Superconductor Science and Technology
Supercond. Sci. Technol. 28 (2015) 125002 (14pp)

doi:10.1088/0953-2048/28/12/125002

Pulsed ﬁeld magnetization of 0°–0° and
45°–45° bridge-seeded Y–Ba–Cu–O bulk
superconductors
M D Ainslie1, J Zou1, H Mochizuki2, H Fujishiro2, Y-H Shi1, A R Dennis1 andD A Cardwell1
1

Bulk Superconductivity Group, Department of Engineering, University of Cambridge, Trumpington
Street, Cambridge CB2 1PZ, UK
2
Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, 4-3-5 Ueda,
Morioka 020-8551, Japan
E-mail: mda36@cam.ac.uk
Received 19 July 2015, revised 6 September 2015
Accepted for publication 19 September 2015
Published 14 October 2015
Abstract

Large, single-grain (RE)BCO (where RE=rare earth or Y) bulk superconductors withcomplicated geometries are required for a variety of potential applications, such as rotatingmachines, magnetic bearings and magnetic separation. As a consequence, the top multi-seeded
melt growth process has been studied over many years in an attempt to deliver large, single
grains for practical applications. Among these techniques, the so-called bridge-seeding produces
the best alignment of two seeds during melt processing of multi-seed samples. In this paper, thetrapped ﬁeld performance and magnetic ﬂux dynamics of two bridge-seeded, multi-seed samples
magnetized by pulsed ﬁeld magnetization are analyzed: one with a 45°–45° and another with a
0°–0° bridge seed. Based on an analysis of the ﬂux penetration across the seeds and in-between
the seeds of the 45°–45° multi-seed sample, an estimated Jc distribution over the ab-plane isdetermined, which provides the basis for further analysis via numerical simulation. A threedimensional ﬁnite-element model, developed to qualitatively reproduce and interpret theexperimental results, was employed to investigate the inﬂuence of the length of the bridge seed
for such multi-seed samples. The simulation results agree well with the observed experimental
results, in that the multi-seed sample’s particular inhomogeneous Jc distribution acts to distort
the trapped ﬁeld proﬁle from a traditional conical Bean’s proﬁle, which is determined by thelength and direction of the bridge seed on the bulk surface.
Keywords: bulk superconductors, multi-seeding, bridge-shaped seeds, trapped ﬁeld magnets,
pulsed ﬁeld magnetization, numerical modelling, ﬁnite element method (FEM) modelling

1. Introduction

However, there are several factors that limit the commercial
applications of bulk (RE)BCO materials.
Based on the critical state model presented by Bean
[9, 10], the peak trapped magnetic ﬁeld at the centre of discshaped bulk superconductor, Btrap, is given in its simplest
form byLarge, single-grain (RE)BCO (where RE=rare earth element or Yttrium) bulk superconductors have signiﬁcantpotential to trap large magnetic ﬁelds over 17 T at temperatures below 30 K [1, 2] and up to 3 T at the technologicallyimportant temperature of 77 K [3]. Such materials fabricatedinto discs and other shapes are potential candidates to replacepermanent magnets in applications such as rotating machines[4], magnetic bearings [5–7] and magnetic separation [8].
0953-2048/15/125002+14$33.00

Btrap = km 0 Jc a,(1 )where k is a geometric constant to account for the sample’sﬁnite thickness, μ0 is the permeability of free space, Jc is the1© 2015 IOP Publishing Ltd Printed in the UK

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Figure 1. Schematic illustration of the single-grain SmBCO samples fabricated by TSMG and the location of (a) the 0°–0° and (b) the 45°–45° bridge-shaped seeds cut subsequently from the parent single grain. (c) An illustration of a bridge-shaped seed.

critical current density and a is the radius of bulk sample [11].
Therefore, sample size is one of the key factors to improve thetrapped ﬁeld performance of a single-grain sample. Anotherpractical limitation to the fabrication of (RE)BCO samples istheir relatively low growth rate; a single-grain bulk sample ofdiameter around 30 mm takes around one week to complete
the growth process. Hence, developing fabrication techniquesthat reduce the processing time is fundamental to delivering
practical, large-scale growth processing.
The multi-seeding process has the potential to enlarge thesample size of (RE)BCO single grains with improved fabrication speed and also provides an opportunity to investigate
grain boundaries in bulk samples, which are quite different tothose that are formed in thin ﬁlms and tapes due to the presence of RE-211 components in the bulk material fabricatedby top-seeded melt-growth (TSMG). Multi-seeding also
allows the development of more complex bulk superconductor shapes, such as bars/rods, rings and cylinders.
Due to these merits, multi-seeding using two or more
separate seeds has been investigated over many years [12–18]. However, among the reported studies, poorly-connectedgrain boundaries form between the two seeds, characterized
by a build-up of impurity phases [12–15]. Compared with thetrapped ﬁeld typically generated by single grains, the trapped
ﬁeld in the reported multi-seeded samples have generally
been relatively low [16]. In our previous studies on multiseeding [19–21], a signiﬁcant improvement was made in thealignment of the seeds in such samples using a novel bridgeseeding technique, which minimizes any misinterpretation of
the properties of the multi-seeded sample that may be associated with seed misalignment, rather than with the grain
growth itself.
In this paper, the trapped ﬁeld performance of multiseeded samples with 45°–45° and 0°–0° aligned bridge seeds
magnetized by pulsed ﬁeld magnetization (PFM) is investigated. The effects of the particular inhomogeneous Jc distribution on the better-performing 45°–45° multi-seed sample
on PFM are modelled numerically using a three-dimensional(3D) ﬁnite-element model, developed to qualitatively reproduce and interpret the experimental results. The results agree

qualitatively with the observed experimental results, in thatthe particular inhomogeneous Jc distribution of the multi-seedsample acts to inﬂuence the magnetic ﬂux dynamics during
PFM and distort the trapped ﬁeld proﬁle, which is determinedby the length, L, and direction of the bridge seed on the bulk
surface. This modelling framework will allow further investigation of the inﬂuence of different lengths and directions ofbridge seeds for such multi-seed samples, to assist in the
optimization of the particular setup and characteristics of the
PFM process, as well as provide valuable input for the
improvement of multi-seed sample processing techniques.

2. Bridge-seeded, multi-seed bulk superconductor
sample details
2.1. Fabrication of the 0°–0° and 45°–45° bridge-seeds

Due to its higher melting temperature, single-grain Sm–Ba–
Cu–O (SmBCO), which forms a suitable seed for the melt
processing of YBCO, was fabricated by TSMG using ageneric seed [22, 23], from a mixed precursor powder ofcomposition 70 wt% Sm-123+30 wt% Sm-211+0.1 wt%
Pt. The as-grown single grains were cut into slices of length
10 mm parallel to the a direction of the crystallographic lattice, as shown in ﬁgure 1(a), and parallel to a growth facet
line on the top surface of the grain, as shown in ﬁgure 1(b).
These slices were subsequently machined into bridge-shaped
seeds, as shown in ﬁgure 1(c). The so-called 45°–45° and 0°–0° bridge seeds, labelled according to their relative orientationin the parent grain, were then used to multi-seed the bulk
YBCO samples based on controlled alignment and relativeorientation of the two legs of the seed [19].
2.2. Melt-processing of multi-seed bulk samples using 45°–45°
and 0°–0° bridges

Precursor powders of YBa2Cu3O7 (Y-123), Y2BaCuO5 (Y211) and Pt (99% purity) with a starting composition of 70
wt% Y-123+30 wt% Y-211+0.1 wt% Pt were mixed
thoroughly using a motorized mortar and pestle [21]. The
2

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Figure 2. Photographs of the bridge-seeded, multi-seed samples under analysis: (a) 45°–45° orientation, and (b) 0°–0° orientation. The
locations of the seeds (and the growth sector boundaries (GSBs) in the case of the 45°–45° sample) are shown by the solid white lines.

mixed powder was pressed uniaxially into pellets of diameter
32 mm and thickness 20 mm. Bridge-shaped seeds with a leg
separation of 10 mm were placed on the top surface of eachpellet. The TSMG technique was used to fabricate the samples, which involves heating each pellet to 1045 °C, holding
for 1 h, cooling at 100 °C h−1 to 1005 °C, and then coolingmore slowly at 0.4 °C h−1 to 970 °C. Finally, the samples
were furnace-cooled down to room temperature at
200 °C h−1. The multi-seed samples, after machining thebottom surface and polishing, were approximately 25 mm indiameter and 9 mm in height.
Photographs of the 45°–45° and 0°–0° bridge-seeded
samples are shown in ﬁgure 2, and in the case of ﬁgure 2(b), it
is clear that the seeds in the 0°–0° conﬁguration have growndifferently, resulting in different sizes after polishing. In thefollowing sections, the performance of the samples is analyzed
after ﬁeld cooling (FC) magnetization from around 40 K and
PFM at operating temperatures of around 40 K and 65 K.

Figure 3. Field cooling (FC) magnetization results for the 45°–45°

and 0°–0° bridge-seeded samples, measured at the centre of the top
surface with external applied ﬁeld around 7 T.

has resulted in a reduced trapped ﬁeld. This is one of the
difﬁculties in growing such multi-seed samples.

3. Experimental results
3.1. FC magnetization

3.2. Pulsed field magnetization

The FC magnetization technique gives the best indication of
the trapped ﬁeld capability of a bulk superconductor sample.
The temperature dependence of the trapped ﬁeld at the bulk
centre is shown in ﬁgure 3. FC magnetization was performed
with an external ﬁeld of 7 T at around 40 K. The bulk washeated at a rate of 0.5 K min−1 up to 100 K and the temperature dependence of the trapped ﬁeld, Bz(T), was measured. At around 40 K, the trapped ﬁeld at the centre of the
top surface of the 45°–45° and 0°–0° oriented samples is
3.15 T and 1.93 T, respectively, and 1.01 T (45°–45°) and
0.67 T (0°–0°) at 65 K. 2D trapped ﬁeld distributions at 77 K
obtained by FC magnetization are also shown for each sample
in ﬁgure 4, as measured approximately 1 mm above the top
surface using a scanning system consisting of a linear array ofHall probes. It is apparent that the variation in the growth of
the seeds in the 0°–0° oriented sample, in this particular case,An overview of the PFM experimental setup is described in[24]. The bulk samples were mounted tightly on a sample
holder fabricated from 316 stainless steel of inner diameter
slightly larger than the diameter of the samples and outer
diameter 56 mm to match the dimensions of the available cold
stage of the pulse system. Stycast 2850 FT, Catalyst 23 LV
was used to mount the samples in the holder, with the epoxy
set under vacuum to ensure void-free embedment. The samples were mounted on the cold stage of a Gifford–McMahon,closed cycle helium refrigerator, and a copper magnetizing
solenoid pulse coil, cooled using liquid nitrogen, was placedoutside the vacuum chamber. The direction of external
applied ﬁeld is parallel to the c-axis of the bulk samples. The
magnetizing coil can provide pulsed external ﬁelds up to3Supercond. Sci. Technol. 28 (2015) 125002

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Figure 4. Trapped ﬁeld distributions for each sample, obtained by ﬁeld cooling (FC) magnetization at 77 K in an external magnetic ﬁeld of
1.5 T and measured approximately 1 mm above the top surface using a scanning system consisting of a linear array of Hall probes: 45°–45°
orientation (left), 0°–0° orientation (right). The samples are aligned in the same position as shown in ﬁgure 2.

Figure 6. Total trapped ﬂux, ΦT, for 45°–45° and 0°–0° samples at
operating temperatures of 40 K and 65 K, measured at 1 mm above
the bulk surface (z=1 mm). ΦT is calculated from the 2D trapped
ﬁeld proﬁles presented in section 3.2.2.

Figure 5. Trapped ﬁelds for the 45°–45° and 0°–0° samples after
PFM at operating temperatures of 40 K and 65 K, measured at thecentre of the top bulk surface (z=1 mm).

Bapp=6.4 T with a rise time of tr=12 ms and duration of
approximately td=120 ms [24].
After PFM of the sample, the two-dimensional trapped
ﬁeld distributions were measured inside the vacuum chamberusing an x–y stage controller and an axial-type Hall sensor
positioned above the top surface of the samples. The trapped
ﬁeld close to the centre of the sample were measured dynamically during the application of each pulsed ﬁeld using thesame Hall sensor (located on the top surface of the samples).

both samples. When the external ﬁeld exceeds the full
activation ﬁeld (deﬁned as the minimum ﬁeld required to fully
magnetize the bulk sample [24]), and with increasing
magnitude of the external applied ﬁeld, the maximum
trapped ﬁeld decreases, due to an increasing temperaturerise from the more rapid movement of ﬂux lines within thesample [24].
Compared with the FC magnetization results (seeﬁgures 3 and 4), which indicate a signiﬁcantly higher trapped
ﬁeld capability for the 45°–45° multi-seed sample, themaximum, central trapped ﬁeld for PFM appears to be lower
than that for the 0°–0° bulk sample and the optimal activationﬁeld is slightly higher at both operating temperatures (40 K
and 65 K).

3.2.1. Trapped field performance using PFM. Figure 5 shows

the trapped ﬁeld for both samples magnetized by PFM at
operating temperatures around 40 K and 65 K, measured at
the centre of the top bulk surface (z=0 mm). For the lower
operating temperature, the trapped ﬁeld is almost doubled in4Supercond. Sci. Technol. 28 (2015) 125002

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Figure 7. 2D trapped ﬁeld proﬁles measured on the top surface (z=1 mm) for the 45°–45° multi-seed sample at 65 K. The central panel

shows the corresponding central trapped ﬁeld, as shown in ﬁgure 5. The samples are arranged in the same position as shown in ﬁgure 2.

Figure 6 presents the total trapped ﬂux, ΦT, for both
samples at 40 and 65 K, measured 1 mm above the bulk
surface, as a function of the applied pulsed ﬁeld, Bapp. ΦT is
calculated from the 2D trapped ﬁeld proﬁles presented in thenext section. Although both samples have an almost similar
total ﬂux trapping capability when magnetized by PFM, theﬂux dynamics and trapped ﬁeld proﬁles for the two samples
are very different, and this behaviour is examined in detail in
the following section.

section 4. When the external applied ﬁeld is lower than theactivation ﬁeld, the trapped ﬁeld is localized at particularlocations around the edge of the bulk sample. However, when
fully magnetized, two well-deﬁned peaks appear in thetrapped ﬁeld proﬁle of the sample. For the lower temperature(40 K), the magnitude of the trapped ﬁeld proﬁle increases,
but the dynamics of the ﬂux penetration show a similar trend
to those at 65 K.
The 2D trapped ﬁeld proﬁles for the 0°–0° multi-seedsample at 65 K and 40 K are shown in ﬁgures 9 and 10,
respectively. The trapped ﬁeld proﬁles here differ from the
45°–45° multi-seed sample due to the different orientation of
the seeds, and hence the growth boundaries (as shown inﬁgure 1). There are clearly deﬁned symmetric twin peaks inthe trapped ﬁeld proﬁle for the 45°–45° sample; however, the
0°–0° sample shows an asymmetric trapped ﬁeld with peaksof different magnitude. Since a well-deﬁned, symmetrictrapped ﬁeld proﬁle is desirable for practical applications, the3.2.2. 2D PFM trapped field profiles. Figures 7 and 8 show

the 2D trapped ﬁeld proﬁles for the 45°–45° multi-seedsample at 65 K and 40 K, respectively. The trapped ﬁeld
distribution is distorted due to the inhomogeneous Jc
distribution generated during the growth process, but this issigniﬁcantly different in comparison with standard YBCO
samples [24]. This will be analyzed numerically in detail in
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Figure 8. 2D trapped ﬁeld proﬁles measured on the top surface (z=1 mm) for the 45°–45° multi-seed sample at 40 K. The central

panel shows the corresponding central trapped ﬁeld, as shown in ﬁgure 5. The samples are arranged in the same position as shown inﬁgure 2.

45°–45° sample exhibits a better trapped ﬁeld proﬁle withmore potential for practical/commercial applications.

Bapp<2 T at 65 K), resulting in only partial magnetization,
the ﬂux is trapped in the regions other than the seed positions
with a relatively small Jc. However, for a larger external
pulsed ﬁeld (close to or higher than the full activation ﬁeld
(Bapp>4–5 T at 40 K and Bapp>3 T at 65 K), the ﬂux istrapped in regions of higher Jc [24]. Therefore, based on
ﬁgure 12, when Bapp=3.01 T at 40 K, the trapped ﬁeld has apattern as a ‘high-low-high-low-high’ characteristic, which
implies the Jc at around ±5 mm across the seed, where thebridge seed is located, is relatively high. When the appliedﬁeld increases, ﬂux is trapped around the seed, which also
implies that Jc around seeds is relatively high, compared to Jc
over the bulk surface. In both ﬁgures 12 and 13, x=0 mm
corresponds to the same point: the centre of the top surface ofthe bulk samples.
Figure 13 shows the cross-section of the trapped ﬁeld
proﬁle along the B-line (see ﬁgure 11) for various appliedmagnetic ﬁelds, Bapp. At Bapp=3.01 T at 40 K and 1.98 T at

3.2.3. Dynamics of magnetic flux penetration during PFM (45°–45° multi-seed sample). In this section, we analyze themagnetic ﬂux penetration into the 45°–45° multi-seed sample
at 65 and 40 K, in order to better understand the ﬂux
dynamics and provide guidance for the numerical simulations
carried out in section 4. From the trapped ﬁeld proﬁlespresented in ﬁgures 7 and 8, the ﬂux penetrates along the Aand B-lines shown in ﬁgure 11: the A-line is along the growth
sector boundaries (GSBs) through the two seed positions andthe B-line passes across the GSB between the two seeds.
Figure 12 shows the cross-section of the trapped ﬁeld
proﬁle along the A-line (see ﬁgure 11) for various appliedmagnetic ﬁelds, Bapp, at operating temperatures of around
65 K (top) and 40 K (bottom). When the external magnetic
ﬁeld is relatively small (e.g., Bapp<3 T at 40 K and6

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Figure 9. 2D trapped ﬁeld proﬁles measured on the top surface (z=1 mm) for the 0°–0° multi-seed sample at 65 K. The central panel shows

the corresponding central trapped ﬁeld, as shown in ﬁgure 5. The samples are arranged in the same position as shown in ﬁgure 2.

65 K, there is a valley in the trapped ﬁeld proﬁle in between
the seed, which implies that Jc across the facet line between
the seeds is relatively large compared to other regions along
the B-line. When the applied ﬁeld is over the activation ﬁeld,
it exhibits a well-deﬁned peak similar to a traditional trapped
ﬁeld proﬁle.
Therefore, Jc across the two seeds (along the A-line) ishighest around the seeds, and Jc in between the seeds (along
the B-line), along the facet line (GSB) between the two seeds,
also has high Jc, but is slightly lower. These analyzes provide
the basis for the assumptions made in the numericalsimulation in the next section.

two seeds in both 45°–45° and 0°–0° oriented samples, which
results in the successful fabrication of multi-seed samples
with trapped ﬁelds that are comparable to those obtainedusing single seeds. However, as shown in ﬁgure 3, the grainboundaries created by using 45°–45° seeds have a less signiﬁcant effect on the overall trapped ﬁeld when magnetizedby FC. An impurity-free boundary can be engineered between
the two seed legs of the bridge when 45°–45° bridge seeds areused to enlarge YBCO single grains [21]. Since in the
numerical simulation a more ideal case needs to be considered
and we need to deduce the inﬂuence of boundary effects inthe model, the 45°–45° multi-seed sample at 65 K is used as
an example to carry out the numerical analysis in this section.

4. Numerical simulation

4.1. Modelling framework

Here, the trapped ﬁeld performance of a 45°–45° bridgeseeded multi-seed sample is investigated qualitatively using a

The alignment of the seeds in the multi-seeding process iscritical and the bridge seeds provide the best alignment of the7Supercond. Sci. Technol. 28 (2015) 125002

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Figure 10. 2D trapped ﬁeld proﬁles measured on the top surface (z=1 mm) for the 0°–0° multi-seed sample at 40 K. The central
panel shows the corresponding central trapped ﬁeld, as shown in ﬁgure 5. The samples are arranged in the same position as shown inﬁgure 2.

3D ﬁnite-element model. This model is based on the H-formulation [25–31], which has been employed previously by
the authors to investigate the trapped ﬁeld performance andcharacteristics of bulk superconductors [24, 32–34], and is
implemented using COMSOL Multiphysics 4.3a [35].
In the model, the governing equations are based on
Maxwell’s equations (Faraday’s and Ampere’s laws), shownas (2) and (3), respectively:¶B¶H= -m 0,¶t¶t ´ H = J.

´E=-

3D model is based on the model framework presented in [24],but the assumptions regarding Jc must be changed appropriately to account for the particular Jc distribution of themulti-seed samples, which differs from that presented in [24]for a standard YBCO sample. In order to simplify thesituation, the ﬁeld dependence of Jc is not considered here.
Based on the analysis in section 3.2.3, Jc varies aroundthe ab-plane of the multi-seed sample, where Jc is slightly
higher along the facet lines (assumed as 1.2×Jc0, whereJc0=3.2×108 A m−2 at 65 K) and the lowest Jc is aroundthe edge of the sample (assumed as 0.4×Jc0), with Jc
varying as a cosine function, as shown as in ﬁgure 14. Jcalong the c-axis (i.e., along the thickness of the sample) is
considered to have the same Jc distribution. This varying Jc
distribution around the ab-plane can be described using a setof mathematical functions and a polar coordinate system as
described below.

(2 )
(3 )

The electrical properties of the superconductor are modelledusing an E–J power law relation [36, 37], E α J n, wheren=21. An external pulsed magnetic ﬁeld is applied to thebulk along the c-axis of sample, perpendicular to the top
surface, by setting appropriate boundary conditions [24]. This
8

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electromagnetic model using equations (8) and (9):r⋅CdT
=  ⋅ (k T ) + Q .
dt

(7 )

The temperature dependence of Jc0 (T) is given by:
1.5⎡⎛ T ⎞2 ⎤Jc0 (T ) = a ⎢ 1 - ⎜ ⎟ ⎥ ,⎝ Tc ⎠ ⎥⎦⎢⎣(8 )where α=9.1×108 A m−2 is the critical current density
extrapolated to T=0 K. The heat source, Q, in the thermal
model is calculated from the product of the electric ﬁeld andcurrent density throughout the sample, deﬁned as
Q = E ⋅ J,

where E =Ex 2 + Ey 2 + Ez 2 and J =(9 )Jx 2 + Jy 2 + Jz 2 .

4.2. Comparison of experimental and numerical simulation
results
Figure 11. Schematic illustration of ﬂux penetration analysis for the
45°–45° multi-seed sample: the A-line is along the GSBs through thetwo seed positions and the B-line passes across the GSB between thetwo seeds.

The trapped ﬁeld proﬁles as simulated numerically are compared with the experimental results for external applied ﬁelds
of 1, 2, 3 and 4 T, as shown in ﬁgures 15–18. These ﬁgures
show that the simulation results agree qualitatively well withthe experimental data. When the external ﬁeld is muchsmaller than the activation ﬁeld, the ﬁeld required to fully
magnetize the bulk sample, the ﬂux only penetrates and stays
within regions with relatively lower Jc (see ﬁgures 15 and 16).
However, when the applied pulse is above the activation ﬁeld
(approximately 3 T in this case), there are two peaks in thetrapped ﬁeld proﬁle (ﬁgure 17), and when Bapp is much larger
than the activation ﬁeld, the trapped ﬁeld decreases overall,but still presents two peaks (see ﬁgure 18). The shape of thetrapped ﬁeld distribution from PFM is determined by thelength of bridge seed and the boundary generated during the
growth process. These results also agree with the experimental data presented previously in [19–21].

In ﬁgure 14, region 1 represents the relatively higher Jc
around the seeds and facet lines/GSBs of the multi-seedsample. Region 4 exhibits the lowest Jc, and regions 2 and 3
represent a gradually decreasing Jc between the GSB towards
the growth sector region (GSR). The mathematical equations
describing Jc for each region are as follows, where the angle θis deﬁned anti-clockwise from the horizontal dashed line
dividing region 4 and regions 1, 2 and 3:
Region 1 (45  q  135):
Jc = Jc0 (1+0.2 ´ cos (4q )) .

(4 )Regions 2 (135  q  180) and 3 (0  q  45):Jc = 0.4Jc0 (1 - cos (2q )) + 0.4Jc0.

(5 )4.3. Influence of bridge seed length

In this section, the inﬂuence of the length of the bridge seed isinvestigated using the same numerical model. The length of
the bridge seed, L, is varied between 2 and 12 mm and it isobserved in ﬁgure 19(a) that with increasing distance between
the two seeds, the maximum trapped ﬁeld of any peakdecreases, as does the trapped ﬁeld at the centre of the bulk.
Another important measure of the performance of bulk
superconductor samples is the total trapped ﬂux, ΦT, in thesample and ﬁgure 19(b) shows ΦT increases as the length of
the bridge seed increases, although the peak trapped ﬁeld
decreases. Finally, ﬁgure 20 shows the trapped ﬁeld distribution across the top surface of the bulk for lengths of 2, 4,
8 and 12 mm. When the bridge length is short, e.g., 2 mm,there is only one peak observed in the trapped ﬁeld distribution. However, as the bridge length is increased, a twopeak pattern begins to emerge and is clearly observed for the
longest bridge lengths. It should be noted that the slightasymmetry in the trapped ﬁeld distribution is an artefact of theﬁne, but ﬁnite, mesh discretization used. These simulation

Region 4 (0° θ −180°):
Jc = 0.4Jc0.

(6 )Equation (4) describes the variation of Jc in region 1, with amaximum 1.2Jc0 close to the GSBs and 0.8Jc0 around the
GSRs. Equation (5) describes the Jc distribution in regions 2
and 3, varying from 0.8Jc0 to 0.4Jc0, and region 4 is governedby equation (6).
Since the temperature of bulk superconductors can change
signiﬁcantly during PFM [9], the electromagnetic model iscoupled with a thermal model in this simulation, which isextended from our previous models [24, 33]. A thermallyisolated model of a bulk superconductor is used to simulate thebulk sample being submersed in sub-cooled liquid nitrogen at
65 K, with the speciﬁc heat and thermal conductivity along
the ab- and c-planes assumed as C=164.25 J/(kg K),
κab=15.49 W/(m K), and κc=3.63 W/(m K), respectively.
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Figure 12. Flux penetration proﬁles for the 45°–45° multi-seed sample across the seeds (from the left and right, along the A-line, as shown inﬁgure 11) at operating temperatures of around (a) 65 K and (b) 40 K.

The samples were ﬁrstly magnetized using the FC magnetization technique, which gives the best indication of thetrapped ﬁeld capability of a bulk superconductor sample.
Although the FC results indicated a signiﬁcantly higher
trapped ﬁeld capability for the 45°–45° multi-seed sample, themaximum, central trapped ﬁeld for PFM was lower than thatfor the 0°–0° bulk sample and the total ﬂux trapping capability when magnetized by PFM was almost the same at bothtemperatures. However, the ﬂux dynamics during the PFM
process for the two samples are very different, which were
investigated using 2D trapped ﬁeld proﬁles measured acrossthe top surface of each sample.
By analyzing the ﬂux penetration into the better-performing 45°–45° multi-seed sample, an estimated Jc distribution over the ab-plane was determined, and this was input into
a 3D ﬁnite-element model, which was then used to qualitatively reproduce the experimental results to good effect. This
numerical model was then used to investigate the inﬂuence ofthe length of the bridge seed on the trapped ﬁeld distribution

results agree qualitatively well with the experimental resultspresented in [19] and this kind of 3D modelling framework
can provide useful guidance for the processing of multi-seedsamples to optimize their performance for a particularapplication.

5. Conclusion
The multi-seeding process has the potential to enlarge thesample size of bulk (RE)BCO superconductors with improved
fabrication speed in order to deliver large, single grains forpractical applications and the so-called bridge-seeding produces the best alignment of two seeds when melt-processing
such samples. In this paper, two multi-seed samples—one
with a 45°–45° and another with a 0°–0° bridge seed—weremagnetized by PFM at temperatures of 65 and 40 K and thetrapped ﬁeld performance and magnetic ﬂux dynamics werestudied.
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Supercond. Sci. Technol. 28 (2015) 125002

M D Ainslie et al

Figure 13. Flux penetration proﬁles for the 45°–45° multi-seed sample in between the seeds (from the top and bottom, along the B-line, as
shown in ﬁgure 11) at operating temperatures of around (a) 65 K and (b) 40 K.

and total trapped ﬂux. For increasing bridge length, the trapped
ﬁeld distribution shows a clear two-peak pattern and there is areduction in the peak and central magnetic ﬂux densities.
However, the total trapped ﬂux is increased with increasing
bridge length. This modelling framework will provide usefulguidance for the processing of such multi-seed samples in the
future in order to optimize their performance.

Acknowledgments
Mark Ainslie would like to acknowledge the support of a
Royal Academy of Engineering Research Fellowship. Jin Zou
would like to acknowledge the support of Churchill College,
Cambridge, the China Scholarship Council and the Cambridge Commonwealth, European and International Trust.
Hiroyuki Fujishiro would like to acknowledge support in part

Figure 14. Schematic illustration of the mathematical function andpolar coordinate system (left) and the Jc distribution across the abplane (right). The Jc distribution includes the locations of the seeds
and the GSBs, shown by the solid white lines.

11Supercond. Sci. Technol. 28 (2015) 125002

M D Ainslie et al

Figure 15. Comparison of (a) experimental and (b) numerical simulation results for the PFM trapped ﬁeld proﬁle at 1 mm above the 45°–45°

multi-seed sample when Bapp=1 T.

Figure 16. Comparison of (a) experimental and (b) numerical simulation results for the PFM trapped ﬁeld proﬁle at 1 mm above the 45°–45°

multi-seed sample when Bapp=2 T.

Figure 17. Comparison of (a) experimental and (b) numerical simulation results for the PFM trapped ﬁeld proﬁle at 1 mm above the 45°–45°

multi-seed sample when Bapp=3 T.

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Supercond. Sci. Technol. 28 (2015) 125002

M D Ainslie et al

Figure 18. Comparison of (a) experimental and (b) numerical simulation results for the PFM trapped ﬁeld proﬁle at 1 mm above the 45°–45°

multi-seed sample when Bapp=4 T.

Figure 20. Numerical simulation results showing the trapped ﬁeld

distribution across the top surface of each bulk sample for bridge
seed lengths of 2, 4, 8 and 12 mm. The centre of the bulk
corresponds to x = 12.5 mm.

by a Grant-in-Aid for Scientiﬁc Research from the Ministry of
Education, Culture, Sports, Science and Technology, Japan.
This research was also supported in part by a Royal SocietyInternational Exchanges Scheme grant, IE131084.

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