IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 20 (2007) 1009–1014

doi:10.1088/0953-2048/20/10/020

Trapped field and temperature rise on a
φ 65 mm GdBaCuO bulk by pulse fieldmagnetization
Hiroyuki Fujishiro, Tetsuya Tateiwa, Kosuke Kakehata,
Takuya Hiyama and Tomoyuki Naito
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
E-mail: fujishiro@iwate-u.ac.jp

Received 13 June 2007, in final form 31 July 2007
Published 31 August 2007
Online at stacks.iop.org/SUST/20/1009
Abstract
The trapped field BT and temperature rise T on a large GdBaCuO
superconducting bulk (65 mm in diameter) have been investigated during
pulse field magnetization (PFM), and compared with those on GdBaCuO
bulk with a diameter of 45 mm. The maximum trapped field at the bulk
center BT (C) on the φ 65 mm bulk is as small as 1.9 T at Ts = 40 K for the
single pulse field application of Bex = 6.7 T, which is smaller than that of theφ 45 mm bulk ( BT (C) = 3.2 T). The total trapped flux T on the φ 65 mm
bulk is, however, about twice as large as that on the φ 45 mm bulk. The
magnetic fluxes cannot sufficiently intrude into the center of the φ 65 mm
bulk at Ts = 40 K for pulse field applications up to 6.7 T, whereas a large
number of the magnetic fluxes are trapped at the peripheral region of thebulk. The trapped field characteristics for both bulks with different diameters
can be roughly interpreted by a simple critical state model under zero fieldcooling (ZFC).

1. Introduction
For practical applications of a high-temperature superconducting bulk as a quasi-permanent magnet, pulse field magnetization (PFM) instead of conventional field cooled magnetization (FCM) has been intensively investigated because of theinexpensive and mobile experimental setup involved [1]. The
trapped field BT P found using PFM was considered to be low,compared with the trapped field BT FC from FCM due to thelarge temperature rise caused by the dynamical motion of themagnetic fluxes. The BT P value was improved at around77 K by multi-pulse techniques such as an iterative magnetizing operation with gradually reduced pulse field amplitude(IMRA) [2] and a multi-pulse technique with stepwise cooling (MPSC) [3]. At a bulk temperatures Ts as low as 30–
40 K, however, BT P was still low. We have systematicallyinvestigated the time and spatial dependence of trapped field
BT P (t, x) and temperature rise T (t, x) for various applied
pulse fields Bex , temperatures Ts , and the various superconducting bulks with different pinning ability [4–6]. To enhance
BT P , it was found that both lowering of Ts and lowering of T0953-2048/07/101009+06$30.00

must be realized at the same time during the PFM procedure.
However, T is generally large at lower Ts due to the large heatgeneration by the large pinning force Fp and/or the small heat
capacity of the bulk. Based on the obtained results, we proposed a new PFM method, called a modified multi-pulse technique combined with stepwise cooling (MMPSC) [7]. Using
the MMPSC method, which consists of two-stage PFM procedures, we have succeeded in producing a highest field trappingof BT P = 5.20 T on the GdBaCuO bulk (45 mm in diameter), which is a record high BT P by PFM to date [8]. Thismethod has been proved to be a universal and effective method
to enhance BT P using other bulks such as the SmBaCuO bulk
disk (φ 45 mm) [9] and the rectangular-shaped GdBaCuO bulk
(33 × 33 × 15 mm3 ) [10].
Recently, a superconducting bulk with diameter larger
than 60 mm appeared on the commercial market, and a singlegrain bulk with 140 mm diameter can also be realized [11].
The trapped field BT and the total trapped flux T increase
with increasing diameter of the bulk disk, if the critical current
density Jc of the bulk superconductor is identical [12]. Then, asuperconducting bulk with large diameter is useful for practical© 2007 IOP Publishing Ltd Printed in the UK1009

H Fujishiro et al

Table 1. The specification of the used bulks and pulse coils.
Bulk nameφ 65 mm bulk

φ 45 mm bulk

Bulk species
Diameter (mm)Height (mm)BT F C (T) at 77 K

GdBaCuO
65
18
1.90

GdBaCuO45
18
1.72

Used pulse coil
I.D. (mm)O.D. (mm)Height (mm)Inductance, L (mH)Resistance, R ()Turns

Coil L
99
121
61
1.08
0.28
103

Coil S
83
114
50
1.07
0.26
112

applications such as in electric motors and generators. Kimura
et al reported the trapped field BT P = 0.8 T on the φ 60 mm
GdBaCuO bulk at 77 K using a vortex-type pulsed coil, which
was, however, smaller than that on φ 45 mm bulk [13]. The
application of the PFM technique to the large bulk at lower Ts
is desired. However, there are no systematic data of BT P by
PFM for the large bulks.
In the present paper, we investigate the trapped fieldcharacteristics on the φ 65 mm GdBaCuO bulk at temperatures
lower than 77 K. We compare the results with those for theφ 45 mm GdBaCuO bulk, and discuss the applicability of the
PFM technique for superconducting bulks with large diameter.

2. Experimental details
Highly c-axis-oriented GdBaCuO bulk disks with φ 65 mm andφ 45 mm (18 mm in thickness; Nippon Steel) were magnetizedby the PFM method. Table 1 shows the specification of thebulks and the used pulse coils. The bulks are composedof GdBa2 Cu3 O y (Gd123) and Gd2 BaCuO5 (Gd211) with amolar ratio of Gd123:Gd211 = 1.0:0.4, 10.0 wt% Ag2 O and
0.5 wt% Pt. The trapped field BT FC by the FCM method at
the center surface of the φ 65 mm bulk was 1.9 T at 77 K.
Figure 1(a) shows the experimental setup around the φ 65 mm
bulk and the pulse coil. The bulk was mounted on a soft ironyoke 40 mm in diameter and 20 mm in thickness and tightly
anchored onto the cold stage of a Gifford–McMahon (GM)cycle helium refrigerator (Sumitomo Heavy Industry). The
bulk was evacuated in the vacuum chamber and was cooled
to the temperature from Ts = 60 down to 30 K. The bulk
was magnetized using the condenser bank (60 mF) and thesolenoid pulse coil, which is abbreviated to Coil L, dipped inliquid N2 . A soft-iron cylinder (65 mm in diameter and 40 mm
in thickness) was inserted in the Coil L and was faced to thebulk in the vacuum chamber. The rise time of the pulse field
generated by the Coil L was tr = 12 ms and the pulse duration
was td = 120 ms. Two Hall sensors (F W Bell, model BHT
921) were attached at positions C (bulk center) and E (20 mmfrom the bulk center) on the bulk surface. The time evolutionsof the local fields [ BL (C)(t) and BL (E)(t)] were monitored
using a digital oscilloscope. The trapped field BT (C) was
defined as BL (C)(t → ∞). The temperatures, T 1, T 2, andT 3 were measured at the positions shown in figure 1(a) on thebulk surface using a fine thermocouple.
Figure 1(b) shows the experimental setup around theφ 45 mm bulk and the pulse coil (Coil S). BT FC at the center
1010

Figure 1. The experimental setup of the (a) φ 65 mm GdBaCuO bulk
and pulse coil (Coil L), and (b) φ 45 mm GdBaCuO bulk and pulse
coil (Coil S). The dimension of the bulks and coils are shown intable 1. The measuring positions of magnetic fields ( B(C) and B(E))
and temperatures (T 1, T 2, and T 3) after applying the magnetic pulse
are indicated.

surface of the φ 45 mm bulk was 1.72 T at 77 K. The bulk
was cooled to Ts = 40 K using the same refrigerator andwas magnetized using Coil S. The rise time of the pulse field
generated by the Coil S was tr = 11 ms and the pulse duration
was td = 80 ms, both of which are somewhat shorter thanthose of Coil L due to the small inductance and resistance ofthe coil. Two Hall sensors were attached at positions C (bulkcenter) and E (15 mm from the bulk center) on the bulk surface.
The time evolutions of the local fields [ BL (C)(t) and BL (E)(t)]were monitored. The time dependences of temperatures T 1–
T 3 on the bulk surface were measured.
For both bulks, the applied field μ0 Ha (t), of which the
maximum strength was defined as Bex , was monitored byobserving the current I (t) flowing through the shunt resistor.
The Bex value was changed up to 6.7 T, which was a maximum
Bex in the present experimental apparatus. The total trappedmagnetic flux T (5 mm) parallel to the c-axis of the bulk
was measured using an axial-type Hall sensor, which scanned
stepwise on the vacuum chamber 5 mm above the bulk surface
with a pitch of 1.2 mm.

3. Results and discussion
3.1. Single pulse application
Figure 2 shows the trapped field BT (C) at the bulk center ofthe φ 65 mm bulk as a function of the applied field Bex at
Ts = 60, 40 and 30 K. The results of the φ 45 mm bulk at
Ts = 40 K are also shown. For the φ 65 mm bulk, BT (C)at Ts = 60 K starts to increase at around Bex = 3.2 T, andincreases with increasing Bex . BT (C) takes a maximum of
1.9 T at Bex = 6 T and then decreases for higher Bex . For thepulse field application of the identical strength of Bex , BT (C)decreases with lowering Ts due to the increase of the pinning
force Fp . At Ts = 40 and 30 K, magnetic fluxes start to
intrude into the bulk center for Bex higher than 4 T and 5 T,
respectively. On the other hand, for the φ 45 mm bulk at

Pulse field magnetization of φ 65 mm GdBaCuO bulk

Figure 2. The trapped field BT (C) at the center of the φ 65 mm
GdBaCuO bulk as a function of the applied pulse field Bex at
Ts = 60, 40 and 30 K. For comparison, the results of the φ 45 mm
GdBaCuO bulk at Ts = 40 K are also shown. The marks from (a) to(e) point to the conditions at which the time dependences of theapplied field μ0 Ha (t) and the local fields BL (C)(t), BL (E)(t) areindicated in figure 3 (see text).

Ts = 40 K, the magnetic fluxes start to reach the bulk center
for Bex  4.2 T, which is slightly higher than that for the
φ 65 mm bulk. BT (C) for the φ 45 mm bulk steeply increases
with increasing Bex , takes a broad maximum of BT (C) = 3.2 T
at Bex = 6 T and then decreases. As shown in table 1, BT FC
by FCM on the φ 65 mm and φ 45 mm bulk is 1.9 and 1.72 T
at 77 K, respectively, which suggests that the effective Jc ofthe φ 65 mm bulk is lower than that of the φ 45 mm bulk
because BT FC is nearly proportional to the diameter of the bulk
under an identical Jc of the bulk material. Since a diameter of
65 mm is roughly 1.5 times (exactly 1.44 times) larger than adiameter of 45 mm, BT FC on the φ 65 mm should be 2.48 T
at 77 K, if the bulks are homogeneous and the Jc value of the
φ 65 mm bulk is equal to that of the φ 45 mm bulk. The result,
BT (C), of the φ 45 mm bulk is higher than that of the φ 65 mm
bulk, suggesting that the magnetic fluxes are easy to intrude
and be trapped at the center of the bulk with small diameter,even though the effective Jc value, that is, the pinning force Fp
is large at an identical Ts .
Figures 3(a)–(e) show the time evolutions of applied field
μ0 Ha (t) and local fields, BL (C)(t) and BL (E)(t) at positions
C and E for conditions (a)–(e) shown in figure 2, respectively.
In figures 3(a) and (b), the results after applying a pulse fieldof Bex = 4.7 T at Ts = 40 K are compared for the φ 65 mm
and φ 45 mm bulks. At the position E in the peripheral region
for both bulks, BL (E)(t) shows a peak with nearly the sameheight as μ0 Ha (t) without any time delay, and then moderately
decreases. The magnetic field of BT (E) = 1.5–2.0 T was
finally trapped. However, at the bulk center of the φ 65 mm
bulk, the magnetic fluxes cannot intrude and are hardly trapped( BT (C)  0). For the φ 45 mm bulk, a small number ofmagnetic fluxes intrude into the bulk center; the maximum
BL (C)(t) was only 1.5 T and the final trapped field, BT (C) was
1.1 T.
In figures 3(c) and (d), the results at Ts = 40 K arecompared for both bulks after applying a pulse field of Bex =6.7 T, which is the maximum strength of the magnetic pulsein this study. In the periphery region, nearly the same strengthof magnetic field as applied field is detected for both bulks.

At the bulk center, BL (C)(t) for the φ 65 mm bulk shows atiny peak of 2.2 T and then finally reaches a trapped field of
BT (C) = 1.8 T. On the other hand, for the φ 45 mm bulk,
the maximum magnetic field of BL (C)(t) = 5.7 T, which isslightly smaller than the applied field μ0 Ha (t), enters the bulk
center and then decreases. The flux jump takes place due to thelarge temperature rise by the excess applied field, and the final
trapped field BT (C) decreases to 2.4 T.
Figure 3(e) presents similar results for the φ 65 mm bulk
at Ts = 60 K after applying a pulse field of Bex = 6.7 T. It
should be noted that nearly the same magnetic field BL (C)(t)as applied field μ0 Ha (t) enters the bulk center, which resultsfrom the decrease of the pinning force Fp due to the higher Ts .
As a result, the magnetic field of BT (C) = 1.7 T was trapped.
The local fields, BL (C)(t) and BL (E)(t) on the φ 65 mm bulk
quickly decrease after rising to a peak, compared with thosefor the φ 45 mm bulk shown in figures 3(b) and (d). This result
suggests that the magnetic flux easily escapes due to the local
temperature rise for the φ 65 mm bulk.
3.2. Temperature rise
To investigate the difference between the trapped fieldcharacteristics of φ 65 mm and φ 45 mm bulks, the temperaturechanges during the PFM procedure are compared. Figures 4(a)and (b) show the temperature change T (t) after applying apulse field of Bex = 4.74 T at Ts = 40 K for the φ 65 mm
and φ 45 mm bulks, respectively. The temperature rise at
the periphery region is fast and large. On the other hand, thetemperature rise at the bulk center is moderate and relatively
small for each bulk, because the magnetic fluxes always intrude
into the bulk from the bulk periphery. For the φ 65 mm bulk
shown in figure 4(a), T (t) changes depending on the measuring
positions in the periphery. The temperature rise of T 3 is larger,
which suggests that the magnetic fluxes preferentially movearound this position. On the other hand, for the φ 45 mm bulk
shown in figure 4(b), the temperature changes in T 2 and T 3,
both of which are situated in the bulk periphery, are moreorless
identical and the magnetic fluxes seem to enter uniformly fromthe bulk periphery. The temperature rise at the bulk center(T 1) for the φ 45 mm bulk is larger than that for the φ 65 mm
bulk. The generated heat Q is the sum of the pinning loss Q p
due to the flux trap and the viscous loss Q v due to the flux
movement [14]. For the φ 45 mm bulk, BT (C) is larger and themagnetic fluxes move around the center of the bulk with finite
velocity. As a result, Q p is dominant at the center of the bulk.
For the φ 65 mm bulk, Tmax at the bulk center (T 1) is always
smaller than that at T 3, since the magnetic fluxes cannot allreach the bulk center and a large number of magnetic fluxes aretrapped at the bulk periphery. For both bulks, the maximum
temperature rise Tmax increases with increasing Bex due tothe increase in the flux velocity and decreasing Ts due to theincrease in Fp .
3.3. Total trapped flux T
Figure 5 shows the total trapped flux T (5 mm) for the
φ 65 mm and φ 45 mm bulks at Ts = 40 K as a function of
applied field Bex . T (5 mm) is estimated by the integration of
BT (5 mm) on the vacuum sheath, at which the distance fromthe bulk surface is 5 mm. T (5 mm) of the φ 65 mm bulk
1011

H Fujishiro et al

Figure 3. The time dependence of applied field μ0 Ha (t) and the local fields BL (C)(t), BL (E)(t) at positions C and E of φ 65 mm andφ 45 mm GdBaCuO bulks for the various conditions of Ts and Bex . Figures (a)–(e) show the results under conditions (a)–(e), which weremarked in figure 2.

increases with increasing Bex , takes a maximum at Bex = 5 T
and then decreases for higher Bex . The T (5 mm)– Bex curve isdifferent from the BT (C)– Bex curve shown in figure 2; BT (C)does not take a maximum up to Bex = 6.7 T at Ts = 40 K.
T (5 mm) of the φ 65 mm bulk is about twice as large asthat of the φ 45 mm bulk, in spite of BT (C) of the φ 65 mm
bulk being lower than that of the φ 45 mm bulk. These results
suggest that the volume of the φ 65 mm bulk is about twiceas large as that of the φ 45 mm bulk and that a large numberof the magnetic fluxes are trapped at the bulk periphery. The
enhancement of the total trapped flux is a merit for the practicalapplications of large bulks.
3.4. Sequential pulse application (SPA)
Figure 6 shows the estimated cross section of the trapped field
profile on the φ 65 mm bulk at Ts = 40 K for applying
three pulse fields (No. 1–No. 3) with identical strength Bex
from 4.74 to 6.74 T, which are applied after recovering to
Ts = 40 K. In this figure, the trapped field profile was
1012

supposed to be symmetrical along the circumferential direction
and was roughly estimated using only the measured BT (C)and BT (E), and BT = 0 at the bulk edge. For the No. 1
pulse application, the trapped field profile is the concave (‘Mshaped’) profile for Bex  5.61 T and changes to the convex
profile (‘cone-shaped’) for Bex  6.03 T. For Bex = 4.74 T,
BT (E) increases with increasing number of magnetic pulses,
though BT (C) nearly remains constant. On the other hand,for Bex = 6.67 T, BT (E) decreases with increasing numberof magnetic pulses, but BT (C) slightly increases. The total
trapped flux T (5 mm) after the No. 3 pulse application isshown in figure 5 for the φ 65 mm bulk at Ts = 40 K as afunction of Bex . T (5 mm) gradually increases with increasing
pulse number and is about 30% enhanced after the No. 3 pulse
application. For the φ 45 mm bulk, both the trapped fields
BT (C) and BT (E) increase with increasing pulse number andthen saturate to final values due to the decrease of T [14].
A similar effect of the T enhancement was confirmed to besmall, possibly due to the small volume of the bulk.

Pulse field magnetization of φ 65 mm GdBaCuO bulk

Figure 6. The estimated cross section of the trapped field profile on
the φ 65 mm bulk at Ts = 40 K after applying three successive pulse
fields (No. 1–No. 3) with identical strength Bex from 4.74 to 6.67 T.

Figure 4. The time dependences of the temperature changes T (t) inT 1, T 2, and T 3 for the (a) φ 65 mm and (b) φ 45 mm GdBaCuO
bulks after applying a pulse field of Bex = 4.74 T at Ts = 40 K.

Figure 7. The conceptional view of the trapped field profiles for theφ 45 mm bulk ((a) and (b)) and the φ 65 mm bulk ((c)–(e)) after the
ZFC magnetizing process at constant Ts .

Figure 5. The total trapped flux T (5 mm) on the φ 65 mm andφ 45 mm bulks at Ts = 40 K as a function of the applied pulse field
Bex , which is estimated by the integration of BT (5 mm), 5 mm above
the bulk surface on the vacuum sheath. The T (5 mm)– Bex curve on
the φ 65 mm bulk after the No. 3 pulse application with identicalstrength is also shown (see section 3.4).

3.5. Discussion
A PFM technique can be regarded as a kind of ZFC
magnetization; in PFM, the applied magnetic fluxes promptly
intrude to the superconducting bulk under the ZFC condition
and then some of the magnetic fluxes are trapped and others
extrude from the bulk. However, there are some differences;
the ZFC magnetization is performed under the quasi-staticmode, in which the temperature rise and the flux velocity
should be negligible. On the other hand, PFM is performed
under the dynamical mode, in which a large heat generation
takes place. The flux velocity cannot be negligible andseriously influences the viscous loss Q v . We discuss thedifference in the BT (C) and the trapped field distribution shownin the previous subsections between φ 65 mm and φ 45 mm
bulks, based on Bean’s critical state model [15] as a first
approximation. The influence of the temperature rise during
the PFM method is also commented.
Figure 7 shows a conceptional view of the trapped field
profiles for the φ 45 mm (figures (a) and (b)) and φ 65 mm bulk
(figures (c)–(e)) after the ZFC magnetizing process at constantTs (for example, Ts = 40 K). As shown in section 3.1, theeffective Jc value of the φ 65 mm bulk was estimated to belower than that of the φ 45 mm bulk. But, for simplicity, weboldly suppose that the Jc value is identical for both bulks,
namely, the slope (d B/dx ), which is proportional to Jc , isidentical [15]. In figure 7, B ∗ denotes the applied field, atwhich the φ 45 mm bulk is fully magnetized by FCM. In the
ZFC magnetization, 2 B ∗ must be applied to fully magnetize
the φ 45 mm bulk. In the φ 65 mm bulk, 1.5 B ∗ and 3 B ∗ arenecessary to magnetize fully by the FCM and ZFC magnetizing
processes, respectively.
When a magnetic field of B ∗ is applied to the φ 45 mm
bulk, the magnetic fluxes just reach the center of the bulk asshown in figure 7(a). On the other hand, the magnetic fluxes
1013

H Fujishiro et al

do not reach the center of the φ 65 mm bulk as shown infigure 7(c). Figures 7(b) and (d) show the trapped field profiles
after applying a magnetic field of 2 B ∗ . For the φ 45 mm
bulk shown in figure 7(b), the magnetic fluxes fully enter thebulk center and are trapped with a cone-shaped profile which
nearly corresponds to the experimental result for Bex = 6 T
at Ts = 40 K shown in figure 2. On the other hand, for the
φ 65 mm bulk shown in figure 7(d), the trapped field profile isan ‘M-shaped’ one and the BT (C) at the bulk center is half ofthat for the φ 45 mm bulk. The differences in BT (C) and thetrapped field profile for both bulks with different diameters canbe interpreted by the ZFC magnetizing mechanism.
In the practical PFM procedure, however, the explanation
mentioned above must be modified slightly, because a large
temperature rise takes place. The B ∗ value and the slope(d B/dx ) decrease with increasing temperature. As a result,the height of the cone-shaped profile should be lower. Itoet al investigated the trapped field characteristics by PFM,
compared with those by ZFC magnetization [16]. They
concluded that the dynamical motion of the magnetic fluxes
during PFM could be explained by taking into accountthe significant contribution of the viscous force under heatgeneration. The slope d B/dx became steeper as it approached
the bulk edge due to the viscous force in their experimental
results. The average temperature rise in the φ 45 mm bulk isnearly equal to that in the φ 65 mm bulk, notwithstanding theinhomogeneity in the temperature rise as shown in figure 4.
Though the time evolution of the flux distribution during PFM
is different from that of the quasi-static ZFC, the final trapped
flux distribution by PFM can be qualitatively understood using
the behaviors of the ZFC magnetization as shown in figure 7.
If a magnetic pulse field with a magnitude of 3 B ∗ isapplied to the φ 65 mm bulk under ZFC magnetization, BT (C)is enhanced and the trapped field profile changes from the‘M-shaped’ profile to the ‘cone-shaped’ one, as shown infigure 7(e). In this case, BT (C) is 1.5 times larger than thatof the φ 45 mm bulk ( BT (C) = 1.5 B ∗ for the φ 65 mm bulk).
Since the power supply, which can generate higher pulse fields,
for example Bex  7 T, is expensive in cost, large in size, andheavy in weight, the use of a large power supply is unrealistic
for practical applications. To enhance BT (C) for the bulk disk
with large diameter, an improved PFM technique such as the
MMPSC method [16] may be one possible solution.

4. Summary
The trapped field BT and temperature rise T on large
GdBaCuO superconducting bulk (65 mm in diameter) havebeen investigated during the pulse field magnetization (PFM)
method, and compared with those on GdBaCuO bulk with adiameter of 45 mm. The important experimental results andconclusions obtained in this study are summarized as follows.

1014(1) The maximum trapped field at the bulk center BT (C) on
the φ 65 mm bulk is as small as 1.9 T at Ts = 40 K forthe single pulse field application of Bex = 6.67 T, whichis smaller than that of the φ 45 mm bulk ( BT (C) = 3.2 T).
(2) The total trapped flux T of the φ 65 mm bulk is, however,about twice as large as that of the φ 45 mm bulk. The
magnetic fluxes cannot intrude into the center of the
φ 65 mm bulk at Ts = 40 K sufficiently for the applied
pulse field up to 6.7 T, and a large number of the magnetic
fluxes are trapped at the peripheral region of the bulk.
(3) The trapped field characteristics for the two bulks withdifferent diameters can be roughly interpreted by a simple
critical state model under zero field cooling magnetization.

Acknowledgments
The authors thank Professor Tetsuo Oka of Niigata University,
Japan for valuable discussions. This work is supported in partby a Grant-in-Aid for Scientific Research from the Ministryof Education, Culture, Sports, Science, and Technology, Japan(No. 17560001) and from Iwate Prefecture, Japan.

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