Superconductor Science and Technology
Supercond. Sci. Technol. 29 (2016) 084001 (10pp)

doi:10.1088/0953-2048/29/8/084001

Trapped ﬁeld of 1.1T without ﬂux jumps inan MgB2 bulk during pulsed ﬁeld
magnetization using a split coil with a softiron yoke
H Fujishiro1, H Mochizuki1, M D Ainslie2 and T Naito1
1

Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, 4-3-5 Ueda,
Morioka 020-8551, Japan2
Bulk Superconductivity Group, Department of Engineering, University of Cambridge, Trumpington
Street, Cambridge CB2 1PZ, UK
E-mail: fujishiro@iwate-u.ac.jp
Received 14 March 2016, revised 5 May 2016
Accepted for publication 27 May 2016
Published 16 June 2016
Abstract

MgB2 superconducting bulks have promising potential as trapped ﬁeld magnets. We haveachieved a trapped ﬁeld of Bz=1.1 T on a high-Jc MgB2 bulk at 13 K without ﬂux jumps bypulsed ﬁeld magnetization (PFM) using a split-type coil with a soft iron yoke, which is a recordhigh trapped ﬁeld by PFM for bulk MgB2 to date. The ﬂux jumps, which frequently took placeusing a solenoid-type coil during PFM, were avoided by using the split-type coil, and the Bz
value was enhanced by the insertion of soft iron yoke. The ﬂux dynamics and heat generation/
propagation were analyzed during PFM using a numerical simulation, in which the magnetic ﬂux
intruded and attenuated slowly in the bulk and tended to align along the axial direction due to thepresence of soft iron yoke. The advantages of the split-type coil and the simultaneous use of asoft iron yoke are discussed.
Keywords: pulsed ﬁeld magnetization, MgB2 bulk, numerical simulation, ﬂux jump, split-type
coil, soft iron yoke
(Some ﬁgures may appear in colour only in the online journal)
Pulsed-ﬁeld magnetization (PFM) has been also investigated to magnetize bulk superconductors, usually using asolenoid-type copper coil and a condenser bank. However,
the trapped ﬁeld, Bz, by PFM is generally lower than that by
FCM because of a large temperature rise caused by the
dynamic motion of the magnetic ﬂux. Multi-pulse techniques
are effective to enhance Bz for REBaCuO bulks due to the
reduction of this temperature rise [8, 9]. Bz (PFM)=5.20 T
has been attained on a GdBaCuO bulk 45 mm in diameter at
30 K using a modiﬁed multi-pulse technique with stepwise
cooling [10], which is a record-high Bz for REBaCuO bulk by
PFM to date. The PFM technique has also been applied to
MgB2 bulks [11, 12]. However, Bz (PFM)=0.81 T at 14 K is
the highest value so far for a high-Jc MgB2 bulk fabricated by
the hot isostatic pressing (HIP) method, on which Bz

1. Introduction
MgB2 superconducting bulks have promising potential as
trapped ﬁeld magnets, such as being rare-earth-free, lightweight and presenting a homogeneous trapped ﬁeld distribution[1], which are in clear contrast with REBaCuO bulk magnets[2]. The problem of weak-links at grain boundaries can beignored in MgB2 polycrystalline bulks due to their longcoherence length, ξ, which enable us to realize better and larger
polycrystalline bulk magnets below the transition temperatureTc=39 K [3]. Recently, MgB2 bulks with high critical current
density, Jc, have been fabricated by various methods and activated by ﬁeld-cooled magnetization (FCM) [4–6]. A recordhigh trapped ﬁeld of Bz=5.4 T has been attained at 12 K on asingle MgB2 bulk 20 mm in diameter [7].
0953-2048/16/084001+10$33.00

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Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et al(FCM)=2.23 T was trapped at 16 K by FCM [13]. However, ﬂux jumps took place frequently during PFM in thehigh-Jc MgB2 bulks and consequently the Bz (PFM) value
decreased for higher applied magnetic ﬁelds. On the other
hand, ﬂux jumps are scarcely observed in low-Jc MgB2 bulks
and even for lower applied ﬁelds in high-Jc MgB2 bulks. The
ﬂux dynamics and heat generation in the MgB2 bulk around20 K are in clear contrast with those in the REBaCuO bulk ataround typical operating temperature of 40 K because of thesmall speciﬁc heat, large thermal conductivity, and a narrowtemperature margin against Tc for the MgB2 bulk. We havepreviously analyzed and discussed the electromagnetic andthermal instability of a high-Jc MgB2 bulk using conventional
relations, such as the critical thickness, dc, and the minimum
propagation zone length, lm [14].
Ida et al proposed a new PFM technique using a vortextype coil, which consists of a couple of copper coils [15].
They demonstrated that, using the vortex-type coil at 77 K,
the magnetic ﬂux starts to be trapped in the center of the
REBaCuO bulk, even for lower pulsed ﬁelds, and that the
maximum Bz was enhanced in comparison to that obtainedusing the solenoid-type coil. We have performed the numerical simulation of trapped ﬁeld, Bz, and temperature, T,
after applying a magnetic pulse using the vortex-type coil,and the results of the simulation can reproduce the experimental results well [16]. In this case, the magnetic ﬂux
intrudes into the bulk not from the periphery, but mainly
from the surface, and the temperature rise during the ﬂux
intrusion for the vortex-type coil is smaller than that for thesolenoid-type coil. We also performed the PFM experiments for REBaCuO bulks using split-type coil, which is ofa similar structure to the vortex-type coil [17, 18]. The
trapped ﬁeld can be enhanced using the split-type coilexperimentally, but there are no reports on PFM experiments using the split-type coil for MgB2 bulks yet. Ikuta
et al investigated the effect of sandwiching the bulk with apair of ferromagnetic iron yoke pieces on the trapped ﬁeld,
Bz, and total trapped ﬂux, Φz [19]. The magnetic ﬂux distribution became more homogeneous and Φz was enhancedby the existence of the yoke, because the magnetic pulse
was more effectively applied to the bulk. Gony et alreported the effect of iron core during PFM at 77 K using asolenoid-type coil and repeated the insertion and removal of
the iron core on the magnetized bulk [20]. The trapped ﬁeld
was enhanced by the existence of the iron core, whichcomes from the orientation of the ﬂux in the direction of theiron core.
On the basis of our experience with PFM and someindications for the improvement of the PFM technique[15, 19], we expect to avoid ﬂux jumps and enhance thetrapped ﬁeld during PFM for high-Jc MgB2 bulks using the
split-type coil with soft iron yokes. In this study, we investigate the PFM procedure for the high-Jc MgB2 bulk using a
split-type coil and compared this to those for a solenoid-type
coil. We also study the effect of the soft iron yoke for the
split-type coil to enhance the trapped ﬁeld, Bz.

Figure 1. Experimental setup for (a) ‘split coil with two yokes’ and(b) ‘solenoid coil with one yoke’. The PFM experiments were also
performed using ‘split coil without yoke’ in (a).

2. Experimental details
A bulk MgB2 superconducting disk was fabricated by a HIP
method [6]. The diameter and thickness are 22 mm and
15 mm, respectively, and the relative mass density was ashigh as 93% of the ideal mass density. Bz(FCM)=2.23 T
was achieved at the center of the bulk surface at 16 K by
FCM. Figure 1 shows the experimental setup of PFM using
the split-type and solenoid-type coils. For the split-type coilshown in ﬁgure 1(a), the MgB2 bulk was fastened in a copper
holder with thin indium foil (0.2 mm in thickness) and connected to the cold stage of a Gifford–McMahon cycle, helium
refrigerator in the vacuum chamber. A Hall sensor (BHT 921;
F W Bell) was adhered to the center of the bulk surface, andthe thermometer (Cernox™) was tightly connected to thecopper holder. The split-type coil (72 mm inner diameter (ID),
124 mm outer diameter (OD), 35 mm height, wire crosssection of 1.3×3.0 mm2 and 117 turns of each coil), which
was submerged in liquid nitrogen, was placed outside thevacuum chamber, in which a pair of soft iron plain, Ni-plated
yokes (60 mm in diameter and 65 mm in height) was inserted
in the central bores of the coil. This coil setup is named ‘split
2Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et al(n=100) was used to describe the nonlinear E–J characteristic of the MgB2 bulk. The results of the numerical simulation strongly depend on the Jc(B, T) characteristics of thesuperconductor [21]. The Jc(B) curve of the MgB2 bulk at
20 K, which was measured using a small piece cut from asimilar bulk by a commercial SQUID magnetometer (MPMS5T; Quantum Design), was ﬁtted using the following equationcoil with two yokes’. For comparison, the bulk was magnetized using the split-type coil with the absence of the soft ironyokes, which is named ‘split coil without yoke’. The initial
temperature, Ts, of the bulk was set to 13 and 20 K, andmagnetic pulses, Bex(t), with a peak up to 2.95 T, a rise timeof 0.018 s and a duration of 0.18 s were applied via a pulsed
current in the coil. The peak of the generated magnetic ﬁeld is
proportional to the ﬂowing current, I; for example, to achieve
Bex(max)=1.5 T at the center of the split coil without any
superconductor inserted, I=440 A and 850 A was ﬂown forthe ‘split coil with two yokes’ and ‘split coil without yoke’,
respectively. During PFM, the time evolution of the temperature, T(t), the central ﬁeld, Bz(t), and the subsequent trapped
ﬁeld, Bz, which was deﬁned as the ﬁnal value of Bz(t) at 60 s,
were measured at the center of the bulk surface. After theremoval of the split-type coil 15 min after the pulse application, two-dimensional trapped ﬁeld proﬁle of Bz was mapped
at 2 mm above the bulk surface (on the outer surface of thevacuum chamber) by scanning a Hall sensor (BHA 921; F W
Bell) using an x–y stage controller.
In the case of using the solenoid coil, as shown inﬁgure 1(b), the same MgB2 disk was mounted in a stainlesssteel (SS) ring (22.1 mm ID, and 56.0 mm OD) using epoxy
resin (Stycast 2850™) and was tightly anchored onto the SS
holder with a soft iron yoke (40 mm diameter (D) and 20 mm
height (H)). This was then connected to the cold stage of arefrigerator using an indium foil [6, 11]. The soft iron yoke is
ﬁxed to the magnetizing ﬁxture, so cannot be removed after
the PFM is carried out. This coil setup is named ‘solenoid coilwith one yoke’. The solenoid copper coil (99 mm ID, 121 mm
OD, 50 mm H, wire cross-section of 1.3×3.0 mm2 and 112
turns), which was submerged in liquid nitrogen, was placedoutside the vacuum chamber. The initial temperature, Ts, ofthe bulk was set to 20 K. Magnetic pulses, Bex, up to 2.2 T,with a rise time of 0.013 s and duration of 0.15 s were applied
via a pulsed current in the coil. For example, I=1040 A wasapplied to achieve Bex(max)=1.5 T at the center of thesolenoid coil without any superconductor inserted. The time
evolution of the central ﬁeld, Bz(t), and the subsequent trapped ﬁeld at 60 s, Bz, at the center of the bulk surface weremonitored by a Hall sensor (BHA 921; F W Bell). Twodimensional trapped ﬁeld proﬁles of Bz were mapped in a
vacuum chamber 15 min after the pulse application, stepwise
with a pitch of 1 mm, by scanning the same Hall sensor using
an x–y stage controller. The time evolution of the temperature,
T(t), was also measured separately using a thermometer
adhered to the bulk surface.

3⎡ ⎛ B ⎞b ⎤⎧⎛ T ⎞2 ⎫ 2
Jc (B , T ) = a ⎨1 - ⎜ ⎟ ⎬ exp ⎢ - ⎜ ⎟ ⎥ ,⎢⎣ ⎝ B0 ⎠ ⎥⎦⎝ Tc ⎠ ⎭
⎩
⎪

⎪

⎪

⎪

(1 )

where Tc=39 K, α=4.5×109 A m−2, B0=1.3 T andβ=1.7 are the ﬁtted parameters. When these parameters
were used in the simulation for FCM, a trapped ﬁeld ofmagnitude at least twice the expected trapped ﬁeld, wasobtained. It was found that the parameter α should be
adjusted to a lower value of α=5.8×108 A m−2 toadequately reproduce the experimental results. This isbecause the Jc (B, T) value estimated from the magnetization
measurement might be overestimated, compared to the realtransport Jc (B, T) value, which is in clear contrast to thenumerical simulation in MgB2 bulk for FCM [1].
The applied pulsed ﬁeld, Bex(t), which is proportional tothe current ﬂowing in the coil, was approximated using thefollowing equation with a rise time of τ=0.018 s for the split
coil without yoke and τ=0.013 s for the solenoid coilwithout yoke, respectively, which were determined from theexperimental results.
Bex (t ) = Bex⎛tt⎞
exp ⎜1 - ⎟ .
⎝
t
t⎠

(2 )

In the numerical analysis, we set the spacing plate with athermal conductivity κcont=0.5 W mK−1 between the MgB2
bulk and the metal holder, which artiﬁcially represents thecooling power of the refrigerator, the thermal contact conductivity and the thermal conductivity of the inserted indium
foil. The temperature dependence of the thermal conductivity,
κ(T), the speciﬁc heat, C(T), and the mass density, d, of the
MgB2 bulk and the SS ring were introduced into the model[14], and these values for the soft iron yoke(κ=2.4 W mK−1, C=12.7 J kg−1 K−1, d=7840 kg m−3)C=8.0 J kg−1 K−1,
andcopper(κ=50 W mK−1,−3d=8960 kg m ) are assumed to be temperature independent. The saturation magnetization, μ0Msat, the initial relative
permeability, μr,max (B<μ0Msat), and the electrical conductivity, σ, of the soft iron yoke were assumed to be
μ0Msat=1.6 T, μr,max=2000 and σ=1.264×107 S m−1,
respectively. When the temperature of the bulk exceeds Tc,
the electrical conductivity of the region of the bulk is assumed
to be 1×105 S m−1. Iterative calculations were performed
for analyzing the combined problem of electromagnetic ﬁelds
and heat diffusion using the ﬁnite element method implemented in the commercial software package, Photo-Eddy,
combined with Photo-Thermo (Photon Ltd, Japan).

3. Numerical simulation
Based on the experimental setup, three types of models wereconstructed for the numerical simulation of PFM as shown inﬁgure 2, in which the physical phenomena occurring during
the magnetization process are described using the fundamental electromagnetic and thermal equations in axisymmetric coordinates. The details of the numerical simulation
have been described elsewhere [14]. The power-n model3

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H Fujishiro et al

Figure 2. Three types of models for numerical simulation during PFM using (a) split coil with two yokes, (b) split coil without yoke and (c)solenoid coil with one yoke. The dimensions of the MgB2 bulk, magnetizing coils and the inserted soft iron yokes are also shown.

4. Experimental results

the yoke along the z-direction. The similar reduction of Bz by
the removal of the yoke was reported in [20].
Figure 4 depicts the time evolution of the applied pulsed
ﬁeld, Bex(t), of 2.2 to 2.3 T in the cases using each pulsed coil,which were measured on the bulk surface at Ts=50 K above
Tc. The difference of Bex(t) can be observed for each case,although the proﬁles for the split coils are quite noisy, which
is a result of incomplete electrical shielding of the probe usedwith the oscilloscope. The time, at which the pulsed magnetic
ﬁeld takes a maximum, was 0.018 s and 0.013 s for the split
coil and the solenoid coil, respectively, due to the differenceof the coil inductance, L. The presence of the soft iron yoke
seems to stop more ﬂux leaving at the bulk position as thepulse reduces during its descending stage. Note that the eddy
current may affect the experimental data for heat generationand so on, but we have not considered the inﬂuence of theeddy current in the present study.
Figure 5 shows the time evolution of the applied ﬁeld,
Bex(t), and the local ﬁeld, Bz(t), at the center of the bulk
surface using each magnetizing coil. For the case using thesolenoid coil at 20 K, shown in ﬁgures 5(a) and (b), themagnitude of Bz(t) is smaller than that of Bex(t) with a veryslight time delay around the peak of the pulse. After the Bz(t)peak, Bz(t) smoothly decreases and approaches its ﬁnal value.
For Bex=2.20 T, shown in ﬁgure 5(b), a ﬂux jump occurred,
and a decrease of Bz and the inhomogeneity of the trapped
ﬁeld proﬁle was observed.
On the other hand, for the case using the ‘split coilwithout yoke’ at 20 K, shown in ﬁgures 5(c) and (d), there isno time delay in Bz(t) at the peak and the peak height of Bz(t)is nearly the same as that of Bex(t). After the peak of the pulse,Bz(t) decreases, then shows an inﬂection and approaches to its

Figure 3(a) presents the trapped ﬁeld, Bz, on the MgB2 bulk at
Ts=20 K by PFM using the three magnetizing coil cases, asa function of the applied pulsed ﬁeld, Bex. For the results
using the ‘solenoid coil with one yoke’, which were reported
brieﬂy elsewhere [13], the Bz value increases steadily fromBex=1.2 T and attains a maximum value of Bz=0.81 T at
Bex=2.0 T. However, a ﬂux jump occurred for a higher ﬁeldof Bex=2.2 T. In the case of using the ‘split coil without
yoke’, the magnetic ﬂux starts to intrude into the bulk centerfrom Bex=0.7 T, which is lower than that for the solenoid
coil, and the Bz value takes a maximum value of Bz=0.75 T
at Bex=1.3 T, and then decreases with further increasing Bex.
For the case using the ‘split coil with two yokes’, the maximum trapped ﬁeld was enhanced to 1.05 T at Bex=1.5 T,
and then decreased with increasing Bex. It is important to notethat no ﬂux jump occurred, even at higher Bex up to 2.95 T in
the case of using the split coil, both with and without theyoke. Figure 3(b) shows Bz at 13 K using the ‘split coil with
two yokes’ as a function of Bex. The trapped ﬁeld wasenhanced with decreasing starting temperature, Ts=13 K;
Bz=1.10 T was realized at Bex=1.55 T with no ﬂux jump.
The detailed time dependences of the local ﬁeld, Bz(t), will be
discussed later.
The results shown in ﬁgure 3(a) were measured under thecondition that the soft iron yoke was loaded on the bulk. In
this case, the trapped magnetic ﬂux was forced to align along
the z-direction due to the existence of yoke. The Bz value after
the removal of the split coil with yoke is also shown inﬁgure 3(b). The inset shows the Bz change at 13 K and for
Bex=1.61 T. The Bz value decreased from 1.10 to 1.04 T,
which results from the absence of the ﬂux alignment effect of4

Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et al

ﬁnal value, which is in clear contrast to that for the ‘solenoid
coil with one yoke’.
In the case of using the ‘split coil with two yokes’ at
13 K, shown in ﬁgures 5(e) and (f), the peak height of Bz(t) is
nearly the same as that of Bex(t), which is a common characteristic for the split coil. However, it should be noticed thatthe intrusion of the magnetic ﬂux was delayed in the case withthe yoke, which is in clear contrast to the case without theyoke, as shown in ﬁgures 5(c) and (d). The local ﬁeld, Bz(t),takes a maximum and then becomes ﬂat with increasing time.
For Bex=1.61 T, a Bz=1.10 T (1.04 T after the yoke isremoved) was achieved. For Bex=2.31 T, Bz decreases and a
ﬂux jump was not observed up to Bex=2.95 T.
Figure 6(a) shows the time dependence of the temperature, T(t), after applying pulsed ﬁelds at 20 K using the split
coil with two yokes. The maximum temperature, Tmax, as afunction of Bex is also shown in the inset. Note that T(t) was
measured on the copper holder shown in ﬁgure 1(a). T(t) takes
a maximum within 2 s for each case and the maximum
temperature, Tmax, increases with increasing Bex, which is
independent of the cases with and without yoke. Figure 6(b)shows the T(t) after applying pulsed ﬁelds at 20 K using thesolenoid coil with one yoke, which was measured on the bulk
surface shown in ﬁgure 1(b). Tmax, as a function of Bex, is also
shown in the inset. T(t) increases with increasing Bex. The
temperature rise was recovered within 30–40 s, which islonger than that for the case using split coil, and the temperature rise seems to be larger than that for the split coil.
However, we must be careful not compare the results ofﬁgures 6(a) to (b) directly, because the position of thetemperature measurement was different and the temperature
for the split coil was not measured on the bulk surface.

Figure 3. (a) Applied pulsed ﬁeld, Bex, dependence of the trapped
ﬁeld, Bz, for each case at Ts=20 K: using the split coil with two
yokes, split coil without yoke and solenoid coil with one yoke. (b)Bex dependence of Bz before and after the removal of the soft ironyokes at 13 K. The trapped ﬁeld change for Bex=1.61 T is also
shown in the inset.

5. Numerical simulation results and discussion
Figure 7 presents the results of the numerical simulation for anormalized magnetic pulse, Bex(t), using the split coils withand without two yokes and the solenoid coil with one yoke.
An imaginary Bex(t) curve for the solenoid coil without theyoke is also shown, which corresponds to the current pulse
shown in equation (2), and takes a maximum at τ=0.013 s.
For Bex(t) for the solenoid coil with one yoke, the yoke
resulted in a moderately slower decay of the magnetic pulse,
compared to Bex(t) for the solenoid coil without yoke. On theother hand, Bex(t) takes a maximum at τ=0.018 s for the
split coil without yoke, according to equation (2). A more
moderate decrease in the magnetic pulse took place for the
split coil with two yokes due to the existence of the yoke.
These results can qualitatively reproduce the experimental
results shown in ﬁgure 4.
Figure 8 shows the results of the numerical simulation of
the trapped ﬁeld, Bz, at 20 K, as a function of the applied
pulsed ﬁeld, Bex, when using each magnetizing coil. The
experimental results in ﬁgure 3(a) are shown again forreference. In all cases, the magnetic ﬂux intruded and wastrapped in the center of the bulk surface, which took a

Figure 4. Time evolution of the applied pulsed ﬁeld, Bex(t), for ‘split
coil with two yokes’, ‘split coil without yoke’ and ‘solenoid coilwith one yoke’.

5Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et al

Figure 5. Time dependence of local ﬁeld, Bz(t), at the center of the bulk surface and the applied ﬁeld, Bex(t), using the ‘solenoid coil with one

yoke’ at Ts=20 K and (a) Bex=1.58 T and (b) Bex=2.20 T; using the ‘split coil without yoke’ at Ts=20 K and (c) Bex=1.29 T and (d)Bex=2.24 T, and using the ‘split coil with two yokes’ at Ts=13 K and (e) Bex=1.61 T and (f) Bex=2.31 T. The 2D trapped ﬁeld
proﬁles, Bz (1 mm), measured 1 mm above the bulk surface are shown in the insets of (a) and (b), and Bz (2 mm), measured 2 mm above thebulk surface are shown in the insets from (c) to (f).

maximum and then decreased with increasing Bex. The
maximum Bz for the ‘split coil with two yokes’ is larger thanthose for the ‘split coil without yoke’ and for the ‘solenoid
coil with one yoke’. These results of the simulation reproduce

the experimental ones well. However, the actual Bex values, atwhich the magnetic ﬂux starts to intrude into the center of thebulk surface, are not consistent with those obtained by theexperiments. These results may result from differences
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H Fujishiro et al

Figure 8. The results of the simulation of trapped ﬁeld, Bz, versus
applied ﬁeld, Bex, at 20 K using the split coils with/without two
yokes and the solenoid coil with one yoke.

between the experimental conditions and the ideal numericalsimulation. However, on the whole, the results of the numerical simulation can qualitatively reproduce the experimental
results for the trapped ﬁeld, Bz.
Figures 9(a) and (b) present the time dependences of thelocal ﬁeld, Bz(t), at Ts=20 K and Bex=1.6 T for the split
coils with/without two yokes and the solenoid coil with one
yoke, respectively. The applied ﬁeld, Bex(t), is also shown foreach case. For the split coil with yoke shown in ﬁgure 9(a),the magnetic ﬁeld, Bz(t), takes a maximum with a slight timedelay and with nearly the same amplitude of the Bex peak,
gradually decreases and then takes a constant Bz value att>0.1 s. For the split coil without yoke, the time delay at thepeak is smaller than that for the split coil with two yokes andthe Bz value is smaller. For the solenoid coil with one yokeshown in ﬁgure 9(b), the peak height of Bz(t) is smaller thanthat of Bex(t) and the peak occurred at nearly the same time.
These results reproduce the experimental ones shown inﬁgure 5 well.
Figures 10(a) and (b) show the numerical simulation
results of the time dependence of the temperature, T(t), atTs=20 K and Bex=1.6 T for the split coil with two yokes
and the solenoid coil with one yoke, respectively. The T(t)values are extracted at three positions; center (x, z)=(0, 0),
middle (x, z)=(5 mm, 0) and side (x, z)=(10 mm, 0) in thebulk. The maximum T(t) increased from the bulk peripheryfor both cases, took a maximum around the peak of theapplied pulse and then decreased from the bulk periphery.
The temperature recovery to the initial temperature,Ts=20 K, for the split coil is faster than that for the solenoid
coil with one yoke, which results from the difference of thesurface area attached to the holder and the difference in its
thermal conductivity. The faster T(t) peak and the prompt T(t)recovery within 1 s results from the small speciﬁc heat, C, andlarge thermal conductivity, κ, of the present MgB2 bulk at
Ts=20 K, which is in clear contrast with the similar numerical simulation results for REBaCuO at Ts=40 K [22], inFigure 6. Time dependence of temperature, T(t), after applying thepulsed ﬁeld using (a) split coil with two yokes and (b) solenoid coilwith one yoke at Ts=20 K for various applied pulsed ﬁelds, Bex.
The maximum temperature, Tmax, as a function of applied ﬁeld Bex,
is also shown in the insets. T(t) was measured on the copper holderin (a) and on the bulk surface in (b).

Figure 7. Time evolution of the normalized applied pulsed ﬁelds,
Bex(t), for the split coil (with and without yokes) and the solenoid
coil (with and without yoke), obtained by numerical simulation.
7

Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et al

Figure 9. Numerical simulation results of the time dependence of thelocal ﬁeld, Bz(t), and applied pulsed ﬁeld, Bex(t), at the center of thebulk at Ts=20 K and Bex=1.6 T for (a) split coils with/without
yokes and (b) the solenoid coil with yoke.

which T(t) takes a maximum at around 1 s at the center of thebulk surface due to the large C value of 132 J kg−1 K−1 andrelatively small κ value along the c-axis of 4 W mK−1. On theother hand, the C and κ values of the MgB2 bulk used in thesimulation are 2.9 J kg−1 K−1 and 20 W mK−1, respectively[14]. These results imply that the heat generation and propagation in the present MgB2 bulk are quite different to thosein the GdBaCuO bulk.
Figure 10(c) shows the numerical simulation results ofthe maximum temperature, Tmax, during the PFM process at
Ts=20 K, as a function of the applied pulsed ﬁeld, Bex, forthe cases using split coil with and without yoke and thesolenoid coil with yoke. In all cases, Tmax increases withincreasing Bex. The Tmax versus Bex relation seems to be
independent of the type of the magnetizing coil and whether
or not the yoke is present. These results suggest that theexperimental results of Bz shown in ﬁgure 3 cannot be
explained by the difference of the temperature rise directly.
The kink behavior at around Bex=1 T may be related to theabrupt ﬂux intrusion to the bulk center.

Figure 10. Numerical simulation results of the maximum temper-

ature, Tmax, during PFM at Ts=20 K, as a function of the applied
pulsed ﬁeld, Bex, for the cases using the split coils with/without two
yokes and the solenoid coil with one yoke.

Finally, let us consider the effect of the soft iron yoke on
the enhancement of the trapped ﬁeld, Bz. Figure 11 shows
images of the magnetic ﬂux vector distribution at t=0.3 s
after the magnetic pulse application of Bex=1.6 T at
Ts=20 K using the split coils with and without the soft ironyoke. For the split coil with yoke shown in ﬁgure 11(a), theinduced magnetic ﬂux in the bulk was pulled along the yoke
(z-direction) during the PFM process, and, as a result, the ﬁnal
8Supercond. Sci. Technol. 29 (2016) 084001

H Fujishiro et alalignment of the trapped magnetic ﬂux in the z-direction wasalmost maintained, even if the split coil with yoke wasremoved after the PFM procedure.
The ﬂux dynamics and heat generation/propagation wereanalyzed during these PFM processes using numericalsimulations and these can qualitatively reproduce the experimental results well. The magnetic ﬂux intrudes and thenattenuates more slowly in the bulk and tends to be aligned
along the z-direction due to the presence of soft iron yoke.

Acknowledgments
This work was supported by Open Partnership Joint Projectsof Japan Society for the Promotion of Science (JSPS) Bilateral Joint Research Projects, and JSPS KAKENHI grant
number 23560002 and 15K04646. Dr Mark Ainslie would
like to acknowledge the support of a Royal Academy ofEngineering Research Fellowship and a Royal SocietyInternational Exchanges Scheme grant, IE131084.
Figure 11. Images of the magnetic ﬂux vector distribution aroundthe bulk after applying a magnetic pulse of Bex=1.6 T at
Ts=20 K using (a) split coil with two yokes and (b) split coilwithout yoke.

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Bz value was enhanced. The trapped ﬂux distribution, aligned
to the z-direction, remained, even if the yoke was removed
after the PFM procedure. On the other hand, for the split coilwithout yoke shown in ﬁgure 11(b), the ﬂux lines curved outof the bulk, and the component in the z-direction, i.e., the Bz
value, became relatively smaller. In this way, the soft ironyokes on both bulk surfaces is signiﬁcantly effective toenhance the Bz value and the subsequent total trapped ﬂux Φz.

6. Conclusion
We have investigated the PFM for a high-Jc MgB2 bulk using
a split-type coil and compared the results to those using asolenoid-type coil. We have also studied the effect of the softiron yoke inserted in the bores of split-type coil to enhance
the trapped ﬁeld, Bz.
A trapped ﬁeld of Bz=1.1 T was achieved on the MgB2
bulk at 13 K without ﬂux jumps by PFM using a split-type
coil with soft iron yoke, which is a record-high trapped ﬁeld
by PFM on an MgB2 bulk to date. Flux jumps, which frequently took place using a solenoid-type coil during PFM,
were avoided by using the split-type coil, even for higher
applied pulsed ﬁelds, Bex. The applied magnetic ﬁeld, Bex(t),rises up slowly and decreases slowly, compared to that for thesolenoid coil with one yoke, which is one of the possible
reasons to avoid the ﬂux jumps.
The Bz value was signiﬁcantly enhanced by the insertionof soft iron yokes in the bores of the split coil, which mainly
results from the ﬂux alignment effect of the yoke. The

9

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