Superconductor Science and Technology
Supercond. Sci. Technol. 29 (2016) 034005 (8pp)

doi:10.1088/0953-2048/29/3/034005

Trapped magnetic-ﬁeld properties ofprototype for Gd-Ba-Cu-O/MgB2 hybrid-type
superconducting bulk magnet
Tomoyuki Naito1, Hidehiko Mochizuki1, Hiroyuki Fujishiro1 and
Hidekazu Teshima2
1
2

Faculty of Engineering, Iwate University, Morioka 020-8551, Japan
Nippon Steel & Sumitomo Metal Corporation, Futtsu 293-8511, Japan

E-mail: tnaito@iwate-u.ac.jp
Received 21 October 2015, revised 1 December 2015
Accepted for publication 10 December 2015
Published 25 January 2016
Abstract

We have studied experimentally and numerically the trapped magnetic-ﬁeld properties of a
hybrid-type superconducting bulk magnet, which comprised an inner Gd-Ba-Cu-O (GdBCO)
disk-bulk and an outer MgB2 ring-bulk, under ﬁeld-cooled magnetization (FCM) and pulsedﬁeld magnetization (PFM). The trapped ﬁeld by FCM at the centerof the hybrid bulk was 4.5T
at 20K, which was 0.2T higher than that of the inner GdBCO disk-bulk without MgB2 ringbulk. The experimental results by FCM were quantitatively reproduced by the numericalestimations for a model, which makes itpossible to understand the trapped ﬁeld properties of thehybrid bulk. The total magnetic ﬂux by FCM, which was estimated numerically, was enhanced
by about 1.7 times from 0.91mWb of the single GdBCO bulk to 1.53mWb of the hybrid bulk.
We also succeeded in magnetizing the whole hybrid bulk by applying multi-pulsed-ﬁelds. The
central trapped ﬁeld of 1.88T was not enhanced, but the total magnetic ﬂux, which was obtained
experimentally, was evidently increased by 2.5 times (0.25 0.62 mWb) for the hybrid bulk.
The obtained results suggest that the hybridizationis effective to enhance the total magnetic ﬂux.
To conﬁrm the reinforcing effect of the MgB2 ring to the GdBCO disk during the cooling andmagnetizationprocesses, we have measured the thermal dilatation, dL (T ) L (300 K ), of the
GdBCO, MgB2 and stainless steel. As a result, the thermal dilatation of MgB2 was smaller thanthat of GdBCO. MgB2 ring-bulk shows no compression effect to resist the hoop stress of the
GdBCO disk-bulk during the FCM process. The reinforcing material such as the stainless steel
ring mustbe set outside the GdBCO disk-bulk.
Keywords: superconducting bulk magnet, hybrid bulk, ﬁeld-cooled magnetization, pulsed-ﬁeld
magnetization, MgB2, Gd-Ba-Cu-O(Some ﬁgures may appear in colour only in the online journal)
radius of bulk) is a magnetic gradient. A total magnetic ﬂux,
F T , which is the surface integral of BT , is also an importantparameter for the practical applications such as magnetic
separation [2], motor [3], wind power generator [4] and so on.
For the enhancement of the efﬁciency of magnetic devices,
the magnetic ﬁeld must reach long distance from the bulk
surface. Using the Bean’s critical state model [5], BT is proportional to both the bulk diameter, d, and the critical current
density, Jc . To enhance the BT value, d and/or Jc must be

1. Introduction
High ﬁeld magnet is one of the promising applications forhigh-temperature superconductors. In addition to a solenoid
coil wound by superconducting wire or tape, a superconducting bulk as a ‘quasi-permanent’ magnet is anothercrucial candidate [1]. The superconducting bulk magnet offers
not only a Tesla-class strong magnetic ﬁeld, BT , buta large
magnetic force ﬁeld, BT · (dBT dr ), where, dBT dr (r is a0953-2048/16/034005+08$33.00

1© 2016 IOP Publishing Ltd Printed in the UK

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T Naito et al

increased. In this case, the output power of both motor andgenerator is enhanced through the enhancement of the torque,τ, which is proportional to the FT value.
Melt-processed single-domain RE-Ba-Cu-O bulk
(REBCO; RE denotes rare-earth element) allows a high Jc
over 105Acm−2 to ﬂow through inside itself at 77K, which
generates magnetic ﬁeld, BTFCM , of several Tesla using ﬁeldcooled magnetization (FCM) [6, 7]. The higher BTFCM can berealised at lower temperatures because of the increase in Jc .
Therefore, a 10T class bulk magnet can be realised around
40K using bulks 45–60mm in diameter and 15mm inthickness reinforced by a stainless steel ring [8]. Further high
BTFCM over 17T was obtained for the specially reinforced
YBCO [9] and GdBCO [10] bulks below 30K. It is difﬁcult
to fabricate a large single-grain REBCO bulk over 100mm indiameter due to the difﬁculty in controlling the crystal growth.
Several unique techniques including a multi-seeding [11], an
RE compositional gradient [12, 13] techniqueand a novelinﬁltration process using Gd2BaO4 and Ba-Cu-O precursors[14] enable us to grow the large REBCO bulks with
140–150mm diameter. In addition, a welding of plural bulks
possibly offers a large bulk-tile [15]. On the other hand, alarge MgB2 bulk magnet over 100mm diameter can be fabricated more easily, because ‘polycrystalline’ MgB2 bulks(20–65 mm diameter) are known to trap Tesla-class magnetic
ﬁeld [16–21]. However, their trapped ﬁeld is smaller than thatof the REBCO bulk because of the strong suppression in Jc
under magnetic ﬁeld. BTFCM =5.4T at 12K is the highest
trapped ﬁeld on the MgB2 bulk to date [19].
Pulsed-ﬁeld magnetization (PFM) is promising to magnetize the superconducting bulks set in the practical applications. However, it is well known that the large temperaturerise due to the intense motion of vortices strongly suppresses
the trapped ﬁeld, BTPFM , which is generally lower than thatobtained by FCM. A multi-pulsed-ﬁelds application, which
reduced the vortex motion, realised BTPFM =5.2T at 30K on
the GdBCO bulk with 45mm diameter, which is known to bea record-high value [22]. The smaller BTPFM =3.0T at 40K
on the larger GdBCO bulk with 65mm diameter suggests thatthe pulsedﬁeldup to about 7T, which is generally determined by a capacitor bank, is insufﬁcient to magnetize thelarge bulks over 65mm in diameter [23]. MgB2 bulks, whichwere fabricated by various techniques, have been magnetizedby PFM [24–26]. The BTPFM of 0.80T at 14K on the highly
dense MgB2 bulk with 38mmdiameter is the highest value[26]. The ﬂux-jump phenomena prevent theenhancementofthe BTPFM in MgB2 bulk in spite of the abundant magnitudeof pulsedﬁelds.
To overcome the weaknesses for each bulk and themagnetizationtechniques, we propose a hybrid-type bulk
magnet in the present study, which consists of the inner
REBCO disk-bulk and the outer MgB2 ring-bulk. The hybridbulk is expected to offer the enhancement of the trapped ﬁeld
and total trapped ﬂux simultaneously due to the enlargementof the bulk diameter. Since the BT proﬁle on the bulk isconical under full magnetization, a bulk with high Jc (m0 H )must be placed inside and that with low Jc (m0 H ) outside in
the hybrid bulk, where m0 H is the external magneticﬁeld.

Figure 1. Photograph of the hybrid bulk with stainless steel rings.
The centercircle is the GdBCO disk and the ring is MgB2. The black
space between the bulks is the epoxy resin. Two-dimensional
orthogonal coordinate axes are deﬁned. The x- and y-axes are in theplane parallel with the bulk surface and the origin is set at thecenterof the bulk surface.

The Jc (m0 H ) value of the GdBCO bulk was reported to be~10 5 Acm−2 at 20K under 3T [27], which is about twoorders of magnitude larger than that of the dense MgB2 bulk
under the identical conditions [18]. If one fabricates the
hybrid bulk with the opposite conﬁguration, that is, the inner
MgB2 disk-bulk and the outer REBCO ring-bulk, the trapped
ﬁeld of the central MgB2 should be fairly reduced by themagnetic ﬁeld generated by the REBCO ring-bulk. In thissense, this type of hybrid bulk is unrealistic. In this paper, we
produce a prototype for the hybrid bulk magnet using theinner GdBCO disk- and outer MgB2 ring-bulks, evaluate its
trapped ﬁeld properties by FCM and PFM experimentally andnumerically, and discuss thepossibility of producing ahybrid-type bulk magnet. The present hybrid bulk magnet is
operated around 20K taking the mechanical strength of the
GdBCO bulk into account, because the bulk is often brokenby the hoop stress due to the Lorentz force, FL [28].
Therefore, we also measured the thermal dilatation of the
GdBCO, MgB2 bulks and the stainless steel, to evaluate
thepossibility of a compression effect of MgB2 ring-bulk on
the hoop stress to the GdBCO disk-bulk.

2. Experimental procedure
2.1. Hybrid bulk preparation

Figure 1 shows a photograph of the hybrid bulk, which
consists of the central disk-shaped GdBCO bulk (20 mm indiameter and 7 mm in thickness), the ring-shaped MgB2 bulk
(22 mm in inner diameter, 38 mm in outer diameter, and 7 mmin thickness) with outer stainless steel (SS) rings. GdBCO
bulk was grown by the modiﬁed quench and melt growth(QMG) method [29], which was described in detail elsewhere[8]. As-grown bulk machined into a disk of 20mm in2

Supercond. Sci. Technol. 29 (2016) 034005

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diameter and 7mm in thickness was annealed at 673K for
100h in ﬂowing 0.1MPa oxygen gas. MgB2 disk-bulk with
38mm diameter and 7mm thickness was fabricated by aninsitu hot isostatic pressing (HIP) method [18] and wasmachined by dry process. After the evaluation of the trapped
ﬁeld, the MgB2 disk was drilled into a ring with the innerdiameter of 22mm by a wire electric discharge machine (wetprocess). The GdBCO and MgB2 bulks and outer SS rings
were glued using a thermal conductive epoxy resin STYCAST 2850GT.
2.2. Measurements

The hybrid bulk was magnetized by ﬁeld cooling (FC) in astatic magneticﬁeld of 5T parallel to the thickness direction
at 20K using a 10-T cryogen-free superconducting magnet(JMTD-10T100, Japan Superconductor Technology (JASTEC), Inc.) and then the applied magnetic ﬁeld was ramped
down to 0T at a rate of 0.022–0.222Tmin−1. In PFM, amagnetic pulse up to 6T with a rise time of 12ms and a
duration time of 150ms was applied to the zero-ﬁeld-cooled
hybrid bulk at the target temperature. For both FCM and PFM
measurements, the bulk was placed on the cold-stage of a
Gifford–McMahon-type helium refrigerator by inserting athin indium sheet to obtain a good thermal contact. The
temperature of the cold-stage was controlled with a Pt-Co
thermometer and 50W heater. The trapped ﬁeld was measured by a transverse-type cryogenic Hall sensor (BHT-921,
F.W. Bell Inc.) mounted on the bulk surface using GE7031
varnish in FCM. During PFM, the trapped ﬁeld at the centralbulk surface was measured by a ﬁxed axial-type Hall sensor.
The map of the trapped ﬁeld by PFM was measured at 1mmabove the bulk surface by scanning the Hall sensor using thex-y stage. The temperature of the bulk was monitored by a
Cernox thermometer which was adhered beside the Hallsensors on the bulk surface in the FCM and was ﬁxed on theSS ring in the PFM.
The thermal dilatation, dL(T)/L(300 K)(=(L(T)–L(300 K))/L(300 K)), was estimated against for the sample
length at 300K, L(300 K), using a strain gauge method. A
commercial strain gauge (CLFA-350–11, gauge factor=2.09, Tokyo Sokki Kenkyujo Co., Ltd.) was adhered on
the surface of a rectangular-shaped sample with similar
superconducting characteristics using an epoxy resin adhesive(EA-2A, Tokyo Sokki Kenkyujo Co., Ltd.). The dL(T)/L(300 K) of the GdBCO was measured in the ab-plane.

Figure 2. Temperature dependence of the trapped ﬁeld by FCM,

BTFCM (T ), for the GdBCO disk- and MgB2 disk- and MgB2 ringbulks. The bulk and the position of the Hall probe are depicted
schematically.

elsewhere [30]. The nonlinear relationship between the electricﬁeld, E, and the current density, J, for each superconductor was described by the power-n model,⎛ J ⎞nE = Ec ⎜ ⎟ ,⎝ Jc ⎠(1 )where Ec of 1μVm−1 is an electric-ﬁeld criterionand n=8
for GdBCO and n=100 for MgB2. The Jc (m0 H ) form0 Hc -axis obtained experimentally for GdBCO bulk was
ﬁtted by the following Kim model [31],1
2⎧⎛ T ⎞2 ⎫⎪⎪m 0 H0⎬Jc (m 0 H ) = a1 ⎨
1
.
⎜
⎟
⎪
⎪
⎝
⎠
T
H
∣
m
c ⎭
⎩
0 ∣ + m 0 H03

(2 )Here, a1 of 2.5 ´ 106 Acm−2 is the Jc at 0T and 0K,
Tc =94K and m0 H0 = 5T. For the MgB2 bulk, the different
Jc (m0 H ) ﬁtting function [32] was used as follows,3⎧⎧⎛ m H ⎞b ⎫⎛ T ⎞2 ⎫ 2⎪⎪
Jc (m 0 H ) = a2 ⎨1 - ⎜ ⎟ ⎬ exp ⎨,⎜ 0 ⎟ ⎬⎪⎪⎝ Tc ⎠ ⎭⎩⎩ ⎝ m 0 H0 ⎠ ⎭
⎪

⎪

⎪

⎪

(3 )

where the ﬁtting parameters are a2 = 4.5×105 Acm−2,
m0 H0 = 1.3T, b = 1.7 and Tc =39K; a2 is also the Jc at 0T
and 0K.

2.3. Numerical model for simulation

Trapped ﬁeld properties of the hybrid bulk were estimatednumerically by analyzing the electromagnetic ﬁelds using acommercial ﬁnite-element-method (FEM) software, PhotoEddy (PHOTON Co., Ltd., Japan). The simulation was performed at a constant temperature of 20K, because theexperimental temperature rise during the FCM was as small
as 0.1K on the bulk surface. The numerical model with twodimensional axisymmetric coordinates was developed on thebasis of the experimental set-up, which was detailed

3. Results and discussion
3.1. Field-cooled magnetization (FCM)
3.1.1. Trapped field properties of the individual GdBCO andMgB2 bulks by FCM. Figure 2 shows the temperaturedependence of the trapped magneticﬁeld determined by
FCM, BTFCM (T ), for the GdBCO disk-bulk, MgB2 disk-bulk
and MgB2 ring-bulk. Hereafter, we call the single bulk using3Supercond. Sci. Technol. 29 (2016) 034005

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Figure 3. Magnetic-ﬁeld dependence of the magnetic-ﬂux density, B,
at both the (0, 0) and (−11, 0) positions for the hybrid bulk atT=20K under the ﬁeld-cooled magnetizationprocess.

preﬁx ‘s-’ as withs-GdBCO and s-MgB2. Two-dimensional
orthogonal coordinate axes are deﬁned as shown in ﬁgure 1.
The x- and y-axes are in the plane of the bulk surface and theorigin is set at the centerof the hybrid bulk. The position of
the Hall probe is schematically shown in ﬁgure 2. The
s-GdBCO disk-bulk was magnetized from m0 H =5T at
22K, and the trapped ﬁeld of 4.3T was achieved at the (0, 0)
position. Quite a moderate decrease in BTFCM (T ) with elevatedtemperature was observed from 22to around 50K, andsubsequently BTFCM decreases rapidly with increasing
temperature above 50K and ﬁnally reaches zero at thecritical temperature, Tc =94K.
On the other hand, the s-MgB2 disk-bulk was magnetizedat 14.5K and the BTFCM of 2.5T was obtained at the (0, 0)
position. BTFCM decreases monotonically with increasing
temperature, and reaches zero at Tc =39K. After thes-MgB2 disk-bulk was manufactured as a ring form, thes-MgB2 ring-bulk was magnetized at 16K. A glass-ﬁbre
reinforced plastic(GFRP) disk with 22mm diameter and
7mm thickness was inserted into the hollow of the ring, andtwo Hall probes were set at the bulk center(0, 0) and the edgeof the inner circle (−11, 0) positions, respectively. The BTFCM
values at both positions, respectively, are 1.5T and 1.8T at
16K, which come from the fact that the magnetic ﬂux of thering-shaped bulk tends to concentrate around the inner edge.

Figure 4. (a) Experimentally obtained trapped ﬁeld by FCM, BTFCM ,at the C(0, 0) and D(−11, 0) positions for the hybrid bulk at 20K.
The BTFCM at the A(0, 0) position for the single GdBCO disk-bulk
and at the B(−11, 0) position for the hollow MgB2 ring-bulk are alsoplotted for comparison. (b) Cross-sections of the trappedﬁeld
proﬁles obtained by numerical simulation for various bulks studied
here (see text). The simulated plots A’, B’, C’ and D’ correspond to
the experimental plots A, B, C and D.

the trapped ﬁelds, BTFCM , of 4.5and 1.4T, respectively, ateach position.
Figure 4(a) shows the BTFCM values of the hybrid bulk atthe (0, 0) and (−11, 0) positions at 20K, which wereextracted from ﬁgure 3. The BTFCM values of eachsinglebulk
at the identical position are also plotted, which were extracted
from ﬁgure 2. Hereafter, we call each constitutional part in the
hybrid bulk using the preﬁx ‘h-’ as withh-GdBCO andh-MgB2. The BTFCM of 4.5T at the (0, 0) position of thehybrid bulk (point C) is enhanced by 0.2T compared to thatfor the s-GdBCO disk-bulk at the same position (point A).
This originates from the superposition of the trappedmagnetic ﬁelds within the h-GdBCO disk and h-MgB2 ring.
However, the magnitude of the BTFCM increase is rathersmaller than that expected from the sum of BTFCM ofeachsingle bulk. In addition, the BTFCM value at the (−11,0) position reduces from 1.5T of the hollow s-MgB2 ringbulk (point B) to 1.4T of the hybrid bulk (point D). The

3.1.2. Trappedfield properties of hybrid bulk by FCM.

Figure 3 shows the magnetic-ﬁeld dependence of themagnetic-ﬂux density, B, at both the (0, 0) and (−11, 0)
positions for the hybrid bulk under the FCM process at 20K.
The sweep rate of m0 H was changed from −0.222 to−0.022Tmin−1 at m0 H =2T, to avert the quench
phenomenon. The B values at each position decrease
monotonically with decreasing m0 H . We ﬁnally obtained4Supercond. Sci. Technol. 29 (2016) 034005

T Naito et al

Figure 5. (a) Applied pulsed-ﬁeld dependence of the trapped ﬁeld, BTPFM , of the hybrid bulk by PFM for various temperatures, Ts . The BTPFM

mapping of the hybrid bulk at Ts =20K for (b)m0 H =1.78T and (c) 5.99T.

h-MgB2 ring (∣ x ∣ = 11 - 19 mm) relative to the BTFCM of thehollow s-MgB2 ring-bulk. The BT -reduction of about 0.5T at∣ x ∣ = 11 mm from point B′ (1.43 T) to D′ (0.92 T) is
somewhat larger than the experimental one of 0.2T between
points B (1.51 T) and D (1.35 T). These discrepancies
between the simulated and experimental results come fromthe slightly large simulated BTFCM of the h-GdBCO disk
compared to the experimental one. In the simulation, thelarger Bleak due to the larger BTFCM of the h-GdBCO disk
causes the smaller BTFCM of the h-MgB2 ring, and then resultsin the small increase of the central BTFCM by hybridization. In
this way, the experimental results are qualitatively reproducedby the numerical simulations.
We compare the total magnetic ﬂux, F T , between the
hybrid bulk and the s-GdBCO disk-bulk. The F T of thehybrid bulk is calculated to be 1.53mWb from the BTFCM
proﬁle at 20K, which is 1.7 times lager than that of
0.91mWb for the s-GdBCO disk-bulk. Therefore, the hybrid
conﬁguration is quite effective to enhance F T .

trapped ﬁeld surely leaks outside the bulk. This leakage ﬁeld,
Bleak , along the z-axis has an opposite direction compared tothe internal BTFCM . Thus, the inverse Bleak of the h-GdBCO
disk reduces the BTFCM of the h-MgB2 ring.
The BTFCM values were obtained experimentally only atx=0 and −11mm. To investigate precisely the experimental results, we simulated the cross-section of thetrappedﬁeld proﬁle by FCM at 20K for the hybrid bulk,
as shown in ﬁgure 4(b). The results of the simulation for the
single bulks (s-GdBCO disk and s-MgB2 ring) were also
shown. The BTFCM proﬁle of the hybrid bulk shows the twostep change due to the contribution of each constitutional part.
The BTFCM of the h-GdBCO disk (∣ x ∣ = 0 - 10 mm)
enhances entirely as compared with that of the s-GdBCO
disk-bulk. The simulated BT -increase at ∣ x ∣ = 0 mm frompoints A′ (4.55 T) to C′ (4.63 T) is about 0.1T, which israther small but qualitatively consistent with the experimental
one of 0.2T between points A (4.26 T) and C (4.49 T). On
the other hand, a suppression in BTFCM is found for the entire5Supercond. Sci. Technol. 29 (2016) 034005

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Figure 6. The mapping of the trapped ﬁeld, BTPFM , by the multi-pulsed-ﬁelds application (MPA) of the hybrid bulk at 20K for (a)m0 H1st =5.98T and (b) m0 H2nd =1.78T. (c) The cross-section of the BTPFM proﬁles at 20K for SPA of 1.78T extracted from ﬁgure 5(b)and for MPA extracted from ﬁgures6(a) and (b).

the BTPFM is 0.07T at m0 H =1.78T, increases suddenly
above m0 H =4.94T, and reaches the highest BTPFM of
1.71T at m0 H =5.99T. Figures5(b) and (c) show thetrappedﬁeld maps at m0 H =1.78 and 5.99T, respectively.
For m0 H =1.78T, the magnetic ﬂux was mainly trapped in
the h-MgB2 ring, and was hardly trapped around the centerofthe h-GdBCO disk. On the other hand, the magnetic ﬂux ismainly trapped in the h-GdBCO disk for m0 H =5.99T.
However, the h-MgB2 ring was not magnetized at all, which
possibly originated from the large temperature rise, similartoprevious reports [24–26]. To magnetize the whole hybridbulk, the multi-pulsed-ﬁeldsapplication (MPA) which consists of the ﬁrst ﬁeld of m0 H1st =5.98T and the second
m0 H2nd =1.78T was carried out. The BTPFM proﬁles in the

3.2. Trappedfield properties of hybrid bulk by pulsed-fieldmagnetization (PFM)

Figure 5(a) shows the trapped ﬁeld, BTPFM , at the centerof thehybrid bulk in dependence on the applied pulsedﬁeld forvarious temperatures, Ts. At Ts=70K, the BTPFM increases
moderately with increasing applied ﬁeld, takes a maximum of
0.67T at m0 H =4.42T, and subsequently decreases. The
steep increase in BTPFM above m0 H =4.95T and the BTPFM
peak of 1.36T at m0 H =5.52T are observed at Ts=50K,
which originates from the enhancement of Jc by cooling.
These results are quite similar to those reported for the single
GdBCO bulks [22], because of the non-superconducting
h-MgB2 ring at both temperatures. At Ts=20K, in which
both h-GdBCO disk and h-MgB2 ring are superconducting,6Supercond. Sci. Technol. 29 (2016) 034005

T Naito et al

4. Summary
We fabricated a prototype of the hybrid bulk magnet consisting of inner GdBCO disk-bulk and outer MgB2 ring-bulk
and evaluated its trapped ﬁeld properties by experiments andnumerical simulations. As a result, we could demonstrate theeffectiveness of the hybridizationfrom the obtained results asfollows.
i. The trapped ﬁeld of the centerof the hybrid bulk wasincreased by the contribution of the MgB2 ring-bulk
byFCM. The maximum trapped ﬁeld of 4.5T wasachieved at the centerof the hybrid bulk by FCM,
which was 0.2T higher than that of the single GdBCO
disk-bulk without MgB2 ring-bulk. The trapped ﬁeld of
the MgB2 ring in the hybrid bulk was reduced by the
inverse leakage magneticﬁeld of the GdBCO disk,
compared with that of the single MgB2 ring-bulk.
ii. Numerical simulations reproduced qualitatively theexperimental results of the trapped ﬁeld properties by
FCM, which helped us to understand the magnetizing
mechanism of the hybrid bulk. The total magnetic ﬂux
calculated numerically increased from 0.91mWb of thesingle GdBCO disk-bulk to 1.53mWb of thehybrid bulk.
iii. The whole hybrid bulk was successfully magnetized byapplying the multi-pulsed-ﬁelds. Although the trapped
ﬁeld at the central hybrid bulk was about 1.88T and
was not improved by MPA, the total magnetic ﬂux was
remarkably increased from 0.25mWb for the single
GdBCO disk-bulk to 0.62mWb for the hybrid bulk.
iv. The thermal dilatation of the MgB2 bulk was smaller
than that of the GdBCO bulk, which suggested that the
MgB2 ring did not protect the GdBCO disk from theelectromagnetic force and that areinforcing material
such as stainless steel should be inserted into the space
between the bulks.

Figure 7. Temperature dependence of the thermal dilatation for

GdBCO in the ab-plane, MgB2 and stainless steel.

xy-plane for both stages are shown in ﬁgures6(a) and (b).
Similarto the single-pulse application (SPA) of 5.99T(ﬁgure 5(c)), only the h-GdBCO disk is magnetized at
m0 H1st =5.98T. By applying the second pulse, the h-MgB2
ring trapped the magnetic ﬂux. Figure 6(c) shows the crosssection of the BTPFM proﬁles of MPA and SPA of 1.78T at
20K. The central BTPFM of 1.88T at the ﬁrst pulse wasslightly reduced to 1.80T at the second one, and asimilar
reduction of BTPFM is found around the centerof theh-GdBCO disk, which is caused by the heat generation due tothe vortex motion. The BTPFM of the h-MgB2 ring by MPA
was slightly smaller than that by SPA, which comes from theleakage magneticﬁeld of the h-GdBCO disk. The estimatedtotal magnetic ﬂux, F T , is substantially enhanced from0.25mWb for the ﬁrst pulse application to 0.62mWb for thesecond one, which suggests that the hybrid conﬁguration with
the MPA technique is quite effective to enhance F T .

Acknowledgments

3.3. Thermal dilatation of each constitutional part of thehybrid bulk

This work was partly supported by JST A-STEP(AS242Z02673L), Hitachi Metals Materials Science Foundation, and JSPS KAKENHI Grant Numbers 23560002,
15K04718, 15K04646.

Finally, let us consider the temperature dependence of thethermal dilatation, dL(T)/L(300 K), of the constitutional
materials such as GdBCO(ab-plane), MgB2 and stainless steel(SS), as demonstrated in ﬁgure 7. All the materials shrink
monotonically with decreasing temperature, and the dL(T)/L(300 K) value is nearly constant below 30K. The dL(T)/L(300 K) value of MgB2 is smaller than that of both GdBCO
bulk and SS, meaning that no reinforcement effect by theh-MgB2 ring on the yield stress of the h-GdBCO disk is
expected in the hybrid conﬁguration. Therefore, to achieve
higher mechanical strength, we need to insert the SS ring into
the space between the h-GdBCO disk- and h-MgB2 ringbulks. The dL(T)/L(300 K) value of SS was larger than that of
MgB2 bulk, which suggested the reinforcement effect of theSS ring on the MgB2 bulk.

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