Physica C 463–465 (2007) 394–397
www.elsevier.com/locate/physc

Importance of initial ‘‘M-shaped’’ trapped ﬁeld proﬁlein a two-stage pulse ﬁeld magnetization (MMPSC) method
H. Fujishiro a,*, T. Hiyama a, T. Tateiwa a, Y. Yanagi b, T. Oka cabFaculty of Engineering, Iwate University, 3-4-5 Ueda, Morioka 020-8551, JapanIMRA MATERIAL R&D Co., Ltd., 5-50 Hachiken-cho, Kariya 448-0021, Japanc
Faculty of Engineering, Niigata University, Niigata, Niigata 950-2181, Japan
Accepted 2 March 2007
Available online 18 May 2007

Abstract
The inﬂuence of a shape of a trapped ﬁeld distribution at a ﬁrst stage on the ﬁnal trapped ﬁeld BT at a second stage has been investigated in the two-stage pulse ﬁeld magnetization technique named as a modiﬁed multi-pulse technique with stepwise cooling (MMPSC).
The ﬁnal trapped ﬁeld BT strongly depends on the shape and the strength of the trapped ﬁeld at the ﬁrst stage. The ‘‘M-shaped’’ proﬁlewith a moderate number of magnetic ﬂuxes at the ﬁrst stage maximizes the ﬁnal BT. The optimization of the applied ﬁeld B2 and thelowering of the operating temperature T2 at the second stage are also eﬀective to enhance BT. The ﬂux intrusion and the ﬂux trap
are eﬀectively promoted at low temperatures by the existence of already trapped ﬂuxes during the ﬁrst stage.
Ó 2007 Elsevier B.V. All rights reserved.
PACS: 74.25.Bt; 74.80.Bj; 74.60.Ge
Keywords: Pulse ﬁeld magnetization; MMPSC method; Trapped ﬁeld proﬁle; Bulk superconductor

1. Introduction
Highly c-axis oriented REBaCuO superconducting
bulks (RE: rare earth element) can trap a magnetic ﬁeld
as high as 17 T at 29 K by ﬁeld-cooled magnetization(FCM) because of the improvements in their pinning properties and the mechanical reinforcement [1]. A cryocooled
superconducting bulk magnet, which can generate over
5 T in open space, has been developed by FCM for theapplications to the sputtering cathode [2]. A pulse ﬁeld
magnetization (PFM) is another technique to magnetize
the bulk and has been intensively investigated because of
the relatively compact, inexpensive and mobile setup [3].
In PFM, however, a large temperature rise occurs in thebulk due to the dynamical motion of magnetic ﬂuxes andthen the trapped ﬁeld component BT parallel to the c-axis*

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

0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2007.03.440of the bulk is fairly smaller than that by FCM due to thedecrease in a critical current density Jc at elevated temperatures. The highest BT value ever reported had been 3.80 Ton the SmBaCuO bulk (35 mm in diameter) at 30 K [4]. We
have systematically studied the temperature rise DT and thetrapped ﬁeld BT on REBaCuO bulks during PFM [5–7]
and have suggested that both the reduction in DT andthe lowering of the operating temperature Ts are indispensable issues to enhance BT [8].
Based on the obtained results, we proposed a new PFM
technique, named as a modiﬁed multi-pulse technique combined with a stepwise cooling (MMPSC) method [9] andhave succeeded a highest ﬁeld trapping of BT = 5.20 T on
the GdBaCuO bulk (45 mm in diameter) [10]. In this technique, a small number of magnetic ﬂuxes should be trappedin the bulk at T1 after applying pulse ﬁeld B1 at a ﬁrst
stage. After the bulk is cooled down to the lower temperature T2, a higher and optimum pulse ﬁeld B2 (>B1) should
be applied at a second stage. The so-called ‘‘M-shaped’’H. Fujishiro et al. / Physica C 463–465 (2007) 394–397

trapped ﬁeld proﬁle at the ﬁrst stage, in which the trapped
ﬁeld at the bulk center is lower than that at the bulk periphery, is also necessary in order to enhance the BT value [11].
If a ‘‘cone-shaped’’ proﬁle is realized at the ﬁrst stage, a sizable enhancement of BT cannot be realized by the succeeding pulse [11]. In the previous studies, however, wemeasured the time evolution of local ﬁelds BL(t) and thetrapped ﬁelds BT at only three points (center, middle andperiphery of the bulk disk) using Hall sensors adhered on
the bulk surface [10]. In order to enhance the BT value still
more using the MMPSC method, the role of the ‘‘Mshaped’’ proﬁle at the ﬁrst stage must be clariﬁed.
In this paper, we measure the two-dimensional trapped
ﬁeld proﬁle 0.5 mm above the bulk surface at both ﬁrst
and second stages in the MMPSC method. The inﬂuenceof the shape of the trapped ﬁeld distribution at the ﬁrst
stage on the ﬁnal BT value at the second stage is discussed.
2. Experimental procedure
The GdBaCuO bulk disk (Nippon Steel Corporation)used in this study was 45 mm in diameter and 18 mm inthickness, which was diﬀerent with that attained
BT = 5.20 T [10]. The bulk was mounted on soft iron yoke
cylinder 40 mm in diameter and 20 mm in thickness andtightly anchored onto the cold stage of a Giﬀord–McMahon (GM) cycle refrigerator. The experimental apparatus
for PFM is described elsewhere [6]. The temperature of
the bulk was controlled over the range from 30 K to70 K. The magnetizing solenoid coil, which generated thepulse ﬁeld up to Bex = 6.29 T with a rise time of 12 ms,
was placed outside the vacuum chamber that the central
axis of the resulting ﬁeld coincides with that of the bulk.
Fig. 1 shows the experimental sequence of the MMPSC
technique. Four magnetic pulses were applied at diﬀerent
initial temperatures T1 and T 2 on the bulk surface. At
the ﬁrst stage, a pulse ﬁeld B1 was applied twice at T1(=70 K or 60 K) in order to trap a small number of magnetic ﬂuxes in the bulk. Hereafter, we refer to these two

Fig. 1. The experimental sequence of the MMPSC technique. At the ﬁrst
stage, a pulse ﬁeld B1 is applied twice (No. 1 and No. 2) at T1. At thesecond stage, the bulk is cooled down to T2 and a higher pulse ﬁeld B2 isapplied twice (No. 3 and No. 4).

395

pulses as No. 1 and No. 2. At the second stage, the bulk
was cooled down to T 2 (=40 K or 30 K) and a higher pulse
ﬁeld B2 was applied twice (No. 3 and No. 4 pulses). At
each stage, the trapped ﬁeld component BT parallel to thec-axis of the bulk was measured 0.5 mm above the bulk
surface by scanning a Hall sensor (F W Bell, BHA 921)
inside the vacuum chamber using a scanning device, which
has an x–y stage controller with a ﬂexible bellows. The
total trapped ﬂux UT was calculated from the trapped ﬁeld
distribution by integrating BT over the area where its value
was positive.

3. Results and discussion
In order to conﬁrm the ﬁeld trapping ability of the bulk
and determine the conditions in the MMPSC method, asingle magnetic pulse was applied and the BT distribution
was measured for various applied ﬁelds Bex at temperatures
T (=30–70 K). Fig. 2a and b show the vertical section of
the BT proﬁle after applying pulse ﬁelds Bex at T = 70 K
and 40 K, respectively. In the inset of Fig. 2a, an exampleof the two dimensional BT proﬁle is shown for
Bex = 2.66 T. All the vertical sections shown in this study
were made along the central line in a same manner. At
T = 70 K, the trapped ﬁeld increases with increasing
applied ﬁeld Bex, takes a maximum for Bex = 4.52 T andthen decreases for higher Bex. The ‘‘M-shaped’’ BT proﬁlecan be observed for Bex < 3.84 T, and a symmetric ‘‘coneshaped’’ proﬁle can be seen for Bex > 4.52 T. On the other
hand, at T = 40 K shown in Fig. 2b, BT(C) at the bulk center is small, even if the pulse ﬁeld with the same strength isapplied as that at T = 70 K. The maximum BT(C) increases
BT = 1.8 T for the highest applied ﬁeld Bex = 6.29 T, but
the ‘‘cone-shaped’’ proﬁle cannot be realized because of
the strong pinning force Fp at low temperatures.
Fig. 3a–d show the BT proﬁles of the cases A–D undervarious conditions (T1, B1, T 2 and B2) in the MMPSC

Fig. 2. The vertical section of the BT proﬁle after applying pulse ﬁelds Bex
at (a) T = 70 K and (b) 40 K. The inset of (a) shows an example of the twodimensional BT proﬁle for Bex = 2.66 T.

396

H. Fujishiro et al. / Physica C 463–465 (2007) 394–397

Fig. 3. The BT proﬁles in the cases A–D under various conditions (T1, B1,
T2 and B2) in the MMPSC method.

method. In cases A and B shown in Fig. 3a and b, the inﬂuence of the shape of the trapped ﬁeld distribution at theﬁrst stage (T1 = 70 K) on that at the second stage(T 2 = 40 K) is indicated. A small number of magnetic
ﬂuxes were trapped on the bulk and the typical ‘‘Mshaped’’ proﬁle was observed at the ﬁrst stage in thecase A (B1 = 3.25 T). The BT proﬁle in the case B(B1 =3.84 T) shows a ‘‘trapezoid-shaped’’ proﬁle rather thanthe ‘‘M-shaped’’ one due to the higher B1. After applying
identical higher pulse ﬁeld B2 = 6.29 T for both cases atthe second stage (T 2 = 40 K), the shape of the ﬁnal BT
proﬁle is quite diﬀerent; a cone-shaped proﬁle with higher
BT(C) = 2.8 T can be observed in the case A, but the‘‘M-shaped’’ proﬁle is more emphasized and BT(C) remains
the low value of 1.4 T in the case B. A slight increase in the
total trapped ﬂux UT in the No. 2 and No. 4 pulse applications, compared with that in the No. 1 and No. 3 pulses,
respectively, is due to the decrease in the temperature riseby the identical pulse ﬁeld applications [7]. In Fig. 3c,
where a very small number of the magnetic ﬂuxes aretrapped only in the bulk periphery at the ﬁrst stage(T1 = 60 K, B1 = 3.25 T), the cone-shaped proﬁle wasobtained at the second stage (T 2 = 40 K, B2 = 6.29 T).
The maximum BT(C) = 2.4 T value was low, comparedwith that of the case A, but BT(C) value and the BT proﬁlewere nearly the same as those obtained by the single pulse

application. In the case D, where a slight diﬀerent ‘‘Mshaped’’ proﬁle from that in Fig. 3a is formed at the ﬁrst
stage (T1 = 60 K, B1 = 3.84 T), the BT proﬁle is asymmetric and the BT(C) is not large at the second stage(T 2 = 40 K, B2 = 6.29 T). In this way, the trapped ﬁeld
proﬁle and the BT(C) value at the second stage strongly
depend on the shape of the trapped ﬁeld proﬁle and theUT value at the ﬁrst stage. The optimum ‘‘M-shaped’’ proﬁle exists at the ﬁrst stage for enhancing the ﬁnal trapped
ﬁeld in MMPSC.
The inﬂuences of the strength of B2 and the lowering T 2
at the second stage were studied under the similar shape of
the BT proﬁle at the ﬁrst stage. Fig. 4a shows the trapped
ﬁeld distribution after applying No. 3 pulse ﬁeld with various B2 values at T 2 = 40 K under the identical ‘‘Mshaped’’ proﬁle at the ﬁrst stage (T1 = 70 K, B1 =3.25 T). For B2 = 5.95 T, a nearly symmetrical trapped
ﬁeld distribution with BT(C) = 2.8 T was observed. On
the other hand, for B2 = 5.60 T and 6.29 T, the BT proﬁles
are asymmetric and the maximum BT values are rather
small. These results suggest that the optimum strength of
B2 exists in order to enhance the trapped ﬁeld and thatthe optimum B2 value changes depending on the shapeof the BT proﬁle at the ﬁrst stage. Fig. 4b shows the resultsof the BT proﬁle, where the temperature T 2 decreased to
30 K and the B2 = 6.29 T was applied under the similar
BT proﬁle at the ﬁrst stage to that shown in Fig. 4a(T 2 = 40 K). A symmetrical trapped ﬁeld distribution
was observed and BT(C) was enhanced over 3 T. An optimum pulse ﬁeld was probably B2 = 6.29 T at T 2 = 30 K
in the bulk which slightly shifts to higher ﬁeld due to theenhancement of the pinning force by lowering T 2. The
lowering T 2 is a possible solution to enhance BT.
Fig. 5a shows the BT(C) value for the No. 3 pulse(T 2 = 40 K) as a function of B2 after the ‘‘M-shaped’’
trapped ﬁeld distribution as shown in Fig. 4a is realized

Fig. 4. (a) The BT proﬁle after applying No. 3 pulse with various B2
values at T 2 = 40 K under the identical trapped ﬁeld distribution at theﬁrst stage (T1 = 70 K, B1 = 3.25 T). (b) The BT proﬁle after applying
B2 = 6.29 T at T 2 = 30 K under the identical BT proﬁle at the ﬁrst stage
to that shown in (a).

H. Fujishiro et al. / Physica C 463–465 (2007) 394–397

397

4. Summary
We have investigated the inﬂuence of a shape of atrapped ﬁeld distribution at a ﬁrst stage on the ﬁnal
trapped ﬁeld at a second stage in a modiﬁed multi-pulse
technique with stepwise cooling (MMPSC). The ﬁnal
trapped ﬁeld BT strongly depends on the shape and thestrength of the trapped ﬁeld at the ﬁrst stage. The optimum‘‘M-shaped’’ proﬁle with a moderate number of magnetic
ﬂuxes at the ﬁrst stage maximizes the ﬁnal BT. The ﬂux
intrusion and trap are promoted eﬀectively by the existenceof already trapped ﬂuxes in the bulk at low temperature.
References
Fig. 5. The BT(C) value for the No. 3 pulse ((a) T2 = 40 K and (b) 50 K)
as a function of B2 after the ‘‘M-shaped’’ trapped ﬁeld distribution isrealized at the ﬁrst stage. The BT(C) values for the single pulse application
are also shown.

at the ﬁrst stage (T1 = 70 K, B1 = 3.25 T). The BT(C) values for the single pulse application at T = 40 K are also
shown. BT(C) of the single pulse application monotonicallyincreases with increasing applied ﬁeld Bex up to 6.29 T. In
the MMPSC method, BT(C) is larger than that in a single
pulse application. It should be noted that BT(C) in the
MMPSC method also increases with increasing B2 andthen takes a maximum at B2 = 6 T. These results suggestthat the magnetic ﬂuxes are easy to intrude and trap inthe bulk for the existence of a moderate number of trapped
ﬂuxes at the ﬁrst stage. Fig. 5b shows the similar results at
T 2 = 50 K. BT(C) in the MMPSC method takes a maximum at 5 T which is larger than that for a single pulse
application. The B2 value at which BT(C) takes a maximum at T 2 = 50 K is lower than that at T 2 = 40 K due
to the decrease in the pinning force Fp.

[1] M. Tomita, M. Murakami, Nature 421 (2003) 517.
[2] Y. Yanagi, T. Matsuda, H. Hazama, K. Yokouchi, M. Yoshikawa,Y. Itoh, T. Oka, H. Ikuta, U. Mizutani, Physica C 426–431 (2005)
764.
[3] U. Mizutani, T. Oka, Y. Itoh, Y. Yanagi, M. Yoshikawa, H. Ikuta,
Appl. Supercond. 6 (1998) 235.
[4] Y. Yanagi, Y. Itoh, M. Yoshikawa, T. Oka, T. Hosokawa, H.
Ishihara, H. Ikuta, U. Mizutani, in: T. Yamashita, K. Tanabe (Eds.),
Advances in Superconductivity XII, Springer-Verlag, Tokyo, 2000, p.
470.
[5] H. Fujishiro, K. Yokoyama, T. Oka, K. Noto, Supercond. Sci.
Technol. 17 (2004) 51.
[6] H. Fujishiro, M. Kaneyama, K. Yokoyama, T. Oka, K. Noto, Jpn. J.
Appl. Phys. 44 (2005) 4919.
[7] H. Fujishiro, K. Yokoyama, M. Kaneyama, T. Oka, K. Noto, IEEE
Trans. Appl. Supercond. 15 (2005) 3762.
[8] K. Yokoyama, M. Kaneyama, H. Fujishiro, T. Oka, K. Noto,
Physica C 426–431 (2005) 671.
[9] H. Fujishiro, M. Kaneyama, T. Tateiwa, T. Oka, Jpn. J. Appl. Phys.
44 (2005) L1221.
[10] H. Fujishiro, T. Tateiwa, A. Fujiwara, T. Oka, H. Hayashi, Physica C
445–448 (2006) 334.
[11] H. Fujishiro, M. Kaneyama, T. Tateiwa, T. Oka, J. Phys. Conf. Series
43 (2006) 405.