 T was predicted at the final step at T=20 K in the bore of MgB 2 cylinder for B app =3.09 T. The lower B c value in the present experiment results from the lower J c (B, T) of the present MgB 2 cylinder, compared with that used in the simulations in [19].

Magnetic shielding capability of the single GdBaCuO bulk lens
The magnetic shielding capability of the GdBaCuO bulk lens was measured using the single GdBaCuO bulk lens during the ZFC process. Figure 5(a) shows the time evolution of the magnetic field, B c , at the center of the single GdBaCuO bulk    Figure 5(b) shows the time evolution of the temperatures of GdBaCuO bulk lens and the cold stage under the same process. In the ascending stage, a clear magnetic field concentration was observed; B c =3.76 T was achieved, which resulted in a magnetic field concentration ratio of B c /B app =1.88. A temperature rise of about 2.1 K took place during ascending stage from 0 to 10 min, originating from magnetic flux penetration into the magnetic lens. When the temperature of the cold stage was set to 20 K, the minimum temperature of the GdBaCuO bulk lens encapsulated by the SS holder was only 26.5 K, which may come from an imperfect thermal contact between the bulk lens and the SS holder. It should be noted that the final B c value was not zero, but a negative one of −0.48 T. This result suggests that some magnetic flux penetrated into the surface of the bulk lens and a residual magnetic field along the -z-direction existed due to the vortex pinning effect. Figure 6 shows the TS dependence of the magnetic field, B c , at the center of the single GdBaCuO bulk lens during the ZFC process under applied magnetic fields of B app =1.0−3.0 T. In the ascending stage from TS=0 to 5, the magnetic field was concentrated by the shielding current. For lower B app =1 and 2 T, B c =2.04 and 3.76 were achieved at TS=5, which correspond to magnetic field concentration ratios, B c /B app , of 2.04 and 1.88, respectively. The B c values increased for higher B app , which were 4.55 T and 5.19 T for B app =2.5 and 3.0 T at TS=5, respectively. However, the magnetic field concentration ratio, B c /B app , gradually decreased due to increased magnetic flux penetration into the bulk lens. For the final stage (TS=10), at which the external field was zero, the B c value increased negatively with increasing B app for the same reason. For all the cases, the minimum temperature of the GdBaCuO bulk lens encapsulated by the SS holder was only 26.5 K. To improve the performance of the magnetic lens, lowering its temperature is necessary.

Realization of the HTFML
Finally, we present the experimental realization of the HTFML using GdBaCuO magnetic lens, combined with the MgB 2 bulk cylinder. Figure 7(a) shows the time evolution of the magnetic field, B c , at the center of the HTFML during the magnetizing process shown in figure 2 under an external magnetic field of B app =2.0 T. Figure 7(b) shows the time evolution of the temperatures measured at each position. In the ascending stage, the B c value reached 3.65 T and then slightly decreased to 3.55 T at the end of the descending stage due to flux flow. The magnetic field concentration ratio, B c /B app , was 1.76 at the end of the ramp. The temperatures of the MgB 2 cylinder and the GdBaCuO bulk lens on the SS holder were 20.0 and 26.5 K, respectively. These results demonstrate the HTFML effect experimentally for the first time. Figure 8 shows the TS dependence of the magnetic field, B c , at the center of the HTFML during the magnetizing process under applied fields of B app =1.0-3.0 T. At the end of the ascending stage (TS=5), the B c value for each B app was nearly the same as that for the single GdBaCuO magnetic lens case, as shown in figure 6. In the descending stage, for B app =1.0 and 2.0 T, the B c value was nearly the same as that at TS=5. On the other hand, for B app =2.5 and 3.0 T, the B c value gradually decreases with increasing TS. As a result, the final B c value for B app =2.5 and 3.0 T was smaller than that for B app =2.0 T. The concentrated magnetic field, B c , at  In the concept paper, in which the HTFML was proposed to be constructed using a REBaCuO magnetic lens and MgB 2 TFM cylinder, a concentrated magnetic field B c =4.73 T was predicted for an external magnetizing field B app =3 T using numerical simulations [19]. However, the maximum B c value was as low as 3.55 T experimentally under the same magnetizing process for B app =2.0 T. This difference occurs for the following reasons. Firstly, the assumed J c (B, T) characteristics of the MgB 2 and GdBaCuO bulks used in the simulations were higher than those of the actual bulks used in the experiments. Secondly, the minimum temperature of the GdBaCuO bulk lens was only 26.5 K, when the temperature of the cold stage was set to 20.0 K. To enhance the HTFML effect for the present MgB 2 cylinder and GdBaCuO bulk lens, the thermal contact between the GdBaCuO bulk lens and the SS holder must be improved. Nevertheless, we have realized the HTFML effect experimentally for the first time. Our final goal is to build and test an HTFML using a GdBaCuO cylinder and GdBaCuO lens, for which a B c value in excess of 10 T (e.g. B c =13.5 T [19]) is predicted for a magnetizing process with B app =10 T. A cryocooled 10 T superconducting solenoid magnet with a large room temperature bore (e.g. 100 mm in ID) has become more readily available in the science and engineering research communities outside of the field of superconductivity. Thus, building on these findings, we aim to provide easily a concentrated magnetic field higher than 10 T in an open space using this HTFML system.

Conclusion
We have presented, for the first time, the experimental realization of a HTFML, based on the device design and magnetizing procedure recently proposed in [19,20]. The important results and conclusions in this study are summarized as follows.
(1) The HTFML effect was demonstrated experimentally using GdBaCuO magnetic lens and MgB 2 TFM cylinder for the first time, such that a magnetic field can be generated in the central bore of the magnetic lens that is higher than both the trapped field in the single cylindrical bulk TFM and the external magnetizing field, even after the externally applied field decreases to zero. (2) A maximum concentrated magnetic field of B c =3.55 T was achieved in the central bore of the HTFML device after removing an applied field of B app =2.0 T at T=20 K. The maximum B c value was smaller than the one estimated by numerical simulations, which results from the lower J c (B, T) and higher operating temperature, compared with those of the numerical predictions. (3) For higher B app , the B c value was not enhanced because of a weakened lens effect due to magnetic flux penetration into the bulk GdBaCuO material comprising the lens. To enhance the HTFML effect, improving the thermal contact between the HTFML and the cold stage and lowering temperature of the GdBaCuO lens and MgB 2 TFM cylinder is necessary for the present setup.