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

6802405

Trapped Field Properties of GdBaCuO Bulk
Superconductors of Various Diameters Magnetizedby Pulsed Fields Using an Identical Split CoilFumiya Shimoyashiki , Hiroyuki Fujishiro , Tomoyuki Naito , and Mark D. Ainslie , Senior Member, IEEE

Abstract—In this paper, the trapped field properties of
GdBaCuO disk bulk superconductors of various diameters during pulsed-field magnetization (PFM) using an identical split coilat 65 K have been investigated both experimentally and numerically. The maximum trapped field, BT max , of the φ43-mm bulk
was larger than that of the φ30-mm bulk. However, BT max of the
φ65-mm bulk was smaller than that of the φ43-mm bulk and thetrapped field profile exhibited a distorted “C-shaped” profile. Using the numerical simulation, these results for the φ65-mm bulk
can be explained by an inhomogeneous temperature profile andthe larger generated heat, Q, due to the lower cooling power of therefrigerator compared to the generated heat. The important issues
to achieve higher and homogeneous trapped fields are discussed
when using split-coil PFM for larger bulks.
Index Terms—Bulk superconductors, numerical simulation,pulsed-field magnetization, split coil, trapped field magnet.

I. INTRODUCTIONULK superconductors, acting as trapped field magnets(TFMs), can achieve higher magnetic fields of magnitude
over ten times higher than the maximum field of conventional
permanent magnets. The pulsed-field magnetization (PFM) isa practical magnetizing technique using a copper coil magnet,
which is a clear contrast to field-cooled magnetization (FCM)
using a superconducting coil magnet [1]. However, the trappedfield, BT , by PFM is generally much smaller than that by FCM
because of a large temperature rise due to the dynamical motion of magnetic flux [2]. To enhance the BT value, multi-pulse
techniques have been shown to be effective [3], [4], in which wehave achieved a record-high BT of 5.2 T at 30 K on a GdBaCuO
bulk by using a modified multi-pulse technique combined witha stepwise cooling (MMPSC) using a solenoid coil [5].
Based on Bean’s critical-state model [6], the trapped field at
the center of the disk bulk is proportional to the bulk diameter

B

Manuscript received October 27, 2018; accepted February 12, 2019. Date of
publication February 25, 2019; date of current version April 23, 2019. This research is supported in part from JSPS KAKENHI Grant 15K04646. The work of
M. D. Ainslie was supported by an Engineering and Physical Sciences ResearchCouncil (EPSRC) Early Career Fellowship EP/P020313/1. (Corresponding author: Fumiya Shimoyashiki.)
F. Shimoyashiki, 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:,g0317083@iwate-u.ac.jp;
fujishiro@iwate-u.ac.jp; tnaito@iwate-u.ac.jp).
M. D. Ainslie is with The Bulk Superconductivity Group, Department ofEngineering, 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.2019.2901349

for an identical critical current density, Jc . The trapped field
properties by PFM have been investigated for larger disk bulks
60 mm in diameter at 40 K using a solenoid coil [7], and 60 and
140 mm diameters at 77 K using a vortex coil [8], [9]. However,the BT value was not necessarily enhanced, compared to that forsmaller bulks 30–45 mm in diameter [5], [10]. This is because
the Jc value of the larger bulks was not necessarily as large as thatof the smaller bulks and the Jc distribution was inhomogeneous.
The use of vortex or split coils has also been shown to beeffective to enhance the BT value for smaller bulks during PFM,
both experimentally and numerically [11], [12]. It is easier forthe magnetic flux to penetrate via flux jumps, which can enhance the trapped field for REBaCuO bulks. We have previously reported the trapped field properties of a 30 mm diameter
GdBaCuO bulk magnetized by a split coil, for which BT = 3.2 T
was achieved at 40 K using a single magnetic pulse of 5.0 T [13].
However, there has not yet been a systematic investigation of
the trapped field properties by PFM using such a split coil forthe disk bulks of various diameters at lower temperatures. The
research of the large-sized TFMs and the enhancement of thetrapped field using the split coil are valuable for engineering
applications such as superconducting rotating machines, which
requires large field poles.
In this paper, the trapped field properties of GdBaCuO bulk
superconductors 43 and 65 mm in diameter using the split coil at
65 K are investigated experimentally and numerically, and compared with our previous data for the 30 mm diameter GdBaCuO
bulk [14]. The possibility of trapped field enhancement for larger
disk bulks using the split coil is discussed.
II. EXPERIMENTAL AND NUMERICAL FRAMEWORK
A. Experimental PFM Procedure
GdBaCuO disk bulks of various diameters (φ43 mm ×
H18 mm, and φ65 mm × H20 mm; Nippon Steel & Sumitomo Metal) were magnetized using a split coil (72 mm in innerdiameter (I.D.), 124 mm in outer diameter (O.D.) and 37 mm
in height (H)), in which a set of permendur yokes (60 mm indiameter and 65 mm in height) was inserted. Each disk bulk was
fastened in brass sample holders of different sizes using a thinindium sheet and was thermally connected to the cold stage ofGM-cycle He refrigerator (5 W at 20 K), as shown in Fig. 1,
in which the bulk was cooled from the periphery along the abplane of the bulk. The detailed experimental setup for PFM is
described in [14]. The 65 mm bulk was also magnetized using
a solenoid coil (95 mm in I.D., 121 mm in O.D. and 50 mmin H) for comparison. The results are then compared to our1051-8223 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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6802405

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

Fig. 1. A schematic view of the disk bulk and brass sample holder, which isthermally connected to the cold stage of the refrigerator.

previous PFM results using the same split coil for a GdBaCuO
disk bulk (φ30 mm × H14 mm) fabricated by the University ofCambridge [14]. A single magnetic pulse, Bex , with a rise timeof 18 ms was applied, ranging from 2.7 to 6.0 T at Ts = 65 K.
The results at 65 K can clearly compare with the numericalones. The time evolution of the magnetic field, BT (t), and thefinal trapped field, BT , were measured at the center of bulk
surface by a Hall sensor (F. W. Bell, BHT921) (adhered to thesurface), and a two-dimensional (2D) trapped field profile wasmeasured at a distance of 3 mm above the bulk surface, stepwise
with a pitch of 1 mm, by scanning an axial-type Hall sensor (F.
W. Bell, BHA921). The time evolution of the temperature, T(t),was also measured using the CernoxTM thermometer connectedto the sample holder as shown in Fig. 1. A heater was used tocontrol the operating temperature using a Pt-Co thermometer.
B. Numerical Simulation Framework
Based on our experimental setup [14], a three dimensional(3D) numerical model was constructed using the finite element
method (FEM). The commercial software package, Photo-Eddy,
combined with Photo-Thermo (Photon Ltd, Japan), was used forthe analysis. The following magnetic field dependence of Jc (B),proposed by Jirsa, was used in the simulation [15],BB
Jc (B) = Jc1 exp −
+ Jc2
BL
Bm ax
 

k 
B
1
1 −
.
(1)
exp
k
Bm ax
The experimental Jc (B, T) data [16] were fit up to 10 T between 65, 70, 75 and 80 K using eq. (1) and the parameters(Jc1 , BL , Jc2 , Bm ax and k) were determined at each temperature.
For example, each parameter value at 65 K was Jc1 = 1.17 ×
109 A/m2 , BL = 0.57 T, Jc2 = 7.56 × 108 A/m2 , Bm ax = 3.0 T
and k = 1.3. The Jc (B, T) profiles at intermediate magnetic fields
and temperatures are interpolated based on each parameter [17].
III. RESULTS AND DISCUSSION
A. Experimental Results
Fig. 2(a) shows the trapped field, BT , at 65 K at the centerof the surface of the φ65 mm bulk, as a function of the appliedfield, Bex , using the split and solenoid coils. The typical trappedfield profiles are also shown in Figs. 2(b)–2(e). For both coils,
BT increases with increasing Bex , takes a maximum, and thendecreases. The maximum trapped field, BT max , was 1.73 T forthe solenoid coil and 1.57 T for the split coil without (w/o) thepermendur yoke. However, BT max was enhanced to 2.24 T by

Fig. 2. (a) The trapped field, BT , at the center of the bulk surface, as a functionof the applied field, Be x , at Ts = 65 K for the solenoid and split coils. The typicaltrapped field profiles are shown in (b) ∼ (e) for selected points from (a).

about 29% by inserting the magnetic yoke into the bore of the
split coil. For the split coil, a higher BT max can be achieved forlower Bex than for the solenoid coil. For lower Bex , as shownin Fig. 2(b) for the split coil and Fig. 2(c) for the solenoid
coil, the trapped field profiles were homogenous. For higher
Bex using the solenoid coil, as shown in Fig. 2(d), the trappedfield profile exhibited a conical shape, which suggests that the
Jc distribution is homogeneous in the bulk. However, for higher
Bex , as shown in Fig. 2(e) for the split coil, the trapped field
profile was fairly distorted and exhibited a “C-shaped profile”.
The similar distorted profile to Fig. 2(e) was also observed forthe bulk with yoke. However, it is hypothesized that the distorted
profile does not come from an inhomogeneous Jc distribution,
but rather that the temperature distribution within the bulk is
inhomogeneous during PFM in the case of the split coil at higher
Bex , for which a large amount of heat is generated in the bulk
due to pinning loss and viscous loss, if the cooling power of therefrigerator is smaller than the generated heat. A large amount ofheat generated in the region opposite the cooling side is difficult
to be extracted out to the cold stage.
As a result, the temperature rise in that region causes a localized decrease in Jc , and then the trapped flux leaves the bulk
easily. On the other hand, for the solenoid coil, the bulk wascooled along c-axis through a large area, and the temperature in
the ab-plane of the bulk is relatively homogeneous. The detail
discussion is performed later with the aid of numerical simulations.
Fig. 3 shows the trapped field, BT , at the center of the bulk
surface for the various diameters, as a function of the appliedfield, Bex , at 65 K using a split coil with the permendur yoke. For
all bulks, BT increases, takes a maximum and then decreases
with increasing Bex . The BT max of the φ43 mm bulk was larger
than that of the φ30 mm bulk. However, BT max of the φ65 mm

SHIMOYASHIKI et al.: TRAPPED FIELD PROPERTIES OF GdBaCuO BULK SUPERCONDUCTORS

Fig. 3. The trapped field, BT , at the center of the bulk surface for the bulks ofvarious diameters magnetized by a split coil with yoke at 65 K, as a function of
the applied field, Be x .

Fig. 4. (a) The maximum temperature rise, ΔTm a x , of the sample holder ofthe bulks of various diameters. (b) The generated heat, Q, as a function of theapplied field, Be x , which was estimated using eq. (2).

bulk was lower than that of the φ43 mm bulk, and BT abruptly
increased and then decreased, compared to the other bulks. If the
Jc (B, T) characteristics of the bulks are assumed to be identicaland homogeneous, the magnetic flux starts to penetrate into thebulk center at a higher Bex , and the larger disk bulk should
trap a higher magnetic field at the higher Bex . The experimental
results for the 65 mm bulk suggest that an inhomogeneous Jc
distribution (due to the large heat generation) exists in the bulk
and, as a result, the magnetic flux easily penetrates at lower Bex
and easily escapes at higher Bex . The maximum BT max among
all the bulks was 2.34 T for the φ43 mm bulk. This discrepancy
mainly comes from the inhomogeneous Jc distribution in the
65 mm bulk due to the inhomogeneous heat transfer to thesample holder and cold stage.
Fig. 4(a) shows the maximum temperature rise, ΔTm ax , asa function of the applied field, Bex , for the bulks with various
diameters, which was measured on the bulk holder. ΔTm ax increases with increasing Bex for each bulk and the gradient of
ΔTm ax /Bex becomes steeper with increasing diameter of thebulk. Fig. 4(b) shows the Bex dependence of the generated
heat, Q, for each bulk, which was estimated using following
equation [7].
Q= (T s +Δ T m a x )(T s )

C(T )V dT,(2)6802405

Fig. 5. Numerical simulation results of the trapped field, BT , at the center ofthe bulk surface at 65 K using the split coil without yoke, as a function of theapplied field, Be x , for the bulks of various diameters.

where, C(T) is specific heat per unit volume and V is the volumeof the GdBaCuO bulk [14]. The Q value in Fig. 4(b) shows asimilar Bex dependence to ΔTm ax shown in Fig. 4(a), which
results from the pinning loss due to flux pinning and the viscous
loss due to flux movement, but also changes depending on the
Jc (B, T) value. The Q values of the φ65 mm bulk indicate larger
values, compared to those of the other bulks. Since V = 66.3 cm3for the φ65 mm bulk, 26.1 cm3 for the φ43 mm bulk, and 10.6
cm3 for the φ30 mm bulk, the Q values are nearly proportional
to the V value more than Bex = 3.5 T. It should be noted that
Jc (B, T) characteristics of the bulks used in the experiment havenot been measured/estimated and may be different to each other.
The cooling power of the refrigerator used in this study was 5 W( = 5 J/s) at 20 K, which is quite smaller than the generated heat
during PFM. The brass holder for each bulk has different sizeand heat capacity, which also influences the temperature rise
and the heat propagation. As a result, the temperature of thebulk increases due to the generated heat exceeding the coolingability, especially for the larger bulk.
B. Numerical Simulation Results
In the numerical simulation, the Jc (B, T) characteristics are
assumed to be identical and homogeneous for all the bulks.
Fig. 5 shows the trapped field, BT , at the center of the bulk
surface without yoke, as a function of the applied field, Bex . In
all cases, BT increased with increasing Bex , took a broad peak
and then decreased. It is easier for the magnetic flux to penetrate to the center of the bulk (and be subsequently trapped)
for a smaller diameter sample. The BT max value increases withincreasing bulk diameter, which does not reproduce the experimental results shown in Fig. 3. The Bex value to achieve BT max
increases with increasing bulk diameter. These results suggestthat it is harder for the magnetic flux penetration into the centerof the larger bulk. The sudden increase and steep decrease in
BT for the 65 mm bulk shown in Fig. 3 was not reproduced by
the simulation under these initial assumptions.
Fig. 6(a) shows the maximum temperature rise, ΔTm ax , asa function of the applied field, Bex , for the bulks of various
diameters, which was estimated at the same position as theexperiment in Fig. 1. ΔTm ax increases with increasing Bex foreach bulk. However, the magnitude of ΔTm ax is larger than thatof experimental results. Furthermore, the gradient of ΔTm ax /Bex
is nearly identical, which is quite different to the experimental
results.

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

Fig. 6. Numerical simulation results of (a) maximum temperature rise,
ΔTm a x , and (b) generated heat, Q, as a function of the applied field, Be x ,for the bulks of various diameters.

Fig. 8. (a) The trapped field, BT , at the center of the bulk surface, as a functionof the Be x for the φ65 mm bulk assuming the initial inhomogeneous temperature
distribution shown in Fig. 7 and (b)–(e) typical trapped field profiles.
Fig. 7. Initial temperature distribution of the φ65 mm bulk, in which regions
1.5 and 3 K higher than the rest of the bulk ( = 65 K) were assumed.

Fig. 6(b) shows the Bex dependence of the generated heat, Q,
for each bulk, which was estimated using eq. (2). The results
show a similar trend as the experimental results in Fig. 3(b).
However, the maximum Q value for the φ65 mm bulk is about
twice as large as that measured in the experiments. In the actual bulks, there exist regions of lower Jc , through which themagnetic flux penetrates easily, even at lower Bex . As a result,the generated heat becomes small. The “C-shaped” trapped field
profile in Fig. 2(e) suggests the possibility of an inhomogeneoustemperature distribution in the large bulk due to the insufficientcooling power of the refrigerator. The numerical simulation was
performed assuming an inhomogeneous initial temperature distribution in the bulk.
Fig. 7 shows the initial temperature distribution for the
φ65 mm bulk, in which the regions 1.5 and 3 K higher than
the rest of the bulk ( = 65 K) were assumed on the offside opposite to the cold stage. Fig. 8(a) shows the trapped field, BT , at thecenter of the bulk surface, as a function of Bex for the φ65 mm
bulk in the case of the initial inhomogeneous temperature distribution shown in Fig. 7. The similar relationship for the bulk
under the uniform Ts is also shown. The BT vs Bex curve forthe inhomogeneous Ts distribution shifted to the lower Bex side,
and BT max was decreased, compared to the uniform Ts case. The
typical trapped field profiles are also shown in Figs. 8(b)–8(e).
In Figs. 8(c) and 8(d), for the inhomogeneous Ts distribution,
the “C-shaped” trapped field profile can be reproduced at low
and high Bex . On the other hand, for the uniform Ts case, homogeneous trapped field profiles are observed, as shown in Figs.

8(b) and 8(e). These results indicated that the inhomogeneous
Ts profile can reproduce the “C-shaped” trapped field profile.
Finally, we should comment on the mechanical reinforcement required to withstand the large repulsion force during theascending stage of PFM. The repulsion force increases withincreasing the diameter of the bulk and with decreasing temperature due to the increase in the Jc value. Sufficient mechanicalsupport is necessary to avoid damage to the refrigerator and/or
the PFM apparatus.
IV. CONCLUSION
We have investigated the trapped field properties of GdBaCuO
bulks with various diameters at 65 K during PFM using the split
coil. The maximum trapped field, BT max , of the φ43 mm bulk
was larger than that of the φ30 mm bulk. However, BT max of the
φ65 mm bulk was smaller than that of the φ43 mm bulk and thetrapped field profile showed distorted “C-shaped” one. Using
the numerical simulation, these results can be explained by theinhomogeneous temperature profile and by the larger generated
heat, Q, for the φ65 mm bulk due to the lower cooling power ofthe refrigerator than the generated heat. To achieve the higher
and homogeneous trapped field profile for the larger bulk for
PFM using the split coil, it is necessary to consider the coolingmethod and cooling power of the used refrigerator.
ACKNOWLEDGMENT
All data are provided in full in the results section of this paper.

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