Physica C 470 (2010) 1181–1184

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

Temperature measurements in small holes drilled in superconducting bulk
during pulsed ﬁeld magnetization
H. Fujishiro *, T. Naito, D. Furuta, K. Kakehata
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japana r t i c l e

i n f oArticle history:
Available online 15 May 2010
Keywords:
Pulsed ﬁeld magnetization
Temperature rise
Flux intrusion
Bulk superconductora b s t r a c t
The time dependence of the temperatures T(z, t) has been measured along the thickness direction z inseveral drilled holes in a superconducting bulk during pulsed ﬁeld magnetization (PFM) and the heat generation and heat transfer in the bulk have been discussed. In the previous paper [H. Fujishiro, S. Kawaguchi, K. Kakehata, A. Fujiwara, T. Tateiwa, T. Oka, Supercond. Sci. Technol. 19 (2006) S540], we calculated
the T(z, t) proﬁles in the bulk by solving a three-dimensional heat-diffusion equation to reproduce themeasured T(t) on the bulk surface; the heat generation took place adiabatically and the calculated T(z,t) was isothermal along the z direction. In this study, the measured T(z, t) at the top surface was higher
than that at the bottom surface just after the pulse ﬁeld application at t < 0.5 s, and then became isothermal with increasing time. These results suggest that the magnetic ﬂux intrudes inhomogeneously into thebulk from the edge of the top surface and the periphery at the early stage. The inhomogeneous magnetic
ﬂux intrusion and the ﬂux trap during PFM change depending on the strength of the pulsed ﬁeld and thepulse number in the successive pulse ﬁeld application.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
For practical applications of superconducting bulks as a quasipermanent magnet, a pulsed ﬁeld magnetization (PFM) is a suitable technique because of mobile and inexpensive experimental
setups [1]. The trapped ﬁeld BPT by PFM is, however, fairly smaller
than the trapped ﬁeld BFC
T by a ﬁeld-cooled magnetization (FCM)
because of a large temperature rise by means of the dynamical motion of the magnetic ﬂux. To clarify the magnetizing mechanism
during PFM and to enhance BPT , the measurements and analysesof the temperature rise in the bulk are valuable. We have systematically investigated the time and spatial dependence of the temperatures T(x, t), local ﬁelds BL(x, t) and the trapped ﬁeld BT(x) on
the surface of the cryo-cooled REBaCuO bulk during PFM, as functions of an initial temperature Ts and an applied ﬁeld Bex [2]. Furthermore, we estimated the generated heat Q during PFM by useof the temperature rise DT and the speciﬁc heat C of the bulk [3].
Taking these results into consideration, we proposed a new PFM
method named a modiﬁed multi-pulse technique with stepwise
cooling (MMPSC) and attained 5.2 T on the GdBaCuO bulk 45 mm
in diameter at 30 K, which is a record high BPT value to date [4].
Furthermore, we estimated a temperature distribution in thebulk by solving a three-dimensional heat-diffusion equation.
Fig. 1 shows the time evolution of the calculated temperature proﬁle T(z, t) along the thickness (z) direction for the YBaCuO bulk
* Corresponding author. Tel./fax: +81 19 621 6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).
0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2010.05.069

after applying the pulsed ﬁeld of 3.83 T at 40 K [5]. The calculated
proﬁles under an ideal condition are shown in Fig. 1a, where thethermal contact resistance Rc between the bottom of the bulk disk
and the surface of the cold stage of the refrigerator was ignored.
After the pulse ﬁeld application, the temperature of the bottom
surface of the bulk was ﬁxed at 40 K and T(z) increased withincreasing z. The T(z, t) took a peak at each z at as short as t = 1 s
and then returned to 40 K only at 20 s, which were unrealistic estimation. Because the measured T(t) on the bulk surface recovered to40 K at about 900 s. The discrepancy comes from the magnitude of
the generated heat Q, which was about two orders of magnitudelarger than the cooling power Qp of the used refrigerator. Fig. 1bshows the optimum estimation for T(z, t), in which the calculatedT(t) well reproduced the measured T(t) on the bulk surface. In thiscase, the calculated T(z, t) might increase adiabatically and show
no z dependence. However, we do not know whether the measured
T(z) shows z dependence in the bulk or not.
In this paper, we measured directly the time dependence of thetemperatures T(z, t) in several drilled holes in the bulk during PFM,
and discussed the heat generation and heat transfer in the bulk.
The temperature measurement in the hole was performed by othergroup [6], but the z dependence of temperature T(z, t) has not beenmeasured.
2. Experimental procedure
A c-axis oriented SmBaCuO bulk superconductor (Dowa Mining
Corp.) of 45 mm in diameter and 15 mm in thickness was used. The

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was magnetized by pulsed ﬁelds using a solenoid-type copper coildipped in liquid N2. The detailed experimental setup for the coiland the bulk was described elsewhere [2]. Three magnetic pulses(Nos. 1–3) with nearly the same amplitude Bex from 3 to 6.5 T wereapplied sequentially after re-cooling to 40 K.

3. Results and discussion

Fig. 1. Time dependence of calculated temperature changes T(z, t) as a function of
the distance z from the bottom of the YBCO bulk after the pulse ﬁeld application,
which were shown in Ref. [5]: (a) is for the ideal but unrealistic case with thecontact thermal resistance of Rc = 0 and (b) is for the optimum case.

stainless steel (SUS304) ring with 2.0 mm in thickness and 15 mm
in height was ﬁxed onto the bulk disk using Stycast 2850GT. The
bulk was tightly anchored onto the cold stage of a Gifford–McMahon (GM) cycle helium refrigerator and was cooled to Ts = 40 K in a
vacuum chamber. In this study, two settings (‘‘set A” and ‘‘set B”)
were performed for the temperature T(z, t) and magnetic ﬁeld
BL(t) measurements as shown in Fig. 2. Several small holes 1 mm
in diameter were drilled at the center and the periphery of thegrowth sector regions (GSRs) in the bulk, and T(z, t) was measured
using ﬁne chromel-constantan thermocouples (76 lm in diameter). In ‘‘set A”, a through hole was drilled at the bulk peripheryand the time dependence of temperatures was measured at thesurface (T1(t)), middle (T2(t)) and bottom (T3(t)). T4(t) and T5(t)were also measured at the bottoms of the holes 7.5 mm in depth.
Two Hall sensors (F.W. Bell, model BHT 921) were adhered at thepositions C (bulk center) and M (10 mm distant from the bulk center) in GSR and the time evolutions of the local ﬁelds BL(t) and thetrapped ﬁelds BT = BL(t ? 1) were monitored by using a digital
oscilloscope. In ‘‘set B”, the temperatures at the surface (T6(t)),
middle (T7(t)) and bottom (T8(t)) were measured. T1(t) and T4(t)were also measured for comparison. For both settings, the bulk

Fig. 2. The measuring position of temperatures T(t) and magnetic ﬁelds BL(t) for (a)‘‘set A” and (b) ‘‘set B”.

Fig. 3a shows the trapped ﬁelds BT(C) and BT(M) as a function of
the applied ﬁeld Bex for the No. 1 pulse. The magnetic ﬂux starts to
intrude and to be trapped into the bulk for Bex > 3.5 T. BT(C) andBT(M) took a maximum at Bex = 4.8 T and then decreased withincreasing Bex because of a large heat generation. BT(C) was larger
than BT(M) for Bex < 5 T, but decreased drastically for Bex > 5.5 T because of the ﬂux jump. Fig. 3b shows the time evolution of the applied ﬁeld Bex(t) and local ﬁelds (BL(C)(t) and BL(M)(t)) after
applying the pulsed ﬁeld of Bex = 4.8 T. The rise time and the duration of Bex(t) was 12 ms and 150 ms, respectively. BL(M)(t) rises up
ﬁrstly and then BL(C)(t) rises up. BL(t) takes a maximum and thenslowly decreases to the ﬁnal value.
Figs. 4a and 4b depict respectively the time evolution of thetemperatures T(z, t) at each position in ‘‘set A”, after applying theNos. 1 and 3 pulses of Bex = 4.8 T. For the No. 1 pulse, T(t) showsa peak within 1 s at each position and decreases slowly to 40 K
for about 600 s. Let us take notice of the temperature change along
the z direction at the bulk periphery. T1(t), T2(t) and T3(t) rise up in
this order and take a peak. These results suggest that the larger
heat generation took place ﬁrstly on the bulk surface. For the No.
3 pulse shown in Fig. 4b, a similar tendency in the temperature
was observed at T1(t), T2(t) and T3(t) with a slight decrease in temperature. It is noteworthy that T4(t) and T5(t) for the No. 3 pulse
are clearly smaller than those for the No. 1 pulse. These results suggest that the magnetic ﬂux does not move violently and is nottrapped around these positions for the No. 3 pulse because of theexistence of the already trapped ﬂux for the Nos. 1 and 2 pulses.
Figs. 4c and 4d display the time evolution of temperature T(z, t),
as a function of the distance z from the bottom of the bulk, which
are re-plotted using Figs. 4a and 4b, respectively. For t < 0.5 s, alarge temperature gradient exists along the z direction and becomes isothermal with increasing time (t > 1 s). The measured
T(t) is quite contrast with the calculated T(t) shown in Fig. 1b fort < 0.5 s. The experimental results suggest that the magnetic ﬂux
does not intrude into the bulk parallel to the z direction, but

Fig. 3. (a) The trapped ﬁeld BT as a function of applied ﬁeld Bex at the center (C) andthe middle (M) positions on the bulk. (b) The time evolution of the applied ﬁeld
Bex(t) and local ﬁelds (BL(C)(t) and BL(M)(t)) after applying pulsed ﬁeld of Bex = 4.8 T
at Ts = 40 K.

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Fig. 4. Time evolution of temperatures (T1(t)–T5(t)) for ‘‘set A” after applying
pulsed ﬁeld of Bex = 4.8 T of the (a) No. 1 and (b) No. 3 pulse. The temperaturechanges for the (c) No. 1 and (d) No. 3 pulse, as a function of the distance z from thebottom of the bulk, which were re-plotted using (a) and (b), respectively.

Fig. 5. Time evolution of temperatures (T1(t), T4(t), T6(t)–T8(t)) for ‘‘set B” after
applying pulsed ﬁeld of Bex = 4.8 T of the (a) No. 1 and (b) No. 3 pulse. (c) The
temperature changes for the No. 1 pulse, as a function of the distance z. (d) The
temperature changes for the No. 1 pulse as a function of the distance r.

obliquely intrudes from the edge of the bulk at early stage of PFM.
As a result, a large temperature gradient exists along the z
direction.
Figs. 5a and 5b show respectively the time evolution of the temperatures T(t) at each position in ‘‘set B”, after applying the Nos. 1
and 3 pulses of Bex = 4.8 T. T1(t) and T4(t), which were also measured similarly to ‘‘set A”, show a similar time dependence andthe maximum temperature rise. These results suggest that theexperimental results can be reproduced by different experimental
setups. It should be noted that the time dependence of temperatures (T6, T7, T8) at the bulk center was quite different from T(t)in the bulk periphery (T1, T2, T3); for the No. 1 pulse, T6(t) andT7(t) reach 60 K at t = 1 s and then slowly increases up to 4 s. Furthermore, for the No. 3 pulse, the temperature rises of T6, T7 and T8
are very small and increases slightly with increasing time. Fig. 5cshows the temperature change along the thickness direction for
the No. 1 pulse in ‘‘set B” for each t, which was re-plotted using
Fig. 5a. The temperature at the bulk center is adiabatically and isothermally rises up along the z direction even at the early time, contrary to that in the bulk periphery. Fig. 5d shows the timedependence of temperature T(r, t) along the radial (r) direction
for the No. 1 pulse in ‘‘set B”, in which the results of T1(t), T4(t)and T7(t) were used. It is noteworthy that the temperature risestarts from the bulk periphery at the early stage (t < 1 s), andquickly decreased with increasing t. On the other hand, T(t) at
the bulk center, T7(t) scarcely changes. As a result, the temperature
gradient along the r direction exists oppositely for t > 3 s andgradually decreased because of the larger thermal diffusivity along
the ab-plane than that along the c-axis in the bulk crystal.
Finally, we present the T(z, t) for lower applied ﬁeld. Figs. 6a and6b display respectively the time evolution of the temperatures T(z,t) as a function of the distance z in ‘‘set A”, after applying the Nos. 1
and 3 pulses of Bex = 3.7 T. The temperature rises were lower thanFig. 6. The time evolution of the temperatures T(t) as a function of the distance z in‘‘set A”, after applying the (a) No. 1 and (b) No. 3 pulses of Bex = 3.7 T at Ts = 40 K.

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those for Bex = 4.8 T shown in Fig. 4c and d because of lower applied ﬁeld. However, a smaller temperature gradient exists fort < 0.5 s along the z direction and becomes isothermal with increasing time (t > 1 s). For the No. 3 pulse, the temperature gradientscarcely exists along the z direction and the temperature rise wasvery small. These results resemble the calculated T(z, t) as shownin Fig. 1b.
In summary, the time dependence of the temperatures T(z, t) inseveral drilled holes in a superconducting bulk during pulsed ﬁeld
magnetization has been measured and compared with the calculated T(z, t) by solving a three-dimensional heat-diffusion equation
reported in the previous paper. The measured T(t) at the top surface of the bulk was higher than that at the bottom surface andthe temperature gradient exists along the thickness direction, justafter the pulse ﬁeld application of t < 0.5 s and then became isothermal with increasing time. In the simulation, T(z, t) rises up adiabatically for t > 0 s and no temperature gradient exists along the
thickness direction. The difference in T(z, t) at the early stage suggests that the magnetic ﬂux intrudes preferentially into the bulk
from the edge of the top surface and the bulk periphery. The asymmetric cooling conﬁguration of the bulk may be another reason;
the bulk is cooled by conduction from the bottom surface on thecold stage of the refrigerator. The inhomogeneous magnetic ﬂux
intrusion and ﬂux trap during PFM changed depending on the applied pulsed ﬁeld Bex and the pulse number.
Acknowledgement
This work is supported in part by a Grant-in-Aid for ScientiﬁcResearch from the Ministry of Education, Culture, Sports, Scienceand Technology, Japan (No. 19560003).
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