Physica C 463–465 (2007) 410–414
www.elsevier.com/locate/physc

Evaluation of current distribution in bulk superconductors
magnetized by pulsed-ﬁelds
K. Yokoyama a,*, T. Oka b, H. Fujishiro c, K. Noto caAshikaga Institute of Technology, 268-1 Omae-cho, Ashikaga, Tochigi 326-8558, Japanb
Niigata University, 8050 Igarashi-2nocho, Niigata, Niigata 950-2181, Japanc
Iwate University, 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan
Accepted 16 February 2007
Available online 2 June 2007

AbstractFor theoretical clariﬁcation of mechanism of a pulsed-ﬁeld magnetization (PFM) and development of more eﬃcient PFM method, we
carried out a detailed computer simulation in consideration of the diﬀerence in the superconducting characteristics between the growth
sector boundary (GSB) and the growth sector region (GSR) parts of the material. The superconducting current was deﬁned in each partand the magnetic ﬁeld induced by the local current was calculated. The entire magnetic ﬁeld distribution was obtained by adding individual distributions. The experiment with a Sm123 bulk superconductor was performed and it was conﬁrmed that the calculated distribution reproduces the experimental one.
 2007 Elsevier B.V. All rights reserved.
PACS: 74.72.h; 74.25.Ha
Keywords: RE123 bulk superconductor; Critical current density; Magnetic ﬁeld distribution; Pulsed-ﬁeld magnetization; Growth sector boundary/region

1. Introduction
According to the recent improvement in the performance of high-Tc REBaCuO (RE = Y, Sm, Gd, etc.) bulk
superconductors, a high trapped ﬁeld exceeding 17 T hasbeen achieved [1]. A superconducting bulk magnet, inwhich a bulk superconductor is magnetized and used likea permanent magnet, is attracting much attention as oneof the applications of bulk materials, because it can generate stronger magnetic ﬁeld than that of permanent magnets
or iron-cored electromagnets. Thus, various industrial
applications such as magnetic separation and magnetron
spattering are considered [2–5]. In the magnetization, apulsed-ﬁeld magnetization (PFM) method is an important
technique for various industrial applications, because abulk can be magnetized with a simple and relatively cheap
apparatus in a short time. However, there is a problem that
*Corresponding author. Tel.: +81 284 62 0605; fax: +81 284 62 4633.
E-mail address: k-yokoyama@ashitech.ac.jp (K. Yokoyama).

0921-4534/$ - see front matter  2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2007.05.027

the strength of trapped ﬁeld (BT) is less than a half of thatmagnetized by a ﬁeld cooled method (FC) at low temperature below about 50 K. The IMRA (iteratively magnetizing
pulsed-ﬁeld operation with reducing amplitudes) method[6,7], MPSC (multi-pulse technique combined with a stepwise cooling) method [8] and MMPSC (modiﬁed MPSC)
method [9] are developed recently aiming at improvement) and BPFMof over 5 T is achieved withof BT in PFM (BPFMTTthe MMPSC method. These are magnetizing methods inwhich several pulsed-ﬁelds are applied with changing thestrength of magnetic ﬁelds and cooled down temperature
based on the idea of controlling heat generation of the bulk
during the magnetization. The heat generation inﬂuences acritical current density Jc, and thus, the resulted BT alsochanges [10,11]. Moreover, it is known that there is a diﬀerence in Jc characteristics between a growth sector boundary(GSB) part and a growth sector region (GSR) part in thesame material, and the characteristics of the former are
more excellent than that of the latter. In the FC magnetization, the diﬀerence between two parts hardly inﬂuences theK. Yokoyama et al. / Physica C 463–465 (2007) 410–414

performance of the trapped ﬁeld because, in this case, heatgeneration is mostly caused by the ﬂux ﬂow during thedecreasing exciting ﬁeld which is very slow in FC method,
and thus the temperature rise is very small. In the PFM, on
the other hand, heat generation originates mainly from ﬂux
jump and it is diﬀerent locally according to the Jc
characteristics.
This paper presents a detailed computer simulation taking into the consideration of the diﬀerence in the Jc characteristics between GSB and GSR parts for the purposeof theoretical clariﬁcation of magnetizing mechanism anddevelopment of more eﬃcient magnetizing method. Firstly,a Sm123 bulk superconductor is magnetized by PFM withchanging the magnitude of applied peak ﬁeld from 3.10 to
5.42 T. Temperature and trapped ﬁeld at the bulk surface
are monitored during the magnetization, and the trapped
ﬁeld distribution of 3.5 mm above the surface is scanned
after the magnetization. The FC magnetization with varying temperature of the material was also performed. Next,
the maximum temperature is obtained from the experimental data of the PFM, and the Jc at that temperature is calculated by using the trapped ﬁeld-versus-temperature dataof the FC assuming that a critical current ﬂows to theentire sample. Here, the current density of GSB andGSR parts is deﬁned, respectively based on the obtained
Jc. Then, changing each current density, the magnetic ﬁeld
distribution is simulated and compared with the experimental distribution map. From these procedures, the validity of the simulation is veriﬁed from the agreement
between experimental and numerical results when thepulsed-ﬁeld of diﬀerent magnitude is applied to a bulk
superconductor.
2. Experimental
2.1. Experimental detail
Using a melt-processed Sm123 bulk superconductor, atemperature rise and a trapped ﬁeld distribution in theFC and the PFM are measured. The bulk material is ahighly c-axis oriented crystal and consists of SmBa2Cu3Oy(Sm123), Sm2BaCuO5 (Sm211) with the molar ratio of
1.0:0.3, 0.5 wt.% Pt powder and 1.5 wt.% Ag2O addition(Dowa Mining Co., Ltd.). The sample size is 45 mm indiameter and 18 mm in thickness, and it is impregnatedby epoxy resin reinforced by glass ﬁber. The epoxy resinon the upper and lower sides of the bulk was removed inorder to establish the thermal contact to the thermocouples
and to measure the precise temperature and to reduce athermal contact resistance to the cold head. The bulk isset on a copper base connected to a cold head of GM
refrigerator (AISIN SEIKI CO., LTD, GR301). Five Teflon-coated chromel-constantan thermocouples (T1–T5) of
76 lm in diameter are adhered on the surface of bulk
superconductor using the GE7031 varnish. T1 is put on
the center of the bulk. T2–T3 and T4–T5 are arranged in
the radial direction of GSR and GSB, respectively as411shown in the insets of Fig. 2. A Hall sensor (F.W. Bell,BHT-921) is set near T1 to monitor a magnetic ﬂux densityof trapped ﬁeld as shown also in the insets. A superinsulation is wound around the bulk superconductor and they arecovered with a vacuum vessel.
In the FC magnetization, a static ﬁeld of 5 T is applied
by a 10 T superconducting magnet at the higher temperature than a critical one, Tc, and the bulk is cooled down
to a prescribed temperature (40, 50, 60 and 70 K at thecold stage). Then, the magnetic ﬁeld is reduced to zerowith a sweep rate of 5.06 mT/s. The temperature andmagnetic ﬁeld are measured every 8 s. In the PFM, after
the bulk is cooled down to 40 K at the cold stage,
pulsed-ﬁeld of 3.10, 3.83, 4.64 and 5.42 T with a risingtime of 10 ms is applied by using a copper coil cooled
at liquid nitrogen temperature and a pulse generator witha condenser bank of 60 mF. The temperature and magnetic ﬁeld are monitored about 7 times per second. Aftereach magnetization, the trapped ﬁeld distribution of parallel direction to the bulk axis is measured by scanning anaxial type Hall sensor (F.W. Bell, BHA-921) above thevacuum vessel, in which the gap between the bulk surface
and the sensor is 3.5 mm.
2.2. Experimental results
Fig. 1 shows the temperature dependence of trapped
ﬁeld. The horizontal and vertical axes indicate the maximum temperature at T1 and the maximum z-direction ﬁeld
measured 3.5 mm above the bulk surface, respectively. The
relationship in the FC magnetization is also presented. The
temperature increases monotonously with the applied ﬁeld.
On the other hand, the trapped maximum ﬁeld increases
with the applied pulsed-ﬁeld from l0H = 3.10 to 4.64 T,
but, thereafter it decreases along the FC line which indicates the upper limit of trapped ﬁeld for each temperature.

Fig. 1. The temperature dependence of the trapped ﬁeld for the various
applied pulsed-ﬁelds. The horizontal and vertical axes indicate themaximum temperature at T1 and the maximum z-direction ﬂux density
in the horizontal plane 3.5 mm above the bulk surface, respectively. Therelationship for the FC magnetization is also presented.

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K. Yokoyama et al. / Physica C 463–465 (2007) 410–414

These results suggest that a high applied ﬁeld causes hightemperature rise, and thus, a trapped ﬁeld is reduced dueto the decrease in Jc.
Fig. 2 shows the time response of normalized temperature rise of T1–T5 for pulsed-ﬁeld of (a) l0H = 3.83 Tand (b) l0H = 4.64 T, respectively. For the case ofl0H = 3.83 T, the temperature of GSR part (T2, T3) risesfaster than that of GSB part (T4, T5) and it means thatmagnetic ﬂux enters in the bulk through the GSR part.
For the case of l0H = 4.64 T, on the other hand, the temperature rises up at the same time at all the points and it isconsidered that magnetic ﬂux enters in the bulk from thewhole periphery.
Fig. 3 illustrates the trapped ﬁeld distribution measured
3.5 mm above the bulk surface for applied pulsed-ﬁeld of(a) l0H = 3.83 T and (b) l0H = 4.64 T, respectively. InFig. 3a, the distribution map draws a diamond shape andone can see that a lot of magnetic ﬂux is trapped in theGSR part. In Fig. 3b, the map is quadrangle and one cansee that the trapped ﬂux of GSB part is more than thatof GSR. From the results of Figs. 2 and 3, in the case ofl0H = 3.83 T, an applied ﬁeld is too small to invade intoFig. 3. Trapped ﬁeld distributions in the horizontal plane 3.5 mm above
the bulk surface for the applied pulsed-ﬁeld of (a) l0H = 3.83 T and (b)l0H = 4.64 T, respectively (Section 2.2).

the GSB part where Jc is higher. In the case ofl0H = 4.64 T, on the other hand, magnetic ﬂux can enter
into the GSB part, but ﬂux creep occurs because of adecline in Jc caused by large heat generation in GSR part,and then, trapped ﬁeld decreases.
3. Simulation

Fig. 2. The time responses of normalized temperature rise at T1–T5 forthe applied pulsed-ﬁeld of (a) l0H = 3.83 T and (b) l0H = 4.64 T,
respectively.

In the simulations of magnetization, an axisymmetricmodel has been usually used. In order to verify the magnetizing mechanism in detail, it is necessary to discuss theGSB and the GSR parts separately because the Jc characteristics are diﬀerent between each area. This paper
attempts to estimate each Jc in two parts by using experimental data and to simulate the magnetic ﬁeld distribution.
In the paper, though the pinning characteristics during themagnetization are not considered, they are evaluated as
distribution of Jc after the magnetization.
An analytical procedure is explained in the applied ﬁeldof 3.83 T. A maximum temperature of Tmax = 57.5 K is

K. Yokoyama et al. / Physica C 463–465 (2007) 410–414

obtained from the experimental data. The Jc at 57.5 K canbe calculated by using the trapped ﬁeld-versus-temperature
data of the FC magnetization is shown in Fig. 1. Assumingthat critical current ﬂows to the whole material, the following expressions for the Jc and the magnetic ﬁeld density B
at an arbitrary position are obtained:)
B ¼ rot A;
ð1Þ
1
r2 A ¼ J cl0
where A and l0 are the vector potential and the magnetic
permeability of the vacuum, respectively. Now, ﬂux density
at the center axis of the bulk 3.5 mm above the surface ismm
¼ 1:56 T in Fig. 3a, and therefore, the critical curB3:5
Trent density is Jc = 5.18 · 108 A/m2 from Eq. (1). Next,
the current density in GSB and GSR parts is deﬁned as
JGSB and JGSR, respectively, based on the above Jc. The
sample is evenly divided into eight regions, each four regions of GSB and GSR. Assuming the current loops in413

each part, the magnetic ﬁeld induced by JGSB and JGSR iscalculated by use of the Biot–Savart law. The entire magnetic ﬁeld distribution is obtained by adding individual distributions. After comparing the obtained distribution withthe experimental one shown in Fig. 3a, JGSB and JGSR areupdated and the magnetic distribution is calculated again.
Fig. 4a shows the simulation result when JGSR/JGSB = 0.3.
The simulation in l0H = 4.64 T is performed as well. Themm¼ 1:60 T from Fig. 3b, and theTmax = 65.7 K and B3:5
Tcritical current density is Jc = 5.89 · 108 A/m2. Fig. 4billustrates the simulation result when JGSR/JGSB = 1.5.
The numerical results shown in Fig. 4 reproduce the experimental results shown in Fig. 3 well, and thus, the validityof the proposed method is conﬁrmed.
4. Conclusions
We proposed a detailed simulation method which took
into account the diﬀerence in the Jc characteristic between
GSB and GSR parts. A Sm123 bulk superconductor wasmagnetized by the PFM as varying the magnitude ofapplied ﬁeld and trapped ﬁeld distribution was measured.
The magnetic ﬂux density of the GSR part was higher thanthat of GSB part for the pulsed-ﬁeld of l0H = 3.83 T, but
the relation was opposite for the case of l0H = 4.64 T. It
was conﬁrmed that the diﬀerence of Jc inﬂuenced the performance of trapped ﬁeld. Next, the numerical analysis
was performed based on the experiment data. The current
density in GSB and GSR parts was separately evaluatedand the magnetic ﬁeld distribution was calculated. The
numerical calculation results of trapped ﬁeld distributionwere corresponding to the experimental one, and therefore,
it was conﬁrmed to be able to analyze the current distribution in detail by the proposed method. We will carry out
the magnetizing simulation on the IMRA, MPSC andMMPSC methods hereafter, and furthermore, there is apossibility that a better magnetizing method can beproposed.
Acknowledgment
This study was partially supported by the CREAT
IWATE Project driven by the Japan Science and Technology Organization.
References

Fig. 4. Results of numerical calculation for magnetic ﬁeld distributions in
the horizontal plane 3.5 mm above the bulk surface for the applied pulsedﬁeld of (a) l0H = 3.83 T and (b) l0H = 4.64 T, respectively.

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