Physica C 468 (2008) 1477–1480

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Physica C
journal homepage: www.elsevier.com/locate/physc

Trapped ﬁeld characteristics on u65 mm GdBaCuO bulk by modiﬁed
multi-pulse technique with stepwise cooling (MMPSC)
H. Fujishiro a,*, T. Tateiwa a, K. Kakehata a, T. Hiyama a, T. Naito a, Y. Yanagi bab

Faculty of Engineering, Iwate University, 3-4-5 Ueda, Morioka, Iwate 020-8551, JapanIMRA Material R&D Co., Ltd., 5-50 Hachiken-cho, Kariya 448-0021, Japana r t i c l e

i n f oArticle history:
Available online 27 May 2008
PACS:
74.25.Bt
74.80.Bj
74.60.Ge
Keywords:
Pulsed ﬁeld magnetization
MMPSC method
Trapped ﬂux density proﬁleBulk superconductora b s t r a c t
A large GdBaCuO superconducting bulk 65 mm in diameter has been magnetized by a two-stage pulse
ﬁeld magnetization method named as a modiﬁed multi-pulse technique with stepwise cooling (MMPSC).
The trapped ﬁeld BPT of 3.0 T was achieved at the bulk center at 40 K by optimizing the trapped ﬁeld proﬁle at the ﬁrst stage of the MMPSC method, on which the maximum BPT was as low as 1.9 T at 40 K for the
single pulsed ﬁeld application. A magnetic gradient along the radius direction larger than that estimatedby a Bean’s model is realized at the ascending stage of the magnetic pulse ﬁeld at the second stage, and alarge amount of magnetic ﬂuxes staying at the bulk periphery ﬂow to the bulk center at the descending
stage.
Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction
Recently, a REBaCuO superconducting bulk of diameter larger
than 60 mm is on the commercial market and a single-grain bulkof 140 mm in diameter can also be fabricated [1]. A trapped ﬁeld
BT and a total trapped ﬂux density UT increase with increasing
diameter of the bulk disk, if the critical current density Jc of thebulk material is identical. Thus, a large bulk is useful for the practical applications such as electric motor and generators. To magnetize the superconducting bulk for the quasi-permanent magnet, thepulsed ﬁeld magnetization (PFM) is suitable, instead of a conventional ﬁeld cooled magnetization (FCM), because PFM is an inexpensive and mobile experimental setup. The trapped ﬁeld BPT by
PFM was, however, pretty smaller than that attained by FCM below
77 K, because of the large temperature rise by the dynamical motion of magnetic ﬂuxes in the bulk [2]. Several approaches havebeen performed and succeeded to enhance BPT around 77 K suchas an iteratively magnetizing pulsed ﬁeld method with reducing
amplitude (IMRA) [3], a multi-pulse technique with stepwise cooling (MPSC) [4] and so on. We have systematically studied the timeand spatial dependences of the temperature T(t, x), the local ﬁeld
BL(t) and the trapped ﬁeld BPT on the surface of cryo-cooled REBaCuO bulks of 45 mm in diameter during PFM for various starting
temperatures Ts and applied ﬁelds Bex [5–8]. We have also investi* Corresponding author. Tel./fax: +81 19 621 6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).
0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2008.05.142

gated the trapped ﬁeld characteristics on the u65 mm GdBaCuO
bulk by the successive pulse application (SPA) method [9]. Contrary to our expectation, the maximum trapped ﬁeld on the
u65 mm bulk was as low as BPT = 1.9 T, which was fairly smaller
than that of the u45 mm GdBaCuO bulk.
To enhance BPT , we proposed a new PFM technique called a modiﬁed MPSC (MMPSC), which consisted of the two-stage temperature procedures [10]. Using the MMPSC method, we havesucceeded a highest ﬁeld trapping of BPT = 5.20 T on the u45 mm
GdBaCuO bulk at 29 K, on which the maximum BPT of 3.6 T was attained by a single pulse application. The value of BPT = 5.20 T is a record high BPT by PFM to date. The MMPSC has been proved to be auniversal and effective method to enhance BPT using other bulks[11,12]. In this paper, we apply the MMPSC method to the
u65 mm GdBaCuO bulk and investigate the ﬂux dynamics andthe BPT enhancement.
2. Experimental procedures
A c-axis oriented GdBaCuO bulk superconductor (Nippon SteelCorporation) of 65 mm in diameter and 20 mm in thickness wasused. The trapped ﬁeld BFC
T by the FCM method was 1.9 T at 77 K.
The stainless steel (SUS304) ring with 1.0 mm in thickness was
ﬁxed onto the bulk disk using Stycast 2850GT. The detailed experimental setup around the bulk and the pulse coil were described
elsewhere [9]. The bulk was tightly anchored onto the cold stageof a Gifford–McMahon (GM) cycle helium refrigerator and was

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cooled down. The bulk was magnetized using a condenser bankand a solenoid-type copper coil dipped in liquid N2. Two Hall sensors (F.W. Bell, Model BHT 921) were adhered at the positions C(bulk center) and E (20 mm distant from the bulk center) on thegrowth sector boundary (GSB). The time evolutions of the local
ﬁelds BL(t) and the trapped ﬁelds BT = BL(t?1) at positions C andE were monitored by using a digital oscilloscope. The applied ﬁeld
l0Ha(t), of which the maximum strength was deﬁned as Bex, wasmonitored by the current I(t) ﬂowing through the shunt resistor.
The rising time of the pulsed ﬁeld was 11 ms and the duration
was 80 ms. The temperature T(t) at the center of the bulk surface
was measured using ﬁne thermocouple. The experimental sequence of the MMPSC technique is shown in the inset of Fig. 1.
At the ﬁrst stage, the pulsed ﬁeld B1 = 3.26, 3.90, 4.75 or 5.18 T
was applied twice (No. 1 and No. 2 pulse) at T1 = 60 K to investigate the inﬂuence of the BT proﬁle at the ﬁrst stage on the ﬁnal
BT. At the second stage, the bulk was cooled to T2 = 40 K and theidentical pulsed ﬁeld of B2 = 6.7 T was applied twice (No. 3 andNo. 4) for each BT proﬁle of the ﬁrst stage.
3. Results and discussion
Fig. 1a shows the time evolution of the applied ﬁeld l0Ha(t) andthe local ﬁelds BL(t) at positions C and E after the No. 1 pulse application (B1 = 4.75 T) at T1 = 60 K in the ﬁrst stage. The local ﬁeld
BL(E)(t) started to rise at t = 3 ms, took a maximum at 15 ms withnearly the same peak height as l0Ha, and then decreased. BL(C)(t)started to rise at 12 ms with a long time delay, at which l0Ha(t)took a maximum of as small as 0.4 T. In this condition, an ‘‘Mshaped” BT proﬁle can be realized, which means the lower trapped

Fig. 1. The time evolution of the applied ﬁeld l0Ha(t) and the local ﬁelds BL(t) at
positions C and E after the (a) No. 1 pulse application (B1 = 4.75 T) at T1 = 60 K in
the ﬁrst stage and (b) the No. 3 pulse application (B2 = 6.7 T) at T1 = 40 K in thesecond stage.

ﬁeld at the bulk center than that at the bulk periphery(BT(C) < BT(E)) [10]. For the No. 2 pulse application (not shown),
BT(C) did not change, but BT(E) slightly increased from 1.1 T to
1.3 T, which was consistent with the previous results [8]. Fig. 1bshows l0Ha(t), BL(C)(t) and BL(E)(t) after the No. 3 pulse application(B2 = 6.7 T) at T2 = 40 K in the second stage. BL(E)(t) increased withincreasing time and the maximum of BL(E) was as large as that of
l0Ha. BL(C)(t) started to rise at 15 ms, took a maximum of 3.5 T
at 20 ms and ﬁnally approached to 3.0 T. The BT(C) = 3.0 T was
higher than that obtained by single pulse application [9]. In thisway, the trapped ﬂuxes at the ﬁrst stage enhance the ﬂux intrusion
and ﬂux trapping at the second stage.
Fig. 2 shows the estimated cross sections of the BT proﬁles on
the bulk after the No. 2 pulse application (B1) with the various
strength at T1 = 60 K, and the subsequent No. 3 pulse applicationof B2 = 6.7 T at T2 = 40 K. If a BT proﬁle is supposed to be symmetrical along the circumferential direction, it is roughly estimatedusing the measured BT(C), BT(E) and BT = 0 at the bulk edge(r = 32.5 mm). Let us compare the BT proﬁles for the No. 2 pulse
at the ﬁrst stage. For the applied ﬁeld B1 lower than 3.90 T, BT(E)increases with increasing B1, but BT(C) is nearly zero. For
B1 = 4.75 T and 5.18 T, a small amount of magnetic ﬂuxes intrude
into the bulk center and the difference between BT(C) and BT(E) becomes small. After the No. 3 pulse application of B2 = 6.7 T at
T2 = 40 K, the BT proﬁle strongly depends on the shape of the already trapped BT proﬁle prepared at the ﬁrst stage; BT(C) after
the No. 3 pulse increases for the BT proﬁle of the ﬁrst stage withincreasing B1. But BT(C) was not enhanced for the BT proﬁle of
B1 = 5.18 T, where BT(C) is as high as 1 T and is comparable with
BT(E). The similar proﬁles for the successive pulse application withidentical strength (SPA) were also shown in Fig. 2, where B = 6.7 T
was applied twice at 40 K to the zero-ﬁeld cooled bulk. The BT proﬁle was cone-shaped, but the BT(C) value was as low as 1.9 T. In thisway, it was found that the optimum ‘‘M-shaped” proﬁle exists at
the ﬁrst stage to maximize the BT(C) value for the No. 3 pulse
application.
Fig. 3a and b show the time dependences of the transient magnetic distribution for the ascending (t 6 11 ms) and the descending(t P 11 ms) stages of the No. 3 pulse ﬁeld (B2 = 6.7 T) at T2 = 40 K
as a function of the bulk radius r, respectively, both of which werereconstructed using Fig. 1b. The bold dotted line in Fig. 3a shows
the initial BT proﬁle at t = 0 ms, which was realized at the ﬁrst stage(B1 = 4.75 T, T1 = 60 K). The local ﬁelds at positions C and E hardly
change for t 6 3 ms and the magnetic ﬂux distribution shows aFig. 2. The estimated cross sections of the BT proﬁles after the No. 2 pulse
application B1 with the various strengths at T1 = 60 K, and the subsequent No. 3
pulse application of B2 = 6.7 T at T2 = 40 K. The similar proﬁles for the successive
pulse application with identical strength (SPA) were also shown.

H. Fujishiro et al. / Physica C 468 (2008) 1477–1480

Fig. 3. The time dependences of the magnetic ﬁeld distribution in the bulk for (a)the ascending (t 6 11 ms) and (b) the descending (t P 11 ms) stages of the No. 3
pulse ﬁeld (B2 = 6.7 T) at T2 = 40 K, where the optimum ‘‘M-shaped” proﬁle wasrealized at the ﬁrst stage.

kink at position E. This result cannot be explained using a Bean’s
critical state model, because the magnetic gradient dB/dr, which
is proportional to a critical current density Jc, should be constant.
This result strongly suggests that the large viscous force FV exists
at the bulk periphery. For t P 4 ms, BL(E)(t) gradually increases
and the ﬂux distribution changes from concave to convex proﬁlewith increasing time. For the descending stage shown in Fig. 3b,
however, BL(C)(t) sharply increases and took a maximum at
t = 14 ms, just after l0Ha(t) takes a maximum. For t P 15 ms,
BL(C)(t) and BL(E)(t) gradually decreased and the cone-shaped
trapped ﬁeld distribution with BT(C) = 3.0 T was ﬁnally obtained.
A magnetic gradient along the radius direction larger than that
estimated by a Bean’s model is realized at the ascending stage ofthe magnetic pulse ﬁeld at the second stage. A large amount ofmagnetic ﬂuxes staying at the bulk periphery ﬂow to the bulk center at the beginning of the descending stage, because of the decrease of FV, at which the ﬂux velocity v is nearly zero and FV is
proportional to v. The optimum ‘‘M-shaped” proﬁle might enhance
the magnetic gradient (dB/dr) and the amount of the magnetic ﬂux
staying at the bulk periphery.
Fig. 4 shows the similar results for the No. 1 pulse of SPA(B = 6.7 T at 40 K), where the magnetic ﬂuxes intrude into the virgin state bulk. A distinct convex trapped ﬁeld proﬁle can be seen at

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Fig. 5. The pulse number dependence of (a) the maximum temperature rise DTmaxand (b) the trapped ﬁelds BT at positions C and E for the MMPSC method (B1 = 4.75 T
at 60 K, B2 = 6.7 T at 40 K) and the SPA method (B = 6.7 T at 40 K).

the end of the ascending stage, compared with the results in Fig.
3a. For the descending stage, the enhancement of BL(C)(t) was
not so large and ﬁnal BT(C) was as small as 1.9 T.
Fig. 5a and b show the pulse number dependence of the maximum temperature rise DTmax and the trapped ﬁelds BT at positions
C and E for the MMPSC method (B1 = 4.75 T at 60 K, B2 = 6.7 T at
40 K) and SPA method (B = 6.7 T at 40 K). For the SPA method,
DTmax gradually decreases and BT(C) gradually increases withincreasing pulse number. For the MMPSC method, DTmax at the second stage is larger than that at the ﬁrst stage because of the larger
pinning loss Qp and viscous loss Qv at low temperature. It should be
noted that the DTmax of the No. 3 pulse in MMPSC is 3.5 K lower
than that of the No. 1 pulse in SPA. The BT(C) value after the No.
3 pulse jumps to 3.0 T and then maintains the value for the No. 4
pulse. The reduction in DTmax is due to the already trapped ﬂuxes
at the ﬁrst stage, which enhances the BPT value in the MMPSC process. The BT(E) value decreases with increasing pulse number forboth MMPSC and SPA, which results from the large temperaturerise in the bulk periphery.
4. Summary
GdBaCuO bulk (u65 mm) has been magnetized by a modiﬁed
multi-pulse technique with stepwise cooling (MMPSC). The
trapped ﬁeld BT of 3.0 T is realized at the bulk center at 40 K by
optimizing the trapped ﬁeld proﬁle (‘‘M-shaped”) at the ﬁrst stage,
on which the maximum BT was 1.9 T at 40 K for the single pulse
application. A moderate amount of the magnetic ﬂuxes should betrapped at the ﬁrst stage to reduce the excess temperature risefor higher pulse ﬁeld (B2) application at lower T2 in the second
stage. A large magnetic gradient (dB/dr) along the radius directionis also necessary at the ascending stage of the pulse ﬁeld (B2) in thesecond stage, where a large amount of magnetic ﬂuxes staying at
the bulk periphery ﬂow to the bulk center at the descending stage.
The optimum ‘‘M-shaped” proﬁle might enhance the magnetic gradient (dB/dr) and the amount of the magnetic ﬂux staying at thebulk periphery.
Acknowledgements

Fig. 4. The time dependences of the magnetic ﬁeld distribution in the bulk for (a)the ascending (t 6 11 ms) and (b) the descending (t P 11 ms) stages of the SPA
process (B = 6.7 T) at T = 40 K.

The authors thank Professor T. Oka of Niigata University for thevaluable discussions. This work is supported in part by a Grant-inAid for Scientiﬁc Research from the Ministry of Education, Culture,
Sports, Science and Technology, Japan (No. 19560003).

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