Physica C 445–448 (2006) 334–338
www.elsevier.com/locate/physc

Higher trapped ﬁeld over 5 T on HTSC bulk by modiﬁed pulse
ﬁeld magnetizing
Hiroyuki Fujishiro a,*, Tatsuya Tateiwa a, Atsushi Fujiwara a,
Tetsuo Oka b, Hidemi Hayashi caIwate University, 3-4-5 Ueda, Morioka 020-8551, JapanIMRA Material R&D Co., Ltd., 5-50 Hachiken-cho, Kariya 448-0021, Japanc
Kyushu Electric Power Co., Inc., 2-1-47 Shiobaru, Fukuoka 815-8520, Japanb

Received 21 March 2006
Available online 23 June 2006

Abstract
The trapped ﬁeld BPT ¼ 5:20 T has been realized on the GdBaCuO bulk superconductor by a modiﬁed multi pulse technique combinedwith a stepwise cooling (MMPSC), which surpassed the previous highest record of BPT ¼ 4:47 T. At the ﬁrst stage, a small amount of themagnetic ﬁeld 1 T was trapped at the bulk center with a concave ﬁeld distribution at a high starting temperature Ts  45 K by the lowpulse ﬁeld application Bex  4.5 T. Following the ﬁrst stage, the higher ﬁeld of Bex  6.7 T was applied at a lower Ts  30 K at the second
stage. The concave trapped ﬁeld proﬁle over the bulk at the ﬁrst stage and the optimization of the higher applied pulse ﬁeld at the second
stage are key points to enhance BT above 5 T.
Ó 2006 Elsevier B.V. All rights reserved.
PACS: 74.25.Bt; 74.80.Bj; 74.60.Ge
Keywords: Pulse ﬁeld magnetizing; Temperature rise; Bulk superconductor; Trapped ﬁeld

1. Introduction
The pulse ﬁeld magnetizing (PFM) on high-Tc bulks has
been recently intensively investigated instead of the ﬁeld
cooled magnetizing (FCM) because of the relatively compact, inexpensive and mobile setup [1]. However, thetrapped ﬁeld BPT by PFM had been pretty smaller than thatattainable by FCM at low temperatures possibly due to thelarge temperature rise DT by the dynamical motion of themagnetic ﬂux. The highest BPT value ever reported had been
3.80 T on the SmBaCuO bulk at 30 K by an improved iterative pulse ﬁeld magnetization method with reduced amplitude (IMRA) [2]. We have systematically measured thetime evolution of the temperature rise DT(t) on the surfaceof the cryo-cooled REBaCuO bulks during the PFM and*

Corresponding author. Tel./fax: +81 19 621 6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).

0921-4534/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2006.04.077

investigated the relation between DT and BPT [3–5]. The heatgeneration results from both the pinning loss Qp related to
the ﬂux trapping and the viscous loss Qv related to the ﬂux
movement. The successive pulses with the same strength
make the DT value decrease and the BPT value increase withincreasing number of the pulse application. The loweringof the bulk starting temperature Ts is expected to resultin a higher BPT due to the enhanced pinning force Fp but
it also brings about a larger DT due to an increase of Qp
and a decrease of the speciﬁc heat C(T). As a result,
BPT at Ts = 10 K was not enhanced contrary to our expectation [6]. Recently, we proposed a new PFM technique
named as a modiﬁed multi-pulse technique combined witha stepwise cooling (MMPSC) [7]. This technique consists of
two stages; ﬁrstly, a small amount of magnetic ﬁeld
(BPT  1 T) is trapped in the bulk center by applying a lower
ﬁeld Bex(1)  4.5 T at a higher temperature Ts(1)  45 K,
realizing a concave trapped ﬁeld distribution over the bulk

H. Fujishiro et al. / Physica C 445–448 (2006) 334–338

sample. Secondly, the bulk is cooled down to Ts(2)  30 K
and the higher pulse ﬁelds of Bex(2)  6.7 T are applied
twice. As a result, we obtained BPT ¼ 4:47 T on the surfaceof the GdBaCuO bulk, which was the highest record using
PFM technique at that time [8]. The reduction of DT due tothe already trapped ﬂux at the ﬁrst stage and the application of the higher Bex(2) at the second stage are key points
to enhance BPT .
In this paper, we inquire into this technique and report
the renewed highest BPT value of 5.20 T by the MMPSC
technique. We elucidate the importance of the optimizationof Bex(2) at the second stage and investigate the eﬀect of thestainless steel ring set onto the bulk disk on the BPT value.
2. Experimental
A highly c-axis oriented GdBaCuO bulk disk (45 mm indiameter and 15 mm in thickness, Nippon Steel Co., Ltd.)was used. The experimental setup around the bulk is shownin the inset of Fig. 1(a). The stainless steel ring with 4 mm
in thickness and 15 mm in height was tightly set onto thebulk disk using Apiezon-N grease in order to reduce DT
during PFM [8]. The bulk with the ring was stacked on
the soft-iron disk on the cold stage of the GM cycle helium
refrigerator and was magnetized using a solenoid-type
pulse coil dipped in liquid N2 with a soft-iron cylinder[7]. Three Hall sensors (F.W. Bell, model BHA 921) were

Fig. 1. The applied ﬁeld [l0Ha(t)] and the local ﬁelds [BL(C)(t), BL(C)(t),
BL(E)(t)] for RUN-1 after applying the (a) pulse No. 1 and (b) pulse No. 3.

335

adhered to the position C (bulk center), M (8 mm distantfrom the bulk center) and E (16 mm distant from the bulk
center) and the time evolutions of the local ﬁelds [BL(C)(t),
BL(C)(t) and BL(E)(t)] were monitored on a digital oscilloscope. The applied ﬁeld l0Ha(t), of which the maximum
strength was deﬁned as Bex, was monitored by the current
I(t) ﬂowing through the shunt resistor. The rising time ofthe pulse ﬁeld was 13 ms and the duration was 80 ms.
The bulk temperature T(t) was measured at the position
T using a ﬁne thermocouple.
3. Results and discussion
We have performed three MMPSC runs (RUN-1–
RUN-3). Table 1 summarizes the initial conditions [Tsand Bex] and the results [Tmax, DTmax and BT(C)] for eachrun, where BPT means BL (t ! 1). For RUN-1, at the ﬁrst
stage, the pulse ﬁeld of Bex(1) = 4.8 T was applied twice(pulse No. 1 and No. 2) at Ts(1) = 47 K. Then the bulk
was cooled down to Ts(2)  28 K and the higher
Bex(2)  6.7 T was applied twice at the second stage (pulse
No. 3 and No. 4). The highest BPT ¼ BT ðCÞ ¼ 5:20 T was
attained for the pulse No. 4. The ﬁrst stage procedure of
RUN-2 and RUN-3 was performed under the similar conditions to that of RUN-1 and, for the second stage, thehigher Bex(2) (=7.01 T for RUN-2) and lower Bex(2)(=6.04 T for RUN-3) were applied in order to clarify theimportance of the strength of Bex(2). In Table 1, the initialconditions and the results using the same bulk without thestainless steel ring are also shown as RUN-0, in which
BPT ¼ 4:47 T was obtained [7].
Figs. 1(a) and (b) show the time dependences of theapplied ﬁeld l0Ha(t) and the local ﬁelds [BL(C)(t),BL(M)(t), BL(E)(t)] for RUN-1 after applying the pulse
No. 1 and No. 3, respectively. BL(E)(t), BL(M)(t), andBL(C)(t) rise up in this order, take a maximum and thenslowly decrease to a ﬁnal stable value. The maximum valueof BL(E)(t) is 4.0 T but that of BL(C)(t) reaches only about
0.9 T. The maximum temperature rise DTmax (=18 K) takes
place, which may mainly come from the heat generation
due to the ﬂux trapping. For the pulse No. 2, the maximumof BL(E)(t) decreases to 2.9 T and DTmax also decreases to
5 K due to the already trapped ﬂuxes which obstruct the
intrusion of the magnetic ﬂux. BT(C) shows a slightincrease to 1.10 T but the BT(M) and BT(E) are nearly
unchanged, both of which are higher than BT(C). For thepulse No. 3 as shown in Fig. 1(b), the maximum of BL(E)(t)remains at 4.2 T, while that of BL(C)(t) increases to 6.0 T
and BPT ¼ BT ðCÞ survives at 5.12 T. These results comefrom the DT reduction due to the trapped ﬂuxes during
the ﬁrst stage and the small DTmax (=29 K) and low Tmax(=57 K) prevent the escape of the magnetic ﬂuxes fromthe bulk. For the pulse No. 4, BPT ¼ BT ðCÞ slightly increases
to 5.20 T.
Figs. 2(a) and (b) present the time evolution of the local
ﬁeld BL(t) as a function of the distance along the radiusdirection on the bulk for the pulse No. 1 of RUN-1 for336

H. Fujishiro et al. / Physica C 445–448 (2006) 334–338

Table 1
The initial conditions [Ts, Bex] and the results [Tmax, DTmax, ﬁnal BPT ] of three MMPSC runs; the RUN-0 shows the previous results in which BPT ¼ 4:47 T
was attained [7]
Run

RUN-1
RUN-2
RUN-3
RUN-0

First stage

Ts(Bex)Tmax(DTmax)
Ts(Bex)Tmax(DTmax)
Ts(Bex)Tmax(DTmax)
Ts(Bex)Tmax(DTmax)

Final BPT

Second stage

Pulse No.1

Pulse No. 2

Pulse No. 3

Pulse No. 4

47 K (4.80 T)
65 K (18 K)
47 K (4.80 T)
65 K (18 K)
46 K (4.52 T)
64 K (18 K)
45 K (4.54 T)
62 K (18 K)

47 K (4.80 T)
52 K (5 K)
48 K (4.94 T)
52 K (4 K)
46 K (4.52 T)
50 K (4 K)
48 K (4.60 T)
53 K (5 K)

28 K (6.73 T)
57 K (29 K)
27 K (7.01 T)
59 K (32 K)
29 K (6.04 T)
49 K (20 K)
29 K (6.72 T)
58 K (29 K)

28 K (6.56 T)
50 K (22 K)
29 K (6.72 T)
53 K (24 K)
30 K (6.87 T)
52 K (22 K)
29 K (6.59 T)
53 K (24 K)

5.20 T
3.02 T
4.10 T
4.47 T

Fig. 2. The time evolution of the local ﬁeld BL(t) as a function of the distance along the radius direction for the pulse No. 1 of RUN-1 for the (a) ascending
and the (b) descending processes.

the ascending and descending processes, respectively, bothof which are reconstructed on the basis of Fig. 1(a). For the
ascending process, the ﬂux intrusion starts to increase fromthe periphery and the small amount of the ﬂuxes arrives atthe bulk center. After the l0Ha(t) value takes a maximum
at t = 13 ms, the intruded ﬂuxes gradually escape in theregion outer than r = 10 mm but the local ﬁelds at positions C and E continue to increase slightly. If the BT proﬁleis assumed to be symmetrical along the circumferential
direction, it should be noted that the BT proﬁle for the ﬁrst
stage shows the concave and ‘‘M-shaped’’ one. This BT distribution must be a key point to bring about the trapped
ﬁeld higher than 5 T at the second stage.
Figs. 3(a) and (b) show the similar BL(t) proﬁle for thepulse No. 3 (Bex = 6.73 T) of RUN-1 for the ascending
and descending processes, respectively. BL(E)(t) increases
but BL(C)(t) and BL(M)(t) hardly change for the ascending
process. For the descending process, however, BL(C)(t)sharply increases just after l0Ha(t) takes a maximum andBL(M)(t) also slightly increases and the conical trapped
ﬁeld distribution with BL(C) > BL(M) > BL(E) is obtained.

These behaviors suggest that the already trapped ﬂuxes inthe ﬁrst stage are pushed into the bulk center and thatthe additional ﬂuxes are supplied from the peripheral
region. The ‘‘M-shaped’’ proﬁle in the ﬁrst stage changes
to the ‘‘cone-shaped’’ one at Ts  30 K for the pulse No.
3 with Bex = 6.73 T. It was pointed out in the previous
paper [9] that the height of the cone (=BT(C)) at the second
stage depends on the height of the edge in the ‘‘M-shaped’’
proﬁle; BT(E) should be higher and BT(C) should be lower
at the ﬁrst stage.
Figs. 4(a) and (b) present the time dependences of theapplied ﬁeld and the local ﬁelds for RUN-2 and RUN-3
on applying the pulse No. 3, respectively. In RUN-2, where
Bex = 7.01 T of the pulse No. 3 is higher than that in RUN1, all the maximum values of local ﬁelds, especially
BL(M)(t), increase. Then BL(C)(t) cannot maintain thehigher value and drastically decreases for t > 60 ms by aspontaneous ﬂux jump. As a result, the trapped ﬁelds atthe positions C, M and E decrease to 2 T and the large
heat generation should be the origin for the depression.
For RUN-3 shown in Fig. 4(b), where lower pulse ﬁeld

H. Fujishiro et al. / Physica C 445–448 (2006) 334–338

337

Fig. 3. BL(t) as a function of the distance along the radius direction on the bulk for the pulse No. 3 of RUN-1 for the (a) ascending and the (b) descending
processes.

Fig. 5. The time dependences of temperature T(t) at position T after thepulse No. 3 application of each run.

Fig. 4. The time dependences of the applied ﬁeld and the local ﬁelds for(a) RUN-2 and (b) RUN-3 after applying the pulse No. 3.

of Bex = 6.04 T was applied, the increase of the BL(t) at
each position is small and the BT(C) value attains only
3.6 T with a round shaped BT distribution.
Finally we comment on the eﬀect of the stainless steel
ring. Fig. 5 shows the time dependences of temperatureT(t) after the pulse No. 3 application of each run. For
RUN-1 to RUN-3, T(t) rises up, takes a maximum at

t = 2 s and then slowly decreases. The local heat generationand the large temperature rise must mainly occur in the
inner part of the bulk within the pulse duration t  0.1 s,
but the temperature change is observable with a long timedelay determined by the thermal diﬀusivity. The maximum
temperature rise DTmax increases with increasing Bex of thepulse No. 3. T(t) of RUN-0 without stainless steel ring is
also shown in Fig. 5 for comparison. It is to be noticed that
T(t) for RUN-0 is much diﬀerent; T(t) slowly increases andtakes a maximum at t  7 s in spite of the identical DTmax
and Tmax values to those in RUN-1. These results suggestthat the heat propagation changes owing to the metal ringsetting and, as a result, the BPT is enhanced from 4.47 T to
5.20 T.
In summary, we performed the MMPSC method on the
GdBaCuO bulk under several conditions and clariﬁed what
are the important factors to enhance BPT over 5 T. At theﬁrst stage in the MMPSC process, the ‘‘M-shaped’’ trapped
ﬁeld proﬁle should be realized on the bulk; BT(C) at thebulk center should be as low as 1 T and the barrier height
BT(E) at the periphery region must be enhanced to 2.5–3 T.

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H. Fujishiro et al. / Physica C 445–448 (2006) 334–338

At the second stage at lower Ts, the optimum higher ﬁeld
Bex, which is 6.7 T for this bulk, should be applied. The
BPT value increased from 4.47 T to 5.20 T as a result of
the stainless steel ring setting onto the bulk disk. The
microscopic change in the heat propagation should takeplace by the ring setting onto the bulk. The detailed study
is in progress.
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