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Realisation of Hybrid Trapped Field Magnetic Lens (HTFML) consistingof REBCO bulk lens and REBCO bulk cylinder at 77 K
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14th European Conference on Applied Superconductivity (EUCAS 2019)
IOP Publishing
Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

Realisation of Hybrid Trapped Field Magnetic Lens (HTFML)
consisting of REBCO bulk lens and REBCO bulk cylinder at
77 K
S Namba1, H Fujishiro1, T Naito1, M D Ainslie2 and D Zhou3
1

Department of Physical Science and Materials Engineering, Faculty of Science andEngineering, Iwate University, 4-3-5 Ueda Morioka, Japan2
Bulk Superconductivity Group, Department of Engineering, University ofCambridge, Trumpington Street, Cambridge CB2 1PZ, UK
3
Department of Physics, Shanghai University, Shanghai, 200444, China
E-mail: g0318128@iwate-u.ac.jp

Abstract. A hybrid trapped field magnet lens (HTFML) can reliably generate a concentrated
magnetic field, Bc, in the centre of the magnetic lens higher than the trapped field of thetrapped field magnet (TFM) and the applied magnetic field, Bapp, even after the external
magnetizing field decreased to zero. In this paper, the performance of HTFMLs consisting of
EuBaCuO bulk TFM with various heights and a GdBaCuO bulk magnetic lens wasinvestigated at 77 K using liquid nitrogen. A concentrated magnetic field of Bc = 0.80 T wasachieved at the centre of the HTFML for the tallest TFM after removing an applied magnetic
field of Bapp = 0.50 T. The influence of the height of the outer TFM cylinder on the final
concentrated field was studied experimentally and discussed using numerical simulation.

1. Introduction
REBaCuO (where RE is rare earth element or Y) bulk superconductors have a potential to trap
magnetic fields much higher than that of a conventional Nd-Fe-B magnet. Thus, the magnetized
REBaCuO bulk can be used as a promising compact, high-strength trapped field magnet (TFM) for
many engineering applications. The world record magnetic field of 17.6 T at 26 K was achieved in a
GdBaCuO disk pair reinforced by shrink-fit stainless steel [1]. Furthermore, the trapped field of 4.3 T
was generated in a GdBaCuO disk pair even at 77 K [2]. An EuBaCuO ring-shaped bulk
superconductor is suitable for practical applications such as a nuclear magnetic resonance (NMR)
spectrometer and magnetic resonance imaging (MRI) equipment because of its low relative magnetic
permeability (𝜇r = 1.0013), compared with that of GdBaCuO (𝜇r = 1.0194) [3–5].
In addition, a ‘magnetic lens’ using cone-shaped bulk superconductors has been investigated, inwhich a magnetic field is concentrated in the bore of the lens using the ‘diamagnetic shielding effect’of superconducting materials and the magnetic field in the lens is higher than the applied field
generated by an external magnetizing coil [6–11]. A higher concentrated field of Bc = 12.42 T has beenachieved at 20 K for a background field of Bapp = 8 T using a bulk GdBaCuO lens [6]. Using an MgB2
magnetic lens, Bc = 2.1 T was also achieved at 17 K for Bapp = 1 T [12].
We proposed a new concept of a hybrid trapped field magnet lens (HTFML) in 2018, which
consists of a TFM cylinder exploiting the ‘vortex pinning effect’, combined with a bulk magnetic lensContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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14th European Conference on Applied Superconductivity (EUCAS 2019)
IOP Publishing
Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

exploiting the ‘diamagnetic shielding effect’ [13]. The HTFML can reliably generate a concentrated
magnetic field in the centre of the magnetic lens higher than the trapped field of the TFM and theapplied magnetic field, even after the external magnetizing field decreases to zero. Very recently, we
confirmed the experimental realization of the HTFML using a GdBaCuO magnetic lens and MgB2
TFM cylinder [14], in which a maximum concentrated magnetic field of Bc = 3.55 T was achieved at
the central bore of the HTFML device after removing the applied field of Bapp = 2.0 T at T = 20 K.
It is better for the HTFML consisting of both REBaCuO magnetic lens and TFM cylinder toachieve higher HTFML effect. In this paper, the performance of HTFML consisting of a GdBaCuO
bulk magnetic lens and EuBaCuO bulk TFM cylinder was investigated at 77 K using a liquid nitrogen.
2. Experimental Procedure
Figure 1 shows the experimental setup for the HTFML device. As outer bulk cylinder, three ringshaped EuBaCuO bulks were stacked (TFM-A, B and C), which were fabricated by QMGTM methodby Nippon Steel Corporation, Japan [15]. The dimension of the TFM-A and C is 60 mm in outer
diameter (OD), 36 mm in inner diameter (ID) and 17 mm in height (H). The TFM-B is 60 mm in OD,
36 mm in ID and 20 mm in H. Each EuBaCuO ring bulk was reinforced by an Al alloy ring 5 mm inthickness (70 mm in OD, 60 mm in ID) with the same height of each bulk, which is a suitable material
for the reinforcement of the bulk applied to NMR apparatus because of non-magnetic and higher
mechanical strength [3]. A GdBaCuO magnetic lens was prepared by the following process: stacked
double GdBaCuO cylindrical bulks (OD = 36 mm, ID = 10 mm, H = 30 mm) fabricated by QMGTM
method were machined into a cone-shaped lens (OD = 30 mm, ID = 10 mm, ID2 = 26 mm, outerheight (OH) = 30 mm and inner height (IH) = 8 mm), as shown in Fig. 1(b). The dimensions of thebulk lens were optimized using numerical simulations [16]. Thin slits 200 μm in width were made todisrupt the circumferential flow of the shielding current during the zero-field-cooled magnetization(ZFCM) process. The GdBaCuO magnetic lens was encapsulated in a stainless steel (SS) holder toprevent mechanical fracture from the Lorentz force. The time evolution of the concentrated magnetic
field, Bc, at the central bore of the HTFML was measured by an axial-type Hall sensor (F. W. Bell,
BHA-921). The similar experiments were performed for the case of double TFMs (TFM-A and B) andsingle TFM (TFM-B).
Since magnetic lens and TFM cylinder are made of the similar REBaCuO materials, an individual
temperature control is necessary to realize the HTFML effect. Figure 2 shows the time sequence of theexternal magnetic field, Bex, and the temperatures, T, of the EuBaCuO TFM cylinders and GdBaCuO
magnetic lens during the magnetizing procedure, which comprises the following five stages.
(1) The long outer glass fibre reinforced plastic (GFRP) container (96 mm in OD, 80 mm in ID) was
set in the room temperature bore (100 mm in diameter) of the cryocooled superconducting solenoid
magnet (170 mm in OD, 120 mm in ID, 200 mm in H, JASTEC JMTD-10T100). The GdBaCuO
magnetic lens encapsulated by SS holder was set in the inner GFRP container (35 mm in OD, 33
mm in ID), and was placed at the centre of the outer GFRP container. The liquid nitrogen waspoured into both GFRP containers.
(2) The external magnetic field, Bex, was linearly ramped up to the maximum magnetic field of
Bapp = 0.50 T at +0.222 Tmin−1. This process corresponds to ZFCM for the GdBaCuO lens, inwhich the magnetic field at the central position is higher than Bapp because of the shielding effect by
the magnetic lens.
(3) After Bex reached to Bapp = 0.50 T, the EuBaCuO TFMs in the plastic container were immersed
slowly to the bottom of the outer GFRP container filled with liquid N2.
(4) Bex was decreased linearly at −0.222 Tmin−1 down to zero. During this process, the outer EuBaCuO
TFMs were magnetized by field-cooled magnetization (FCM) and magnetic flux was trapped. A
magnetic field at the centre of the magnetic lens still remains due to the existence of the trappedfield in the EuBaCuO TFMs.
(5) As a result, the HTFML can reliably generate a magnetic field higher than the trapped field in the
EuBaCuO TFMs and Bapp, even after Bex = 0.

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14th European Conference on Applied Superconductivity (EUCAS 2019)
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Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

Figure 1. (a) The schematic illustration of the experimental setup for the HTFML using liquid
nitrogen, which corresponds to the magnetizing stage of (3) (see text). (b) Cross-sectional and top
views of the GdBaCuO magnetic lens with slits. When a magnetic field is applied to the lens along the+z-direction, the shielding current flows like red arrows and the magnetic flux penetrates into the boreof the lens through the slits. As a result, the magnetic field along the +z-direction is amplified due tothe shielding current.

Figure 2. Time sequence of the external magnetic field, Bex, at the centre of the HTFML and thetemperatures, T, of the EuBaCuO TFMs and GdBaCuO magnetic lens during the magnetizing
procedure.
3. Numerical simulation
Based on the experimental setup of the HTFML as shown in Fig. 1, a three-dimensional numericalsimulation model was constructed, which consists of the bulk magnetic lens, bulk cylinders and amagnetizing solenoid coil. The magnetic lens and solenoid coil were assumed to be the same size as
those used in the experiments. The magnetic lens has two slits with 5 deg. along the y-direction. Allbulk TFMs were assumed to be the same size of 60 mm in OD, 36 mm in ID and 20 mm in H for
simplicity. The numerical simulation was carried out using the commercial finite element method
software package, Photo-Eddy (Photon Ltd., Japan), which helped us to understand electromagnetic
phenomena of HTFML during the magnetization process. The details of fundamental equations for thesimulations are described elsewhere [17–19]. The nonlinear relationship between the electric field, E,
and current, J, of the superconducting bulk was given by the power–n law (n = 20). The magnetic fielddependence of the critical current density, Jc(B), for the bulks used in this simulation was describedusing the following equation [20–22],3

14th European Conference on Applied Superconductivity (EUCAS 2019)
IOP Publishing
Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

𝐽𝑐 (𝐵) = 𝐽𝑐1 exp (−

𝐵
𝐵
1
𝐵 𝑘
) + 𝐽𝑐2
exp [ (1 − (
) )],
𝐵𝐿
𝐵𝑚𝑎𝑥
𝑘
𝐵𝑚𝑎𝑥

(1)

where Jc1, Jc2 are magnitudes of the central and secondary peaks, respectively: Bmax is the secondary
peak position, BL and k are coefficients. These free fitting parameters, Jc1, BL, Jc2, Bmax and k inequation (1) for the EuBaCuO TFM cylinders and GdBaCuO magnetic lens are shown in table 1,
which reproduced the experimental results of the time evolution of the measured magnetic field during
FCM for the single EuBaCuO TFM (TFM-B) and ZFCM for the single GdBaCuO magnetic lens,
respectively.
Table 1. Fitting parameters of the Jc(B) characteristics for the EuBaCuO TFM cylinder and GdBaCuO
magnetic lens, shown in eq. (1).
Jc1 (A m−2)
BL (T)
Jc2 (A m−2)
Bmax (T)k
8
EuBaCuO TFM cylinder
5.9 × 100.4
1.8 × 109
1.7
2.4
GdBaCuO magnetic lens
7.2 × 1080.4
2.2× 109
1.7
2.4
4. Results and discussion
4.1. FCM for single GdBaCuO cylinder and ZFCM for single GdBaCuO lensFigure 3(a) shows experimental and simulation results of the time dependence of the trapped field,
Bc, at the centre of the single TFM (TFM-B) and the external field, Bex, during FCM, ramped downfrom 1.0 T at 77 K. The experimental Bc value of 0.82 T was trapped finally after the flux creep in thedescending stage, which suggested the trapped field ability of the TFM-B at 77 K. The simulation
curve of the field-dependent Bc reproduced the experimental one.
Figure 3(b) shows the experimental and simulation results of the time dependence of the magnetic
field, Bc, at the centre of the single GdBaCuO lens and the external field, Bex, during the magnetizing
process of HTFML for Bapp = 0.50 T at 77 K. The effect of magnetic field concentration by themagnetic lens was confirmed experimentally. The negative magnetic field of Bc was observed after themagnetization, which resulted from the magnetic flux penetration into the bulk lens. Just after the
ascending stage in the simulation, the concentrated magnetic field sharply increased, which is in clear
contrast to the experimental result. This discrepancy originates from the width of slits gap. In thesimulation, slit gap is 5 deg., which is wider than the actual slit gap. Therefore, more magnetic flux
generated by the external magnetizing coil is intruded in the lens bore, compared to the situation.
However, simulated Bc gradually decreased with time and was nearly the same as experimental one in
the descending stage and after magnetization.

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14th European Conference on Applied Superconductivity (EUCAS 2019)
IOP Publishing
Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

21.5(a) single TFM

Bc (exp)

B

Bc (sim)app= 1.0 T(b) GdBaCuO lensBapp = 0.5 T

1Bc (exp)

1

Bc (sim)

B (T)

B (T)

Bex

0.5

Bex
0

0
0

10

20

0

30

Time (min)

10

20

30

Time (min)Figure 3. Experimental results of the time dependence of measured magnetic field, Bc, for (a) the
single EuBaCuO bulk cylinder (TFM-B) during FCM from Bapp = 1.0 T at 77 K, and for (b) the single
GdBaCuO magnetic lens during HTFML magnetizing process, shown in Fig. 1, for Bapp = 0.5 T at
77 K. The simulation results of Bc are also shown in each figure.
4.2. Comparison of FCM for triple, double and single EuBaCuO TFMs
Figures 4(a) - 4(c), respectively, show the time evolution of the measured magnetic field, Bc, at thecentre of the triple, double and single EuBaCuO TFM and external field, Bex, during the HTFML
magnetization process for Bapp = 0.50 T. In the ascending stage, the magnetic field, Bc, increased
linearly with increasing Bex and the magnitude of Bc was the same as the external field because the
EuBaCuO cylinders were in the normal state. In the descending stage, in which the bulk cylinders
were cooled in liquid N2 and then FCM was performed, the final trapped field of the triple and double
EuBaCuO TFMs was 0.50 and 0.49 T, respectively. For the single TFM (TFM-B), as shown in Fig.
4(c), a small amount of flux flow was observed and the final trapped field was decreased to Bc =0.46 T.
Figure 5 shows the numerical simulation results of magnetic field, Bc, at the centre of the triple,
double and single EuBaCuO TFMs and external field, Bex, during the magnetizing process for
Bapp = 0.50 T at 77 K. Final trapped field of these cases at 35 min (after approximately 15 min laterfrom the ramp end) was 0.50, 0.50 and 0.46 T, respectively. For the single TFM, a small flux flow
observed experimentally in the descending stage was reproduced in this simulation.

Figure 4. Time evolution of the measured magnetic field, Bc, at the centre of the (a) triple, (b) doubleand (c) single EuBaCuO TFM at 77 K and external field, Bex, during the magnetization process for
Bapp = 0.5 T.

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14th European Conference on Applied Superconductivity (EUCAS 2019)
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Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

simulation

1

B (T)

triple TFMs
double TFMs
single TFM
Bex

0.5

0
0

10

20
Time (min)30

40

Figure 5. The numerical simulation results of magnetic field, Bc, during the magnetizing process for
Bapp = 0.5 T at the centre of the EuBaCuO cylinder using triple, double and single TFM.
4.3. HTFML effect using triple, double and single EuBaCuO TFM with GdBaCuO lensFigure 6 presents the confirmation of the HTFML effect consisting of GdBaCuO magnetic lens and
EuBaCuO cylinder with triple, double and single TFM during the HTFML magnetization process for
Bapp = 0.50 T. In the ascending stage using triple TFMs, as shown in Fig. 5(a), Bc was higher than Bex
due to the diamagnetic shielding effect in the GdBaCuO magnetic lens and then finally Bc = 0.81 T
was achieved. In the descending stage, after cooling process, Bc decreased slightly to 0.80 T. This
result suggests that the HTFML effect at 77 K was confirmed. However, the final Bc value for the
HTFML device using double and single EuBaCuO TFMs was decreased to 0.74 T and 0.56 T,
respectively, as shown in Figs. 6(b) and 6(c). Although the trapped field ability for each TFM is almost
the same (see Fig. 4), the HTFML effect decreased with decreasing height of the TFM cylinder. In
particular, the HTFML effect with the single TFM was less than the other cases.
Figure 7 shows the numerical simulation results of magnetic field, Bc, during the magnetizing
process of HTFML for Bapp = 0.50 T at the centre of the HTFML using triple, double and single
EuBaCuO TFMs. Just after the ascending stage, the concentrated magnetic field gradually decreased
for all cases due to the gradual magnetic flux penetration into the bulk lens because of the lower Jc(B)characteristics at 77 K. For the use of triple and double EuBaCuO TFMs, in the descending stage, thetime dependence of Bc was nearly the same and the final Bc values of 0.77 T were achieved. On theother hand, for the single EuBaCuO TFM case, as shown in Fig. 6(c), an abrupt decrease in Bc can beobserved, which was similar to the experimental result, and the final Bc was 0.58 T. These numericalsimulation results fairly reproduced the experimental ones as shown in Fig. 6.
Finally, we consider the reason of the difference of the HTFML effect for EuBaCuO cylinder withdifferent height. Figures 8(a) and 8(b) show the simulation results of the final trapped field andmagnetic flux line distributions for the HTFML using triple and single TFMs, respectively. The final
trapped field for the HTFML using single TFM was Bc = 0.46 T, which was slightly smaller than thatusing triple TFMs (Bc = 0.50 T), as shown in Fig. 5. The magnetic flux penetration can be confirmed
in inner periphery of the bulk lens for each case. The difference of final Bc in the HTFML comes fromthe route of the magnetic flux concentration into the lens. For the HTFML using triple TFMs,
magnetic flux line is along the +z-direction and trapped field generated from the TFMs is concentrated
efficiently in the lens. On the other hand, for the HTFML using single TFM, magnetic flux cannot becollected to the lens effectively because the height of TFM (H = 20 mm) is shorter than that of the lens
(H = 15 mm). From both simulation and experimental results, the HTFML device should be consistedof TFMs with at least higher than the lens for better HTFML performance.

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14th European Conference on Applied Superconductivity (EUCAS 2019)
IOP Publishing
Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

Figure 6. Experimental results of measured magnetic field, Bc, during the magnetizing process for
Bapp = 0.5 T at the centre of the HTFML using (a) triple, (b) double and (c) single EuBaCuO TFM.
simulation

1.5

triple TFMs
double TFMs
single TFM
Bex

B (T)

1

0.5

0
0

10

20
Time (min)30

40

Figure 7. The numerical simulation results of magnetic field, Bc, during the magnetizing process for
Bapp = 0.5 T at the centre of the HTFML using triple, double and single EuBaCuO TFM.

Figure 8. Comparison of final distributions of the magnetic field and magnetic flux lines for the
HTFML using (a) triple and (b) single TFM. Schematic view of the magnetic flux distribution is also
shown in each case.

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14th European Conference on Applied Superconductivity (EUCAS 2019)
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Journal of Physics: Conference Series
1559 (2020) 012079 doi:10.1088/1742-6596/1559/1/012079

5. Summary
The performance of HTFML consisting of EuBaCuO bulk TFMs with various heights and a
GdBaCuO bulk magnetic lens was experimentally investigated at 77 K using liquid nitrogen. A
concentrated magnetic field, Bc = 0.80 T, at the centre of the HTFML was achieved for the longer TFM
after removing an applied magnetic field of Bapp = 0.50 T. The experimental results were reproduced
well by the numerical simulation. The HTFML effect was reduced with decreasing height of
EuBaCuO TFM cylinder under the identical GdBaCuO bulk magnetic lens. To enhance the HTFML
effect using both REBaCuO bulk TFMs and REBaCuO bulk magnetic lens, it is necessary to lowering
the operating temperature.
Acknowledgements
The authors thank Mr. Y. Yanagi of IMRA Material R&D Co., Ltd., Japan, for valuable experimental
supports. This research is supported by Adaptable and Seamless Technology transfer Program throughTarget-driven R&D (A-STEP) from Japan Science and Technology Agency (JST), Grant No.
VP30218088419 and by JSPS KAKENHI Grant No. 19K05240. M. D. Ainslie would like toacknowledge financial support from an Engineering and Physical Sciences Research Council (EPSRC)
Early Career Fellowship, EP/P020313/1.
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Journal of Physics: Conference Series
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