IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 22 (2009) 095006 (6pp)

doi:10.1088/0953-2048/22/9/095006

Enhancement of trapped field and total
trapped flux on GdBaCuO bulk by the
MMPSC + IMRA method
Hiroyuki Fujishiro1 , Takuya Hiyama1 , Tomoyuki Naito1 ,Yousuke Yanagi2 and Yoshitaka Itoh2
1
2

Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, JapanIMRA Material R&D Company Limited, 2-1 Asahi-cho, Kariya 448-0032, Japan

E-mail: fujishiro@iwate-u.ac.jp

Received 25 March 2009, in final form 2 June 2009
Published 5 August 2009
Online at stacks.iop.org/SUST/22/095006
Abstract
The trapped field BTP (z) and the total trapped flux T (z) as a function of the distance z from thebulk surface have been measured on a GdBaCuO superconducting bulk of 45 mm in diameter,
which was magnetized by a sequential pulsed field application (SPA) method, a modified
multi-pulse technique with stepwise cooling (MMPSC), and a subsequent iterative magnetizing
operation with gradually reduced pulse field amplitude (IMRA). A trapped field of BTP = 3.10 T
was realized by the MMPSC method, which was higher than that attained by SPA( BTP = 2.35 T). T (0.5 mm), which was 1.64 mWb after the MMPSC method, was enhanced
by about 53%, to 2.51 mWb, by the subsequent IMRA method due to the additional flux
trapping. The MMPSC method combined with the IMRA process (MMPSC + IMRA) is aneffective and promising pulse field magnetizing technique to enhance both BTP and T on any
superconducting bulks.

because of its compact, mobile and inexpensive setup. The
trapped field BTP by PFM was, however, pretty small comparedwith BTFC , due to the large temperature rise from the dynamical
motion of the magnetic flux. The maximum BTP ever reported
is as low as 3.8 T at 30 K from an iteratively magnetizing
pulsed field method with reducing amplitude (IMRA) [5]. We
have systematically studied the time and spatial dependencesof the temperature T (t, x), local field BL (t) and trapped field
BTP on the surface of cryocooled REBaCuO bulks during PFM
for various starting temperatures Ts and applied fields Bex , andhave suggested the importance of the precise measurements ofT (t, x) on the bulk surface [6, 7].
To enhance BTP , the reduction in temperature rise T
is an indispensable issue. The lowering of Ts down to 10–
20 K, which is effective for FCM due to the enhancementof the critical current density Jc , is not necessarily effectivefor PFM because of the large heat generation due to theincrease of pinning loss and the decrease of the specificheat of the bulk material. Taking the obtained experimental
results into consideration, we proposed a new PFM technique
named a modified multi-pulse technique with stepwise cooling(MMPSC) [8], and have attained the highest field trapping of

1. Introduction
Recently, practical applications using REBaCuO superconducting bulks (RE: rare earth ions and Y) as a strong
quasi-permanent magnet have been intensively investigatedfor magnetic separation for environmental cleaning [1], adrug delivery system (DDS) for medical applications [2] anda sputtering cathode to grow thin films for semiconductor
devices [3]. For the magnetic separation and the DDS, it isnecessary to enhance not only the magnetic field B , but also themagnetic field gradient (grad B ) in order to achieve a stronger
magnetic force. On the other hand, for the sputtering cathodeand the motor/generator applications [4], a large amount of
total trapped flux T with a flat magnetic field distribution
is necessary to make the uniform magnetic field reach fartheraway.
In the applications, the magnetizing technique of thesuperconducting bulks is very important. A field-cooledmagnetization (FCM) is the conventional method and thetrapped field BTFC and the total trapped flux FC
T by FCM areas high as the maximum abilities of the bulk. Recently, apulsed field magnetization (PFM) has been intensively studied
0953-2048/09/095006+06$30.00

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Figure 1. (a) The experimental setup around the bulk and the magnetizing pulse coil. (b) The experimental sequence of the MMPSC + IMRA
technique.

BTP = 5.20 T at 29 K on a GdBaCuO bulk of 45 mm indiameter, on which only 3.6 T was trapped by a single pulse
application at 40 K [9]. BTP = 5.20 T is the highest recorded
value by PFM to date. We applied the technique to other bulkswith different pinning ability and confirmed that the MMPSC
was a universal and effective method to enhance BTP [10].
The IMRA method has been reported to be valuable forthe enhancement of the T value [5]. The MMPSC method
followed by the IMRA method is expected to enhance both
BTP and T values. In the previous paper, we reported BTP(5 mm) and T (5 mm) on a SmBaCuO bulk using the
MMPSC + IMRA method, on which the T (5 mm) value wasenhanced by the subsequent IMRA method [11]. However, the
BTP (z) and T (z) values as a function of the distance z fromthe bulk surface have not been systematically investigated.
In this paper, we applied the PFM techniques to the
GdBaCuO bulk with a higher trapped field ( BTFC = 1.8 T at
77 K) than that on the SmBaCuO bulk. The trapped field BTP (z)and the total trapped flux T (z) are investigated as a functionof the distance z for the MMPSC and the subsequent IMRA
methods.

thickness and tightly anchored onto the cold stage of a Gifford–
McMahon (GM) cycle helium refrigerator. The temperatureof the bulk Ts was controlled over the range from 30 to70 K. The bulk was magnetized using a copper pulse coil
( L = 1.08 mH and R = 0.25  at 100 K) dipped inliquid N2 , which was placed outside the vacuum chamber.
The applied field μ0 Ha (t), of which the maximum strength
was defined as Bex , was monitored by observing the current
I (t) flowing through the shunt resistor. The maximum Bex
was 6.3 T and the rise time of the pulsed field was 12 ms.
Three magnetic pulses with the same amplitude Bex , whichwere named the 1st, 2nd and 3rd pulse, were applied tothe bulk sequentially after re-cooling to Ts . We abbreviate
this technique as the sequential pulsed field application (SPA)
method. The trapped field characteristics of the bulk for the 1stpulse were reported elsewhere [13]. The trapped field profile
BT (0.5 mm) was measured 0.5 mm above the bulk surface byscanning an axial-type Hall sensor (F W Bell, BHA921) inside
the vacuum chamber using a scanning device, which has anx – y stage controller with flexible bellows. The total amountof the trapped magnetic flux density T = T (0.5 mm)
was calculated by integrating the BT (0.5 mm) value over theregion where it was positive. The BTP (z) at the bulk centerand the T (z) values were also measured as a function of the
distance z .
Figure 1(b) shows the experimental sequence of the
MMPSC + IMRA technique. In the MMPSC part, four
magnetic pulses were applied at different initial temperatures
T 1 and T 2 on the bulk surface. At the first stage, a pulse fieldof B 1 (=B 2 = 3.3 T) was applied twice at T 1 = 70 K inorder to realize the concave-shaped profile of the trapped fieldon the bulk. Hereafter, we refer to these two pulses as No. 1
and No. 2. At the second stage, the bulk was cooled down
to T 2 = 30 K and a higher pulse field B 3 (=B 4 = 6.3 T)
was applied twice (No. 3 and No. 4), after recovering to T 2.
After the termination of the MMPSC part with pulse No. 4,
the IMRA process is started to enhance the T value, in which

2. Experimental details
A GdBaCuO bulk superconductor (Nippon steel) with a 45 mm
diameter and 15 mm thickness was used in this study. The
trapped field BTFC and the total trapped flux FC
T by FCM wereas high as 1.80 T and 0.84 mWb, respectively, at 77 K on thebulk surface. A stainless-steel (SUS304) ring with a 6.0 mm
thickness and 15 mm height was fixed onto the bulk disk
using epoxy resin (Stycast 2850GT) to enhance the mechanicalstrength of the bulk and to reduce the temperature rise due tothe increase in heat capacity [12].
Figure 1(a) shows the experimental setup around the bulk
and the magnetizing pulse coil. The bulk was mounted on asoft iron yoke cylinder of 40 mm in diameter and 20 mm in2

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Figure 2. (a) The total trapped flux T (0.5 mm) and (b) the trapped field BTP = BT (0.5 mm) at the bulk center, after the 1st and 3rd pulses in
the SPA process, as a function of the applied field Bex for various temperatures Ts . In the inset of (b), the concept of the SPA process is
schematically shown.

increment rate increased with decreasing Ts . In this way, the
SPA technique is effective for the enhancement of T .
Figure 2(b) shows the trapped field BTP = BT (0.5 mm) at
the bulk center after the 1st and 3rd magnetic pulse application,
as a function of Bex at various Ts . For the 1st pulse, BTP
at Ts = 70 K starts to increase for Bex  2.7 T, takes amaximum at Bex = 4.5 T and then decreases with increasing
Bex . The BTP – Bex curve can usually be observed for PFM
techniques, which is attributed to a large temperature rise in
the bulk for higher Bex , due to the fast motion of the magnetic
flux lines in the presence of resistive forces; the pinning force
Fp and the viscous force Fv . The applied pulsed field, atwhich the magnetic flux starts to be trapped at the bulk center,increases with decreasing Ts , which comes from the increaseof the shielding current in the superconductor. For the 1stpulse application, the maximum BTP was 1.90 T at 50 K for
Bex = 6.3 T and was enhanced to 2.35 T for the 3rd pulse
application in SPA. The slight increase in the BTP value for the
3rd pulse comes from the decrease of the temperature rise [10].

Figure 3. The pulse number dependence of (a) the applied field Bexand (b) the total trapped flux T (the left ordinates) and the trappedfield BTP (right ordinates) for the MMPSC + IMRA method.

3.2. MMPSC + IMRA method

several magnetizing pulsed fields with reduced amplitude were
iteratively applied to the bulk at Ts = 30 K.

In a previous paper, we investigated the optimization of the
MMPSC method for the bulk used in this study [13]. As aresult, the conditions (T 1 = 70 K, B 1 = B 2 = 3.3 T,
T 2 = 30 K, B 3 = B 4 = 6.3 T) were confirmed to be
the optimum ones to attain a higher BTP than 3 T on the bulk
surface. Figure 3(a) shows the pulse number dependence of
the applied field Bex for the MMPSC + IMRA method. In
the IMRA part, the applied field Bex was decreased step bystep from 6.01 T (No. 5 pulse) to 3.58 T (No. 13 pulse) at
Ts = 30 K. Figure 3(b) shows the pulse number dependenceof the total trapped flux T = T (0.5 mm) and the trappedfield BTP = BT (0.5 mm) for the MMPSC + IMRA method.
BTC was drastically enhanced to 2.95 T for the No. 3 pulse
and 3.10 T for the No. 4 pulse in the MMPSC part, due tothe cone-shaped field trapping and, as a result, T was alsoenhanced to 1.64 mWb for the No. 4 pulse. In the IMRA
part, T gradually increases and tends to saturate for n  10;

3. Results and discussion
3.1. Sequential pulsed field application (SPA)
In order to investigate the field trapping ability of the
GdBaCuO bulk used, it was magnetized by a single
pulse application and SPA, both of which are conventional
techniques in PFM. Figure 2(a) shows the total trapped flux
T = T (0.5 mm) after the 1st and 3rd pulse application
in SPA as a function of the applied field Bex at Ts = 70,
50 and 30 K. All the T – Bex curves take a maximum. The
maximum T value increases, and the Bex value, at which Ttakes a maximum, shifts to a higher value with decreasing Ts .
It should be noted that the T value increases noticeably for
the SPA technique; the T value for the 3rd pulse was 20–40%
larger than that for the 1st pulse at each Ts , and also that the3Supercond. Sci. Technol. 22 (2009) 095006

H Fujishiro et al

Figure 4. The trapped field BT = BT (0.5 mm) profiles for the (a) No. 2 and (b) No. 3 pulses in the MMPSC part, and (c) No. 6 and(d) No. 13 pulses in the IMRA part in the MMPSC + IMRA method.
Table 1. Summary of the T (z) and BTP (z) values. The decrement rates T (z)/T (0.5 mm) and BTP (z)/BTP (0.5 mm) are also shown inparentheses.
Methodz = 0.5 mm

z = 5 mmz = 10 mm

z = 20 mm

MMPSCT = 1.64 mWb

T = 1.17 mWb(71%)
BTP = 1.63 T(53%)
T = 1.79 mWb(71%)
BTP = 1.86 T(59%)

T = 0.86 mWb(52%)
BTP = 0.99 T(32%)
T = 1.30 mWb(52%)
BTP = 1.21 T(39 %)

T = 0.49 mWb(29%)
BTP = 0.42 T(14%)
T = 0.72 mWb(29%)
BTP = 0.56 T(18%)

BTP = 3.10 T
MMPSC + IMRAT = 2.51 mWb
BTP = 3.14 T

T = 2.44 mWb (No. 10) and T = 2.51 mWb (No. 13).
The T behavior in the IMRA part comes from the additional
flux trapping due to the smaller temperature rise, which resultsfrom the lower Bex . The IMRA process might be ineffective
for a lower Bex than the critical value, even if the pulse number
increases. On the other hand, BTP is slightly increased from
3.10 T (No. 4) to 3.14 T (No. 13) during the IMRA process,which suggests that additional magnetic flux might be trappedat the bulk periphery.

Figure 4 shows the BT (0.5 mm) profiles for a typicalstep in the MMPSC + IMRA method. In figure 4(a) for theNo. 2 pulse in the MMPSC part, the magnetic flux is trappedwith a concave distribution due to the lower Bex , which can beunderstood on the basis of Bean’s critical state model. For the
No. 3 pulse application, the BT profile changes to a convex one
as shown in figure 4(b), which indicates that a large amount ofmagnetic flux intrudes into the bulk center. In figure 4(c) for
the No. 6 pulse in the IMRA part, most of the magnetic flux4

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H Fujishiro et al

the No. 13 pulse was enhanced to 2.51 mWb, which was 53%
larger than that after the No. 4 pulse (1.64 mWb). T (z) for
the No. 4 and No. 13 pulse decreases with increasing z andthe decrement rate is nearly the same; T (z)/T (0.5 mm) forz = 10 and 20 mm is 52% and 29%, respectively.
Figure 6(b) shows the results of BTP (z). Similarly
to the results of T (z), BTP (z) monotonously decreases
with increasing z . The decrement rate of BTP (z) in the
MMPSC + IMRA method is slightly smaller than that in
the MMPSC method; BTC (z) (20 mm)/BT (0.5 mm) for the
MMPSC and MMPSC + IMRA is 14% and 18%, respectively.

4. Summary
The trapped field BTP and the total trapped flux T (z)as a function of the distance z from the bulk surface
have been investigated on a GdBaCuO superconducting
bulk which was magnetized by a sequential pulsed field
application (SPA) method, a modified multi-pulse techniquewith stepwise cooling (MMPSC), and a subsequent iterative
magnetizing operation with gradually reduced pulse field
amplitude (IMRA). The important experimental results andconclusions obtained in this study are summarized as follows.

Figure 5. The cross section of the BT (0.5 mm) profiles for each stepof the MMPSC + IMRA method.

is trapped at the bulk periphery, and finally for the No. 13
pulse, the magnetic flux is additionally trapped as shown infigure 4(d).
Figure 5 shows the cross sections of the BT (0.5 mm)
profiles along the x -axis shown in figure 4 for each step in
the MMPSC + IMRA method. For the No. 2 pulse, a small
amount of magnetic flux was trapped on the bulk periphery anda concave or ‘M-shaped’ profile was observed. After the No. 3
pulse application, a cone-shaped profile with a higher BTC canbe observed. As shown in figures 4(c) and (d), the magnetic
flux is trapped at the bulk periphery.

(1) A trapped field of BTP = 3.10 T was realized at T 2 = 30 K
at the end of the MMPSC method (No. 4 pulse), which
was higher than that attained by SPA at 50 K ( BTP = 2.35 T
for the 3rd pulse). The BTP of 3.10 T was slightly enhanced
to 3.14 T by the subsequent IMRA method. The MMPSC
method is valuable to enhance the trapped field at the bulk
center.
(2) T (0.5 mm) after the MMPSC method was 1.64 mWb,
which was enhanced significantly to 2.51 mWb by thesubsequent IMRA method due to additional flux trapping.
(3) The MMPSC method combined with the IMRA process(MMPSC + IMRA) is an effective and promising pulse
field magnetization technique for enhancing both BTP andT on any superconducting bulks.

3.3. The distance z dependence of T (z) and BTC (z)We measured the total trapped flux T (z) and the trapped field
BTP (z) as a function of the distance z . Table 1 summarizes the
T (z) and BTP (z) values after the MMPSC part (No. 4) andthe IMRA part (No. 13), in which the decrement rate of T (z)and BTP (z) compared with those at z = 0.5 mm are also shownin parentheses. Figure 6(a) shows the results of T (z). By
performing the IMRA process, the T (0.5 mm) value after

Figure 6. (a) The total trapped flux T (z) and (b) the trapped field BTP (z) as a function of the distance z from the bulk surface for the
MMPSC + IMRA method. The results after the No. 4 and No. 13 pulse application, respectively, are indicated.

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H Fujishiro et al

Acknowledgments[5] Yanagi Y, Itoh Y, Yoshikawa M, Oka T, Hosokawa T,
Ishihara H and Ikuta Hand Mizutani U 2000 Advances inSuperconductivity XII (Tokyo: Springer) p 470[6] Fujishiro H, Oka T, Yokoyama K, Kaneyama M andNoto K 2004 IEEE Trans. Appl. Supercond. 14 1054
[7] Fujishiro H, Yokoyama K, Oka T and Noto K 2004 Supercond.
Sci. Technol. 17 51[8] Fujishiro H, Kaneyama M, Tateiwa T and Oka T 2005 Japan. J.
Appl. Phys. 44 L1221[9] Fujishiro H, Tateiwa T, Fujiwara A, Oka T and Hayashi H 2006
Physica C 445–448 334[10] Fujishiro H, Tateiwa T, Kakehata K, Hiyama T, Naito T and
Yanagi Y 2008 Physica C 468 1477
[11] Fujishiro H, Tateiwa T and Hiyama T 2007 Japan. J. Appl.
Phys. 46 4108
[12] Fujishiro H, Yokoyama K, Kaneyama M, Oka T and
Noto K 2005 IEEE Trans. Appl. Supercond. 15 3762
[13] Fujishiro H, Hiyama T, Tateiwa T, Yanagi Y and Oka T 2007
Physica C 463–465 394

This work is supported in part by a Grant-in-Aid for Scientific
Research from the Ministry of Education, Culture, Sports,
Science and Technology, Japan (No. 19560003).

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