IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 2, JUNE 2008

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Numerical Analysis of Bulk Superconducting Magnet
Magnetized by Pulsed-Field Considering a Partial
Difference of Superconducting Characteristics
K. Yokoyama, T. Oka, H. Fujishiro, and K. Noto

Abstract—On the pulsed-field magnetization (PFM) of superconducting bulk magnets, a detailed analysis taking into accountthe difference in superconducting characteristics between a growth
sector boundary (GSB) and a growth sector region (GSR) parts ofthe material was carried out. The current density was defined ineach part and a magnetic field induced by the local current wascalculated. The entire magnetic field distribution was obtainedby adding individual distributions. The experiment with a Sm123
bulk superconductor was performed and it was confirmed that thecalculated distribution agreed with the experimental result.
Index Terms—Bulk superconductor, growth sector boundary/region, magnetic field distribution, pulsed-field magnetization.

I. INTRODUCTION
SUPERCONDUCTING permanent magnet with RE123(, Sm, Gd, etc) bulk materials is attracting muchattention as one of strong magnetic field generators. This magnet
is superior to conventional permanent magnets or iron-coredelectro- magnets in strength of generated magnetic field, andthus, various industrial applications such as magnetic separationand magnetron spattering are considered [1]–[4]. The magnetizing method of bulk magnets is roughly divided into a fieldcooling (FC) and a pulsed-field magnetization (PFM). In theformer, a high magnetic field can be captured and a magnetic
field exceeding 17 T at 29 K is achieved [5]. On the other hand,
PFM is an important technique for various industrial applications because a bulk can be magnetized with a simple and relatively cheap apparatus in a short time. However, there is a
is less than aproblem that the strength of trapped field
half of that magnetized by 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 recentlyA

in PFM
andof
aiming at improvement ofover 5 T is achieved by the MMPSC method. These are magnetizing methods in which several pulsed-fields are applied withchanging the strength of magnetic fields and cooled down temperature based on the idea of controlling heat generation of thebulk during the magnetization. The heat generation influencesalso
a critical current density , and thus, the resulted
changes [10], [11]. Moreover, it is known that there is a difference in characteristics between a growth sector boundary(GSB) and a growth sector region (GSR) parts in the same material, and the characteristics of the former are more excellent thanthat of the latter [7]. In FC method, the difference between two
parts hardly influences the performance of the trapped field because, in this case, heat generation is mostly caused by the flux
flow during the decreasing exciting field which is very slow in
FC method, and thus the temperature rise is very small. In PFM,
on the other hand, heat generation originates mainly from flux
jump and it is different locally according to .
This paper presents a detailed analysis method taking into theconsideration of the difference in the characteristics between
GSB and GSR parts for the purpose of theoretical clarificationof magnetizing mechanism and development of more efficientmagnetizing method. Firstly, a Sm123 bulk superconductor ismagnetized by PFM with changing the magnitude of applied
peak field from 3.10 to 5.42 T. Temperature and trapped fieldat the bulk surface are monitored during the magnetization, andthe trapped field distribution above 3.5 mm from the surface isscanned after the magnetization. Next, a current distribution isestimated from the experimental results and the magnetic field
distribution is calculated by using the proposed analysis modeland the obtained current distribution. The validity of the simulation method is verified from the agreement between experimental and numerical results.
II. EXPERIMENT

Manuscript received August 28, 2007. This work was supported in part by the
CREAT IWATE Project driven by the Japan Science and Technology Organization.
K. Yokoyama is with the Department of Electrical and Electronic Engineering, Ashikaga Institute of Technology, 268-1 Omae-cho, Ashikaga, Tochigi
326-8558, Japan (e-mail: k-yokoyama@ashitech.ac.jp).
T. Oka is with Education Center for Engineering and Technology, Faculty ofEngineering. Niigata University, 2-8050, Ikarashi, Nishi-ku, Niigata 950-2181,
Japan (e-mail: okat@eng.niigata-u.ac.jp).
H. Fujishiro is with the Faculty of Engineering, Iwate University, 4-3-5 Ueda,
Morioka 020-8551, Japan (e-mail: fujishiro@iwate-u.ac.jp).
K. Noto is with Iwate University (e-mail: notokoshichi@yahoo.co.jp).
Digital Object Identifier 10.1109/TASC.2008.920530

A. Bulk Material and Measurement Procedure
Fig. 1 shows a melt-processed Sm123 bulk superconductorused in this experiment. The growth sector boundaries (GSB)
that appear in the process of the crystal growth can be clearly
seen. The bulk material is a highly c-axis oriented crystal and(Sm123),(Sm211)consists ofwith the molar ratio of 1.0:0.3, 0.5 wt.% Pt powder and 1.5 wt%
addition. The size of the sample is 46 mm in diameterand 15 mm in thickness and it is impregnated by epoxy resin
reinforced by glass fiber. The epoxy resin on the upper and1051-8223/$25.00 © 2008 IEEE

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 2, JUNE 2008

Fig. 1. A melt-processed Sm123 bulk material and set-up for measurement of
temperature and trapped field.

lower sides of the bulk was removed in order to establish
the thermal contact to the thermocouples and to measure theprecise temperature and to reduce a thermal contact resistanceto the cold head.
The bulk is set on a copper base connected to a cold head ofGifford-McMahon (GM) cycle refrigerator (AISIN SEIKI CO.,LTD, GR301). Five Teflon-coated chromel-constantan thermoin diameter are adhered on the surcouples (T1–T5) of 76
face of bulk superconductor using the GE7031 varnish. T1 is
put on the center of the sample and T2–T5 are arranged in four
GSRs as shown in the insets of Fig. 1. A Hall sensor (F.W.Bell,
BHT-921) is set near T1 to monitor a magnetic flux density of
trapped field as shown also in the insets.

Fig. 2. The time responses of temperature at T2–T5 for the applied pulsed-field H 3.10 T and 4.64 T.

=

B. Magnetization and Results
A temperature and a trapped field distribution in FC and PFM
are measured. In FC magnetization, a static field of 5 T is applied to the bulk material at an initial temperature of 100 K by
a solenoid type superconducting magnet with a field of 10 T
and a room-temperature-bore of 100 mm in diameter (JASTEC,JMTD-10T100), and afterward the bulk is cooled down to a prescribed temperature (40, 50, 60 and 70 K at the cold stage). Aftertemperature of all thermocouples steady, the magnetic field is reduced to zero with a sweep rate of 5.06 mT/s. A temperature
and a magnetic field are measured every 8 seconds. In PFM,
the bulk is cooled down to 40 K at the cold stage, and afterward pulsed-field of 3.10, 3.83, 4.64 and 5.42 T with a risingtime of 10 ms is applied. A temperature and a magnetic field
are monitored about 7 times per second. After each magnetization, the axial components of trapped magnetic flux density
above 3.5 mm from the bulk surface are scanned by a Hall sensor(F.W.Bell, BHA-921).
Fig. 2 shows the time response of temperature of T2–T5 forand 4.64 T. For the case of
pulsed fields of
3.10 T, the temperature at T4 and T5 rise faster andhigher than ones at other parts. It means that magnetic flux entersin the bulk only through T4 and T5parts. For the case of
4.64 T, on the other hand, the temperature at all the points rise
up at the same time. It is considered that magnetic flux entersin the bulk from the whole periphery. When each maximum
4.64
temperature is compared, it reaches about 70 K for
T though it is about 50 K for3.10 T. It is because heatgeneration caused by pinning loss grows with increase in theamplitude of applied pulsed-field.

Fig. 3. The temperature dependence of trapped flux density for the various applied pulsed-fields. The horizontal and vertical axes indicate the maximum temperature at T1 and the maximum z-direction flux density in the horizontal plane
above 3.5 mm from the bulk surface, respectively. The relationship for the FC
magnetization is also presented. A right axis indicates the estimated current density.

Fig. 3 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 above
3.5 mm from the bulk surface, respectively. The relationship in
FC magnetization is also presented. The temperature increases
monotonously with the applied field. On the other hand, thetrapped maximum field increases with the applied pulsed field
3.10 T to 4.64 T, but, thereafter it decreases along
fromthe FC line which indicates the upper limit of trapped field foreach temperature. These results suggest that a high applied field
causes high temperature rise, and thus, a trapped field is reduced
due to the decrease in .
Fig. 4 illustrates the two- and one-dimensional trapped field
distributions measured above 3.5 mm from the bulk surface for3.10 T and (b) 4.64 T,
an applied pulsed-field of (a)respectively. For the reference, the result in FC with a static
applied field of 5 T and the bulk temperature of 70 K is presented in Fig. 4(c). One-dimensional distributions show crosssections of two- dimensional maps cut by GSR1, GSR2, GSB1

YOKOYAMA et al.: NUMERICAL ANALYSIS OF BULK SUPERCONDUCTING MAGNET MAGNETIZED BY PULSED-FIELD

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Fig. 5. Simulation model of the bulk magnet. The sample is evenly divided into
eight regions, each four regions of GSB and GSR.

III. NUMERICAL ANALYSIS
A. Simulation Model

Fig. 4. Two- and one-dimensional distributions of trapped magnetic field. Twodimensional maps are measured in the horizontal plane above 3.5 mm from thebulk surface in PFM of (a)  H
3.10 T and (b) 4.64 T, and (c) FC with theapplied static field of 5 T and the bulk temperature of 70 K. One-dimensional
maps show cross sections of two-dimensional maps cut by GSR1, GSR2, GSB1
and GSB2 lines indicated in (a). (Experimental results).

=

and GSB2 lines indicated in Fig. 4(a). For the case of
3.10 T, there are two peaks at T4 and T5 parts with the maximum magnetic flux densities of 0.72 T and 0.76 T, respectively.
The same experiment was carried out several times and it was
confirmed that the magnetic flux was always trapped only at thecharacterissame parts. From this result, it is estimated thattics at T4 and T5 parts are low compared with other parts. For
4.64 T, the distribution almost agrees withthe case of
one for FC with a static applied field of 5 T and the bulk temperature of 70 K. This is corresponding to the result that the points
4.64 T and FC at 70 K almost overlap asof PFM ofshown in Fig. 3. Although both draw a concentric circle with apeak value of 1.56 T, one can see that a lot of magnetic flux istrapped at GSR part in PFM, but the relationship is opposite in
FC. Because there is little influence of flux creep by heat genercharacteristic is directly reflected in theation in FC and themagnetic field distribution, it is understood thatin GSB is
4.64 T, on the otherhigher than one in GSR. In PFM ofhand, it is thought that the strength of applied field is not enoughfor the magnetic flux to be trapped in the GSB parts.

A numerical analysis of PFM is carried out on the basis of
the experimental results. Although the final aim is to imitate
the movement of magnetic flux during the magnetization, thedynamic pinning characteristics are not considered and they areafter the magnetization in thisevaluated as distribution of
paper.
Fig. 5 shows a simulation model of the bulk magnet. The
sample is evenly divided into eight regions, each four regionsof GSB and GSR, and it is assumed that the area of each part isequal for convenience. The current densities in GSB and GSR
and, respectively, assuming thatparts are defined asones in four regions of each part are equal. These values are calculated from the slope of the one-dimensional distributions oftrapped field shown in Fig. 4 in accordance with the Bean model,
though a bulk superconductor is not necessarily a critical state.
By using estimated current density and the proposed simulation
andis calcumodel, the magnetic field induced bylated by the following expression.

(1)
are the vector potential and the magnetic perwhere andmeability of the vacuum, respectively. The entire magnetic field
distribution is obtained by adding individual distributions.
B. Results and Discussion
A critical current corresponding to the maximum flux denis calculated from experimental resity of trapped fieldsults of FC by (1). The estimatedis indicated in the rightis almost equal to andaxis in Fig. 3. In the case of FC,
A/m . Also,is 2.2% smaller than
. In the case of PFM of
4.64 T,
andare
A/m and
A/m , respectively, andis 16.9% larger. In the case of
3.10 T,A/m and
A/m , andis.
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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 2, JUNE 2008

IV. CONCLUSIONS
A bulk superconductor magnetized by PFM was analyzed indetail by using a simulation model taking into account the difcharacteristic between GSB and GSR parts.
ference in theFirstly, the experiment of PFM with a Sm123 material was performed. A temperature and magnetic flux density at the bulk
surface were measured during the magnetization and a trappedfield distribution above 3.5 mm from the surface was scanned.
For a low applied field of 3.10 T, magnetic flux was trapped
only in GSR parts. For a high applied field of 4.64 T, the distribution drew a concentric circle as well as the result in FC, but
the trapped magnetic flux in GSR parts was more than that in
GSB parts. Next, current densities in GSB and GSR parts were
estimated from experimental results, and magnetic distributions
were calculated by using the obtained values and the simulation model. The numerical results agreed with the experimental
ones, and thus, it was confirmed to be able to analyze the current
distribution in detail by the proposed method. We will carry out
the magnetizing simulation considering magnetic flux motion
during the magnetization.
REFERENCES

Fig. 6. Two- and one-dimensional distributions of trapped magnetic field. Twodimensional maps are measured in the horizontal plane above 3.5 mm from thebulk surface in PFM of (a)  H
3.10 T and (b) 4.64 T. A result by theordinary method in PFM of  H 4.64 T is presented in (c). One-dimensional
maps show cross sections of two- dimensional maps cut by GSR1, GSR2, GSB1
and GSB2 lines indicated in (a). (Numerical results).

==

A magnetic field distribution is calculated by using a simuand
lation model shown in Fig. 5 and the above
values. Fig. 6 shows the simulation results of two- and one-dimensional distributions of magnetic field for PFM of (a)3.10 T and (b) 4.64 T. A result by an ordinary model in whichandis not considered is also
the difference between
presented in Fig. 6(c) for the reference. In Fig. 6(a), the current
loops in T2 and T3 parts are deleted according to the experimentis difficult, the agreement
result. Though the estimation of
between the numerical and experimental results is obtained. In
Fig. 6(b), a local characteristic at GSB parts is appeared while
the result by the ordinary model is a complete concentric circle
shown in Fig. 6(c). Moreover, a good correspondence to theexperimental result is shown. As mentioned above, the experimental results are reproduced well by this analysis, and the validity of the proposed method is confirmed.

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