Field-cooled magnetization of Y-Ba-Cu-O
superconducting bulk pair reinforced by full
metal encapsulation under high magnetic
fields up to 22 T
Cite as: J. Appl. Phys. 126, 243901 (2019); https://doi.org/10.1063/1.5124010
Submitted: 09 August 2019 . Accepted: 07 December 2019 . Published Online: 23 December 2019
Tomoyuki Naito, Hiroyuki Fujishiro, and Satoshi Awaji

J. Appl. Phys. 126, 243901 (2019); https://doi.org/10.1063/1.5124010© 2019 Author(s).

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Field-cooled magnetization of Y-Ba-Cu-O
superconducting bulk pair reinforced by full metal
encapsulation under high magnetic ﬁelds up to 22 T
Cite as: J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
Submitted: 9 August 2019 · Accepted: 7 December 2019 ·Published Online: 23 December 2019
Tomoyuki Naito,1,a)Hiroyuki Fujishiro,1View Online

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CrossMarkand Satoshi Awaji2

AFFILIATIONS
1Faculty of Science and Engineering, Iwate University, Morioka 020-8551, Japan

2

High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University, Sendai 980-8577,
Japan

a)

Electronic mail: tnaito@iwate-u.ac.jp

ABSTRACTWe report on the ﬁeld-cooled magnetization (FCM) process under magnetic ﬁelds of up to 22 T for the stacked Y-Ba-Cu-O (YBCO) bulk
pair reinforced by a stainless steel (SUS316) container. On the basis of the numerically simulated mechanical stress in a bulk during FCM,
the SUS316 container was designed by the numerical simulation to oﬀer the suﬃcient hoop stress tolerance to the bulk trapping themagnetic ﬁeld of 20 T. As a result, we obtained successfully the trapped ﬁeld, BT , of 15.1 T by FCM from 18 T at 28 K at the center of the
YBCO bulk pair. However, the extremely large-scale vortex jumps and large temperature rise occurred suddenly during FCM from a higher
ﬁeld of 22 T at a lower temperature of 23 K, and then a small crack was conﬁrmed at the periphery of “both” YBCO bulks from the distorted
contour maps of BT . The simultaneous break of both YBCO bulks probably in spite of suﬃcient mechanical reinforcement led us toconclude that the thermal instability triggered oﬀ the large-scale vortex jumps and large heat generation. The stress concentration induced
thermally at the hot spot brought about the cracking.
Published under license by AIP Publishing. https://doi.org/10.1063/1.5124010
I. INTRODUCTION
Two kinds of superconducting magnets, a conventional coilmagnet and a quasipermanent bulk magnet, are well known. Although
not only the shape and structure but also the excitation method iscompletely diﬀerent from each other, both magnets interestingly havethe same crucial issues relating to the electromagnetic stress tolerance
under a strong magnetic ﬁeld generalized by themselves.
The superconducting wires in a coil magnet experience bothcompressive and tensile stresses on cooling and under the excitation,
which deteriorates the superconducting properties such as the upper
critical ﬁeld, Bc2 , and the critical current density, Jc .1–4 Speciﬁcally,
the tensile hoop stress of several hundreds of megapascals by theelectromagnetic force along the circumferential direction is applied
to the superconductors in a high-ﬁeld magnet.5,6 Therefore, to utilize
the intrinsic Jc of superconductors and to protect the magnet itself,
the superconductors and magnets must be reinforced to withstandthe hoop stress. A Ni-based alloy with a high yield stress of

J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
Published under license by AIP Publishing.

0.8–1.4 GPa at low temperatures7,8 is well known to be used as a substrate for the REBa2 Cu3 O7δ (RE is the rare earth element, RE123)
coated conductors9 and as a reinforcing lamination for the(Bi, Pb)2 Sr2 Ca2 Cu3 O10þx wires sheathed with silver alloy.10 Actually,
these wires equipped in the cryogen-free 25 T superconducting
magnet at the High Field Laboratory for Superconducting Materials(HFL-SM), Institute for Materials Research (IMR), Tohoku University,
have operated safely to date.5,11,12 In addition to the enhancement of
the yield stress of wires, the “Yoroi-coil” was proposed to give structurally an additional stress tolerance to the coil.13 The double-pancake
coils wound with the (Gd,Y)123 coated conductor tapes were fully
covered by the glass ﬁber reinforced plastic (GFRP). As a result, theYoroi-coil withstood the hoop stress of 2.0 GPa exceeding the yieldstress of the Hastelloy substrate (1.3–1.4 GPa), suggesting that the
GFRP full-cover successfully took charge of a part of the hoop stress.
Single grain RE-Ba-Cu-O (REBCO) bulks, which mainly
consist of the superconducting REBa2 Cu3 O7δ (RE123) matrix andthe nonsuperconducting RE2 BaCuO5 (RE211) phases, are usually

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reinforced by a metal ring [typically, stainless steel (SUS)] to trap
magnetic ﬁelds of several Teslas without mechanical fracture.14
This is because they are the brittle ceramics with quite a low
mechanical strength against the electromagnetic tensile hoop stress.
The widely scattered fracture strength of 20–160 MPa, which wascommonly evaluated by the three point bending test, has beenreported for REBCO bulks.15 This results from the fact that themechanical strength is sensitive to the microstructure of each tested
bulk that contains intrinsically the diﬀerent amount of voids, impurity particles, crystal defects, and so on. Thus, the enhancement of
the internal mechanical strength of bulk is essential. The additionof Ag enhanced the bending strength from 90 MPa of the pristine
YBCO bulk to 110–140 MPa of the 10–20 wt. % Ag added one by
reducing the preexisting microcracks and preventing the crack
propagation.16 Since the tensile strength is commonly about half ofthe bending one,17 we can consider roughly the tensile strengthof 50–70 MPa for the Ag-added YBCO bulk. The bending strengthof YBCO bulks increased from 76.7 MPa to 115.1 MPa at 77 K byﬁlling up the pores and microcracks in the bulk by the impregnation of epoxy resin.18 Further external reinforcement by the epoxy
resin with carbon ﬁber realized the trapped ﬁeld, BT , of 17.24 T at
29 K in the center of the stacked two YBCO bulks by the ﬁeldcooled magnetization (FCM) from the applied ﬁeld, Bapp , of 18 T.19
Later, the shrink-ﬁt stainless steel ring, which is a simple and easy
reinforcement technique, also enabled to trap a magnetic ﬁeld of
17.6 T at 26 K in the stacked GdBCO bulk pair, in which Bapp was
also 18 T.20 The evolution of the shape of the BT proﬁle withrespect to temperature, found in both reports, demonstrated that
BT of 17 T-class was limited by Bapp of 18 T and the potential of
the REBCO bulks trapping a magnetic ﬁeld of over 20 T.
The hoop stress tolerance of the cylindrical bulk has often
been discussed against the maximum hoop stress, which is proportional to the square of the maximum trapped ﬁeld, expected at
the center of bulk.21 In a realistic case, on the other hand, theinteraction between the bulk and the reinforcing material must be
considered. Therefore, we performed the numerical simulations
to estimate precisely the hoop stress in the disk bulk during FCM
from Bapp ¼ 22 T to achieve the trapped ﬁeld of 20 T for two
types of reinforcements, a stainless steel (SUS316) ring and a
SUS316 full-cover capsule, under three Jc values such as 4Jc* , 3Jc* ,and 2Jc* .22 Jc* was deﬁned as the critical current density, which was
assumed to be independent of the magnetic ﬁeld, to achieve thetrapped ﬁeld of B* from the following relation, B* ¼ μ0 Jc* R, by the
Bean’s critical state model.23 Here, we used Jc* of 1:75  109 Am2 for B* of 22 T, μ0 is the magnetic permeability in vacuum,and R is the radius of disk bulk. For the most severe case of
Jc ¼ 4Jc* , we clariﬁed that the bulk encapsulated fully by the
SUS316 container withstood the electromagnetic “tensile” hoop
stress up to þ150 MPa by applying the thermal “compressive”
hoop stress of about 200 to 140 MPa, i.e., the net tensile stress
was suppressed from þ150 MPa to below þ10 MPa, rather
smaller than the typical tensile strength of þ50 to þ70 MPa mentioned above.
In this paper, we report the ﬁeld-cooled magnetization processof the stacked YBCO bulk pair reinforced by the stainless steel
capsules, which were expected to apply the suﬃcient hoop stress
tolerance against the trapped ﬁeld of 20 T by the numerical

J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
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simulation results,22 under magnetic ﬁelds of up to 22 T at various
temperatures of 23–40 K.
II. EXPERIMENTAL PROCEDURE
We stacked two YBCO disk bulks (Bulk#1 and #2) with 20 mm
in diameter and 10 mm in thickness reinforced by the stainless steel(SUS316) capsule that consisted of a ring and two thin plates, as
shown schematically in Fig. 1. Three-dimensional orthogonal coordinate axes were deﬁned. The x- and y-axes were parallel to thesurface of disk bulks and the z-axis along the thickness direction of
the bulks, and the origin was set at the center of the stack.
The YBCO bulks were grown by a top seeded melt-growthmethod at the Nippon Steel Corp.24 The SUS316 capsules were
designed to keep the mechanical strength of bulks against the hoop
stress during FCM from the applied magnetic ﬁeld, Bapp , of 22 T,
which was based on the numerical simulations described elsewhere.22
Each YBCO bulk was inserted into the SUS316 ring (31 mm in outer
diameter, 20 mm in inner diameter, and 10 mm in height), and thencovered from both sides by two types of SUS316 thin disk plates,“A” and “B,” using six screws. Both plates (A and B) were 31 mm indiameter and 1.5 mm in thickness, and one face of the plate A had asingle groove with 3 mm in width and 0.5 mm in depth. As found in
Fig. 1, the groove of each plate A, which was faced in stacking theencapsulated YBCO bulks, oﬀered the space with 3 mm in width and
1 mm in height, in which four cryogenic miniature Hall probes(HGT-2010, Lakeshore Inc.) were set at x ¼ 0, 2, 5, and 9 mm along
the x-axis. It is noteworthy that the seed crystal side and the opposite(bottom) side of each bulk were covered by the plates A and B,
respectively, that is, the seed crystal side of each bulk faced eachother in the stack. This is because the crystallinity and the superconducting properties are well known to be diﬀerent from the seed
crystal and bottom sides. The temperature of the stacked YBCO
bulks was monitored by a Cernox thermometer set at the bottom of
the stack.

FIG. 1. Schematic image of the stacked YBCO bulk pair (Bulk#1 and #2) reinforced by the stainless steel (SUS316) capsule, which consists of one ring andtwo different plates A and B. The numbered four small square boxes set along
the x-axis are the miniature cryogenic Hall probes. The small square box set atthe bottom of the stack is a Cernox thermometer.

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The stacked YBCO bulk pair was inserted into a magnetizing
coil with a gas He ﬂow type cryostat. The temperature was controlled by the Cernox thermometer and 50 W heater. We used thefollowing two magnets of the HFL-SM, IMR, Tohoku University;
one was a commercial cryogen-free 15 T superconducting magnet(JASTEC Inc.), named 15T-CSM, and the other was the speciallydesigned 28 T hybrid magnet consisting of 16 T water-cooled and
12 T superconducting magnets, named 28T-HM. After the FCM
experiment under high magnetic ﬁelds, the bulk was evaluated by
the trapped ﬁeld proﬁle measured by scanning an axial-type Hall
probe (BHA-921, F.W. Bell Inc.) in liquid nitrogen (LN2 ) using acommercial cryogen-free 10 T superconducting magnet (JASTEC
Inc.) at Iwate University.
III. RESULTS AND DISCUSSION
We measured the local vortex density at four positions,
B1 (x ¼ 0 mm), B2 (x ¼ 2 mm), B3 (x ¼ 5 mm), and B4 (x ¼ 9 mm),and temperature of the stacked YBCO bulk pair during FCM fromthe initial applied magnetic ﬁeld, Bapp , of 15 T at two temperaturesof sample, Ts ’s, 40 and 30 K using the 15T-CSM magnet.
Figure 2(a) shows the typical results taken at Ts ¼ 40 K as afunction of the time step (TS) of the descent of the magnetic ﬁeld
during FCM. TS was deﬁned by the following relation:
TS ¼

Bapp  Bex
 10,
Bapp

(1)

where Bex was the actual external magnetic ﬁeld, changing from
Bapp (TS ¼ 0) down to 0 T (TS ¼ 10). Bex was decreased from 15 T
down to 0 T at a constant rate of 0:04 T/min. Both local vortex
densities, B1 and B2 , decreased quite moderately and ﬁnallyreached 10.0 T and 9.35 T, respectively, just at the ramp-end[Bex ¼ 0 T (TS ¼ 10)] and Ts ¼ 40 K, which were the trapped ﬁeld
at x ¼ 0 and 2 mm, named BT1 and BT2 , respectively. Somewhat
quick decrease in B3 was observed, and the trapped ﬁeld at
x ¼ 5 mm, BT3 , was 6.08 T. B4 decreased monotonically with Bex
and reached 0.59 T at TS ¼ 10. One can notice the decay of thetrapped ﬁelds at TS ¼ 10 due to the vortex creep, which will be
discussed later (in Fig. 5). The nearly constant temperature wasobserved during the FCM process, suggesting that the slowly swept
Bex suppressed the heat generation due to the vortex dynamics.
Note that BT1 of 13.5 T at the ramp-end was also successfully
obtained during FCM from Bapp ¼ 15 T at Ts ¼ 30 K (not shownhere); the somewhat elevated BT1 originated from the increase of Jc
by lowering Ts .
Figure 2(b) shows the FCM process for the stacked YBCO
bulk pair under Bapp ¼ 18 T at Ts ¼ 28 K using the 28T-HM
magnet. As shown schematically in the inset of Fig. 2(b), Bex was
decreased stepwise from 18 T down to 0 T, to avoid the heat generation due to the vortex dynamics by the high sweep rate, 0:20 to0:32 T/min, of 28T-HM. The interval of the applied magnetic
ﬁeld, ΔBex , was 0:05 to 0:1 T with the duration, Δt, of 0.5 min,which corresponded to the pseudo-sweep rate of about 0:1 to0:2 T/min. Although the gradual decrease of the vortex density
was observed below TS ¼ 6, the vortices began to be excluded

J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
Published under license by AIP Publishing.

FIG. 2. Time step (TS) dependence of the local vortex density (left verticalaxis) and temperature (right vertical axis) of the stacked YBCO bulk pair during
the FCM process under (a) Bapp ¼ 15 T and Ts ¼ 40 K and (b) Bapp ¼ 18 T
and Ts ¼ 28 K, respectively. The inset of (b) shows schematically the stepwisechange and the pseudoswept Bex as a function of time, t.

swiftly beyond TS ¼ 6. Consequently, the YBCO bulk pair trapped
successfully the magnetic ﬁeld of 15.1 T at x ¼ 0 mm just at theramp end. The temperature was stable during FCM, although thepresent 28T-HM experiment had somewhat faster pseudo-sweep rateof Bex than that in the 15T-CSM experiments. No vortex jumps andno abrupt temperature rise suggest strongly that both YBCO bulks
were protected during FCM from 18 T by the present SUS316 capsules, as expected from the numerical simulation results.22 In addition, we conﬁrmed that this YBCO bulk pair trapped 15.1 T again in
the second FCM experiment under the same condition (Bapp ¼ 18 T
and Ts ¼ 28 K), which also support no fracture of both bulks. If a
crack was created at the ﬁrst FCM experiment, the second trapped
ﬁeld should deteriorate by the crack propagation.
Figure 3 shows the mappings of trapped ﬁeld, BT , in the x-yplane, which were taken at 2.5 mm distance from both surfaces of
YBCO bulks after FCM under Bapp ¼ 1 T in LN2 . The concentric

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FIG. 3. The proﬁle of the trapped magnetic ﬁeld at 2.5 mm distance from thesurface of bulk for each YBCO bulk
after FCM under Bapp ¼ 1 T in theliquid nitrogen. (a-1) and (a-2), respectively, are for the plate A and B sidesof the #1 bulk (Upper bulk). (b-1) and(b-2), respectively, are for the plate A
and B sides of the #2 bulk (Lowerbulk).

circular proﬁles without the distortion were observed at eachsurface of both upper #1 and lower #2 bulks. This also supports
strongly no fracture of both bulks during FCM under Bapp ¼ 18 T
at Ts ¼ 28 K. If the cracking happens partially in a bulk during
FCM, the induced supercurrent should circumvent a crack, resulting in the distorted BT proﬁle. The maximum trapped ﬁelds,
BT, max ’s, were 0.27 and 0.28 T, respectively, at the plates A (seedcrystal) and B (bottom) sides for the upper #1 bulk, and those were0.25 and 0.28 T for the lower #2 bulk. Somewhat higher trapped
ﬁelds with larger area at the plate B (bottom) side than those at theplate A (seed crystal) one are found for both bulks. This diﬀerence
seems to originate from the low superconducting properties of theseed crystal side because of the existence of the a(b)-growth region
with relatively low crystallinity and less Y211 particles acting as thepinning centers.
Figure 4 shows the trapped ﬁeld proﬁle, BT (x), just at the
ramp-end under various indicated FCM conditions for the stacked
YBCO bulk pair. The domelike shaped BT (x) came from themagnetic ﬁeld dependent Jc (B), which suggested that the induced

J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
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supercurrent ﬂew through the whole region of bulks, that is, both
YBCO bulks were fully magnetized. BT independent of x should
appear, if a region with no induced supercurrent ﬂowing exists.
Figure 5 shows the time dependence of the reduced trapped
ﬁeld at the center (x ¼ 0 mm), BT1 (t)=BT1 (0), of the stacked YBCO
bulk pair for various FCM conditions. The start time, t ¼ 0 min,was deﬁned as the time at the ramp-end. The lower two experimental data were taken using the 15T-CSM. At Ts ¼ 40 K, thetrapped ﬁeld began to decay steeply around t ¼ 5 min, and the
decay of about 3% was observed at t ¼ 10 min. The decay
became moderate at a lower temperature of Ts ¼ 30 K, because
the increase of pinning potential and the decrease of thermal
ﬂuctuation were brought about simultaneously by lowering temperature. As a result, the 3% decay of BT1 was observed at
t ¼ 50 min. However, BT1 after FCM under Bapp ¼ 18 T at
Ts ¼ 28 K using the 28T-HM decayed somewhat rapidly just likeas at Ts ¼ 40 K using the 15T-CSM. This indicates that more
vortices were activated in the 28T-HM experiment, compared to
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FIG. 6. Temperature dependence of the trapped ﬁeld at x ¼ 0 mm, BT1 (T) of
the stacked YBCO bulk pair after FCM from Bapp ¼ 18 T at 28 K.
FIG. 4. Trapped ﬁeld at the ramp-end along the x-axis for the stacked YBCO
bulk pair under various indicated FCM conditions.

larger induced electromotive force, dΦ=dt(¼d(BexS)=dt), at thechange in Bex , which depends on the original sweep rate of the
28T-HM (0:20 to 0:32 T/min). Here, Φ is the magnetic ﬂux,
and S is the cross-sectional area of bulk surface perpendicular to
the z-axis.
Figure 6 shows the trapped ﬁeld at x ¼ 0 mm, BT1 (T), as afunction of the temperature after the successful FCM experiment at
Bapp ¼ 18 T and Ts ¼ 28 K for the stacked YBCO bulk pair. BT1 (T)FIG. 5. Time dependence of the reduced trapped ﬁeld at the center(x ¼ 0 mm), BT1 , of the stacked YBCO bulk pair for various indicated FCM
conditions.

J. Appl. Phys. 126, 243901 (2019); doi: 10.1063/1.5124010
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decreased monotonically with the negative curvature with increasing temperature. No temperature-independent BT1 (T) also supportsthat both YBCO bulks were fully magnetized. Extrapolating of thiscurve toward the low temperatures suggested that the trapped ﬁeld
over 20 T can be achieved below 20 K for this YBCO bulk pair.
To obtain a higher trapped ﬁeld, therefore, the FCM experiment was performed at the lower temperature of Ts ¼ 23 K underBapp ¼ 22 T for the same YBCO bulk pair using the 28T-HM, as
shown in Fig. 7; the target trapped ﬁeld was not 20 T but 18 T to
avert the thermal instability. Bex was decreased from 22 T down to
20 T with somewhat fast constant sweep rate of 0:2 T/min, andsubsequently stepwise with ΔBex ¼ 0:05 T and Δt ¼ 0:5 min.
Both local vortex densities, B1 and B2 , decreased moderately with

FIG. 7. Time step (TS) dependence of the local vortex density (left verticalaxis) and temperature (right vertical axis) of the stacked YBCO bulk pair during
the FCM process under Bapp ¼ 22 T and Ts ¼ 23 K.

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decreasing Bex . However, both B1 and B2 jumped abruptly from20.5 T to (5 T) at TS ¼ 6:9 (Bex ¼ 6:9 T), and, at the same time,
the temperature of the YBCO bulk pair increased steeply from 23 K
to  63 K. Just after the vortex jumps occurred, the Bex sweeping
was immediately stopped, and then Ts was increased slowly up to
Tc to protect the YBCO bulks from the further crack propagation,
assuming that the cracking occurred. Note that both lower B1 andB2 compared to Bex at the vortex jumps are artiﬁcial because they
showed about 5 T even at 100 K. The Hall probes themselves
seemed to be broken by the overvoltage due to the large induced
electromotive force at the sudden change in the magnetic ﬁeld.
Figure 8 shows the mappings of the trapped magnetic ﬁeld at
2.5 mm distance from both surfaces of each YBCO bulk after FCM
under Bapp ¼ 1 T in LN2 . The degradation of BT, max from 0.27 T
down to 0.25 T and the distorted BT proﬁle were found at the plate
A side of the upper #1 bulk [Fig. 8(a-1)]. On the other hand,
BT, max was kept as high as 0.28 T at the plate B side of the upper#1 bulk, although the BT proﬁle was slightly distorted, as shown in
Fig. 8(a-2). Further deterioration of BT, max and distortion of the BT

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proﬁles were observed for the lower #2 bulk; BT, max ’s of the plate A
and B sides, respectively, decreased from 0.25 T down to 0.20 T andfrom 0.28 T down to 0.24 T. These results indicate that the cracking
occurred at the periphery of the plate A side for both YBCO bulks,
and the size of crack of lower #2 bulk seems to be larger than thatof upper #1 bulk.
The vortex jumps originate possibly from the bulk fracture or
thermal instability. First, let us consider the vortex jumps triggeredby the partial fracture of YBCO bulks at the periphery in spite of
the mechanical reinforcement. In our simulation results for thesame experimental setup and condition (Bapp ¼ 22 T), the trapped(sim)’s, of 21.5, 21.1, andﬁelds at the center (x ¼ y ¼ z ¼ 0 mm), BT
18.8 T, respectively, were estimated for three Jc values such as 4Jc* ,3Jc* and 2Jc* .22 Thus, BT of 18 T expected experimentally suggeststhat Jc of the present YBCO bulks at 23 K is probably somewhat
smaller than 2Jc* . For Jc ¼ 2Jc* , the bulk encapsulated by the present
SUS316 capsule felt only the compressive stress during FCM from
Bapp ¼ 22 T and under BT ¼ 18:8 T.22 One can notice that an area
between the ﬁxing screws might weaken the reinforcement

FIG. 8. The proﬁle of trapped magnetic
ﬁeld at 2.5 mm distance from thesurface of bulk for each YBCO bulks
after the FCM under Bapp ¼ 1 T in theliquid nitrogen. (a-1) and (a-2), respectively, are for the plate A and B sides of
the #1 bulk (Upper bulk). (b-1) and(b-2), respectively, are for the plate A
and B sides of the #2 bulk (Lower bulk).

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ARTICLEmechanically; however, only the SUS316 ring (without ﬂaps) was
conﬁrmed numerically to apply the compressive stress of about
100 MPa thermally to the periphery of bulk.22 In any case, thebulk fracture should not happen at the periphery under the present
mechanical reinforcement. In addition, the observed one large
vortex jumps during FCM indicates that the present two YBCO
bulks probably broke simultaneously. Because of the diﬀerent
microstructure of each bulk, it is extremely diﬃcult to consider thata lack of mechanical reinforcement causes the bulk fracture “simultaneously.” Thus, we conclude that the YBCO bulks were protectedmechanically by the present SUS316 capsules, as expected, andhave to consider an alternative possibility of the bulk fracture.
Next, we consider the inﬂuence of thermal shock due to theabrupt local heat generation by the vortex jumps on the mechanicalbehavior. This is because the vortex jumps are usually known to becaused by the thermal instability owing to the small speciﬁc heat of
the bulk at low temperatures. The local heat generation leads thetemperature gradient in the bulk, which results in the thermal compressive stress at the hot spot under the conditions that restrain
free expansion. In addition, the sudden decrease in both BT and Jc
reduces quickly the electromagnetic hoop stress, and then the bulk
might be subjected to the additional compressive stress by thesudden contraction. There are a few reports for the compressive testsof REBCO bulks.25,26 The compressive strength of a YBCO bulk wasreported to be over 196 and 115 MPa along the c-axis and theab-planes, respectively.25 For a SmBCO bulk, the average compressive
strengths were 466 and 368 MPa along the c-axis and the ab-planes,
respectively.26 The cleavage at the ab-planes gives rise to the lower
compressive strength along the ab-plane. Therefore, the compressive
stress of several hundreds of megapascals is required to break thebulk.
The thermal stress at any point, σ th , which depends on thediﬀerence in temperature between that point, Tp , and the average,
Tave , of an inﬁnite slab sample, is given by the following relation:27

σ th ¼Eα(Tave  Tp ),1νPublished under license by AIP Publishing.

IV. CONCLUSION
We have studied the ﬁeld-cooled magnetization (FCM) of
stacked Y-Ba-Cu-O (YBCO) bulk pair reinforced by the stainlesssteel (SUS316) capsule under magnetic ﬁelds of up to 22 T. The
SUS316 capsule was designed to apply the suﬃcient compressive
stress to the YBCO bulks overcoming the electromagnetic tensilestress during FCM from 22 T, which was based on the numericalsimulations reported previously. As a result, the trapped ﬁeld, BT ,of 15.1 T at 28 K was successfully achieved at the center of YBCO
bulk stack. However, the FCM experiment under the magnetic
ﬁeld of 22 T at 23 K failed, that is, the huge vortex jumps occurred
during the withdrawal of the external magnetic ﬁeld. The small
crack was conﬁrmed at the periphery by the two-dimensional BT
proﬁles for both YBCO bulks. The break of both YBCO bulks,
in spite of the suﬃcient mechanical strength estimated by thenumerical simulation, suggested to originate not from a lack ofmechanical reinforcement but from a thermal shock by the heatgeneration due to the abrupt and remarkably large change in thevortex density in the YBCO bulk stack. The importance of thecontrol of the exhaust heat from the bulk was suggested in addition to the mechanical strength.
ACKNOWLEDGMENTS
The authors would like to thank Mr. Y. Sasaki, Mr. K. Fushimi,
and Mr. H. Ishikawa of the High Field Laboratory for
Superconducting Materials, Institute for Materials Research, Tohoku
University for their assistance in the experiments using a Hybrid
magnet, 28T-HM. We also thank Mr. Y. Takeda, Mr. Yuhei
Takahashi, and Mr. Yuya Takahashi of the Iwate University for their
help in part of this work. This work was partly supported by JSPS
KAKENHI under Grant Nos. JP15K04718, JP15K04646, andJP18K04920.
REFERENCES(2)

where E is Young’s modulus, α is the liner thermal expansion
coeﬃcient, and ν is the Poisson ratio. Using the typical mechanicalparameters of REBCO bulks, E ¼ 100 GPa, α ¼ 5:2  106 K1 ,and ν ¼ 0:33, σ th ¼ 0:78  (Tave  Tp ) is obtained. This relationsuggests that the temperature rise over 200 K is roughly needed toinduce the bulk fracture thermally, however, that at the vortex
jumps was as low as approximately 40 K, as found in Fig. 7.
Considering the position of the Cernox thermometer and the low
thermal conductive REBCO bulks,28,29 the actual temperature rise at
the hot spot must be rather larger than the observed experimentally.
The thermal shock eﬀect proposed here will be conﬁrmed by thenumerical simulations combined with the direct observation of thecracks by the X-ray CT technique30 in the near future. In addition to
the mechanical strength, the thermal stability is also a crucial important issue to realize the trapped ﬁeld over 20 T, which can be solved
by inserting a high thermal conductive metal as the heat sink tothe bulk.18

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