Physica C 412–414 (2004) 646–650
www.elsevier.com/locate/physc

Estimation of generated heat in pulse ﬁeld magnetizing
for SmBaCuO bulk superconductor
Hiroyuki Fujishiro a,*, Kazuya Yokoyama b, Masahiko Kaneyama a,
Tetsuo Oka b, Koshichi Noto a,bb

aFaculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
Iwate Industrial Promotion Center, 3-52-2, Iioka-shinden, Morioka 020-0852, Japan

Received 29 October 2003; accepted 19 January 2004
Available online 7 May 2004

Abstract
The generated heat Q during the pulse ﬁeld magnetizing (PFM) has been estimated for a cryo-cooled SmBaCuO bulk
superconductor based on the maximum temperature rise DTmax and speciﬁc heat CðT Þ. Five successive magnetic pulses
with a ﬁxed amplitude (Bex ¼ 3:01 T  5:42 T) are applied and DTmax are measured for the various initial temperature Ts
between 40 and 70 K. Q has shown characteristic dependences on Ts ; Bex and the pulse number of the successive pulses.
The pinning loss (Qp ) and viscous loss (Qv ) have been separated and estimated as a function of Ts and Bex .
Ó 2004 Elsevier B.V. All rights reserved.
PACS: 74.25.Bt; 74.80.Bj; 74.60.Ge
Keywords: Pulse ﬁeld magnetizing; Heat generation; Speciﬁc heat; Pinning and viscous loss; SmBaCuO

1. Introduction
The pulse ﬁeld magnetizing (PFM) method
for the melt-processed REBaCuO bulk superconductors (RE: rare earth ions) has been recently
recognized to have a promising potential andintensively studied to magnetize the bulk system.
However, at present, the trapped magnetic ﬁeld BPT
by PFM is lower than that by the static ﬁeldcooled magnetizing (FCM) [1–3]. The reason has*Corresponding author. Tel./fax: +81-19-621-6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).

been attributed to the temperature rise DT due tothe magnetic ﬂux motion, which reduces the pinning force Fp . We studied the time evolution andspatial distribution of DT ðtÞ at the surface of thecryo-cooled YBaCuO [4] and SmBaCuO [5,6] bulk
superconductors after PFM. The DT ðtÞ behavior
changed depending on the initial stage temperature Ts the applied pulse ﬁeld Bex and the distribution of BPT before applying the pulse ﬁeld. The
measurement on the spatial distribution of DT ðtÞ
enabled us to locate the easy path, through which
the ﬂuxes preferably intrude into the bulk. In order
to elucidate the magnetizing mechanism by PFM
and to enhance BPT it is necessary to estimate thegenerated heat Q for various Ts and Bex because the0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2004.01.083

H. Fujishiro et al. / Physica C 412–414 (2004) 646–650

Q value may oﬀer more exact information thanDT .
In this paper, we estimate the Q values for theSmBaCuO bulk superconductor after applying Bex
iteratively by use of the measured speciﬁc heatCðT Þ and the maximum temperature rise DTmax .
We investigate the Ts ; Bex and the pulse number
dependences of Q to discuss the mechanisms of theheat generation from the viewpoint of the pinningand viscous power losses.

2. Experimental
A highly c-axis oriented SmBaCuO bulk
superconductor of disk shape with 46 mm indiameter and 15 mm in thickness was used, which
was composed of SmBa2 Cu3 Oy (Sm123) andSm2 BaCuO5 (Sm211) with the molar ratio of
Sm123:Sm211 ¼ 1.0:0.3, 15.0 wt.% Ag2 O powder
and 0.5 wt.% Pt powder [6]. The bulk was tightly
stuck on the cold stage of a Giﬀord McMahon
cycle helium refrigerator, which was evacuatedbelow 105 Torr. The initial stage temperature
Ts was changed from 40 to 70 K. The time evolution of temperature T 0ðtÞ at the center of thebulk (P0) was recorded about seven times justafter applying the pulse ﬁeld using chromel–constantan thermocouple adhered to the bulk surface.
The bulk was magnetized using a pulse coil(L ¼ 1:08 mH) dipped in liquid N2 . The rise timeof the pulse ﬁeld Bex was about 10 ms. Five
successive pulse ﬁelds with a ﬁxed amplitude ofBex ¼ 3:01, 3.84, 4.64 or 5.42 T were applied tothe bulk for each Ts . Hereafter we abbreviate theﬁve pulses as Nos. 1–5. BPT just upon the bulksurface was measured by the Hall sensor (F.W.
Bell, model BHT 921) adhered to a position 2.5mm apart from P0. After a set of T 0ðtÞ and BPT
measurements completed for Nos.1–5 pulses at Ts
the bulk was heated up to 120 K in order toeliminate the trapped ﬂuxes completely and thenagain was cooled down below the superconducting transition temperature Tc ( ¼ 93 K). The speciﬁc heat CðT Þ was measured from 4.2 to 300 K
by the commercial PPMS system (Quantum Design Co., Ltd.) using a sample with the same
composition as the bulk crystal.

647

3. Results and discussion
Fig. 1 shows examples of T 0ðtÞ after applying
the Nos. 1 and 5 pulses of Bex ¼ 3:01 and 4.64 T at(a) Ts ¼ 40 K and (b) Ts ¼ 60 K, respectively. In
the inset of Fig. 1(b), the pulse number dependenceof the maximum temperature rise DT 0max is presented. In all the cases, DT 0max is the largest for theNo. 1 pulse and decreases with increasing pulsenumber, approaching a ﬁxed ultimate value after
the No. 3 pulse. This behavior is reasonable because the largest amount of the ﬂux penetrates into
the virgin state bulk during the No. 1 pulse andis trapped in the bulk.
Fig. 2 shows DT 0max for the (a) No. 1 and (b)No. 5 pulse applications as a function of Ts . With
increasing Ts , T 0max values on the ﬁrst pulse

Fig. 1. Examples of the time evolution of temperature T 0ðtÞ
after applying the Nos. 1 and 5 pulse ﬁeld of Bex ¼ 3:01 and4.64 T at (a) Ts ¼ 40 K and (b) Ts ¼ 60 K. The pulse number
dependence of the maximum temperature rise DT 0max is shownin the inset of (b).

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H. Fujishiro et al. / Physica C 412–414 (2004) 646–650

Q¼

Z Ts þDT 0max

CðT ÞV dT ;

ð1Þ

Ts

application only slightly increase for Bex ¼ 3:01 T,
while those for Bex P 3:84 T clearly decrease. Inorder to discuss the heat generation mechanisms
on PFM, however, we must know the exact
amount of generated heat.
Fig. 3 presents the temperature dependence ofthe speciﬁc heat CðT Þ (J/cm3 K) of the bulk. Since
the bulk is a composite material with about 65%
volume fraction of the superconductive Sm123
phase [7], only a faint cusp in C is observable atTc ¼ 93 K as seen in the inset. The generated heat
Q due to the pulse ﬁeld application can be estimated using the following equation:

where V is the volume of the bulk disk. In thepresent case, we can assume that the heat generation occurs under the adiabatic condition because
the heat generation is completed within the pulse
duration (20 ms) and the Q is exhausted in 10–20
min through the bottom surface of the bulk invacuum atmosphere. The hatched region in Fig. 3
shows an example of the calculation of Q per unit
volume for Bex ¼ 4:64 T at Ts ¼ 40 K (DT 0max ¼ 28K). The estimated Q values using DT 0max may beunderestimated because the heat generation occurs
in the peripheral region and the DT 0max value isusually the smallest on the bulk surface [4–6]. Fig.
4 shows the results of the Q values for each Bex as afunction of Ts . It can be seen that the Ts dependences of Q in Fig. 4 and DT 0max in Fig. 2 are
diﬀerent. In Fig. 4(a) for the No. 1 pulse, Q for
Bex 6 4:64 T increases with increasing Ts takes amaximum and decreases with the further increase
in Ts On the other hand, Q for Bex ¼ 5:42 T
monotonically decreases with increasing Ts . In Fig.
4(b) for the No. 5 pulse, Q for Bex 6 3:84 T
monotonically increases with increasing Ts while Q
for Bex P 4:64 T takes a maximum at around 60 K.
The Q (or T 0max ) value was conﬁrmed to be verysmall above Tc possibly because of the disappearance of Fp .

Fig. 3. The temperature dependence of the speciﬁc heat CðT Þ ofthe SmBaCuO bulk.

Fig. 4. The estimated Q values for each Bex as a function of Ts
after the (a) No. 1 and (b) No. 5 pulse application, respectively.

Fig. 2. The maximum temperature rise DT 0max for the (a) No. 1and (b) No. 5 pulse application as a function of the initial stage
temperature Ts .

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The heat generation during PFM is caused by
the pinning loss (Qp ) and viscous ﬂow loss (Qv ) as
expressed by the following equation [1]:Q ¼ Qp þ Qv ¼ ðFp þ Fv ÞvtpBex 2¼ Jc Bex v þ gv tp ;/0

ð2Þ

where Fp is the pinning force, Fv the viscous force,v the ﬂux velocity, g the viscosity coeﬃcient, /0 aﬂuxoid quantum, Jc the critical current and tp is
the pulse duration. g is given by
Bc2 ðT Þ/0Bex1þgðBex ; T Þ ¼;
ð3Þ
qn ðT Þ2Bc2 ðT Þ
where Bc2 ðT Þ is the upper critical ﬁeld and qn ðT Þ isthe resistivity in the normal state. Similarly toDT 0max (or Q) shown in the inset of Fig. 1(b), theBPT value was also found to almost saturate afterthe No. 3 pulse. Accordingly, no additional ﬂux
trapping takes place during the No. 5 pulse and thepinning power loss Qp may be negligible. ThenQ(No. 5) for the No. 5 pulse shown in Fig. 4(b) canbe regarded as almost due to the viscous loss Qv If
we assume that Qv is not much diﬀerent for eachpulse, the diﬀerence DQ ¼ Q(No. 1) ) Q(No. 5)
may roughly stand for Qp for the No. 1 pulse. TheDQ values as a function of Ts are displayed in Fig.
5(a) for each Bex and Fig. 5(b) presents BPT for theNo. 1 pulse. Comparing Fig. 5(a) and (b), we notice that DQ and BPT have much similar Ts dependences, i.e., when DQ is large, BPT is also large. ThisFig. 5. (a) DQ( ¼ Q(No. 1) ) Q(No. 5)) and (b) BPT for each Bex
as a function of Ts .

649

fact supports our assumption that DQ can beroughly regarded as Qp .
In Fig. 5(a), DQQp Þ exhibits the negative Tsdependence as a whole, which is reasonable on thebasis of Eq. (2) because Fp or Jc should decrease
with increasing T . The dQp =dTs values, however,take positive values for Bex ¼ 3:01 and 3.84 T
below 60 and 50 K, respectively. This may be causedby the strong pinning centers in the peripheral
region which obstruct the intrusion of the ﬂux into
the bulk. The existence of the strong pinning centers in the peripheral region was conﬁrmed for thissample in the previous papers [4,5]. In Fig. 4(b),overall Ts dependence of Qv (¼ Q (No. 5)) is positive. This fact is somewhat puzzling because g isexpected to decrease with increasing T owing to
the reduction in Bc2 ðT Þ in Eq. (3). The existence ofthe strong pinning centers in the peripheral region
can also be an origin of the positive dQv =dTs The
strong pinning in the peripheral region obstructs
the free intrusion of the ﬂux and suppresses theamount of the ﬂux ﬂow in the bulk. With
increasing temperature, the peripheral pinning isweakened and a larger amount of the ﬂux canfreely penetrate into the bulk, resulting in the larger viscous loss Qv The another possibility may be
the increase in the eﬀective ﬂux velocity v in Eq.
(2). If the critical state is realized during PFM, v
should be inversely proportional to the pulse
duration tp and should be temperature independent for a ﬁxed Bex . If the critical state is not attained because of too short tp ; v may increase withT owing to the reduced Fp , which may result in theincrease in Qv because Qv is proportional to v2 inEq. (2).
In summary, the generated heat Q after applying the pulse magnetic ﬁeld has been estimated for
the SmBaCuO bulk superconductor using themaximum temperature rise DT 0max and the measured speciﬁc heat CðT Þ. Analyzing the pulse
number dependence of Q for the ﬁve successive
pulse applications with a ﬁxed amplitude Bex , thecontributions of the pinning power loss Qp and theviscous ﬂow power loss Qv to the total Q have beenroughly separated. Qp decreases with increasing
initial stage temperature Ts because of the reduction in the pinning force Fp with increasing T . It
has been conﬁrmed that Qp which is approximately

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H. Fujishiro et al. / Physica C 412–414 (2004) 646–650

by Qp ﬃ DQ ¼ Q(No. 1) ) Q(No. 5), is closely
correlated with the trapped magnetic ﬁeld
BPT dQv =dTs has been found predominantly to bepositive, somewhat in contradiction with the theoretical expectation. The strong pinning centers in
the peripheral region, which suppress the free
intrusion of the ﬂux may provide a plausible origin
for the positive dQv =dTs . Another possibility for
dQv =dTs > 0 may be the deviation from the criticalstate model, permitting the increase in the ﬂux
velocity v and, resultantly, Qv with increasing T .

Acknowledgements
The authors greatly thank Prof. M. Ikebe ofIwate University for valuable suggestions and Dr.
J. Hejetmanek of Institute of Physics, Academy
Science of Czech Republic for the speciﬁc heatmeasurement. This work is partially supported by
Japan Science and Technology Corporation under

the Joint-research Project for Regional Intensive in
the Iwate Prefecture on ‘‘Development of practicalapplications of magnetic ﬁeld technology for use in
the region and in everyday living’’.

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