IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 27, NO. 4, JUNE 2017

6800205

Pulsed-Field Magnetizing Characteristics ofRectangular-Shaped Gd–Ba–Cu–O Bulk Using
Split- and Solenoid-Type Coils
Keita Takahashi, Mark D. Ainslie, Member, IEEE, Hiroyuki Fujishiro, and Tomoyuki Naito

Abstract—We have investigated the trapped-field characteristics
of a rectangular-shaped Gd–Ba–Cu–O bulk (33 × 33 × 15 mm3 )magnetized by pulsed-field magnetization (PFM) using split- andsolenoid-type coils. A soft iron yoke was set below the bulk for thesolenoid coil and two yokes are inserted in the bores of the split
coil. The maximum trapped field BZ m a x at the center of the bulk
surface was 1.73 T at 40 K in the case of the solenoid coil, with adistorted profile. On the other hand BZ m a x was enhanced to 3.05 T
at 40 K for the split coil with two yokes for which a symmetrictrapped-field profile was observed. The behavior of the magnetic
flux motion indicated two conditions for the enhancement of thetrapped field: that the magnetic flux intrudes easily into the bulk
even for lower applied fields and then saturates with minimal flux
creep. We have also investigated the electromagnetic and thermal
properties of the bulk during PFM using a numerical simulationin which the magnetic flux tended to align along the z-axis due tothe presence of the soft iron yoke. The use of the split coil with two
yokes is effective in enhancing the trapped field for the rectangularshaped bulks.
Index Terms—(RE) BaCuO bulk, pulsed field magnetization,
numerical simulation, trapped field, soft iron yoke.

I. INTRODUCTIONULSED field magnetization (PFM) of (RE)BaCuO bulks(RE: rare earth element or Y) has been investigated intensively for practical applications as a substitute for field-cooledmagnetization (FCM) because PFM is an inexpensive and mobile experimental setup with no need for a superconducting
magnet. However, the trapped field, BZ , by PFM is generally
lower than that by FCM, where BZ values over 17 T have beenachieved [1], because of the large temperature rise caused by the
dynamical motion of the magnetic flux [2]. To enhance BZ by
PFM, multi-pulse techniques using a solenoid coil are usuallyeffective due to the reduction of temperature rise [3–6]. Using a
new multi-pulse technique – the so-called modified multi-pulse
technique with stepwise cooling (MMPSC) – we successfully
achieved a highest trapped field of BZ = 5.20 T on a 45 mm

P

Manuscript received September 1, 2016; accepted October 17, 2016. Date of
publication November 7, 2016; date of current version November 22, 2016. This
work was supported by the Open Partnership Joint Projects of Japan Society for
the Promotion of Science (JSPS) Bilateral Joint Research Projects and the JSPS
KAKENHI under Grant 23560002 and Grant 15K04646.
K. Takahashi, H. Fujishiro, and T. Naito are with the Faculty of Science and Engineering, Iwate University, Morioka 020-8551, Japan (e-mail:t2216017@iwate-u.ac.jp; fujishiro@iwate-u.ac.jp; tnaito@iwate-u.ac.jp).
M. D. Ainslie is with the Bulk Superconductivity Group, Department ofEngineering, University of Cambridge, Cambridge CB2 1PZ, U.K. (e-mail:mark.ainslie@eng.cam.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2016.2625764

Gd-Ba-Cu-O bulk disk at 30 K, which is a record-high value todate [7].
In addition, the use of new types of coils, such as a split
coil or a vortex coil was confirmed to enhance BZ both experimentally and numerically [8], [9]. Its cooling procedure
along the ab-plane of the bulk is assumed to improve the heatdissipation and reduce the temperature rise during PFM, because the ab-plane thermal conductivity, κab , is much higher
than along the c-axis, κc [10]. From these reasons, the useof split coil also has a potential to realize a high-trappedfield bulk magnet. A ferromagnetic yoke incorporated in themagnetizing apparatus has been also used to directly improve the available magnetic flux. M. D. Ainslie et al. realized the enhancement of trapped field of BZ = 3.27 T on
the top surface of a 30 mm diameter Gd-Ba-Cu-O bulk at
40 K employing such a split coil with a pair of soft iron yoke[11]. It is also the intention of this study to make a comparison of the magnetic flux dynamics between using solenoid- andsplit-type coils and to acknowledge the nature of the trappedfield enhancement for higher trapped field magnets.
We also reported the PFM results of a rectangular-shapedbulk using a solenoid coil, showing that an inhomogeneous Jc
distribution and the shape of the bulk leads to an asymmetrictrapped field profile [12]. There has been no research reported
in the case of a rectangular-shaped bulk magnetized using a split
coil so far. Additionally, a rectangular-shaped bulk would makethe difference of the magnetic flux dynamics clearly between asolenoid and split coils.
The experimental measurements have shown progress towards a more effective approach to enhance BZ using a split-coilwith a soft iron yoke [11], [13], [14]. To clarify the multi-physics
during the PFM process, numerical simulations are a useful aid
because the experimental measurements are restricted. Several
studies of numerical simulation have been reported for PFM[2], [15–21]. In this study, we experimentally investigate thetrapped field characteristics of a rectangular-shaped Gd-Ba-CuO bulk magnetized by PFM using solenoid and split coil. We
also construct a numerical model to reproduce the experimental
assembly and numerically analyze the time dependence of thelocal field BZ (t, r) in the bulk. The choice of the magnetizing coils and the effect of a soft iron yoke on the trapped fieldcharacteristics are also discussed.
II. EXPERIMENT AND SIMULATION SETUP
A. Experimental Setup and Procedure
The rectangular-shaped Gd-Ba-Cu-O bulk superconductor(Nippon Steel) of area 33 × 33 mm2 in the ab-plane and1051-8223 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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6800205

Fig. 1.

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 27, NO. 4, JUNE 2017

Experimental setup of two kinds of apparatus for PFM and the magnetizing coil, (a) solenoid-type and (b) split-type.

15 mm in thickness was mounted on the cold stage of a GiffordMcMahon (GM) cycle helium refrigerator. A schematic view of
two kinds of apparatus for PFM is shown in Fig. 1. Two types ofmagnetizing coils (solenoid and split coil), which were cooledusing liquid nitrogen, were placed outside the vacuum chamber.
In Fig. 1(a), the bulk was tightly mounted in a stainless steel(SUS304) frame using Stycast 2850GT resin. A soft iron yoke
was set below the bulk in the solenoid type apparatus. In Fig.
1(b), the bulk was mounted in a copper holder and magnetized
between the two coils of the split coil, in which two soft ironyokes were inserted. Single magnetic pulses, Bex , of amplitudes
ranging from 2.2 to 6.0 T were applied individually to the bulk,
which was cooled to either Ts = 65 or 40 K. During PFM,
the time dependence of the local field BZ (t) at the center ofthe bulk surface was measured by using a Hall sensor with adigital oscilloscope. The temperature, T (t), was also measured
by a CERNOX thermometer on the side of the sample holder.
The trapped field profiles were mapped at 2 mm above the bulk
surface by scanning the Hall sensor with a pitch of 1 mm using
an x-y stage controller.
B. Numerical Simulation
Based on our experimental setup shown in Fig. 1, a threedimensional (3D) numerical model was constructed using thefinite element method (FEM). The physical phenomena during
PFM are described by electromagnetic and thermal equations,which were referred to refs. [22], [23]. Commercial software,
Photo-Eddy, combined with Photo-Thermo (Photon Ltd, Japan),
was adopted for the analysis, which was carried out using a personal computer. The simulation procedure and the parameters
used were described elsewhere in detail [24].
The power-n model (n = 8) was used to describe the nonlinear E-J characteristic of the bulk. The Kim model was considered for an approximation that the temperature and magnetic
field dependence of Jc (T, B) was described as, 2  32
T
B0(1)
Jc (T, B) = α 1 −Tc|B| + B0
where Tc ( = 92 K) is the critical temperature of the bulk
at B = 0 T, and B0 ( = 1.3 T) is a constant. An interpolation method, the most accurate method to model theFig. 2. Experimental results of the trapped field B Z at the center of the bulk
as a function of the applied field B e x using the solenoid- and split- coils at
65 K and 40 K.

experimentally measured Jc (T, B) data was adopted in our recent paper [11]. A homogeneous Jc distribution, with a constant
α value of 3.0 × 108 A/m2 , was used in this study, which corresponded to Jc (40 K, 0 T) = 2.2 × 108 A/ m2 . The anisotropic
thermal conductivities κab = 20 Wm−1 K−1 in the ab-planeand κc = 4 Wm−1 K−1 along the c-axis were assumed. The
rectangular shaped bulk, with the same dimensions as that usedin the experiments, was cooled to Ts = 40 K. Three types ofcoils (solenoid without yoke, split without yoke and split withyoke) were analyzed. For solving the models in a reasonable
time, one-fourth of the superconducting bulk was considered.
The magnetic saturation that limits the maximum achievablemagnetic flux density in the soft iron yoke was presumed to be
1.6 T as a practical value of a ferromagnetic material.
III. EXPERIMENTAL RESULTS
Figure 2 presents the trapped field, BZ , at the center of thebulk surface, as a function of the applied field Bex for both thesolenoid- and split- coils. Cooling the bulk sample to a lower
temperature (from 65 K to 40 K) resulted in a higher trappedfield due to an increase in the Jc of the bulk. For the solenoid
coil, BZ at 40 K started to increase at Bex = 4.0 T, became∗= 5.48 T
a maximum trapped field BZm ax = 1.73 T at Bex
and then decreased with further increasing Bex . Hereafter, weabbreviate the optimum applied field to obtain the maximum

TAKAHASHI et al.: PULSED-FIELD MAGNETIZING CHARACTERISTICS OF RECTANGULAR-SHAPED GD–BA–CU–O

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Fig. 3. Temperature rise ΔT measured on the side of the sample holder as afunction of the applied field B e x for the solenoid- and split- coils.
∗
trapped field as Bex. This is a typical result consistent with aprediction by the critical state model (CSM), the ratio of required
applied field to obtain the maximum trapped field Bex / BZm ax
to be over two. On the other hand, in the case of the split coil, themagnetic flux started to be trapped at the center for Bex as low
as 3.5 T at 40 K and BZm ax drastically increased with slightly
increasing Bex . The BZm ax was 3.05 T at 40 K, which was
higher than that obtained by using the solenoid coil at relatively∗= 4.01 T. The measured BZ here still includes thelow Bexinfluence of the presence of the yokes and is slightly reduced(around 0.2 T) when the yokes are removed, as described in[25]. However, the use of the split coil has potential to obtainthe trapped field equivalent to the applied field similar to the
FCM technique.
Figure 3 shows the temperature rise, T, measured on the sideof the sample holder, as a function of the applied field, Bex , forboth the solenoid- and split- coils. T increased monotonicallywith increasing Bex in contrast to the trapped field. T forthe split coil was two times higher than that obtained by using
the solenoid coil. In this case, the thermal properties of thecopper sample holder could not be negligible with possible eddy
current heating at low temperature. These results suggest thatthe enhancement of the trapped field characteristics depends onthe magnetic flux motion ruling out the influence of heating
roughly. We have shown in the numerical simulations in [11]that the magnetizing fixture and presence of the yoke has aminimal effect on the average temperature rise in the bulk.
Figure 4 presents the trapped field profiles of the rectangularshaped bulk using (a) the solenoid- and (b) split- coils measured
at 2 mm above the bulk surface after the optimum magnetization
at Ts = 40 K. Experimental results of a typical disc bulk using(c) the solenoid- and (d) the split- coils reported by M. D. Ainslie
et al. were also shown as a reference [11]. For all cases (a) ∼(d), the trapped field profiles were saturated with a conical shape∗
shown in Fig. 2. In
when applying optimum applied field Bex
Fig. 4 (a) using the solenoid coil for the rectangular shaped bulk,
the trapped field profile was distorted along the growth sector
boundary and resulted in lower trapped field at the center of thebulk. The uniformity of the trapped filed profile is correlation
with the magnetic flux dynamics [12]. For the solenoid coil,the magnetic flux concentrates on the rim and intrudes into

Fig. 4. Experimental results of the trapped field profiles measured at 2 mmabove when full magnetization for the rectangular-shaped bulk, using (a) thesolenoid- and (b) split- coils and for the disc bulk using (c) the solenoid- and(d) split- coils reported by M. D. Ainslie et al. [11] at 40 K.

Fig. 5. Time dependence of the local field B Z (t) at the center of the bulk
surface for each coil, (a) solenoid coil and (b) split coil, after applying the
optimum applied field B e∗x .

the bulk from the periphery. An asymmetric profile was causedby the local temperature rise due to such an inclination of themagnetic flux. However, (b) using split coil, the trapped field
profile is not affected by the influence of the shape of the bulk andcompares favorably with the disc bulk (c) and (d). A symmetrictrapped field profile can be obtained when the magnetic flux
intrudes not from the periphery but from the surfaces for the split
coil [9], following the temperature rise on the whole surface ofthe bulk.
Figure 5(a) and 5(b) present the time dependence of the local
field, BZ (t), at the center of the bulk surface for each mag∗
. The applied pulsed field,
netizing coil when applying Bex
Bex (t), was also shown. Using the solenoid coil shown in
Fig. 5(a), the magnetic flux started to intrude into the center6800205

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 27, NO. 4, JUNE 2017

Fig. 6. Analysis results of the trapped field B Z at the center of the bulk as afunction of the applied as function of the applied field B e x for each coil.

of the bulk at the same time with increasing of the applied fieldand BZ (t) gradually increased while the applied field was fluctuating. The maximum value of BZ (t) was lower than Bex by
2 T at t = 13 ms and then decreased similarly with increasingtime until the end of the magnetizing process. However, by using the split coil shown in Fig. 5(b), the magnetic flux would not
intrude at first during the magnetizing process, but then drastically increased after the pulse peak at t = 26 ms. BZ (t) took amaximum value close toBex and the magnetic flux still remained in the bulk evenafter the whole process of magnetization. This behavior of themagnetic flux motion for the split coil indicated combined conditions in the enhancement of the trapped field: the magnetic∗
and then saturates withflux penetrates fully into the bulk at Bex
minimal flux creep.
IV. SIMULATION RESULTS AND DISCUSSION
In this section, the results of the simulation for PFM using a
split coil without a yoke are also considered. Figure 6 shows thetrapped field BZ at the center of the bulk surface for each coilat 40 K as a function of the applied field Bex . The magnetic flux
starts to be trapped at the center at Bex = 3.00 T. However, BZ
for the split coil with yoke is higher by 0.5 T at Bex ≥ 4.50 T.
These results suggest the effect of the soft iron yoke might exist
in the experimental results shown in Fig. 2. On the other hand,
we can notice that the difference in the BZ − Bex curve for eachmagnetizing coil is relatively small in the case without the yoke,
as observed in [11].
Figure 7 shows the trapped field profiles BZ on therectangular-shaped bulk surface normalized by the maximum
trapped field BZm ax of the bulk center at t = 300 ms when applying Bex = 5.00 T using each magnetizing coil. For the split
coil with the yoke, the amount of the magnetic flux along withz-axis direction is kept even in the outer region of the bulk in
addition to the higher magnitude of the trapped field as shownin Fig. 6. In other words, the trapped magnetic flux can be oriented towards the z-axis direction on the bulk surface if there is
the soft iron yoke. The existence of the soft iron yoke enables
to control the direction of the magnetic flux and encourages anadditional pinning force in the bulk.

Fig. 7. Analysis results of the trapped field profiles on the bulk surface whenfull magnetization for each coil.

Fig. 8. Time dependence of the local field B Z (t) at the center of the bulk
surface for each coil after applying the pulsed field of B e x = 5.00 T.

Figure 8 depicts the results of time dependence of the local
field BZ (t) at the center of the bulk surface when applying
pulsed field of Bex = 5.00 T with each magnetizing coil. The
local field BZ (t) at the center of the bulk surface starts to increase
and approaches the maximum value for t = 13 ms. For the split
coil, one condition for the enhancement of the trapped field, thepenetration of the magnetic flux could not be reproduced asshown in Fig. 5(b). It also suggests that the full penetration of
the magnetic flux does not depend on the split coil. The soft ironyoke is effective for reduction of the flux creep in process ofdemagnetization after the pulse peak. So for now, the proposed
reason for the observed enhancement of the trapped field mainly
depends on the existence of the soft iron yoke in this simulation.
V. SUMMARY
We have investigated experimentally and numerically thetrapped field characteristics of a rectangular-shaped Gd-Ba-CuO bulk magnetized by PFM using split- and solenoid- coils. The
maximum trapped field BZm ax was enhanced to 3.05 T at 40 K
for the split coil with two yokes, for which a symmetric trappedfield profile can be seen. For the split coil, the magnetic flux∗
and then saturates with minpenetrates fully into the bulk at Bex
imal flux creep during PFM. Numerical simulation considering

TAKAHASHI et al.: PULSED-FIELD MAGNETIZING CHARACTERISTICS OF RECTANGULAR-SHAPED GD–BA–CU–O

electromagnetic and thermal properties of the bulk was performed showing that the soft iron yoke is effective in a reduction of the flux creep by aligning the magnetic flux to z-axis
direction. The use of the split coil with two yokes is effective inenhancing the trapped field.
ACKNOWLEDGMENT
Dr. M. Ainslie would like to acknowledge the support of a
Royal Academy of Engineering Research Fellowship.
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