IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 23 (2010) 025013 (6pp)

doi:10.1088/0953-2048/23/2/025013

Estimation of temperature rise fromtrapped field gradient on superconducting
bulk magnetized by multi-pulse technique
Hiroyuki Fujishiro1 , Tomoyuki Naito1 , Kosuke Kakehata1 ,Yosuke Yanagi2 and Yoshitaka Itoh2
1
2

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

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

Received 29 July 2009, in final form 6 October 2009
Published 18 December 2009
Online at stacks.iop.org/SUST/23/025013
Abstract
Trapped field profiles of the GdBaCuO superconducting bulk of 65 mm in diameter have beenmeasured as magnetized using a successive pulsed-field application (SPA) and a subsequent
iterative pulsed-field magnetization with reducing amplitude (IMRA). The trapped field
gradient d BT /dx on the bulk periphery increases concomitantly with increasing pulse numberin the IMRA part. The d BT /dx value on the bulk magnetized by field-cooled magnetization(FCM) was also measured at each temperature TF . The maximum temperature Tmax for eachpulse was estimated by comparing the d BT /dx value for the IMRA part with that for the FCM
at each temperature. Furthermore, Tmax was measured directly for the SPA part in the drilledhole in the bulk. The estimated Tmax was nearly equal to the measured Tmax , which thereby
confirmed that Tmax after applying the pulsed field can be estimated using the d BT /dx value inthe bulk periphery. The enhancement of the total trapped flux PT in the IMRA part withincreasing pulse number results from enhancement of the critical current density Jc because of
the reduction in Tmax .

iteratively pulsed-field magnetization with reducing amplitude(IMRA) [5]. We have studied the time and spatial dependencesof the temperature, local field and trapped field on the surfaceof cryo-cooled REBaCuO bulk samples systematically during
PFM for various starting temperatures Ts and applied fields
Bex [6, 7]. Considering the experimental results obtained,
we have proposed a new PFM technique—designated as
the modified multi-pulse technique with stepwise cooling(MMPSC)—and have produced the highest trapped field of
5.20 T at 29 K on a GdBaCuO bulk sample of 45 mm diameter,in which only 3.6 T had been trapped using a single-pulse
application at 40 K [8].
Recently, REBaCuO superconducting bulks with diameter
larger than 60 mm have been put onto the commercial
market. Even a single-grain bulk of 140 mm diameter can berealized [9]. According to a Bean critical state model [10],a trapped field BT at the bulk centre is proportional to thediameter of the bulk disc d . A total trapped flux density T is
proportional to d 3 , if the critical current density Jc of the bulk
material is of equal value. The large T value is especially

1. Introduction
Practical applications using REBaCuO superconducting bulk
(RE: rare earth ions and Y) as a strong quasi-permanent magnet
have been intensively investigated for magnetic separation forenvironmental cleaning [1], drug delivery systems (DDSs)
in medical applications [2] and sputtering cathodes to growthin films for use in semiconductor devices [3]. Fieldcooled magnetization (FCM) using a superconducting magnet
is a conventional technique to magnetize bulk samples. The
trapped field BTFC and the total trapped flux FC
T by FCM
achieves the maximum abilities of the bulk. On the other hand,pulsed-field magnetization (PFM) has been studied intensively
because it is compact, mobile and uses no superconducting
magnet for practical applications. The trapped field BTP by
PFM was, however, smaller than BTFC because of the large
temperature rise due to the dynamical motion of the magnetic
flux. To enhance BTP , it is necessary to decrease the temperaturerise. Several approaches have been used such as a multipulse technique with stepwise cooling (MPSC) [4] and an
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Supercond. Sci. Technol. 23 (2010) 025013

H Fujishiro et al

Table 1. The trapped field BT and total trapped fluxes T on the
GdBaCuO bulk of 65 mm in diameter and 18 mm in thickness usedin this study magnetized by the SPA, MMPSC and IMRA methods.
Those on the GdBaCuO bulk of 45 mm in diameter and 18 mm inthickness are also shown. (Note: SPA: successive pulsed-field
application. MMPSC: modified multi-pulse technique with stepwise
cooling. IMRA: iteratively pulsed-field magnetization with reducing
amplitude. FCM: field-cooled magnetization.)

BTFC (T)Method

65 mmbulk [11, 13](at 40 K)

45 mmbulk [14](at 30 K)

FCM

1.9 (77 K)

1.8(77 K)
1.9
3.1
—
3.14
1.96
1.64
—
2.51
—
1.79
—

BTP (T)
SPA
1.3
BTP (T)
MMPSC
3.0
BTP (T)
SPA + IMRA
1.4
BTP (T)
MMPSC + IMRA —PT (0.5 mm) (mWb) SPA
2.9
PT (0.5 mm) (mWb) MMPSC—
PT (0.5 mm) (mWb) SPA + IMRA
5.05
PT (0.5 mm) (mWb) MMPSC + IMRA —PT (4 mm) (mWb) SPA + IMRA
4.1
PT (5 mm) (mWb) MMPSC + IMRA —FC
4.44 (48 K)
T (4 mm) (mWb) FCM

Table 2. The conditions from A to C in the SPA + IMRA method
performed in this study.
Condition

Condition A

Condition B

Condition CTs
B 1 (=B 2 = B 3)
B5
B7
B9
B 11
B 13

40 K
6.6 T
6.1 T
5.4 T
4.9 T
4.2 T
3.5 T

40 K
5.4 T
4.9 T
4.2 T
3.5 T
—
—

60 K
6.6 T
6.0 T
5.3 T
4.8 T
4.2 T
3.4 T

As described in this paper, we measure the magnetic field
gradient d BT /dx on the 65 mm GdBaCuO bulk using the
SPA + IMRA method. We estimate the maximum temperature
Tmax using the magnetic field gradient with the IMRA partby comparing the d BT /dx value with that using FCM. We
examine the propriety of the estimation of Tmax using themagnetic field gradient by comparison with the measured Tmax
in a small hole in the bulk.

2. Experimental details
A 18 mm thickness 65 mm GdBaCuO superconducting bulk
disc (Nippon Steel Corp.) was used for this study. The
trapped field characteristics for various magnetizing techniques
are presented in table 1. Figures 1(a) and (b) respectively
show the experimental set-ups for the SPA + IMRA method
and for the FCM method. In figure 1(a), the bulk was mounted
on a soft iron yoke cylinder and was tightly anchored onto
the cold stage of a Gifford–McMahon (GM) cycle helium
refrigerator. The magnetizing solenoid coil, which generated
a pulse field up to Bex = 6.7 T with a rise time of 12 ms,
was placed outside the vacuum chamber. Figure 1(c) presents
the experimental sequence used for the SPA + IMRA method.
Table 2 shows the conditions of the SPA + IMRA method used
for this study. Three conditions A–C were performed withvarious temperatures and applied fields in the SPA part. The
starting temperature Ts of the bulk was maintained at 40 or
60 K. Three magnetic pulses (nos. 1–3) with nearly identicalamplitudes B 1 (=B 2 = B 3) were applied sequentially after
re-cooling to Ts . From the no. 4 pulse, the IMRA process wasstarted; the applied pulsed fields Bn (Bn−1 ) were iteratively
reduced to 3.5 T in 0.3 T steps at constant Ts . Two-dimensional
trapped field profiles of BTP (4 mm) and BTP (0.5 mm) were
mapped at distances z = 4 or 0.5 mm above the bulk surface,
stepwise with a pitch of 1 mm by scanning an axial-type
Hall sensor (F W Bell, BHA 921) inside the vacuum chamberusing an x – y stage controller. The temperature of the bulk
was measured independently during SPA using a Teflon-coatedchromel–constantan thermocouple (76 μm in diameter) in thehole of 1 mm in diameter and 10 mm in depth drilled in the
periphery of the bulk. We confirmed the lack of degradation ofsuperconductivity by drilling a small hole in the bulk.
For the FCM experiment as presented in figure 1(b), thebulk was similarly tightly anchored onto the cold stage of therefrigerator. The FCM was performed at various temperatures
TF from 38 to 85 K using a cryo-cooled superconducting
magnet. During FCM, the static magnetic field of 3 T was

useful for applications such as electric motors/generators andsputtering cathodes.
We have investigated the trapped field characteristics
on the 65 mm GdBaCuO bulk by successive pulsed-field
application (SPA) and the MMPSC method [11, 12]. Table 1
presents results of BT and T on 65 mm GdBaCuO bulk
obtained using several magnetizing techniques. The resultsfor 45 mm GdBaCuO bulk are also shown for comparison.
The maximum trapped field on the 65 mm bulk was as low
as BTP = 1.3 T by SPA and BTP = 3.0 T by MMPSC at
40 K, which was smaller than those on the 45 mm bulk
because of the lower Jc . However, the PT value for a large
bulk can be enhanced easily using the IMRA method; the PT(0.5 mm) value, which was measured at z = 0.5 mm above
the bulk surface, was as high as 5.05 mWb on the 65 mm
bulk at Ts = 40 K using the SPA + IMRA method, which
was about 1.7 times larger than that obtained using the SPA
method (PT = 2.9 mWb) [13]. It was 2.2 times larger thanthat on the 45 mm bulk by the MMPSC + IMRA method(PT = 2.51 mWb) [14]. The PT (4 mm) value (=4.1 mWb)
at 40 K using the SPA + IMRA method was as high as theFC
T (4 mm) value (=4.44 mWb) obtained using FCM under
Bex = 3 T at 48 K [13].
The increase of the PT value obtained using the IMRA
part results from the reduction in temperature rise by reducing
the amplitude of the magnetic pulse [6]. As a result, theeffective Jc increases and the magnetic flux is additionallytrapped in the bulk periphery. The gradient of the magnetic
field, trapped in the bulk periphery, is expected to beclosely related to the maximum temperature after the magnetic
pulse application if Bean’s model governs, even roughly, themagnetizing process during PFM. However, no experimental
results have been reported in the relevant literature.
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H Fujishiro et al

Figure 1. Experimental set-up around the bulk and magnetizing coil for (a) pulsed-field magnetization (PFM) and (b) field-cooledmagnetization (FCM). For PFM and FCM, the trapped field profile was, respectively, measured inside and outside the vacuum chamber.
(c) The experimental sequence of the SPA + IMRA method.

decreased to 0 T at 3 mT s−1 . BTFC (4 mm) profiles were
measured on the vacuum sheath surface, which was 4 mm fromthe bulk surface.

decreasing TF , as indicated by the dashed lines in the bulk
periphery. According to Bean’s model, the gradient of thetrapped field is proportional to Jc [10]. Figure 2(b) presents
the gradient of the trapped field d BTFC (4 mm)/dx as a functionof temperature TF . The gradient decreases with increasing TF
and then falls to zero at Tc = 92 K. Our group reported thatthe temperature on the bulk surface increased slightly during
FCM and that the increase in temperature was enhanced withdecreasing TF and with increasing the descending speed ofthe magnetic field [15]. The descending speed in this study
was 3 mT s−1 . Using the previous results, the respective
temperature rise values were estimated as 4 K at TF = 50 K,
2 K at 60 K and 1 K at 70 K, respectively.

3. Results and discussion
3.1. Trapped field distribution by FCM
Figure 2(a) shows a cross section of the trapped field profile
BTFC (4 mm) by FCM at various temperatures TF . For higher
TF , the cross section of the BTFC (4 mm) profile shows a cone
shape, but the maximum BTFC (4 mm) value is low at the bulk
centre. With decreasing TF , the profile changed from conicalto trapezoidal and the BTFC (4 mm) value increased and thensaturated because of the increase of Jc with decreasing TF . The
FCM was performed under a constant magnetic field of 3 T.
Therefore the saturation tendency took place. It is noteworthy
that the magnetic field gradient increases concomitantly with

3.2. Trapped field distribution by SPA + IMRA
Figures 3(a) and (b) respectively portray the pulse number
dependence of the cross section of the trapped field profile3

Supercond. Sci. Technol. 23 (2010) 025013

H Fujishiro et al

Figure 2. Trapped field profiles BTFC (4 mm) on the bulk for the FCM
from 3 T for various temperatures TF . (b) Magnetic field gradientd BTFC (4 mm)/dx as a function of temperature TF .

Figure 3. The pulse number dependence of the (a) BTP (0.5 mm) and(b) BTP (4 mm) profiles for the SPA + IMRA method of condition A( Ts = 40 K, B 1 = 6.6 T).

BTP (0.5 mm) and BTP (4 mm) for ‘condition A’ (Ts = 40 K,
B 1 = 6.6 T) [13]. In figure 3(a), for the no. 3 pulse in the
SPA part, the concave BTP (0.5 mm) profile is apparent. The
BTP (0.5 mm) value at the bulk periphery increased graduallywith increasing pulse number. On the other hand, the BTP(0.5 mm) value at the bulk centre increases only slightly. For
the no. 13 pulse application ( B 13 = 3.5 T) in the IMRA part,the BTP increment at the bulk periphery seemed to saturate. In
figure 3(b), the profile becomes broad and the magnitude of
the BTP (4 mm) at the periphery becomes small because themeasurement position is distant from the bulk surface. On
the other hand, the magnitude of the BTP (4 mm) at the bulk
centre was nearly the same as the BTP (0.5 mm) because of
the concave BTP profile. The magnitude of the BTP at the bulk
centre becomes small on increasing the distance z to larger
than z = 6 mm. To compare the magnetic gradient by PFM
with that by FCM and to estimate the temperature rise during
the SPA + IMRA method, we adopted the BTP (4 mm) profiles
for the following discussion, although the magnetic gradientshould be measured just above the bulk surface. The BTFC (z )profile cannot be measured at z = 0.5 mm but at 4 mm becauseof the experimental limitation. The magnitude of the magnetic
gradient for BTP (4 mm) was about 60% that for BTP (0.5 mm).
Figure 4(a) depicts the pulse number dependence of thecross section of the trapped field profile BTP (4 mm) for‘condition B’ (Ts = 40 K, B 1 = 5.4 T). The applied field B 1
is smaller than that for condition A. Therefore, the magnetic
flux cannot intrude into the bulk centre. For this reason,
the trapped field profile becomes more concave. However,
the magnetic gradient increased slightly with increasing pulse
number in the IMRA part. Figure 4(b) depicts the pulse number
dependence of the BTP (4 mm) profiles for ‘condition C’ (Ts =60 K, B 1 = 6.6 T). The operating temperature Ts is higher
than that for condition A under an identical B 1. Therefore,
the magnetic flux can penetrate and be trapped at the bulk
centre. The magnetic gradient increases concomitantly withincreasing pulse number and the trapped field profile changes
from conical to trapezoidal. It is noteworthy that the gradient of
the trapped field at Ts = 60 K is smaller than that at Ts = 40 K.
Figure 5 presents the pulse number dependences of themagnetic gradient d BTP (4 mm)/dx for three conditions, whichwere determined from figures 3(b) and 4(a) and (b). The
d BTP (4 mm)/dx value for condition B is larger than that forcondition A because of the smaller temperature rise for lower
applied field. The d BTP (4 mm)/dx value for condition A is
greater than that for condition C because of the larger Jc at
lower Ts . In all cases, the increase of the d BTP (4 mm)/dx value
with increasing pulse number in the IMRA part arises fromthe reduction in the temperature rise. The d BTP (0.5 mm)/dx
versus the pulse number n was also shown for condition A in
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Supercond. Sci. Technol. 23 (2010) 025013

H Fujishiro et al

Figure 6. The time evolution of the temperature T (t) in the bulk for
the SPA part of conditions A–C.

Figure 4. The pulse number dependence of the BTP (4 mm) profiles
for the SPA + IMRA method of (a) condition B ( Ts = 40 K,
B 1 = 5.4 T) and (b) condition C ( Ts = 60 K, B 1 = 6.6 T).
Figure 7. The pulse number dependence of the estimated Tmax foreach applied pulsed field (n  3, dashed lines) and measured Tmax
(1  n  3, solid lines) for conditions A–C.

3.3. Measurement of temperature rise in the bulk
Figure 6 presents the time evolution of the temperature T (t)in a small hole drilled in the bulk periphery for the SPA partof conditions A–C. The temperature rise for the no. 1 pulse is
the largest and becomes small gradually for subsequent pulses.
The maximum temperature Tmax for the no. 1 pulse of condition
A was 78 K; its temperature T (t) was decreased gradually
to 40 K for 15 min. Tmax for condition C remains constantor increases slightly because of the powerful magnetic flux
movement for each pulse.
Figure 5. The pulse number dependence of the magnetic gradientd BTP (4 mm)/dx for conditions A, B and C, which were estimatedfrom figures 3(b) and 4(a) and (b), respectively. The
d BTP (0.5 mm)/dx versus the pulse number was also shown for
condition A.

3.4. Estimation of maximum temperature Tmax during the
SPA + IMRA method
We estimated the maximum temperature Tmax for each stepin the SPA + IMRA method using the results presented infigures 5 and 2(b). Figure 7 shows the pulse numberEdependence of the estimated Tmax
for n  3 as dashed lines.
M
The measured Tmax values for n  3, which are indicated inEfigure 6, are also shown as solid lines. The Tmax
decreasedconcomitantly with increasing pulse number for all conditions
and approaches Ts = 40 K for conditions A and B and to

figure 5. The d BTP (0.5 mm)/dx is about 1.6 times larger thanthe d BTP (4 mm)/dx value and increases concomitantly withincreasing pulse number.
5Supercond. Sci. Technol. 23 (2010) 025013

H Fujishiro et al(1) Tmax after the pulsed-field magnetization can be estimatedusing the gradient of the trapped field d BT /dx in the bulk
periphery by comparison with the magnetic field gradienton the bulk periphery magnetized by FCM.
(2) The estimated Tmax was nearly the same as the measured
Tmax , which was measured directly in the drilled hole inthe bulk during the SPA part.
(3) In a bulk as large as 65 mm in diameter, the total trapped
flux PT is enhanced by the IMRA method because of thedecrease in the temperature rise, which is effective forpractical applications.

Acknowledgment
Figure 8. The pulse number dependence of the total trapped flux PT(4 mm) for each condition. The PT (0.5 mm) values for condition A
are also shown.

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

Ts = 60 K for condition C. It is noteworthy that the measured
and estimated Tmax values for n = 3 are nearly equal, whichsuggests that the gradient of the trapped field profile is usefulfor estimation of Tmax .
Figure 8 depicts the pulse number dependence of the total
trapped flux PT (4 mm) for each condition. The PT (4 mm)
value increases concomitantly with increasing pulse number;
finally it saturates. It is noteworthy that the PT (4 mm) valuesof condition B from n = 3–7 are larger than those of condition
E
A. The estimated Tmax
of condition B is apparently lower. As aresult, the Jc value is higher than with condition A. However,
the maximum PT (4 mm) value of 4.0 mWb was realized forthe subsequent pulsed application of condition A, which was
as high as FCT (4 mm) by FCM under Bex = 3 T at 48 K [13].
The PT (0.5 mm) values for condition B are also shown in the
figure, which are about 1.33 times larger than PT (4 mm).

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4. Summary
The trapped field profiles of the GdBaCuO superconducting
bulk (65 mm in diameter) were measured. The bulk sample
was magnetized using a successive pulsed-field applicationand the subsequent iterative pulsed-field magnetization methodwith reducing amplitude (SPA + IMRA) and a field-cooledmagnetization (FCM). The maximum temperature Tmax after
heat generation for each pulse in the SPA + IMRA method wasestimated through comparison of the magnetic field gradientin the bulk periphery with that after the FCM. Important
experimental results and conclusions obtained in this study aresummarized as follows.

6