INSTITUTE OF PHYSICS PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 16 (2003) 809–814

PII: S0953-2048(03)61076-6

Time evolution and spatial distribution oftemperature in YBCO bulk
superconductor after pulse fieldmagnetizing
Hiroyuki Fujishiro1, Tetsuo Oka2, Kazuya Yokoyama2 andKoshichi Noto112

Faculty 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

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

Received 13 March 2003, in final form 14 May 2003
Published 11 June 2003
Online at stacks.iop.org/SUST/16/809
Abstract
The time evolutions of temperature rise T (t) after pulse field magnetizing
have been measured on the surface of a cryo-cooled YBaCuO bulk
superconductor. The temperature rise T increases with increasing pulse
field strength, and a quite large temperature rise (Tmax ∼ 18.8 K) is
observed just before the trapped magnetic flux reaches the central region of
the bulk. The epoxy resin, impregnated and coated to the bulk crystal formechanical reinforcement, prevents the heat exhaust towards the cold stageof the refrigerator and it needs much time to recover its initial temperature.
The spatial distribution of T (t) has indicated that the magnetic fluxes tend
to enter into the bulk, avoiding the 4-fold growth sector boundaries of thebulk crystal.

1. Introduction
For the application of bulk superconductors as a high strength
magnet, the pulse field magnetizing (PFM) method is a
useful technique as well as the static field cooled magnetizing(FCM) method [1]. Recently, a new PFM method based ona series of iterative magnetizing operations with gradually
reduced pulse field amplitudes, named the IMRA method,has been proposed [2]. In this method, the PFM operations
are repeated so as to efficiently enhance the total trappedmagnetic fluxes in the bulk. It was demonstrated that, by
the IMRA method, the YBaCuO bulk could trap almost an
equal amount of the magnetic flux as the FCM method inliquid nitrogen [3]. However, at temperatures lower than 77 K,
the maximum trapped magnetic flux by PFM even using the
IMRA method is generally lower than that by FCM as shownfor the SmBaCuO bulk superconductors [4, 5]. A possible
origin for this observation can be the temperature rise causedby the viscous motion of the magnetic fluxes, resulting in thedecrease of the trapped field. The realization of the trappedmagnetic field by PFM below 77 K as high as that of FCM is0953-2048/03/070809+06$30.00

greatly desired because the use of a cryo-cooled refrigerator
is now very popular to cool the bulk superconductors far
below 77 K.
Ikuta et al measured the in situ local magnetic flux density
of YBaCuO and SmBaCuO bulks in liquid nitrogen just after
PFM, and then calculated the time and position dependences of
the temperature rise T at the bulk surface [6]. The estimatedT initially increases rapidly and reaches a maximum within
the order of a millisecond. The temperature rises faster inthe outer side of the bulk. The estimated T is only a few
K and increases with increasing pulse field strength. These
calculations, however, have not been testified by experiments.
There have been no calculations nor experimental data as
for the time and position dependences of the temperaturerise T (t, r) of the bulk superconductors cooled by a cryocooled refrigerator. Recently, the epoxy resin impregnation
technique for the bulk materials has been widely applied
for the mechanical reinforcement [7]. The existence of the
low-thermal-conductive epoxy resin on the bulk surface may
prevent the heat exhaust from the bulk and enhance thetemperature rise after PFM. However, there have been no© 2003 IOP Publishing Ltd Printed in the UK809

H Fujishiro et al

Pulse Magnetizing coilor Superconducting Magnet

epoxy resin

Yoke

bulk

(a)

bulk

with epoxy

bulk

(b)

without epoxy

T6
In foilbisect line

Cu rodSapphire plate
Cold stage ofrefrigerator

C3(T3)Hall sensor

C2(T2)(d)

C1(T1)C4(T4)C5(T5)
GSBs
inter-GSB region

Growth sector
boundaries(GSBs)(c)

Vacuum shroud

Figure 1. The experimental setup of the YBaCuO bulk superconductor for the temperature measurements. The cross sections of the bulk for(a) ‘with epoxy’ and (b) ‘without epoxy’ settings are shown. (c) The setting of the bulk in the Gifford McMahon (GM) cycle helium
refrigerator and the position of the temperature measurement T 6 are shown. (d ) The positions of the temperature measurement T 1–T 5 on
the bulk surface are indicated (see the text).

experimental data for the effect of the resin-impregnation on
T of the bulks either.
In this paper, we report and analyse the time and position
dependences of the temperature rise T (t, r) after PFM for
the YBaCuO bulk superconductors with and without epoxy
resin, which are cooled using a cryo-cooled refrigerator down
to ∼40 K.

2. Experimental details
Figure 1 shows the setup of the YBaCuO bulk superconductor
in a Gifford McMahon (GM) cycle helium refrigerator (AISIN,
GR103). The YBaCuO bulk superconductor used in thisstudy is a highly c-axis-oriented crystal fabricated by Dowa
Mining Co, Ltd. The crystal consists of YBa2Cu3Oy (Y123),
Y2BaCuO5 (Y211) with the molar ratio of 1.0 : 0.4 and0.5 wt% Pt powder (without Ag2O addition). The initial sizeof the bulk is 46 mm in diameter and 15 mm in thickness. The
bulk was uniformly impregnated and coated by epoxy resin
in vacuum, the final sample size being 52 mm in diameterand 17 mm in thickness. The epoxy resin layer (∼1 mm inthickness) on the upper side of the bulk was removed in order tomeasure the precise temperature of the bulk surface as shown infigure 1(a). We name this sample setting as the ‘with epoxy’setting. In the setting shown in figure 1(b), the epoxy resinon the lower side was also removed, which we name as the‘without epoxy’ setting.
The YBaCuO bulk was stuck on the sapphire plate on thecold plate of the GM refrigerator using an indium (In) foil
as shown in figure 1(c). Five sets of Teflon-coated chromel–
constantan thermocouples (76 µm in diameter) were adhered
to the bulk surface using GE7031 varnish (figure 1(d )). The
thermocouple at the centre of the bulk is named as C1 and three810

thermocouples (C1, C4, C5) were aligned along one of the 4fold growth sector boundaries (GSBs) with a 9 mm distance.
GSBs are a kind of grain boundaries which are formed in theab-plane of the bulk sample as a result of the collision of thecrystal growth fronts [1]. The other two thermocouples (C2,
C3) were set along a line which makes an angle of 135◦ fromthe first GSB line with a same distance. We name this line,
along which the thermocouples (C1, C2, C3) were put, as thebisect line, and the sector region surrounded by GSBs, as theinter-GSB region. We denote the temperatures measured by
C1–C5 as T 1–T 5. The temperature of the cold stage of the
GM refrigerator, T 6, was also monitored. Since the magnetic
field dependence of the thermoelectric voltage of the chromel–
constantan thermocouple used in this experiment is within 2%
under the field of 5 T and at 40 K [8], the recalibration of thethermoelectric voltage in the field was not performed. Eachthermocouple voltage was monitored about seven times per
second just after applying the pulse fields. The cryo-cooled
YBaCuO bulk was magnetized using a pulse coil dipped inliquid N2 as shown in figure 1(c). The rise time of the pulse wasabout 1 ms. The strength of the pulse field Bex was calculated
from the current flowing through the coil. Bex was applied
iteratively following a typical IMRA procedure. The Hallsensor (F W Bell, model BHA 921) was adhered to theposition with a 3 mm distance from the bulk centre as shownin figure 1(d ), which monitored the trapped magnetic field
BT P . The trapped field BT F C following FCM using the cryocooled superconducting magnet was also measured at several
temperatures. In the FCM procedure, the static magnetic fieldof 5 T was decreased down to 0 T in 18 min (0.278 T min−1).
The distribution of the trapped magnetic flux density was
mapped using an axial-type Hall censor, which was scanned
3 mm above the bulk surface.

Temperature measurements in YBCO magnetized by pulse field

Pulse

Bex (T)T 1max (K)T 1max (K)BT P (T)

#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11

2.322
3.014
3.870
4.644
5.418
5.031
4.644
2.418
3.870
3.014
2.322

3.7
4.3
18.8
19.2
24.5
21.7
18.5
14.0
9.8
4.5
1.7

46.0
45.5
59.8
60.0
66.0
63.0
60.0
56.0
52.5
47.5
44.7

0.056
0.013
0.271
2.029
2.278
2.350
2.394
2.418
2.403
2.437
2.438

(a) without epoxy

90

Temperature (K)Table 1. Summary of the IMRA method for each applied pulsein the case of the ‘without epoxy’ setting; the applied pulse field
Bex (T), the maximum temperature rise T 1max(K) at the centre of
the bulk, the maximum temperature of T 1max(K) and the trappedfield measured by the attached Hall sensor BT P (T).

T1

80
#5
#6

70

#3

#9 #10

#1 #2

#11

50
40
30

T6

0

100

200

300

Time (min)(b) with epoxy

3. Results and discussion#5

Temperature (K)The GM refrigerator used in this study needs about 3 h tocool the cold stage with the YBaCuO bulk superconductor
to the lowest temperature (T = 35 K). However, the time toreach the lowest temperature at the bulk sample surface arevery different between the ‘with epoxy’ and ‘without epoxy’settings; the former takes about 9 h, while the latter takes about
3.5 h. One of the authors (HF) and co-workers measured
the anisotropy of the thermal conductivity κ(T ) and thethermal diffusivity α(T ) of the YBaCuO bulk superconductors
prepared in the same procedure [9]. The κ(T ) values in theab-plane (κab ) and along the c-axis (κc ) are κab = 98 and κc =23 mW cm−1 K−1 at 200 K, and κab = 185 and κc =30 mW cm−1 K−1 at 40 K, respectively. In comparison to
those κ values, κ(T ) of the used epoxy resin is quite low(1.8 mW cm−1 K−1 at 293 K) [7]. The difference of thereaching time to the lowest temperature between the ‘withepoxy’ and ‘without epoxy’ settings may come from theexistence of low-thermal-conductive epoxy resin with 1 mm inthickness between the cold stage and the YBaCuO bulk. The
lowest temperatures of the bulk surface, T 1–T 5 were about∼42 K for both settings and about 7 K higher than T 6. The
vacuum gap between the bulk surface and the inner surfaceof the vacuum shroud is only 1.5 mm and the radiation heatshould intrude into the bulk, which may be the main origin of
the temperature rise at the bulk surface. The temperature riseof 7 K results from the low thermal conductivity and the large
thickness along c-axis of the bulk superconductor. Although asufficient vacuum gap may reduce the temperature difference,
the high trapped magnetic field cannot be fully utilized at theouter surface of the vacuum shroud because of the elongateddistance from the bulk surface.
Table 1 numerically summarizes the strength of thepulse field Bex , the maximum temperature rise T 1max of
T 1, the maximum temperature T 1max and the trapped field
BT P measured by the attached Hall sensor after each Bex
application. In the ‘without epoxy’ setting, 11 magnetic
pulses, which we abbreviate to #1 to #11 in order, wereapplied after the bulk surface temperature T 1 recovers to theinitial temperature (∼42 K). In the ‘with epoxy’ setting, the

#7
#8

60

90

3.1. Temperature rise under pulse field magnetizing

#4

80

#6

#7

#8 #9 #10
#11

#4
#3

70
#2

60

T1

#1

50
40
30
0

T6

100

200

300

Time (min)Figure 2. The full time dependences of the typical temperatures(T 1, and T 6) in the IMRA method for the (a) ‘without epoxy’setting and (b) ‘with epoxy’ setting.

same series of the 11 magnetic pulses Bex were applied withevery 20–30 min time interval before T 1 recovers to the initial
temperature.
Figures 2(a) and (b) present the full time dependences of
the temperatures T 1 and T 6 after PFMs for ‘without epoxy’and ‘with epoxy’ settings, respectively. In figure 2(a), thesurface temperature suddenly increases just after applying
the magnetic pulse and then smoothly decreases to the initial
temperature within ∼30 min. The temperature T 6 of the cold
stage is nearly independent of the pulse field strength. The
maximum temperature rise T 1max increases with increasing
pulse field strength. In figure 2(b) for the ‘with epoxy’ setting,the temperature of the bulk surface cannot recover to theinitial temperature within several decade minutes and, as canbe seen, just before applying the following pulse the surface
temperature gradually increases, in spite of the nearly constant
T 6. These results confirm that good heat exhaust cannot berealized due to the existence of the epoxy resin layer between
the bulk and the cold stage.
Figure 3(a) shows the relation between the trappedmagnetic field BT P by PFM method and the applied
pulse field Bex for both ‘without epoxy’ and ‘with epoxy’settings. For the ‘without epoxy’ setting, the magnetic flux
is hardly trapped for the #1 and #2 pulses at the positionof the Hall sensor near the central position, and the #3811

H Fujishiro et al

4

5

(a)
without epoxy
with epoxy

B TP (T)#11#10#9 #8 #7

#5

#4

2
#11

#10

#9

#4

Hall
sensor

1

#5
#3
#8
#1

0

#6

B TP and BTF C (T)

3

0

1

2

#2

#3

3

4

∆T 1m a x (K)

#3
#3

6

#5

10
#7

#1
#1
#11
#11

0

0

1

2

3

4

5

6

Bex (T)
Figure 3. (a) The relation between the trapped magnetic field BT P
measured by the attached Hall sensor and the applied pulse field Bex ,and (b) the relation between the maximum temperature rise T 1max
of T 1 and Bex for both ‘without epoxy’ and ‘with epoxy’ settings.

pulse (Bex = 3.870 T) can give a slight trap (BT P =0.271 T). Figure 3(b) shows the relation between theT 1max
maximum temperature rise T 1max and Bex .
after the #3 pulse is extremely large (T 1max = 18.8 K)
and the maximum surface temperature T 1max reaches ∼60 K.
Then BT P suddenly increases to 2.029 T for the #4 pulse(Bex = 4.644 T) and moderately increases to 2.278 T for the#5 (Bex = 5.418 T) pulse. For the following pulses from #6
to #11 with gradually reduced Bex values, BT P only slightly
increases. It was reported that the total trapped flux over thebulk increases through these pulses [2]. T 1max versus Bex
can be regarded as a smooth relation except for the case of
the #3 pulse. For the ‘with epoxy’ setting, the trapped field
BT P is generally lower and the BT P versus Bex curve becomes
more complicated than for the ‘without epoxy’ setting. These
results may come from the temperature difference of the bulk
between both settings before applying each magnetic pulse.
Figure 4 displays the relation between the trapped field
BT P and the maximum temperature T 1max after applying thepulse field for both settings. The temperature dependence ofthe trapped field BT FC by the FCM method is also presented
in the figure. BT FC (T ) decreased with increasing bulk surface
temperature T 1max. The maximum temperature rise T 1max FC
was also monitored during the FCM operation, which was
812

#4

BTP

30

40

50

60

70

80

90

100

T 1m a x (K)

#7

#9

5

BTP

Figure 4. The trapped field BT P versus the maximum temperatureof T 1 (T 1max) after applying the pulse field for ‘without epoxy’ and‘with epoxy’ settings. The trapped field by the FC magnetizing
BT FC was also presented.

15

#9

#5

2

0

5

#5

without epoxy
with epoxy

3

1

(b)

20

FCM(BTF C )# 7 #6

Bex (T)25

without epoxy
with epoxy

4

as small as ∼4 K [10]. It was found that BT P could notexceed BT FC for the same bulk surface temperature. In the‘without epoxy’ setting, BT P touches the BT FC –T 1max line forthe #5 pulse and then deviates from this line for the succeedingP
pulses. In the ‘withthe Pepoxy’ setting, BT also touches
FC
BT –T 1max line BT = 1.5 T at T 1max = 73 K for the#4 pulse and then decreases along this line for succeeding
pulses (#6–#9), because the maximum temperature of the bulk
crosses the BT FC –T 1max line. Thus the field trapping ability
due to the PFM technique can be systematically explained on
the basis of the maximum temperature of the bulk surface.
The cold stage temperature T 6 of the GM refrigerator is, atbest, the starting temperature of the bulk crystal before thepulse. The temperature monitor of the bulk is indispensable toanalyse the PFM technique and to take the full advantage of the
IMRA method. The present results are the first experimental
confirmation that the decrease of BT P for higher Bex pulses
is attributable to the BT FC –T 1max line limitation and that the
BT P decrease occurs along this line.
3.2. Position dependence of temperature rise
It is widely accepted that the magnetic fluxes penetrate into
the bulk crystal preferentially through the weaker pinning
regions of the superconductors [4]. The 4-fold GSBs may
act as efficient pinning centres for the magnetic fluxes. The
position dependence of the temperature rise T (t) after
applying the magnetic pulse should also provide useful
information as for the magnetizing mechanism of the PFM
technique. Figures 5(a) and (b) show the time evolution of
the normalized temperature rises (TN (t)(=T (t)/Tmax ) of
T 1–T 5 ( T1N –T 5N) for the ‘without epoxy’ setting after
applying the #3 and #9 pulses, respectively. The strengthof both magnetic pulses is the same (=3.870 T). Since theposition dependence of the temperature rise T (t) is small,the normalized temperature raises TN (t) are introduced
for clarity. Because the pulse width is as short as amillisecond order, the heat generation should also occur withina millisecond order.

Temperature measurements in YBCO magnetized by pulse field

1.0

4

(a )

without epoxyt(60%) (sec)

∆TN

0.8
0.6
0.4 #3

T1
T2
T3
T4
T5

0.2

T3
T2

Hall
sensor

T1

T4
T5

3

2

T1

T1

T4

T4
T2
T5
T3

T2
T5
T3
T2

1 T3

0

0

5

10

15

1.0

T5

0

0

1

2

3

4 5 6 7 8
Pulse Number

9

10 11

(b)

Figure 6. The rising time of T 1–T 5 to reach the 60% of the
maximum temperature rise Tmax after applying each pulse for‘without epoxy’ setting.

0.8

∆TN

T4

20

Time (sec)Hallsensor

T1

without epoxy

0.6
0.4 #9

T1
T2
T3
T4
T5

0.2

T3
T2
T1

GSB
Hall
sensorT

T4
T5

without epoxy

0

0

5

10

15

20

Time (sec)Figure 5. The time dependence of the normalized temperature risesTN (t) of T 1–T 5 for the ‘without epoxy’ setting just after applying
the (a) #3 and (b) #9 pulses.

For the #3 pulse in figure 5(a), T 1N (t) rises more
slowly and the rising times of T 2N (t)–T 5N (t) arehardly different. On the other hand, for the #9 pulse
shown in figure 5(b), which resulted in the trapped field of
BT P = 2.403 T at the central position, the rising timesof T 2N –T 5N are clearly different; the temperature riseis the fastest for T 3N (t) and then becomes slower forT 5N (t), T 2N (t), T 4N (t) and T 1N (t) in this order.
Thus the temperature rising time depends on the pulse number
or the strength of the pulse field. We define the rising time toreach 60% of the maximum change Tmax after applying thepulse as the rising time t (60%). Figure 6 shows t (60%) of T 1–
T 5 for each applied pulse. In the case of the #1 and #2 pulses,
T 3 along the bisect line rises first, followed by T 5 on the GSB
line. This result suggests that the applied magnetic flux prefers
to penetrate into the bulk through the inter-GSB region of thebulk crystal, avoiding the GSB lines. The more violent flux
motion produces more heat in the inter-GSB region, resulting
in the faster temperature rise along the bisect line (T 3, T 2,
T 1) than that along the GSB line (T 5, T 4, T 1). For therespective series of temperature measurements (T 3, T 2, T 1)
and (T 5, T 4, T 1), the temperature rises firstly at the outer
positions (T 3, T 5), secondly at the inner positions (T 2, T 4)
and lastly T 1 rises. The similar behaviours are observablefor the #8–#11 pulses. In this way, the heat generation due
to the intrusion of the magnetic fluxes occurs faster in theouter positions of the bulk. The slower temperature rise of T 1

Figure 7. An example of the distribution of the trapped magnetic
field above 3 mm on the bulk surface after applying the #1 pulse for‘without epoxy’ setting.

may originate as a result of the heat propagation from outersides, which is controlled by the thermal diffusivity αab of
the bulk crystals (αab  20–10 mm2 s−1 for the temperature
range 40–70 K [9]). In the case of #4 to #7 pulses with
the Bex strength higher than ∼4 T, t (60%) of both series of(T 3, T 2, T 1) and (T 5, T 4, T 1) is not explicitly arranged inthis order. As we have mentioned, the magnetic fluxes arriveat the position of the Hall sensor near the central region for the#4 pulse and the flux motion may become complicated under
the following strong magnetic pulses. It is worthwhile noting,however, that the rising time of T 2 is consistently faster thanthat of T 4.
Figure 7 shows an example of the distribution of thetrapped magnetic field above 3 mm from the bulk surface
after applying the #1 pulse for the ‘without epoxy’ setting.
The sample arrangement of this figure is the same as that infigure 1(d ). The distribution of trapped magnetic field shows afaint 4-fold symmetry, the magnetic fluxes being trapped along
GSBs somewhat more strongly than those in the inter-GSB
region. These results also support that there is a larger density813

H Fujishiro et alof pinning centres along the GSBs than in the inter-GSB region
and are consistent with the analyses of the position dependenceof T.

4. Summary
The time evolution and position dependence of the temperaturerise Delta T (t, r) on the surface of the cryo-cooled YBaCuO
bulk superconductor has been measured after the pulse
field magnetizing (PFM). Important experimental results andconclusions obtained in this study are summarized as follows.
(1) The epoxy resin, which is impregnated and coated on thebulk superconductor for the mechanical reinforcement,strongly prevents the heat exhaust from the bulk to thecold stage of the refrigerator. It needs much time for the
resin-impregnated superconductor to recover the initial
temperature (∼the cold stage temperature) after being
heated by the applied pulse field.
(2) The maximum temperature rise Tmax after applying
the pulse field increases with increasing magnetic pulse
field strength and an anomalously large temperature rise(Tmax ∼ 18.8 K) is observed just before the magnetic
field is trapped in the vicinity of the centre of the bulk.
(3) It has been experimentally confirmed that the trapped field
BT P by PFM cannot exceed the trapped field BT FC by
the static field cooled magnetizing (FCM) at the samebulk temperature. These results could be clarified bymeasuring the maximum temperature Tmax of the bulk
surface after the pulse field application.
(4) The time evolution of temperature rise T (t) depends on
the position on the bulk surface and the magnetic fluxes
move more easily through the inter-GSB region which
is surrounded by the growth sector boundaries (GSBs).
The temperature rise first occurs at the outer region of
the bulk crystal and then heat propagates to the centre of814

the bulk crystal. These results are consistent with the
distribution of the trapped field.
(5) The in situ temperature monitor on the bulk surface
gives us valuable information about the magnetizing
mechanism of the bulk superconductors and is
indispensable to the PFM analyses. The efficiency of
the IMRA method must be tested by monitoring the bulk
sample temperature to take full advantage of the iterative
pulse techniques.

Acknowledgments
This work is partially supported by Japan Science andTechnology Corporation under the Joint-research Project for
Regional Intensive in the Iwate Prefecture on Development ofpractical applications of magnetic field technology for use in
the region and in everyday living.

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