IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 29, NO. 5, AUGUST 2019

6801705

Flux Dynamics and Thermal Behavior of a GdBaCuO
Bulk Magnetized by Single- and Double-Pulse
Techniques Using a Split-Type Coil
Tatsuya Hirano, Hiroyuki Fujishiro , Tomoyuki Naito , Mark D. Ainslie , Senior Member, IEEE,and Yun-Hua Shi

Abstract—We have investigated the trapped field properties of a
GdBaCuO disk bulk during single- and double-pulsed field magnetization (PFM) using a split-type coil for various pulse sequences
for the first time. It is well known that the multi-PFM techniqueusing a solenoid-type coil and the single-PFM technique using a
split-type coil are effective to enhance the trapped field due to alower temperature rise. However, it was found, in this work, thatthe trapped field by double-PFM using the split-type coil was notenhanced in spite of lower temperature rise. We analyzed the magnetizing process using two parameters, the “magnetic flux penetration ratio,” Rin , and the “magnetic flux residual ratio,” Ro u t , forvarious pulse sequences for the split-type and solenoid-type coils.
The Rin value was decreased by the double-PFM for both coils,
and the Ro u t value was improved only by the double-PFM using
the solenoid-type coil. As a result, the trapped field for single-PFM
using the split-type coil, which has a higher Rin , reduced after the
double-PFM due to a decrease of Rin and no enhancement of Ro u t .
These results are in clear contrast to those using the solenoid-type
coil.
Index Terms—Bulk high-temperature superconductors, multipulse application, pulsed field magnetization, REBaCuO bulk,
split-type coil, trapped field magnets.

I. INTRODUCTION
EBaCuO (RE: rare earth element or Y) superconducting
bulks have been used as a trapped field magnet (TFM) thatcan provide a magnetic field of several Tesla for engineering applications such as rotating machines [1], magnetic separation[2], and a magnetic drug delivery system [3]. The pulsed fieldmagnetization (PFM) technique is a magnetizing method forsuperconducting bulks with a compact, mobile and inexpensive

R

Manuscript received October 26, 2018; accepted February 12, 2019. Dateof publication February 22, 2019; date of current version March 21, 2019.
This research is supported in part by JSPS KAKENHI under Grant 15K04646.
M. D. Ainslie would like to acknowledge financial support from Engineeringand Physical Sciences Research Council (EPSRC) Early Career Fellowship
EP/P020313/1. (Corresponding author: Tatsuya Hirano.)
T. Hirano, H. Fujishiro, and T. Naito are with the Department of Physical Science and Materials Engineering, Faculty of Science and Engineering,
Iwate University, Morioka 020-8551, Japan (e-mail:,g0318132@iwate-u.ac.jp;
fujishiro@iwate-u.ac.jp).
M. D. Ainslie and Y.-H. Shi are with the Bulk Superconductivity Group,
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ,
U.K. (e-mail:,mark.ainslie@eng.cam.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2019.2900979

setup, compared to field-cooled magnetization (FCM). However, the trapped field by PFM is generally much lower than thatby FCM because of a large temperature rise associated with therapid and dynamical motion of magnetic flux [4]. The PFM technique consists of an ascending (flux penetration) phase on theorder of milliseconds and then a descending (flux flow) phase.
To enhance the trapped field by PFM, a large amount of flux
penetration and a small amount of flux flow should be achieved.
There have been several approaches to enhance the trapped fieldby PFM using the solenoid-type coil. Multi-pulsed field magnetization techniques, which involve iteratively applying pulsed
fields, are effective, such as the successive pulse application(SPA) [5] and the multi-pulse technique with step-wise cooling(MPSC) [6]. The multi-PFM technique achieves a reduction influx flow from lowering the flux pinning and viscous losses dueto the already trapped magnetic flux after the 1st magnetic pulse[7]. Using a modified MPSC (MMPSC) technique, a recordhigh trapped field of 5.20 T was achieved using a solenoid-type
coil with a 45 mm GdBaCuO disk bulk at 30 K [8]. Similarly,
there have been reports to enhance the trapped field by PFM
using a split-type coil with an iron yoke [9], in which the flux
intrudes by a flux jump with reduced flux flow. The cooling of
the bulk for the split-type coil is faster than that for the solenoidtype coil because the bulk is cooled from the periphery along
the ab-plane, which has higher thermal conductivity than thec-axis [9]. However, multi-pulse effects using the split-type coilhave not yet been reported.
In this study, we investigated the trapped field properties of a
GdBaCuO disk bulk during single- and double-PFM using the
split-type coil for various sequences. To understand the doublepulse effect, we compared the trapped field properties to thoseusing the solenoid-type coil.
II. EXPERIMENTAL SETUPA GdBaCuO superconducting disk bulk of 41 mm in diameterand 12 mm in thickness was grown using the top-seeded meltgrowth (TSMG) process at the University of Cambridge [10].
Fig. 1 shows the schematic view of the experimental setup for
the PFM. The split-type coil (72 mm in inner diameter (I.D.),
124 mm in outer diameter (O.D.), and 35 mm in height (H)) andthe solenoid-type coil (99 mm I.D., 121 mm O.D. and 50 mm H)
are used as magnetizing coils. The bulk was fastened in a brass

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6801705

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 29, NO. 5, AUGUST 2019

Fig. 1. Schematic view of the experimental setup for the PFM experiments
using (a) the split-type coil and (b) the solenoid-type coil.

Fig. 3. Applied pulsed field (Be x ) dependence of the trapped field, Bt , at thecenter of the bulk surface using (a) the split-type coil and (b) the solenoid-type
coil for various sequences. The applied field, at which the Bt value begins toincrease, is defined as the rise field, Br .

During the PFM process, the time evolution of the magnetic
field, B(t), at the center of the bulk surface was measured using
a Hall sensor (F. W. Bell, BHT921). B(t) at 300 ms is defined as
the trapped field, Bt . The time evolution of the temperature, T(t),was measured by a CERNOX thermometer on the side surfaceof the brass holder for the split-type coil and on the side surfaceof stainless steel ring for the solenoid-type coil.
III. RESULTS

Fig. 2. Time sequences of the operating temperature settings used in this studyfor (a) 65 K single-pulse, (b) 25 K single-pulse, (c) 65 K - 65 K double-pulseand (d) 65 K - 25 K double-pulse.

sample holder using a thin indium sheet and was cooled fromthe periphery along the ab-plane. A pair of permendur yokes(60 mm diameter and 65 mm H) was inserted in the bores of the
split-type coil [9]. For the solenoid-type coil, the same bulk was
mounted in a stainless steel ring 17.5 mm in width and cooled
from the bottom surface along the c-axis of the bulk, where asoft iron yoke (60 mm in diameter and 20 mm in H) is installed
underneath the bulk [4].
Fig. 2 shows the time sequences of the operating temperature settings used in this study. For the single-pulse application,
shown in Figs. 2(a) and 2(b), the bulk was cooled to Ts1 = 65
or 25 K, and a single-magnetic pulse with a rise time of 18 ms(split-type coil) or 13 ms (solenoid-type coil), Bex1 , ranging
from 3 to 6 T was applied to the bulk. For the double-pulse
application, shown Figs. 2(c) and 2(d), the 1st pulse of Bex1 =3 T was applied at Ts1 = 65 K for all cases. In the 2nd stage, thebulk was cooled to Ts2 = 65 or 25 K and the 2nd pulse, Bex2 ,ranging from 3 to 6 T was applied to the bulk. The magnetic
pulse and temperature sequences for each magnetizing coil are
named as follows.
1) Single-pulse using split-type coil: S-sp(Ts1 )2) Double-pulse using split-type coil: D-sp(Ts1 , Ts2 )3) Single-pulse using solenoid-type coil: S-sol(Ts1 )4) Double-pulse using solenoid-type coil: D-sol(Ts1 , Ts2 )Fig. 3(a) shows the applied pulsed field (Bex ) dependence ofthe trapped field, Bt , at the center of the bulk surface using the
split-type coil for various sequences. Here, the applied field,
at which the Bt value begins to increase, is defined as the risefield, Br . The Bt value for S-sp(65 K) increases from Br =3.06 T by the flux jump and the highest Bt value of 2.79 T wasachieved at Bex = 3.76 T. The Bt value for S-sp(25 K) increased
from Br = 4.17 T and a highest Bt of 3.96 T was achieved at
Bex1 = 5.43 T. These rapid increases in Bt above Br result
from flux jumps [11], [12] (or so-called giant flux leaps (GFLs)
in other works [13]), which are a characteristic behavior whenusing the split-type coil. The rise field, Br , increased and thetrapped field, Bt , was usually enhanced when lowering theoperating temperature during single-PFM [14]. These results
were also obtained for the 2nd pulse application of the D-sp(65K, 65 K) and D-sp(65 K, 25 K). It should be noted that therise field, Br , of the 2nd pulse application increased, but the
maximum Bt value was not enhanced, compared to that ofsingle-pulse application.
On the other hand, for the solenoid-type coil, as shown in
Fig. 3(b), the Bt value for S-sol(65 K) increases monotonicallywith increasing Bex . When Bex is 4.0 T, the Bt value for Dsol(65 K, 65 K) is higher than that for S-sol(65 K), whichindicates that the flux jump also occurs for the double-PFM.
These results are similar to that for S-sol(25 K) and D-sol(65 K,
25 K). These results support the previous reports, in which themulti-PFM using the solenoid-type coil enhances the trappedfield [8], [15].
Fig. 4(a) shows the maximum temperature rise, ΔTm ax , during PFM, as a function of the applied pulsed field (Bex ), for each

HIRANO et al.: FLUX DYNAMICS AND THERMAL BEHAVIOR OF A GdBaCuO BULK MAGNETIZED

6801705

Fig. 4. Maximum temperature rise, ΔTm a x , during PFM, as a function of
applied pulsed field (Be x ), for each sequence using (a) the split-type coil and(b) the solenoid-type coil.

sequence using the split-type coil. ΔTm ax increased with increasing Bex for all cases. The ΔTm ax value of the double-PFM
is lower than that of the single-PFM, which results from lowering the flux pinning and viscous losses due to the already trappedmagnetic flux after the 1st magnetic pulse application [7],[15]. The ΔTm ax value using the solenoid-type coil, shown in
Fig. 4(b), is larger than that using the split-type coil, because thebulk is cooled via the c-axis (solenoid-type coil) of lower thermal conductivity, rather than the ab-plane (split-type coil) [9].
Figs. 5(a) and 5(b) show the time evolutions of the appliedfield, Bex (t), and trapped field, B(t), at the center of the bulk
surface for S-sp(25 K) for Bex1 = 4.17 T and S-sol(25 K) for
Bex1 = 4.14 T, respectively. In Fig. 5(a), the magnetic flux
doesn’t intrude into the center of the bulk for the split-type coil.
In Fig. 5(b), for the solenoid-type coil, B(t) takes a peak valueof Bin = 2.13 T, which is defined as the maximum penetration
field, and then decreases to a final small Bt value due to a large
flux flow.
Figs. 5(c) and 5(d) show similar plots for S-sp(25 K) for Bex1
= 4.89 T and D-sp(65 K, 25 K) for Bex2 = 4.99 T, respectively.
In Fig. 5(c), with increasing Bex1 , compared to Fig. 5(a), themagnetic flux intruded rapidly via a flux jump and the B(t)reached Bin = 4.67 T. After that, B(t) gradually decreased to
Bt = 3.40 T, where the flux flow, defined as ΔB ( = Bin - Bt ),was 1.27 T. For D-sp(65 K, 25 K), shown in Fig. 5(d), after
the 1st pulse of Bex1 = 3 T was applied at 65 K, the magnetic
flux also intruded the bulk center suddenly via a flux jump andthen flow out of the bulk to the final value, Bt . The Bin andBt values were slightly smaller than those for S-sp(25 K) as
shown in Fig. 5(c) at a nearly identical applied field. The final
Bt reduction mainly results from the decrease in Bin for the
double-PFM.
Figs. 5(e) and 5(f) show similar plots for S-sol(25 K) for
Bex1 = 5.56 T and D-sol(65 K, 25 K) for Bex2 = 5.57 T. When
Bex1 is increased, as shown in Fig. 5(e), the Bin and Bt values
increase, compared to those in Fig. 5(b). For D-sol(65 K, 25 K)
in Fig. 5(f), after the 1st pulse of Bex1 = 3 T was applied
at 65 K, the Bin value was smaller than that for S-sol(25 K).
This result is consistent with that obtained using the split-type
coil. The Bt value for D-sol(65 K, 25 K) was also higher thanFig. 5. Time evolution of the applied field, Be x (t), and trapped field, Bt (t)at the center of the bulk surface for (a) S-sp(25 K) for Be x 1 = 4.17 T, (b) Ssol(25 K) for Be x 1 = 4.14 T, (c) S-sp(25 K) for Be x 1 = 4.89 T, (d) D-sp(65 K,
25 K) for Be x 2 = 4.99 T, (e) S-sol(25 K) for Be x 1 = 5.56 T and (f) D-sol(65 K,
25 K) for Be x 2 = 5.57 T.

that for S-sol(25 K). This is in contrast with the double-pulse
effect using the split-type coil. The enhancement of the final Bt
mainly results from the decrease in the flux flow (ΔB) for the
double-PFM.
IV. DISCUSSION
Using the experimental results, we now discuss the doublepulse effect during PFM using the split-type coil, compared withsingle-PFM and the solenoid-type coil. Fig. 6 shows the appliedfield (Bex ) dependence of the “magnetic flux penetration ratio”,
Rin , using the split-type and solenoid-type coils during singleand double-PFM. Here, Rin is defined as Bin /Bex . Rin = 1.0
corresponds to an ideal flux penetration during FCM using theBean model [16]. The Rin value of S-sp increases rapidly andtakes a maximum of higher than 0.9 ∼ 0.95 by the assistance ofa flux jump. There is a temperature rise due to rapid movementof magnetic flux with flux jump, shown in Fig. 4(a). The Rinvalue for D-sp is nearly equal to or slightly smaller than thatfor S-sp because of the existence of a trapped flux after the 1stpulse. Using the solenoid-type coil, Rin gradually increases with

6801705

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 29, NO. 5, AUGUST 2019

Fig. 6. Applied field (Be x ) dependence of the magnetic flux penetration ratio,
Rin , using the split-type and solenoid-type coils at 25 and 65 K to 25 K during
single- and double-PFM.

with increasing Bex using the split-type coil, and becomes a
maximum. And then the Rout value decreases with a further
increase in Bex , which indicates that the flux flow, ΔB, becomeslarge due to the large temperature rise [17]. The maximum valueof Rout is not enhanced by double-PFM using split-type coil.
The Bin for D-sp(65 K, 25 K) is smaller than that for S-sp(25 K)
when the maximum Rout is achieved. The temperature rise of
ΔTm ax = 10.8 K (D-sp(65 K, 25 K)) and ΔTm ax = 15.0 K (Ssp(25 K)) was measured at the maximum Rout for each PFM,
as shown in Fig. 4(a). These results suggest that Rout does
not strongly depend on temperature rise. The reduction of thetrapped field after the 2nd pulse using the split-type coil canbe mainly explained by the reduction of both Rin and Rout . On
the other hand, for the solenoid-type coil, the Rout value for
D-sol(65 K, 25 K) is larger than that for S-sol(25 K) at Binhigher than 3.11 T, which is a different result when using the
split-type coil, although the Rin value is small. The trapped fieldenhancement after the 2nd pulse using the solenoid-type coil, as
shown in Fig. 3, can be mainly explained by the enhancementof Rout .
Fig. 7(b) shows applied field (Bex ) dependence of Rin × Routusing the split-type and solenoid-type coils during single- anddouble-PFM. The Rin × Rout value is equivalent to the magnetic
flux trapping ratio (Bt /Bex ), which was rewritten from Figs. 3(a)and 3(b). The higher Rin × Rout value approaches an ideal PFM
process. The Rin × Rout values for D-sp(65 K, 25 K) are smaller
than those for S-sp(25 K) in spite of a low temperature rise,because of the decrease of Rin and/or Rout . On the other hand,for the solenoid-type coil, the Rin × Rout value for D-sol(65 K,
25 K) increases for higher Bex , compared to that for S-sol(25 K)
because of the enhanced Rout value.
V. CONCLUSION

Fig. 7. (a) Magnetic flux residual ratio, Ro u t , for each sequence, as a functionof Bin . (b) Rin × Ro u t value ( = Bt /Be x ) for each sequence, as a function of
Be x .

increasing Bex due to the absence of flux jumps and is smaller
than that for the split-type coil. Similarly to the split-type coil,
Rin for D-sol is smaller than that for S-sol. The double-PFM byboth magnetizing coils results in a decreased Rin value, because
it is more difficult for the flux to penetrate the bulk due to theexistence of the flux trapped from the 1st pulse [15].
Fig. 7(a) shows the “magnetic flux residual ratio”, Rout , using
the split-type and solenoid-type coils during single- and doublePFM, as a function of Bin . Here, Rout is defined as Bt /Bin ,which is the ratio of the trapped field, Bt , to the maximum
penetration field, Bin . The Rout value increases concomitantly

We have experimentally investigated the trapped field properties of a GdBaCuO disk bulk during single- and double- pulsed
field magnetization (PFM) using a split-type coil for various sequences for the first time. The important results and conclusion
obtained in this study are summarized as follows.
1) The trapped field by double-PFM using the split-type coil
was not enhanced in this study, although a lower temperature rise was achieved. These results are in clear contrast
with those of the multi-PFM technique using a solenoidtype coil.
2) The magnetizing process was analyzed using the parameters of “magnetic flux penetration ratio”, Rin , and “magnetic flux residual ratio”, Rout , for various sequences using
the split-type and solenoid-type coils. The double-PFM byboth coils resulted in a decreased Rin value because of thealready trapped flux after the 1st pulse. For the solenoidtype coil, the Rout value was enhanced by the double-PFM
due to the lower temperature rise. The trapped field during single-PFM using the split-type coil, which exhibits ahigh Rin , was decreased by the double-pulse application
due to the decrease of Rin and no enhancement of Rout .
ACKNOWLEDGMENT
All data are provided in full in the results section of this paper.

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