Superconductor Science and Technology
Supercond. Sci. Technol. 28 (2015) 105004 (7pp)

doi:10.1088/0953-2048/28/10/105004

Trapped ﬁeld properties of a concentriccircled MgB2 bulk composite magnetized bypulsed ﬁeld and ﬁeld cooling
H Mochizuki1, H Fujishiro1, T Naito1, A F Albisetti2 and G Giunchi3
1

Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, 4-3-5 Ueda,
Morioka 020-8551, Japan
2
EDISON S.p.A., Foro Buonaparte 31, 20121 Milano, Italy3
Materials Science Consultant, via Teodosio 8, 20131 Milano, Italy
E-mail: fujishiro@iwate-u.ac.jp
Received 11 May 2015, revised 5 July 2015
Accepted for publication 21 July 2015
Published 24 August 2015
Abstract

We investigated the trapped ﬁeld properties of the concentric-circled MgB2 bulk composite disk
by pulsed ﬁeld magnetization (PFM), which consists of 36 MgB2 thin rings for both surfaces ofthe disk and a small MgB2 central cylinder in the stainless steel disk. MgB2 parts were fabricatedby a reactive Mg-liquid inﬁltration (Mg-RLI) method. The trapped ﬁeld proﬁle just above thecomposite surface was very concentric circled, which suggested that the superconducting current
ﬂows along the azimuthal direction in the MgB2 rings and the cylinder independently, eventhough the magnetic ﬂux dynamically moves in the composite during PFM. The trapped ﬁeld
properties by PFM were reproduced qualitatively by the numerical simulation using the criticalcurrent density Jc(B) of the MgB2 parts estimated by the trapped ﬁeld Bz by the ﬁeld-cooledmagnetization (FCM). The composite disk is a promising candidate to realize the MgB2 bulk
magnet with concentric-circled trapped ﬁeld distribution magnetized by PFM.
Keywords: MgB2, trapped ﬁeld, numerical simulation, critical current density(Some ﬁgures may appear in colour only in the online journal)
1. Introduction

with controlled melt processing of a top-seeded melt growth(TSMG) using a NdBaCuO or SmBaCuO (001) seed crystal,in which a highly textured structure with its c-axis oriented
perpendicular to the bulk surface can be fabricated. In the
TSMG method, however, four-fold growth sector boundaries(GSBs) exist essentially in the a-growth region, in which theJc value is higher than that in the growth sector regions(GSRs) because of the introduction of pinning centers relatedwith crystal defects, etc. As a result, the trapped ﬁeld proﬁlealso shows four-fold symmetry, which is essentially inevitable and is a disadvantage for the application to the NMR
bulk magnet necessary with space uniformity of magnetic
ﬁeld with ppm order [6]. The trapped ﬁeld inhomogeneity isenhanced for the REBaCuO bulk by the PFM rather than the
FCM [7]. The magnetic ﬂux dynamically moves in the bulk
with a large temperature rise during the PFM process and thetrapped ﬁeld proﬁle is sensitive to the local Jc(B, T)

A superconducting bulk magnet using REBaCuO (RE: rareearth element or Y) is one of the typical models for practicalapplications, such as nuclear magnetic resonance (NMR),
magnetic separation, drug delivery systems, and so on [1],which produces quasi-permanent magnets on the order ofseveral tesla. The superconducting properties such as thetrapped ﬁeld Bz and critical current density Jc(B) have been
recently enhanced. The long-standing world record ﬁeld
generated by an arrangement of two YBaCuO bulks of
Bz=17.24 T at 29 K [2] was recently exceeded by
Bz=17.6 T at 26 K in the GdBaCuO bulk pair by improving
the mechanical strength [3]. Some approaches to enhance theBz and Jc have been performed such as the enlargement of
diameter in the bulk disk and the introduction of new pinning
centers [4, 5]. It is customary to fabricate the REBaCuO bulk
0953-2048/15/105004+07$33.00

1© 2015 IOP Publishing Ltd Printed in the UK

Supercond. Sci. Technol. 28 (2015) 105004

H Mochizuki et al

Figure 1. (a) Photograph and (b) schematic view of the cross section of the concentric-circled MgB2 bulk composite.

distribution in the bulk. Recently, Morita et al proposed a new
REBaCuO bulk module, in which several thin bulk plateswith concentric-circled slits were stacked in order to restrict
the supercurrent only in the superconducting slit rings [8].
Sekino et al investigated the circumferential inhomogeneityof the trapped ﬁeld of the bulk composite by FCM [9], inwhich the trapped ﬁeld proﬁles are fairly concentric circled
and the slits have the effect of suppressing the distortion ofsuperconducting currents.
On the other hand, better and larger polycrystalline MgB2
bulk magnets can be recently achieved below the transition
temperature Tc=39 K, since the problem of weak links at thegrain boundaries can be ignored due to their long coherence
length, ξ [10]. MgB2 bulk magnets are expected for the NMR
application because the inhomogeneity of the trapped ﬁeld
proﬁle can be avoided essentially. Several groups have fabricated MgB2 bulks using different techniques by in situ or
ex situ methods, and reported the trapped ﬁeld using FCM
and PFM. Bz=5.4 T at 12 K was achieved by FCM on asingle MgB2 bulk disk with 20 mm diameter fabricated by
hot-pressing ball-milled Mg and B powders [11], which is arecord high trapped ﬁeld on the MgB2 bulk by FCM to date.
Yamamoto et al reported that the concentric-circled trapped
ﬁeld proﬁle with a maximum Bz of 1.0 T was realized by
FCM, 3 mm above the MgB2 bulk (30 mm in diameter and
10 mm in thickness) fabricated by in situ method [12]. As thetrapped ﬁeld proﬁle by FCM is usually measured on thevacuum sheath, which is 3∼4 mm above the bulk surface,ﬁne special trapped ﬁeld distribution might be blurred. It isnecessary to scan the proﬁle just above the bulk surface inorder to investigate the inhomogeneity of the trapped ﬁeld
and Jc.
Giunchi [13] developed MgB2 bulks using the reactive
Mg-liquid inﬁltration (Mg-RLI) technique, which is preferable to fabricate dense and large MgB2 bulk with any form,
such as disks, cylinders, rings and so on, where the maximumBz value was about 1.3 T at 15 K by FCM on the MgB2 bulk

with 55 mm diameter and 15 mm thickness at the center holeof 6 mm. We magnetized the Mg-RLI MgB2 bulk by PFM
and measured the trapped ﬁeld proﬁle 1 mm above the bulk
surface, where the precise trapped ﬁeld inhomogeneity can bemeasured [14, 15]. However, the trapped ﬁeld proﬁle on the
MgB2 polycrystalline bulk magnetized by PFM is notnecessarily concentric circled, even though the proﬁle by
FCM is nearly conical shaped. Using the Mg-RLI technique,a concentric-circled MgB2 bulk module was fabricated[16, 17] and we can investigate the trapped ﬁeld proﬁle on themodule magnetized by PFM just above the surface, in which
the concentric-circled trapped ﬁeld proﬁle can be expected.
In this paper, we investigated the trapped ﬁeld propertiesof the concentric-circled MgB2 bulk composite by PFM
experimentally and numerically, which consists of 36 MgB2
rings and a small MgB2 central cylinder grooved in thestainless substrate.

2. Experimental setup
Figures 1(a) and (b) show the photograph and schematic viewof the cross section of the concentric-circled MgB2 bulk
composite used in this study. The MgB2 parts, which consistof 36 thin rings with slightly different diameter (0.5 mm inwidth and 1.75 mm in thickness) in both surfaces and acentral cylinder (5.7 mm in diameter), were fabricated by MgRLI method in the stainless steel (SUS) substrate 61 mm indiameter and 7.4 mm in thickness. The fabrication process ofthe disk composite is described elsewhere in detail [16, 17].
The experimental setup for PFM is presented in ﬁgure 2.
The detailed experimental apparatus for PFM is shown elsewhere in detail [15]. The bulk composite mounted in astainless steel ring was tightly connected on the cold stage ofa Gifford–McMahon cycle helium refrigerator. The initial
temperature Ts of the composite was set to 15 or 20 K. A
magnetizing solenoid coil (94 mm i.d., 153 mm o.d., and2

Supercond. Sci. Technol. 28 (2015) 105004

H Mochizuki et al

magnetometer (MPMS-5 T; Quantum Design). The Jc-B
relationship was estimated using the extended Bean model[18], Jc=20ΔM/a(1-a/3b), where a and b are the dimensions of the plane of the sample perpendicular to the appliedﬁeld and ΔM is the width of the M(H) hysteresis loop.

3. Numerical model of analysis
Based on the experimental setup, the framework for thenumerical simulation for both PFM and FCM was constructed, in which the physical phenomena occurring during
the magnetization processes are described using the fundamental electromagnetic and thermal equations in axisymmetric coordinates. The detail of the numerical simulation
was described elsewhere [19, 20]. Brieﬂy, the power-n model(n=100) was used to describe the nonlinear E–J characteristic of the MgB2 part. The measured Jc(B) of the MgB2 disk
at 20 K was ﬁtted using the following equation,

Figure 2. Schematic view of the experimental setup for PFM.

50 mm height), which was dipped in liquid nitrogen, wasplaced outside the vacuum chamber. A magnetic pulse Bex(t)with a rise time of 0.013 s and a duration time of 0.15 s wasapplied to the composite with Bex=0.8 to 2.0 T by ﬂowing
the pulsed current from a condenser bank. The time evolutions of the local ﬁeld BL C (t)(z=0 mm) and the ﬁnal trapped
ﬁeld Bz(z=0 mm) were measured by the axial-type Hallsensors (F W Bell, BHA 921) attached on the center of thecomposite surface using a digital oscilloscope. The twodimensional trapped ﬁeld proﬁle Bz(z=1 mm) was mapped
1.0 mm above the bulk surface, stepwise with a pitch of
1.0 mm by scanning the same axial-type Hall sensor inside
the vacuum chamber using an x–y stage controller with aﬂexible bellows. Time dependence of temperature T(t) during
PFM was monitored by a Cernox thermometer connected tothe outer stainless steel ring by a screw.
FCM was also performed for the bulk composite. A static
magnetic ﬁeld of Bex=5 T was applied to the composite
above Tc using a cryo-cooled superconducting solenoid
magnet (JASTEC JMTD-10T100) and then the composite
was ﬁeld-cooled to Ts. Afterwards, the applied ﬁeld was
decreased down to zero at a rate of −0.22 T min−1. The
temperature dependence of the trapped ﬁeld by FCM BzFCM (T)(z=0 mm) was measured by a ‘sweep method,’ that is, after
the FCM procedure at Ts, the composite was warmed slowly
with a heating rate of 0.1 K min−1. The BzFCM (T)(z=0 mm)
values were measured using three Hall sensors (AREPOC s.r.o.,
LHP-NP) adhered on the composite surface at the center(x=0 mm), and at the positions of x=4.5 and 5.5 mm. The
BzFCM (T)(z=0 mm) was also measured for the MgB2 bulk
disk (54 mm in diameter and 15 mm in thickness), which was
fabricated by the same Mg-RLI method [15], in order toestimate the critical current density Jc(B) of the MgB2 parts inthe composite for the numerical simulation. After the FCM
experiments, the MgB2 bulk disk was cut, and a small piece
about 1×1×2 mm3 in size was prepared and the magnetization curve M(H) was measured at 20 K under a magnetic
ﬁeld up to μ0H=5 T using a commercial SQUID⎢ ⎛ ⎞b ⎥B
Jc (B) = Jc0 exp ⎢ - ⎜ ⎟ ⎥ ,⎢⎣ ⎝ B0 ⎠ ⎥⎦(1 )where B0 and β are the ﬁtting parameters. The temperaturedependence of the critical current density Jc0 under the zeroﬁeld is described by the following equation [19],⎫ 3/2⎧⎛ T ⎞2 ⎪⎪Jc0 = a ⎨
1
,
⎜ ⎟⎬
⎪
⎝ Tc ⎠ ⎪⎭⎩(2 )where Tc is the critical temperature and α is a constantrepresenting Jc at 0 K. In order to reproduce the trapped ﬁeld
properties of the composite disk, Jc–B characteristics of the
MgB2 parts were estimated according to equations (1) and (2).
Iterative calculations were performed to analyze the
combined problem of electromagnetic ﬁelds and heat diffusion using the ﬁnite element method (FEM) using commercial
software, Photo-Eddy, combined with Photo-Thermo (Photon
Ltd, Japan). In the model analysis of FEM, the bulk composite was equally divided with 0.25 mm mesh and temperature dependence of thermal conductivity k (T) and thespeciﬁc heat C(T) of the MgB2 and stainless steel wereintroduced in the analysis [21, 22].

4. Experimental results
4.1. PFM

Figure 3 shows the pulsed ﬁeld dependence of the trapped
ﬁeld BzPFM (z=0 mm) at the center of the disk composite
magnetized by PFM at Ts=15 and 20 K. The result of the
MgB2 bulk disk was also shown [15]. Similarly to the previous experimental results of REBaCuO and MgB2 bulks[15, 23], the BzPFM (z=0 mm) value increases, takes a maximum and then decreases with increasing Bex. The maximum
BzPFM (z=0 mm) was slightly increased and the BzPFM(z=0 mm)–Bex relation shifts to higher Bex side with3

Supercond. Sci. Technol. 28 (2015) 105004

H Mochizuki et al

Figure 5. The cross section of the trapped ﬁeld proﬁle BzPFM

Figure 3. Pulsed ﬁeld dependence of the trapped ﬁeld BzPFM(z=1 mm) for each Bex.

(z=0 mm) at the center of the disk composite magnetized by PFM
at Ts=15 and 20 K. The results for the MgB2 bulk disk atTs=14 K are also shown [15].

condition. The proﬁle shows fairly concentric circles with aslightly concave proﬁle near the center.
Figure 5 shows the cross section of the trapped ﬁeld
proﬁle BzPFM (z=1 mm) for each Bex. For Bex=1.06 T, theproﬁle was concave and the trapped ﬁeld increased withincreasing Bex. For Bex=1.41 T, the trapped ﬁeld took amaximum and then decreased with further increase in Bex.
The proﬁle is axisymmetric for all the Bex, even just above thebulk surface. The symmetric proﬁle suggests that the superconducting current ﬂows independently along the azimuthal
direction in each MgB2 ring and cylinder. For the MgB2 bulk
disk, the trapped ﬁeld proﬁle with the concentric circle can beobtained by FCM in principle. However, the trapped ﬁeld
proﬁle of the MgB2 disk bulk by PFM did not necessarily
show the concentric-circled one [14]. Using this bulk composite, the concentric-circled proﬁle can be realized even by
PFM. It should be noted that the proﬁle is not completely
conical but concave or trapezoidal for all the applied ﬁelds.
The reason is discussed later. However, from the viewpoint of
the concentric-circled proﬁle, this type of the composite canbe applicable for NMR magnetized by PFM, in which thetrapped ﬁeld homogeneity is quite severe [6].
Figure 6(a) presents the time evolution of temperature T(t) during PFM in the disk composite at Ts=20 K for various
applied pulsed ﬁelds. For each Bex, temperature rose sharply
within several seconds, which increased with increasing Bex,
and then decreased and quickly recovered to the initial temperature Ts with several hundred seconds. The quick responsein T(t) is similar to that of the MgB2 bulk disk [15] and comesfrom the low speciﬁc heat C(T) and high thermal conductivity
k (T), which is clearly in contrast with those of the REBCO
bulk [25]. Figure 6(b) presents the maximum temperature rise
ΔTmax at Ts=15 and 20 K as a function of Bex. The ΔTmax
for the MgB2 disk bulk at 14 K is also shown [15]. ΔTmax
increases with increasing applied ﬁeld Bex for all the cases
and becomes small in case of the increase in Ts, which is
independent of the structure of the bulk, i.e., a concentriccircled bulk composite or a disk bulk.

Figure 4. Time evolution of the applied ﬁeld Bex(t) and the local ﬁeld

BLC (t) (z=0 mm) at the center of the surface at 20 K after applying
the pulsed ﬁeld of Bex=1.41 T. The inset shows the trapped ﬁeld
proﬁle BzPFM (z=1 mm) of the disk composite after PFM.

decreasing Ts due to the increase in Jc of the MgB2 parts. The
maximum BzPFM (z=0 mm) was 0.29 T at 15 K, which was
smaller than that of the MgB2 bulk disk at 14 K.
Figure 4 presents the time evolution of the applied ﬁeld
Bex(t) and the local ﬁeld BLC (t)(z=0 mm) at the center of thesurface at 20 K after applying the pulsed ﬁeld of
Bex=1.41 T. BLC (t)(z=0 mm) started to increase with aslight time delay, took a maximum of 0.38 T at 0.04 s, gradually decreased and approached to the ﬁnal value with theincrease in time. The ﬂux jump did not happen in the disk
composite under our experimental condition of Ts and Bex,
which frequently takes place for the MgB2 bulk disk withhigher Jc and for the higher Bex [24]. The inset of ﬁgure 4
shows the trapped ﬁeld proﬁle BzPFM (z=1 mm) of the disk
composite 1 mm above the disk surface under the same4

Supercond. Sci. Technol. 28 (2015) 105004

H Mochizuki et al

Figure 7. Temperature dependence of the trapped ﬁeld BzFCM(z=0 mm) at three positions; A (center, x=0 mm), B(x=4.5 mm), and C (x=5.5 mm) of the composite. BzFCM(z=0 mm) of the MgB2 bulk disk at the center is also shown.

Figure 6. (a) Time dependence of temperature T(t) during PFM in

the disk composite at Ts=20 K for various applied pulsed ﬁelds
Bex. (b) The maximum temperature rise ΔTmax at Ts=15 and 20 K
as a function of Bex.
Figure 8. Magnetic ﬁeld dependence of the critical current density

Jc(B) at 20 K for the disk bulk. The ﬁtting curve (dashed line) andthe estimated Jc(B) of the MgB2 part in the composite are also shown(see text).

4.2. FCM

In order to estimate the Jc–B characteristics of the MgB2 partsin the disk composite, FCM was performed. Figure 7 shows
the temperature dependence of the trapped ﬁeld BzFCM(z=0 mm) at three positions; A (center, x=0 mm), B(x=4.5 mm), and C (x=5.5 mm), as shown in the inset. In
the ﬁgure, BzFCM (z=0 mm) at the center of the MgB2 bulk
disk is also shown for comparison. The maximum values of
BzFCM (z=0 mm) at 12.1 K are 1.06 T (x=0 mm), 0.65 T(x=4.5 mm), and 0.69 T (x=5.5 mm), respectively. The Tc
value decided by the zero ﬁeld trap was relatively low;Tc=36 K for position A and 34 K for positions B and C,
which suggests that the superconducting properties of the
MgB2 parts in the composite are a little bit deteriorated. These
results may come from the complicated structure of the disk
composite with many narrow ridges, in which the immersedboron powder poorly reacted with liquid Mg. It should benoticed that the cross section of the trapped ﬁeld proﬁle is not
fully corn-shaped, but BzFCM (z=0 mm) at the position C isslightly higher than that at the position B. This result comesfrom the gap of 4.4 mm between the MgB2 central cylinder
and the innermost MgB2 ring, as shown in ﬁgure 1(b). The
volume fraction of MgB2 parts is estimated to be 15% of thetotal volume of the disk composite. The trapped ﬁeld BzFCM(z=0 mm) lower than that of the bulk disk comes from thesmaller volume fraction and the lower superconducting
characteristics in the MgB2 parts.
5. Results of numerical simulation and discussion
5.1. Estimation of Jc–B characteristics in the MgB2 parts
using FCM

In order to clarify the trapped ﬁeld properties of the bulk
composite, it is necessary to estimate the Jc–B characteristics
in the MgB2 part. The plots in ﬁgure 8 show the magnetic
ﬁeld dependence of the critical current density Jc(B) at 20 K
5Supercond. Sci. Technol. 28 (2015) 105004

H Mochizuki et al

Table 1. Determined parameters in equations (1) and (2) for the Jc–B
characteristics.

MgB2 bulk disk (measured)
MgB2 part in the composite(estimated)α (A m−2)

B0 (T)

β

3.6e9
5.9e8

0.9
1.0

1.4
1.7

for the disk bulk. As can be seen in the typical MgB2 bulks[26], Jc decreases monotonically with increasing magnetic
ﬁeld, which is nearly the same Jc(0) and magnetic ﬁeld
dependence to the bulk fabricated by Mg-RLI method. Using
equations (1) and (2), the ﬁtting parameters were decided asshown in table 1 and the ﬁtting curve is shown in ﬁgure 8 bydashed line.
Figure 9 presents the cross section of the trapped ﬁeld
proﬁle BzFCM (z=0 mm) by FCM at 20 K, as a function of theposition x. The experimental results obtained in ﬁgure 7 areplotted in the ﬁgure, in which the plots at x=−4.5 and−5.5 mm are the axisymmetric assumptions from x=+4.5
and +5.5 mm. The dashed line shows the results of thenumerical simulation using the Jc(B) obtained from the bulk
disk shown in ﬁgure 8. It should be noticed that the dashedline is quite larger than the experimental results. These results
suggest that the Jc(B) for the MgB2 parts in the composite issupposed to be lower than that obtained from the bulk disk.
So we reversely estimated the Jc(B) for the MgB2 parts in thecomposite using the experimentally obtained results. In thisestimation, the parameters of α, B0, and β in equations (1) and(2) were decided as shown in table 1 and the estimated Jc(B)is also shown in ﬁgure 8 by a solid line. It is found that theestimated Jc(B) of the MgB2 parts in the composite is about
one order of magnitude smaller than that of the MgB2 bulk
disk. The result of the numerical simulation is also shown inﬁgure 9 by a solid line, which can reproduce the experimental
data. In the next subsection, the numerical simulation of the
PFM for the composite is shown using the estimated Jc(B)relation of the MgB2 parts.

Figure 9. Results of the experiments and numerical simulations of

the trapped ﬁeld proﬁles for the composite magnetized by FCM(see text).

Figure 10. Results of the simulation for the cross section of thetrapped ﬁeld BzPFM (z=1 mm) proﬁle by PFM at 20 K, as a functionof applied pulsed ﬁeld Bex.

The discrepancy between the experiments and simulations may come from several reasons. One possibility is thedifference in Jc(B) characteristics for the MgB2 ring part andthe cylinder part; Jc(B) characteristics for the MgB2 cylinderpart may be higher or lower than those for the MgB2 ring part.
For the former case, the MgB2 cylinder shields the magnetic
ﬂux, and for the latter case, the MgB2 cylinder cannot trap themagnetic ﬂux. However, both hypotheses cannot be realistic
because the trapped ﬁeld proﬁle by FCM can reproduce theexperimental results by using identical Jc(B) characteristics
for the MgB2 ring part and the cylinder part, as shown inﬁgure 9. Another possibility is inhomogeneous temperature
distribution during PFM. The MgB2 rings in the bottom wereattached directly the cold stage and were cooled. On the other
hand, the MgB2 rings in the upper surface were cooled
through the low thermal conductive stainless steel substrate,of which the thermal conductivity k (T) was about one orderof magnitude smaller than that of the MgB2 bulk [25]. The
generated heat due to the ﬂux movement and trap in the upper5.2. Numerical simulation of trapped field properties by PFM

The numerical simulation of the PFM for the composite was
performed using the estimated Jc(B) of the MgB2 parts shownin ﬁgure 8. Figure 10 presents the results of the simulation forthe cross section of the trapped ﬁeld proﬁle BzPFM (z=1 mm)
by PFM at 20 K, as a function of applied pulsed ﬁeld Bex. For
Bex lower than 0.6 T, the trapped ﬁeld proﬁle shows a large
concave one, which is nearly consistent with the experimental
results shown in ﬁgure 5, although the applied ﬁeld Bex in thesimulation is somewhat smaller than that in the experiment.
However, for Bex larger than 0.8 T, the magnetic ﬂux intrudes
in the central part of the composite and the trapped ﬁeld at thecenter of the composite increases with increasing Bex, which
is clear contrast to the experimental results; in the experiments, the magnetic ﬂux cannot intrude into the center and the
maximum trapped ﬁeld decreased, even if the Bex value
increased.
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H Mochizuki et al

Acknowledgments

surface are removed through the stainless substrate during
PFM. So the temperature on the upper surface can possibly behigher than that on the bottom surface. The thermal contact
resistance between each MgB2 part and the stainless steel
substrate may seriously affect the trapped ﬁeld properties,
which was not considered in the numerical simulation. The
problem of this discrepancy between ﬁgures 5 and 10 remains
as a future study.

This work was supported in part by JSPS KAKENHI grant
number 23560002 and 15K04646.

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6. Conclusion
The trapped ﬁeld properties of the concentric-circled MgB2
bulk composite disk, which consists of 36 MgB2 thin rings forboth sides of the composite and a MgB2 central cylinder inthe stainless steel substrate and was fabricated by a reactive
Mg-RLI method, have been investigated experimentally andnumerically. The important results and conclusions obtained
from this study are summarized as follows.
(1) The trapped ﬁeld proﬁle by PFM, BzPFM (z=1 mm),
1 mm above the disk surface was very concentric
circled, which suggested that the superconducting
current ﬂows along the azimuthal direction in the
MgB2 rings and the cylinder independently, eventhough the magnetic ﬂux dynamically moves in thecomposite during PFM. The trapped ﬁeld proﬁle is not
perfectly conical but slightly concave at the central
region.
(2) The critical current density Jc(B) of the MgB2 parts inthe disk composite was estimated using the experimentally obtained trapped ﬁeld values by FCM and thenumerical simulation. The Jc(B) was about one order ofmagnitude smaller than that of the MgB2 bulk disk
fabricated by the same method.
(3) Using the estimated Jc(B) characteristics of the MgB2
parts, the numerical simulation for the PFM procedures
was performed. For the lower pulsed ﬁeld region, thetrapped ﬁeld properties were reproduced qualitatively
by the numerical simulation.
(4) However, in the simulation, the magnetic ﬂux intruded
into the central MgB2 cylinder for the higher pulsed
ﬁeld region, which is clear contrast to the experimental
results. The discrepancy may come from the inhomogeneous temperature distribution due to the existence ofthe thermal contact resistance between the MgB2 parts
and the stainless steel substrate in the experiment.
Detailed analysis remains about the discrepancy in the
future study.

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