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

6801206

Influence of Inner Diameter and Height of
Ring-Shaped REBaCuO Bulks on Trapped Field andMechanical Stress During Field-Cooled
Magnetization
Hiroyuki Fujishiro , Keita Takahashi, Tomoyuki Naito , Yousuke Yanagi, Yoshitaka Itoh, Takashi Nakamura,and Mark Ainslie , Senior Member, IEEE

Abstract—In this paper, the trapped field Bz , thermal hoop stressσ θ cool by cooling from 300 to 50 K, and electromagnetic hoop stressσ θ FCM during field-cooled magnetization (FCM) from Ba p p = 6.3
and 9.4 T are investigated numerically for ring-shaped REBaCuO
bulks with various inner diameters (I.D.) and heights (H) and reinforced by an Al alloy ring. For simplicity, an identical critical current density Jc (B), which is a typical value at 50 K, is assumed in
the simulation. The Bz value at the center of the ring bulk changes
depending on the I.D. and H values of the ring bulk, which resultsfrom the different distribution of the superconducting current. As aresult, the total hoop stress σ θ total (= σ θ cool + σ θ FCM ) also changes
for each ring bulk and each Ba p p because of the variation of theσ θ cool and σ θ FCM values. The maximum σ θ total value, which affects the bulk fracture at Ba p p = 9.4 T, increases with decreasing
the height of ring bulk. These results can present guidelines fordesigning a trapped-field magnet using ring bulks.
Index Terms—Bulk high-temperature superconductors, finite
element method, field-cooled magnetization, mechanical properties, numerical simulation.

I. INTRODUCTION
OR the practical application of trapped field magnets(TFMs) using superconducting bulks such as RE-Ba-Cu-O(REBaCuO, RE: rare earth element or Y) and MgB2 , it is an
important issue to increase the trapped field in the bulk. The
trapped field capability of a disk-shaped bulk is proportional toF

Manuscript received October 22, 2018; accepted January 28, 2019. Date of
publication January 31, 2019; date of current version February 21, 2019. This
work was supported in part by JSPS KAKENHI under Grant 15K04646. The
work of M. D. Ainslie was supported by an Engineering and Physical Sciences
Research Council Early Career Fellowship EP/P020313/1. (Corresponding author: Hiroyuki Fujishiro.)
H. Fujishiro, K. Takahashi, and T. Naito are with the Department of Physical Sciences and Materials Engineering, Faculty of Science and Engineering,
Iwate University, Morioka 020-8551, Japan (e-mail:, fujishiro@iwate-u.ac.jp;t2216017@iwate-u.ac.jp; tnaito@iwate-u.ac.jp).
Y. Yanagi and Y. Itoh are with the IMRA Material R&D Company Ltd, Kariya
448-0032, Japan (e-mail:,yanagi@ai-i.aisin.co.jp; y-itoh@ai-i.aisin.co.jp).
T. Nakamura is with RIKEN, Wako 351-0198, Japan (e-mail:, ta-kashi.
nakamura@riken.jp).
M. Ainslie is 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.2019.2896782

the critical current density, Jc (B, T), and the diameter, as well as
the height of the bulk. For field-cooled magnetization (FCM),
which is a conventional magnetizing technique, increasing Jc (B,T) by lowering the operating temperature is an effective way toenhance the trapped field. To date, a highest trapped field of 17.6
T has been achieved at 26 K in a disk-shaped GdBaCuO bulk
pair reinforced by shrink-fit stainless steel [1]. During the FCM
process, however, a large Lorentz force, FL (=J × B), is generated due to the interaction between the induced current density(J) and the magnetic field (B), and results in fracture of thebulk when the magnetic stress exceeds the mechanical strengthof the material. Analytical solutions of the mechanical stresses
have been investigated during FCM for the disk and ring bulkswith infinite height, in which the Bean’s critical state model was
mainly used for superconducting characteristics [2]–[4].
A ring-shaped REBaCuO bulk is also useful for practicalapplications such as nuclear magnetic resonance (NMR) spectrometers and magnetic resonance imaging (MRI) apparatus [5],[6], in which the trapped field enhancement is an ongoing challenge to improve their resolution. In addition to Jc (B, T), thedistributions of the trapped field and mechanical stress change
depending on the inner diameter (I.D.), outer diameter (O.D.)and height (H) of the ring bulk. Although several experimental
and numerical results exist for the trapped field and mechanicalstress for the ring-shaped bulk [7]–[10], there have not been systematic investigations for the mechanical stress and the effect ofthe metal ring reinforcement in the ring bulk with finite height.
In the present paper, the trapped field, Bz , thermal hoop stress,σ θ cool , by cooling from 300 to 50 K and electromagnetic hoop
stress, σ θ FCM , during FCM from Bapp = 6.3 and 9.4 T are investigated for ring-shaped REBaCuO bulks (O.D. = 64 mm)with various I.D. and H and reinforced by an aluminum (Al)alloy ring, under the assumption of an identical critical current density, Jc (B), for the bulk. The influence of the shapeof the ring bulk on the risk of the mechanical fracture is also
discussed.
II. NUMERICAL SIMULATION FRAMEWORKA three-dimensional (3D) finite element model was constructed, based on our experimental setup for FCM [8] as shown1051-8223 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

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TABLE IIASSUMED MECHANICAL PARAMETERS OF REBACUO BULK, EPOXY RESIN, AND
AL ALLOY USED IN THE NUMERICAL SIMULATIONa

Young’s modulus, b Poisson ratio, c Thermal expansion coefficient.

following equation [13], [14].
BB
Jc (B) = Jc1 exp −
+ Jc2
BL
Bm ax
 

k 
B
1
1 −
,
× exp
k
Bm ax
Fig. 1. Cross-sectional view of the numerical model of the ring bulk reinforced
by Al alloy ring, which is magnetized using a solenoid coil.

TABLE IDIMENSIONS OF THE FIVE SIMULATED REBACUO RING BULKS

in Fig. 1, for the electromagnetic and mechanical simulation.
Five REBaCuO ring bulks 64 mm in O.D. were investigated, inwhich I.D. was changed from 28 to 40 mm and H was changed
from 20 to 6 mm, as shown in Table I. Each ring bulk was
mounted in an Al alloy (A7075-T6) ring 5 mm in width (74 mm
in O.D. and 64.2 mm in I.D.) with the same height as the ringbulk using an epoxy resin 0.1 mm in thickness. In the FCM process, the ring bulk was cooled to the magnetizing temperatureof Ts = 50 K, based on the experimental setup [5], [6], under
initial applied fields of Bapp = 6.3 and 9.4 T using a solenoid
coil (170 mm in O.D., 120 mm in I.D. and 200 mm in H), andthen, the external field was decreased linearly at −0.222 Tmin−1
down to zero. The Bapp value of 6.3 and 9.4 T is equivalent to
270 and 400 MHz, respectively, considering practical NMR resolution. The time step (TS) of the descent of the magnetic field
during FCM is defined as TS = 10 (Bapp - Bex )/Bapp by 10
steps, in which Bex is the actual time-dependent external field.
The electromagnetic phenomena during FCM are described
elsewhere [10], [11]. The temperature variation during FCM is
ignored for simplicity, assuming isothermal conditions. The E-J
power law is used to simulate the highly non-linear resistivity ofthe superconductor, where the electric field, E, is proportional toJ n , and n = 20 is assumed as a typical value for HTS materials
and a good approximation of Bean’s critical state model [12].
The Jc (B) characteristics of the bulk were assumed using the(1)

where each parameter (Jc1 = 2.3 × 109 A/m2 , Jc2 = 1.57 × 109
A/m2 , BL = 0.8 T, Bm ax = 4.5 T and k = 1.0) can reproduce
actual experimental results at 50 K [15], [16].
The co mmercial finite element method (FEM) software package, Photo-Eddy (Photon Ltd., Japan), was adapted for the analysis of the trapped field, Bz , and induced current density, Jθ ,along the θ-direction in the bulk. Elastic behavior in isotropic
materials can be expressed by Hooke’s law, and a detailed explanation is provided elsewhere [7], [8]. The nodal force on eachnode of the meshed elements calculated by Photo-Eddy was
exported to the software package, Photo-ELAS (Photon Ltd.,
Japan), for the analysis of the hoop stress, σ θ . The assumed
mechanical parameters (Young’s modulus, EY , Poisson ratio, ν,and thermal expansion coefficient, α) of each component usedin the mechanical simulation are su mmarized in Table II, which
are assumed to be isotropic and to be in the elastic region.
III. RESULTS OF ELECTROMAGNETIC SIMULATION
Fig. 2(a) shows the TS dependence of trapped field at thecenter of the five ring bulks, Bz (z = r = 0 mm), during FCM
from Bapp = 6.3 T and 9.4 T. The Bz value gradually decreases
with increasing TS for each case. For each Bapp , the Bz value
at the final step (TS = 10) changes depending on the I.D. andH values. For the ring bulks with identical height of H = 20
(bulks (1) – (3)), the final Bz value increases with decreasing
I.D. For the bulks with identical I.D. = 34 mm, the final Bz
value increases with increasing H. It should be noted that the
final Bz value for bulk (5) (I.D. = 34 mm, H = 6 mm) is thesame for both Bapp values. These results suggest that the thinbulk was fully magnetized for higher Bapp than 6.3 T and thatthe induced supercurrent flows through the entire bulk.
Fig. 2(b) shows the final Bz (z = r = 0 mm) value for the
ring bulks with H = 20 mm for Bapp = 6.3 and 9.4 T, asa function of I.D. Bz decreases with increasing I.D. Fig. 2(c)shows the final Bz (z = r = 0 mm) value for the ring bulks with
I.D. = 34 mm for Bapp = 6.3 and 9.4 T, as a function of H.
Bz decreases with decreasing H. The thinner ring bulks cannot
achieve higher trapped fields at the bulk center.

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Fig. 3. Contour maps of the current density distribution along the circumferential (θ) direction for each bulk after the FCM process (TS = 10) from Ba p p= 6.3 T.

Fig. 2. (a) The TS dependence of the trapped field at the center of the five ringbulks, Bz (z = r = 0 mm), during FCM from Ba p p = 6.3 T and 9.4 T. (b) The
final Bz (z = r = 0 mm) value for the ring bulks with H = 20 mm for Ba p p =6.3 and 9.4 T, as a function of I.D. and (c) for the ring bulks with I.D. = 34 mm,
as a function of H.

Let us compare the current density distribution for each bulk
during FCM. Fig. 3 shows the contour maps of the current
distribution, Jθ , along the circumferential (θ) direction in eachbulk after the FCM process (TS = 10) from Bapp = 6.3 T. Notethat the current flows in the blue region and there is no current in
the red region, as defined in Fig. 1. It was found that the current
distribution changes depending on the shape of the ring bulks.
For the bulks with H = 20 mm (bulks (1) – (3)), the supercurrent
flows at the periphery and the top and bottom regions of thebulk and the no current region increases with decreasing I.D.
On the other hand, for the bulks with I.D. = 34 mm (bulks (3)– (5)), no current region shrinks with decreasing H, and finallythe supercurrent flows through the entire bulk cross-section for
H = 6 mm. The current distribution is closely related to thetrapped field profile and determines the final trapped field shownin Fig. 2(a).
IV. RESULTS OF MECHANICAL SIMULATION
A. Cooling Process
Figs. 4(a) and 4(b), respectively, show the thermal hoop stressprofiles, σ θ cool , at the bulk center (z = 0 mm) and the bulk surfaceof each bulk after cooling from 300 to 50 K. The shape of the ring

Fig. 4. Thermal hoop stress profiles, σ θ cool , at (a) the bulk center (z = 0 mm)
and (b) the bulk surface, for each bulk during cooling from 300 to 50 K. (c) Theσ θ cool value of the ring bulks at r = 30 or 31 mm with H = 20 mm after coolingto 50 K, as a function of I.D. (d) The σ θ cool value of the ring bulks at r = 30 or
31 mm with I.D. = 34 mm after cooling to 50 K, as a function of H.

6801206

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 29, NO. 5, AUGUST 2019bulk influences on σ θ cool profile. At the bulk center, shown in
Fig. 4(a), a large compressive stress is applied to the ring bulk by
the Al alloy ring due to the difference in the thermal expansion
coefficient [7]. The maximum compressive stress takes place atthe bulk periphery (r = 31 mm) for each bulk. On the other hand,on the bulk surface, as shown in Fig. 4(b), the compressive stressat the bulk periphery decreases for all the bulks and changes to atensile stress for the bulks (1) – (3). The maximum tensile stress
was +40 MPa for the smaller I.D. bulk (2) (I.D. = 28 mm,
H = 20 mm) at r = 31 mm.
Fig. 4(c) shows the σ θ cool value at r = 30 or 31 mm for the
ring bulks with H = 20 mm after the cooling to 50 K, as afunction of I.D. The σ θ cool value decreases with increasing I.D.
Fig. 4(d) shows the σ θ cool value at r = 30 or 31 mm for the
ring bulks with I.D. = 34 mm after the cooling to 50 K, as afunction of H. The σ θ cool value on the bulk surface changes froma positive to a negative value with decreasing H and at the bulk
center (z = 0 mm), which has a negative (compressive) value,σ θ cool decreases with decreasing H. In the ring bulk as thin as
H = 6 mm, a compressive σ θ cool is present in all bulk region,
although the trapped field is smaller.
B. FCM Process
Fig. 5(a) shows the time step dependence of electromagnetic
hoop stress, σ θ FCM , during FCM from Bapp = 9.4 T at the inneredge on the bulk surface for each ring bulk, at which the σ θ FCM
value is the maximum in each bulk [7], [9]. σ θ FCM increases
with increasing TS, takes a maximum at an intermediate TS andthen decreases with the increase in TS for each ring bulk, which
is a co mmon tendency for σ θ FCM during FCM. It should be
noted that the σ θ FCM – TS profile for bulk (5) (I.D. = 34 mm,
H = 6 mm) is quite different to that for the other bulks because
the supercurrent flows through the entire bulk cross-section.
Fig. 5(b) shows the maximum electromagnetic hoop stress,σ θ FCM (max), as a function of I.D., for the bulks with H = 20 mm,
at the bulk center and the bulk surface, during FCM from 6.3 and
9.4 T. σ θ FCM (max) occurs at the inner edge of each ring bulk
and at the bulk surface this is slightly larger than at the bulk
center (z = 0 mm). Fig. 5(c) shows σ θ FCM (max) in the bulksof I.D. = 34 mm at bulk center and bulk surface during FCM,
as a function of H. Similar to Fig. 5(b), the difference between
the bulk center and bulk surface is very small. σ θ FCM (max)increases with decreasing H, which suggests that the thin ringbulk fractures more easily during FCM.

Fig. 5. The TS dependence of the electromagnetic hoop stress, σ θ FCM , during
FCM from 9.4 T, at the inner edge on the bulk surface for each ring bulk.
(b) Maximum electromagnetic hoop stress, σ θ FCM (max), in the bulks with H= 20 mm, at the bulk center and bulk surface during FCM, as a function of I.D.
(c) σ θ FCM (max) in the bulks of I.D. = 34 mm at the bulk center and bulk surface
during FCM, as a function of H.

B. Cooling + FCM Process
Figs. 6(a) and 6(b), respectively, show the TS dependenceof the total hoop stress profile, σ θ total ( = σ θ cool + σ θ FCM ),for bulk (3) (I.D. = 34 mm, H = 20 mm) at the bulk center(z = 0 mm) and at the bulk surface (z = 10 mm) during FCM
from 9.4 T. The σ θ total profile at the step 0 shows the σ θ coolwithout FCM, as shown in Fig. 4. The maxmum σ θ total at thebulk center (z = 0 mm) occurs at the inner edge (r = 17 mm)due to the increase from σ θ FCM . On the other hand, on the bulk
surface (z = 10 mm), the maximum σ θ total takes place at the
inner edge (r = 17 mm) and also at the bulk edge (r = 30 mm).

Fig. 6. The TS dependence of the total hoop stress profile, σ θ total ( = σ θ cool+ σ θ FCM ), for bulk (3) at (a) the bulk center (z = 0 mm) and (b) the bulk surface
during FCM from 9.4 T.

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Fig. 8. The relationship between the Bz value and the σ θ total (max) value forthe five cases at Ba p p = 6.3 and 9.4 T.

Fig. 7. (a) The TS dependence of the total hoop stress, σ θ total , at the inneredge on the bulk surface for each ring bulk during FCM from Ba p p = 9.4 T
after cooling to 50 K. (b) The maximum σ θ total value for the ring bulks with
H = 20 mm at the bulk center (z = 0 mm) and the bulk surface during FCM
from 6.3 and 9.4 T, as a function of I.D. (c) The maximum σ θ total value for the
ring bulks with I.D. = 34 mm at the bulk center and the bulk surface during
FCM, as a function of H.

The maximum σ θ total changes depending on the TS dependenceof the σ θ cool and σ θ FCM values.
Fig. 7(a) shows the TS dependence of the total hoop stress,σ θ total , at the inner edge on the bulk surface for each ring bulk
during FCM from Bapp = 9.4 T, after cooling to 50 K. Theσ θ total values decreased, compared to the σ θ FCM values, due
to the addition of the compressive stress by cooling. However,a tensile stress larger than +100 MPa is present during FCM
from 9.4 T, which suggests the possibility of the bulk fracturing,
since the fracture strength of typical Ag-doped REBaCuO bulks
is considered to be 50 ∼ 70 MPa [17], [18].
Fig. 7(b) shows the maximum σ θ total value for the ring bulkswith H = 20 mm at the bulk center (z = 0 mm) and the bulk
surface during FCM from 6.3 and 9.4 T, as a function of I.D.
The maximum σ θ total for Bapp = 9.4 T takes place at the inneredge and the difference is small between the bulk center andsurface. However, for Bapp = 6.3 T, the maximum σ θ total value
at the bulk surface is larger than that at the bulk center, becausethe σ θ total value at the periphery of the bulk surface becomeslarge due to the existence of the tensile stress during the coolingprocess. Fig. 7(c) shows the maximum σ θ total value for the ringbulks with I.D. = 34 mm at the bulk center (z = 0 mm) and thebulk surface during FCM from 6.3 and 9.4 T, as a function of

H. For a similar reason to that for bulk (3), the maximum σ θ total
value at the bulk surface is larger than that at the bulk center
for Bapp = 6.3 T. However, for smaller H values, the maximumσ θ total value takes place at the inner edge and the difference
between the bulk center and the bulk surface is very small.
The results in Figs. 7(b) and 7(c) suggest that the ring bulks
reinforced by Al alloy ring, except bulk (5), may avoid mechanical fracture during FCM from 6.3 T, because the maximumσ θ total value is +62 MPa, which is nearly the same as the fracture strength (50 ∼ 70 MPa) of typical REBaCuO bulks [17],[18]. However, bulk (5) during FCM from 6.3 T, and all fivebulks during FCM from 9.4 T, must suffer fracture based on thepresent simulation.
Fig. 8 shows the relationship between the trapped field, Bz ,and the maximum total hoop stress, σ θ total (max), for the fivering bulks for Bapp = 6.3 and 9.4 T, which was summarizedfrom Figs. 2(a) and 7. It was found that the I.D. should bedecreased and H should be increased to both enhance the trappedfield and reduce the hoop stress simultaneously. This directionmeans the approach to fabricating a long disk bulk. These resultspresent useful guidelines for designing ring-shaped TFMs toavoid the mechanical fracture. However, to achieve a higher
trapped field during FCM from Bapp = 9.4 T without fracture,a new reinforcement method must be applied [10].
IV. CONCLUSION
We have investigated numerically the trapped field, Bz , thermal hoop stress, σ θ cool , by cooling from 300 to 50 K and electromagnetic hoop stress, σ θ FCM , during FCM from Bapp = 6.3 and
9.4 T for ring-shaped REBaCuO bulks of various I.D. and H,
reinforced by an Al alloy ring. The total hoop stress σ θ total ( =σ θ cool + σ θ FCM ) changed at each position and for each Bapp due
to variation of σ θ cool and σ θ FCM . The maximum σ θ total value,at the innermost edge decreases with increasing the height ofring bulk. For Bapp = 6.3 T, the maximum σ θ total value can be
reduced below the fracture strength of 50 ∼ 70 MPa of the bulk
material. However, for Bapp = 9.4 T, the ring bulk must break. It
is necessary to introduce a new reinforcement structure to avoid
the mechanical fracture of the ring bulk to realize the 400 MHz
NMR bulk magnet.

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REFERENCES[1] J. H. Durrell et al., “A trapped field of 17.6 T in melt-processed, bulk
Gd-Ba-Cu-O reinforced with shrink-fit steel,” Supercond. Sci. Technol.,vol. 27, 2014, Art. no. 082001.
[2] T. H. Johansen, C. Wang, Q. Y. Chen, and W.-K. Chu, “Enhancement oftensile stress near a hole in superconducting trapped-field magnets,” J.
Appl. Phys., vol. 88, pp. 2730–2733, 2000.
[3] T. H. Johansen, Q. Y. Chen, and W.-K. Chu, “Pinning-induced stress inclamped superconductors,” Physica C, vol. 349, pp. 201–210, 2001.
[4] T. M. Johansen, “Flux-pinning-induced stress and magnetostriction inbulk superconductors,” Supercond. Sci. Technol., vol. 13, pp. R121–R137,
2000.
[5] T. Nakamura, Y. Itoh, M. Yoshikawa, T. Oka, and J. Uzawa, “Developmentof a superconducting magnet for nuclear magnetic resonance using bulk
high-temperature superconducting materials,” Concepts Magn. Reson. B,
vol. 31B, pp. 65–70, 2007.
[6] T. Nakamura et al., “Development of a superconducting bulk magnet for
NMR and MRI,” J. Mag. Reson., vol. 259, pp. 68–75, 2015.
[7] H. Fujishiro et al., “Simulation studies of mechanical stresses in REBaCuO
superconducting ring bulks with infinite and finite height reinforced bymetal ring during field-cooled magnetization,” Supercond. Sci. Technol.,vol. 30, 2017, Art. no. 085008.
[8] K. Takahashi, H. Fujishiro, T. Naito, Y. Yanagi, Y. Itoh, and T. Nakamura,“Fracture behavior by magnetic stress in EuBaCuO superconducting ringbulk reinforced by a stainless steel during field-cooled magnetization,”
Supercond. Sci. Technol., vol. 30, 2017, Art. no. 115006.
[9] K. Takahashi, H. Fujishiro, T. Naito, Y. Yanagi, Y. Itoh and T. Nakamura, “Numerical simulation of electromagnetic and thermal hoop stresses
in REBaCuO superconducting ring and disk bulks reinforced by stainless steel ring with various thicknesses during field-cooled magnetization,” IEEE Trans. Appl. Supercond., vol. 28, no. 3, Apr. 2018,
Art. no. 6800705.

[10] H. Fujishiro, K. Takahashi, T. Naito, Y. Yanagi, Y. Itoh, and T. Nakamura,“A new proposal of mechanical reinforcement structures to annular REBaCuO bulk magnet for compact and cryogen-free NMR spectrometer,”Physica C, vol. 550, pp. 52–56, 2018.
[11] H. Fujishiro and T. Naito, “Simulation of temperature and magnetic field
distribution in superconducting bulk during pulsed field magnetization,”
Supercond. Sci. Technol., vol. 23, 2010, Art. no. 105021.
[12] M. D. Ainslie, D. Zhou, H. Fujishiro, K. Takahashi, Y.-H. Shi, and J.
H. Durrell, “Flux jump-assisted pulsed field magnetization of high-Jc
bulk high-temperature superconductors,” Supercond. Sci. Technol., vol. 29,
2016, Art. no. 124004.
[13] M. Jirsa, L. P˚ust, D. Dlouhý, and M. R. Koblischka, “Fishtail shapein the magnetic hysteresis loop for superconductors: Interplay between
different pinning mechanisms,” Phys. Rev. B, vol. 55, pp. 3276–3284,
1997.
[14] M. Muralidhar, N. Sakai, M. Jirsa, N. Koshizuka, and M. Murakami,“Direct observation and analysis of nanoscale precipitates in(Sm,Eu,Gd)Ba2Cu3Oy,” Appl. Phys. Lett., vol. 85, pp. 3504–3506,
2004.
[15] M. D. Ainslie and H. Fujishiro, “Modelling of bulk superconductor magnetization,” Supercond. Sci. Technol., vol. 28, 2015, Art.
no. 053002.
[16] T. Kii et al., “Low-temperature operation of a bulk HTSC staggered array
undulator,” IEEE Trans. Appl. Supercond., vol. 22, no. 3, Jun. 2012, Art.
no. 4100904.
[17] D. Lee and K. Salama, “Enhancements in current density and mechanicalproperties of Y-Ba-Cu-O/Ag composites,” Jpn. J. Appl. Phys., vol. 29,
pp. L2017–L2019, 1990.
[18] K. Katagiri et al., “Effects of Ag content on the mechanical properties of(Nd,Eu,Gd)–Ba–Cu–O bulk superconductors,” Physica C, vol. 392-396,
pp. 526–530, 2003.