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Enhancement of Trapped Field and Total Trapped Flux on High Temperature Bulk
Superconductor by a New Pulse-Field Magnetization Method

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2007 Jpn. J. Appl. Phys. 46 4108
(http://iopscience.iop.org/1347-4065/46/7R/4108)
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Japanese Journal of Applied Physics
Vol. 46, No. 7A, 2007, pp. 4108–4112#2007 The Japan Society of Applied Physics

Enhancement of Trapped Field and Total Trapped Flux on High Temperature
Bulk Superconductor by a New Pulse-Field Magnetization Method
Hiroyuki FUJISHIRO, Tatsuya T ATEIWA, and Takuya H IYAMA
Faculty of Engineering, Iwate University, Morioka 020-8551, Japan(Received December 25, 2006; accepted March 19, 2007; published online July 4, 2007)

A higher trapped ﬁeld BT P and larger total trapped ﬂux T have been achieved on a SmBaCuO bulk superconductor (45 mm) by a modiﬁed multipulse technique with stepwise cooling (MMPSC) and a subsequent iterative magnetizing operation
with gradually reduced pulse ﬁeld amplitude (IMRA). BT P ¼ 4:33 T has been realized at the center of the bulk surface by the
MMPSC method, which is higher than that attained by a single-pulse application (BT P ¼ 3:3 T). After the IMRA process, T(5 mm) = 1.55 mWb was achieved 5 mm above the bulk surface, which is about 35% larger than that after the MMPSC
process. The MMPSC method combined with the IMRA process (MMPSC-IMRA) is demonstrated to be a universal andpromising pulse-ﬁeld magnetization technique for enhancing both BT P and T on any superconducting bulks.
[DOI: 10.1143/JJAP.46.4108]
KEYWORDS: bulk superconductor, pulse-field magnetization, temperature rise, trapped field, MMPSC-IMRA method

1.

Introduction

As a practical application of REBaCuO bulk superconductors (RE: rare-earth element or yttrium), a highstrength superconducting bulk magnet has been intensively
developed by pulse-ﬁeld magnetization (PFM) as well as theconventional ﬁeld-cooled magnetization (FCM).1) The trapped ﬁeld BT P obtained by PFM was, however, considerably
smaller than that attained by FCM below 77 K due to thelarge temperature rise (T) caused by the dynamical motionof the magnetic ﬂuxes.2) Several approaches have beensuccessfully performed to enhance BT P including an iteratively magnetizing pulsed-ﬁeld method with reducing
amplitude (IMRA)3) and a multipulse technique with stepwise cooling (MPSC).4) To clarify the dynamics of the ﬂux
motion during PFM and to enhance BT P , we have systematically studied the time and spatial dependences of thetemperature Tðt; xÞ, local ﬁeld BL ðt; xÞ, and the trapped ﬁeld
BT P on the surface of cryocooled REBaCuO bulks during
PFM for various starting temperatures Ts and applied ﬁelds
Bex .5–8) The generated heat Q due to the ﬂux intrusion was
estimated using the speciﬁc heat CðTÞ of the bulk and the
maximum temperature rise Tmax . The pinning loss Qp dueto the ﬂux trapping at the pinning centers and the viscous
loss Qv due to the ﬂux movement in the bulk were separately
analyzed experimentally and estimated (Q ¼ Qp þ Qv ) bysuccessive pulse applications (SPA) with a ﬁxed amplitude.9)
To enhance BT P , both the reduction in T and the loweringof the bulk temperature Ts are crucial issues, because thecritical current density Jc and the resultant trapped ﬁeld BT P
increase with lowering Ts . Taking the obtained experimental results into consideration, we proposed a new PFM
technique, which we refer to a modiﬁed MPSC (MMPSC),
which consists of a two-stage temperature procedure.10) At
the ﬁrst stage, a small number of magnetic ﬂuxes are trappedat the bulk periphery at a relatively high temperature Ts ð1Þ
(< Tc ; superconducting transition temperature) by the lowerpulse ﬁeld application of Bex ð1Þ. At the second stage, thebulk is cooled to a lower temperature Ts ð2Þ [< Ts ð1Þ], anda higher and optimum magnetic pulse ﬁeld of Bex ð2Þ
[> Bex ð1Þ] is applied. The temperature rise T at thesecond stage can be markedly reduced by the alreadytrapped ﬂuxes at the ﬁrst stage, compared with that which

occurred after the bulk was initially cooled to Ts ð2Þ and thesame magnetic ﬁeld as Bex ð2Þ was applied. We have realizeda trapped ﬁeld of BT P ¼ 5:20 T on a GdBaCuO bulk 45 mm
in diameter, which had a trapped ﬁeld as low as BT P ¼ 3:0 T
using a single-pulse application. The value of BT P ¼ 5:20 T
is the highest recorded by PFM to date.11)
In this paper, we apply the MMPSC technique to a
REBaCuO bulk disk instead of the GdBaCuO bulk in which
BT P ¼ 5:20 T was achieved to demonstrate that the MMPSC
method can be universally applied to enhance BT P for any
REBaCuO bulk. The IMRA method is sequentially applied
to enhance the total trapped ﬂux T after the MMPSC
process is complete. The enhancement of T as well as thatof BT P is important for applications such as motor andgenerators using REBaCuO bulks.12)
2.

Experimental Methods

A c-axis-oriented SmBaCuO bulk superconductor (DowaMining) with 45 mm diameter and 18 mm thickness wasused. The bulk is composed of SmBa2 Cu3 Oy (Sm123) andSm2 BaCuO5 (Sm211) with the molar ratio of Sm123 :Sm211 ¼ 1:0 : 0:3, as well as 15.0 wt % Ag2 O powder, and
0.5 wt % Pt powder. A stainless-steel (SUS304) ring with
2.0 mm thickness and 18 mm height was ﬁxed onto the bulk
disk using epoxy resin (Stycast 2850GT) to enhance themechanical strength of the bulk and to reduce the temperature rise due to the increase in heat capacity.13) Figure 1
shows the experimental setup around the bulk and the pulse
coil. The bulk was mounted on a soft iron yoke 40 mm indiameter and 20 mm in thickness and tightly anchored onto
the cold stage of a Giﬀord–McMahon (GM) cycle helium
refrigerator. The system was evacuated in the vacuum
chamber using an oil diﬀusion pump. Three Hall sensors (F.
W. Bell, model BHT 921) were attached at positions C (bulkcenter), M (8 mm from the bulk center), and E (16 mm fromthe bulk center) on the bulk surface. The time evolutionsof the local ﬁelds [BL (C)(t), BL (M)(t), and BL (E)(t)] weremonitored using a digital oscilloscope. The bulk wasmagnetized using a solenoid pulse coil (L ¼ 1:08 mH and
R ¼ 0:25  at 100 K) dipped in liquid N2 . The dimensionsof the coil are 83 mm in inner diameter, 114 mm in outer
diameter, and 112 turns, in which a soft-iron cylinder (40mm in diameter and 65 mm in thickness) is inserted. The

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H. FUJISHIRO et al.

60

20
(a)

SUS ring

4.0T

bulk
C ME
T (K)

yoke

coil

cold stage

15

50
(K)

T

(b)
Ts=45K

Ts=30K

Bex=6.0T

10

max

bulk

6.0T

∆T

yoke

40
Bex=4.0T

Bex(2)

1st stageBex(2)
No.4

No.2

Ts(2)

No.1

Ts(1)

2nd stage
Time

Fig. 2. The concept of the MMPSC technique. The time dependence ofthe temperature change is schematically shown. Two pulse ﬁelds [No. 1
and No. 2; Bex ð1Þ ¼ 4:0 T] are applied at the ﬁrst stage [Ts ð1Þ ¼ 45 K] andthe higher pulse ﬁelds [No. 3 and No. 4; Bex ð2Þ ¼ 6:0 T] are subsequently
applied at the second stage [Ts ð2Þ ¼ 30 K].

applied ﬁeld 0 Ha ðtÞ, of which the maximum strength
was deﬁned as Bex , was monitored by observing the currentIðtÞ ﬂowing through the shunt resistor. The rising time ofthe pulse ﬁeld was 13 ms and the duration was 120 ms.
The temperature on the bulk surface TðtÞ was measured
at position T using a ﬁne thermocouple. The total trappedmagnetic ﬂux T (5 mm) parallel to the c-axis of the bulk
was measured using an axial Hall sensor, which scanned
stepwise on the vacuum chamber 5 mm above the bulk
surface with a pitch of 1.2 mm. Figure 2 shows theexperimental sequence of the MMPSC technique used inthis study. Four magnetic pulses are applied at diﬀerent
initial temperatures, Ts ð1Þ and Ts ð2Þ, on the bulk surface.
At the ﬁrst stage, a pulse ﬁeld Bex ð1Þ ¼ 4:0 T was applied
twice at Ts ð1Þ ¼ 45 K to trap a small number of magnetic
ﬂuxes at the bulk periphery. Hereafter, we refer to these twopulses as No. 1 and No. 2. At the second stage, the bulk wascooled to Ts ð2Þ ¼ 30 K and a higher pulse ﬁeld of Bex ð2Þ ¼
6:0 T was applied twice (No. 3 and No. 4). At each stage, thetemperature rise T, local ﬁelds BL ðtÞ, and the trapped ﬁeld
BT P ¼ BL ðCÞðt ! 1Þ were monitored.
3.

30
0

10 20 30 40 50
Time (s)

0
3

4

5
B

ex

6
(T)

7

8

Fig. 3. (a) The time dependences of the temperature TðtÞ at the position T
after a typical magnetic pulse application. (b) The maximum temperaturerise Tmax as a function of Bex for Ts ¼ 30 and 45 K.

Tc >T s (1)>T s (2)B ex (1) < Bex (2)

No.3

Tc

Bex(1)
Bex(1)

Ts=30K
Ts=45K

Fig. 1. The experimental setup around the bulk and the pulse coil. The
measuring positions of the local ﬁeld BL ðtÞ and temperature TðtÞ areindicated as positions C, M, E, and T on the bulk surface. The trapped
ﬁeld BT P was measured at position C.

Temp

5

Results and Discussion

3.1 Single-pulse application
To conﬁrm the ﬁeld-trapping ability of the SmBaCuO
bulk used in this study, a single magnetic pulse was applied

to the bulk and the trapped ﬁeld BT P , and temperature rise
T was measured at Ts ¼ 30 and 45 K. Figure 3(a) shows
the time dependences of the temperature change TðtÞ atposition T for various strengths of the magnetic pulse Bex .
After applying the pulse ﬁeld, TðtÞ rises and takes a maximum at t  10 s and then slowly decreases to the initial
temperature for t  15 min. The temperature rise increases
with increasing Bex , because a large number of magnetic
ﬂuxes intrude into the bulk and destroy the surface potential
barrier, and then some of the magnetic ﬂuxes are trapped at
the pinning centers. The heat generation results from thepinning loss Qp and the viscous loss Qv .9) Figure 3(b) shows
the maximum temperature rise Tmax as a function of Bex at
Ts ¼ 30 and 45 K. Tmax starts to increase for Bex > 3:8 T at
Ts ¼ 30 K and then increases with increasing Bex . On theother hand, at Ts ¼ 45 K, Tmax starts to increase for Bex >3:5 T and increases less rapidly with increasing Bex . These
results are mainly due to the enhancement of Qp at low
temperatures. The decrease in the speciﬁc heat CðTÞ of thebulk at low temperatures is another reason.
Figures 4(a) and 4(b) show the trapped ﬁeld BT P at
position C and the total trapped ﬂux T (5 mm) as a functionof Bex at Ts ¼ 30 and 45 K. In Fig. 4(a), the magnetic ﬂuxes
start to intrude and are trapped at the bulk center at Ts ¼ 30
K for Bex > 3:8 T. BT P takes a maximum at Bex ¼ 6:0 T andthen slowly decreases with increasing Bex . Note that the
BT P  Bex curve for Ts ¼ 45 K shifts parallel to lower Bex by
0.3 – 0.5 T, compared with that for Ts ¼ 30 K. This behavior
is closely related with the Tmax –Bex curve shown in
Fig. 3(b), suggesting that the ﬂux movement and trapping
result in the generation of heat. The maximum BT P is equal
to almost 3.2 T at Ts ¼ 30 and 45 K. In Fig. 4(b), T (5 mm)
sharply increases for Bex > 3:8 T at Ts ¼ 30 K and Bex >3:5 T at Ts ¼ 45 K, both of which show similar behavior to
BT P , as shown in Fig. 4(a). T (5 mm) at Ts ¼ 30 K is larger
than that at Ts ¼ 45 K due to the enhancement of the pinning
force Fp . The Bex values at which the maximum BT P andmaximum T (5 mm) can be obtained are slightly diﬀerent.
The maximum values of BT P ¼ 3:3 T and T (5 mm) =1.06 mWb can be obtained at Ts ¼ 30 K using the present
SmBaCuO bulk by a single-pulse application.

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Jpn. J. Appl. Phys., Vol. 46, No. 7A (2007)

5

H. FUJISHIRO et al.

5

1.5

(a)
4

20

SPA (6.2T)

4

15
(K)
max

SPA (4.0T)

2

1
0
3

4

5
6
B (T)

7

0
3

4

5
B

6
(T)

ex

7

6

(a) T s(1)=45K, B ex(1)=4.0T

B L(C)B L(M)B L(E)µ H

No.1 pulse

0

T

L

µ H (T), B (T)SUS ring

C ME

a

bulk

a
0

2
1
0

(b)

T (2)=30K, B (2)=6.0T No.3 pulse
s

ex

4
B (C)

a

L

µ H (T), B (T)

5

3

0

L

B (M)

2

L

B (E)
L

µ H

1
0

0

0

50

100

0

8

Fig. 4. (a) The trapped ﬁeld BT P at the bulk center (position C) and (b) the
total trapped ﬂux T (5 mm) as a function of the applied pulse ﬁeld Bex at
Ts ¼ 30 and 45 K.

3

MMPSC
SPA(30K)
SPA(45K)

1

8

4

10

0.5

ex

5

∆T

(T)
T

P

3

T

2

1.0

B

Φ (5mm) (mWb)

P

B

T

(T)

SPA (6.2T)

3

(b)

(a)

(b)

Ts=30K
Ts=45Ka

150

Time (ms)Fig. 5. The time dependences of the applied ﬁeld 0 Ha ðtÞ and the local
ﬁelds [BL (C)(t), BL (M)(t), BL (E)(t)] after applying (a) pulse No. 1 and (b)pulse No. 3.

3.2 MMPSC operation
Taking the experimental results in §3.1 into consideration,
the MMPSC process was applied to the SmBaCuO bulk,
where Bex ð1Þ ¼ 4:0 T was applied twice at Ts ð1Þ ¼ 45 K
as the ﬁrst stage and Bex ð2Þ ¼ 6:0 T was applied twice atTs ð2Þ ¼ 30 K as the second stage. Figures 5(a) and 5(b)show the time dependences of the applied ﬁeld 0 Ha ðtÞ andthe local ﬁelds BL ðtÞ at positions C, M, and E after applying
pulses No. 1 and No. 3, respectively. After applying ‘‘pulse

1

2
3
4
Pulse number

5
SPA (4.0T)

0

1

2
3
4
Pulse number

Fig. 6. The pulse-number dependences of (a) the trapped ﬁeld BT P and (b)the maximum temperature rise Tmax for MMPSC. The results of threepulse applications with the same strength (SPA) are also presented forBex ¼ 4:0 T at Ts ¼ 45 K and Bex ¼ 6:2 T at Ts ¼ 30 K.

No. 1’’ at the ﬁrst stage, BL (E)(t), BL (M)(t), and BL (C)(t)sharply increase in this order and quickly reach a ﬁnal stablevalue without overshooting. BL (M)(t) reaches about 2.1 T,
but BL (C)(t) and BL (E)(t) reach only 1.5 –1.3 T. A maximum
temperature rise Tmax of 5.5 K takes place, which may
mainly result from the heat generation due to the ﬂux
trapping. For pulse No. 2, BT P and BL ðtÞ at C, M, and E
remained, and then Tmax decreased to 2 K due to a small
amount of ﬂux movement. For pulse No. 3 [Bex ð2Þ ¼ 6:0 T]
at Ts ¼ 30 K, as shown in Fig. 5(b), the maximum BL (E)(t)was only 3 T, which then decreased to 1.2 T, suggesting thatthe magnetic ﬂuxes inhomogeneously intruded into the bulk
from areas other than position E. On the other hand, themaximum of BL (C)(t) increased to 5.0 T and was as highas 4.6 T after t ¼ 150 ms. However, BT P ¼ BT ðCÞ gradually
decreased to 4.25 T at t ¼ 15 min due to the ﬂux creep.
BL (M)(t) increased to 4.7 T then gradually decreased to
3.5 T. After the application of pulse No. 4, BT P ¼ BT ðCÞ
slightly increased to 4.33 T. When we applied Bex ð2Þ ¼ 6:2 T
at the second stage, which was slightly higher than Bex ð2Þ ¼
6:0 T, a ﬂux jump occurred and BT P decreased to 3.8 T.
When Bex ð2Þ ¼ 5:8 T was applied at the second stage, BT P
reached only 3.6 T. An optimum Bex ð2Þ value exists thatenhances the ﬁnal BT P value in the MMPSC method.
Figures 6(a) and 6(b) show the pulse-number dependences of the trapped ﬁeld BT P and the maximum temperaturerise Tmax for the present MMPSC method, respectively.
For comparison, the results for three successive magnetic
pulse applications (SPA) with the same strength are also
shown for Bex ¼ 4:0 T at Ts ¼ 45 K, which correspond to theconditions at the ﬁrst stage, and for Bex ¼ 6:2 T at Ts ¼
30 K, which nearly corresponds to the conditions at thesecond stage. In the SPA process at Ts ¼ 30 K, a ﬁeld of
BT P ¼ 3:20 T was trapped after the pulse No. 1, and thetrapped ﬁeld increased very slightly to 3.35 T after the No. 3
pulse. Tmax gradually decreased from 18 K after the pulse
No. 1 to 13 K after pulse No. 3. Similar pulse-number
dependences of BT P and Tmax were also shown after SPA
for Bex ¼ 4:0 T at Ts ¼ 45 K. For the ﬁrst stage (No. 1 andNo. 2 pulses) in the MMPSC process, BT P and Tmax have
similar traces to those after SPA. However, the BT P value4110

Jpn. J. Appl. Phys., Vol. 46, No. 7A (2007)

H. FUJISHIRO et al.

3.3 Enhancement of T by subsequent IMRA method
After the termination of the MMPSC process for pulse
No. 4, the IMRA method was applied to enhance the Tvalue. In the IMRA method, several magnetizing pulsed
ﬁelds with reduced amplitude are iteratively applied to thebulk at constant Ts and the additional ﬂuxes are trappedaround the bulk periphery. As a result, the total trapped ﬂux
T increases.3) Figure 7 shows the pulse-number dependence of the total trapped ﬂux T (5 mm) during the
MMPSC and IMRA processes. The results of the trapped
ﬁeld BT P are also shown. The pulse numbers from No. 5
to No. 14 correspond to the IMRA process, which was
performed at Ts ¼ 30 K. The inset shows the relation
between T (5 mm) and Bex for each pulse in the
MMPSC-IMRA process. T (5 mm) increases with increasing magnetic pulse number; T (5 mm) is 1.15 mWb forNo. 5 and is 1.55 mWb for No. 14, which is an increase of
35% during the IMRA process. On the other hand, BT P on
the bulk surface is not enhanced during the IMRA process.
Figure 8 shows the cross sections of the trapped ﬁeld
proﬁle BT (5 mm) on the surface of the vacuum chamber,which is 5 mm above the bulk surface for diﬀerent pulse
numbers. The trapped-ﬁeld proﬁle shows a symmetric cone-

5
4

1.5

No.7
No.5
1
MMPSC
1st (45K)
0.5

MMPSC
0

2

0

3

4

IMRA
5

(T)

MMPSC
2nd (30K)

T

0.5

P

1.5

T

1.0

B

Φ (5mm) (mWb)3
No.14 No.12
No.9

10
Pulse number

No. 2
No. 4
No. 7
No. 14

1.5

T

1.0

0.5

0
-40

-30

-20

-10
0
10
Distance (mm)

20

30

40

Fig. 8. The trapped-ﬁeld proﬁles BT (5 mm) 5 mm above the bulk surface
in air for the MMPSC process (No. 2 and No. 4) and for the IMRA
process (No. 7 and No. 14).

shaped distribution. The change in the proﬁle from pulse
No. 2 to pulse No. 4 results from the trapped-ﬁeld enhancement due to the MMPSC method. The BT (5 mm) value
increases from 1.4 to 1.7 T after the 10 pulses in the IMRA
method. The enhancement in BT (5 mm) is not due to thetrapped ﬁeld enhancement at the center of the bulk surface
but due to the additional ﬂux trapping at the bulk periphery.
4.

Conclusions

A higher trapped ﬁeld BT P and a larger total trapped ﬂux
T have been achieved on a SmBaCuO bulk superconductor
by a modiﬁed multipulse technique with stepwise cooling(MMPSC) and a subsequent iterative magnetizing operation
with gradually reduced pulse ﬁeld amplitude (IMRA). BT P ¼
4:33 T has been realized on the bulk surface by the MMPSC
method, which is higher than that attained by the singlepulse technique (BT P ¼ 3:3 T). After additional 10 pulses in
the IMRA method, T (5 mm) = 1.55 mWb was achieved
5 mm above the bulk surface, which is about 35% larger thanthat after the MMPSC process. The generated magnetic ﬁeld
BT (5 mm), 5 mm above the bulk surface in air is 1.7 T after
the IMRA process, which is about 21% larger than that
before the IMRA process. Thus, the MMPSC method isdemonstrated to be a universal and promising PFM technique for enhancing both BT P for any REBaCuO bulk, andthe subsequent IMRA technique can be used to enhance theT and BT values in air.
Acknowledgments2TΦ (5mm) (mWb)

2.0

2.0

B (5mm) (T)after pulse No. 3 jumps to BT P ¼ 4:25 T then slightly
increases to 4.33 T after pulse No. 4. Note that Tmax is
14.5 K after pulse No. 3 in MMPSC, which is about 4 K
lower than that after pulse No. 1 in SPA. The reduction inTmax is due to the already trapped ﬂuxes at the ﬁrst
stage, which enhance the BT P value in the MMPSC process.
In the previous paper, we suggested that, at the ﬁrst stage,
the ﬁeld trapping (BT P  1 T) into the bulk center, which has
an M-shaped trapped-ﬁeld distribution, should critically
govern the ﬁnal BT P value.14) The M-shaped distributionmeans that the trapped ﬁeld at position C is lower than thatat position M and/or position E. In the present MMPSC, thedesirable M-shaped proﬁle [BT P ¼ BT ðCÞ ¼ 1:5 T, BT ðMÞ ¼
2:1 T] was realized at the ﬁrst stage. The optimization of
Ts and Bex for each stage is of crucial importance forattaining a BT P value higher than 4 T. Since the SPA
technique is also eﬀective in reducing the temperature rise,
it is necessary to apply the same Bex twice for each stage.

The authors thank Professor T. Oka of Niigata University
for the 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.

1
5

6

7

Bex (T)

14

0

Fig. 7. The pulse-number dependence of the total trapped ﬂux T (5 mm)
and the trapped ﬁeld BT P for the MMPSC-IMRA method. The inset
shows T (5 mm) as a function of applied ﬁeld Bex .

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