INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 15 (2002) 748–753
PII: S0953-2048(02)34137-X
Comparison of pulsed magnetization
processes for HTS bulk parts
M Sander, U Sutter, M Adam and M Kläser
Forschungszentrum Karlsruhe GmbH, ITP, PO Box 3640, D-76021 Karlsruhe, Germany
E-mail: michael.sander@itp.fzk.de
Received 16 July 2001
Published 18 April 2002
Online at stacks.iop.org/SUST/15/748
Abstract
With respect to the potential application as cryo-permanent magnets,
melt-textured YBaCuO bulk parts were used to investigate various pulsed
magnetization processes employing pulsed copper coils. Results for different
multi-pulse processes including different peak fields, pulse durations,
temperatures and geometries are compared. The strong current-carrying
capabilities of HTS material, even for currents above the critical
current Jc, result in strong shielding effects, in particular for short pulse
durations. It turns out that the inhomogeneities present in all real materials
play an important role for the initial magnetic flux penetration. To fully
magnetize the bulk samples, the non-stationary conditions and geometrical
effects require peak fields, which substantially exceed twice the saturation
magnetization measured at the sample surface. Transient magnetizations
as well as shapes and absolute values of trapped flux profiles are reported.
1. Introduction
High-temperature superconductor (HTS) have shown excellent pinning properties especially at lower temperatures and
have therefore a particularly high potential as cryo-permanent
magnets: by field-cooling in 18 T, it could be shown that
magnetic fields beyond 14 T can be trapped in melt-textured
YBCO bulk samples at temperatures of about 20 K [1, 2].
However, for many applications such as magnetic bearings
or electrical machines, the HTS bulk components have to be
magnetized in situ i.e. the use of large superconducting coils is
prohibitive. For such cases, pulsed magnetization employing
copper coils is a prerequisite [3–14]. As regards high trapped
fields practical constraints exist primarily concerning the
maximum achievable pulsed field. Thus, optimizing the
cryo-permanent magnet and the magnetization process for
a specific application requires an improved understanding
of the dynamics of such magnetization processes and of the
influence of the corresponding process parameters. Especially
the effect of the strong shielding properties goes well beyond
a simple Bean’s model [15, 16].
2. Experimental details
The experimental set-up used for the pulsed magnetization
and the flux mapping was essentially already described earlier
0953-2048/02/050748+06$30.00 © 2002 IOP Publishing Ltd
[17]. Briefly, the YBCO samples are magnetized by using a
pulsed Cu coil, which is immersed in LN2 and which together
with a capacitor forms a resonant circuit. A thyristor allows
use of the first half sine-wave only for magnetization, which
has a duration t of about 30 ms or 3 ms, depending on the
Cu coil used [11, 12]. Corresponding peak fields Hp were
up to 3.3 T. Four YBCO cylinders with outer diameters of
about 30–32 mm and heights between 8 and 16 mm were
used. In section 6 also earlier results taken for YBCO
rings with inner/outer diameters of 11/17.5 mm and 3 mm
thickness are included [13]. YBCO samples were either
immersed in LN2, or, by employing a cryocooler, kept at
temperatures between 50 K and 80 K. Thereafter, the remanent
magnetization is recorded with a Hall probe, which is scanned
above the sample in a distance between 1 mm and 6 mm,
depending on the cooling procedure and sample. Transient
magnetizations were taken by recording the transient signal of
the Hall probe with a storage oscilloscope. Maximum values
of the measured surface magnetic fields µ0 H S at 77 K for
the ‘fully magnetized’ cylinder samples were in the range of
620 mT to 406 mT. Estimated saturation fields for the ring
samples were between 80 mT and 40 mT [13].
To allow for a comparison of rather different
measurements, all magnetic fields and magnetization data are
given in relative values H/H S and M/µ0 H S , respectively.
Since especially at lower temperatures samples could not
Printed in the UK
748
Comparison of pulsed magnetization processes for HTS bulk parts
Magnetization M(t) / µ0Hs
Magnetic Field B(t)/µ0Hs
1.2
16mm
4
12mm
8mm
3
4mm
2
0mm
Radial Distance
1
P2: 3.1ms, 3.7H
0.8
s
77K
P1: 3.1ms, 3.9H
s
0.6
P1: 3.1ms, 5.3H
s
0.4
s
3.9H , 77K
0
-1
10
0
1
2
1
3.1 ms
32 ms
s
DC: 5.6 H
-1
77K
-2
s
-µ0H(t) / H
-3
0
1
2
3
1
10
2
10
3
10
4
10
Figure 2. Relaxation of magnetization measured at the centre of the
sample after subsequently applying two 3.1 ms pulses of 3.9H S (P1)
and 3.7H S (P2) at 77 K; for comparison a single pulse P1 with a
peak field of 5.3H S is also shown.
(a)
0
0
10
Time after Pulse [ ms ]
3
Time [ ms ]
Magnetization M(t) / µ0Hs
1.0
4
Applied Magnetic Field H(t) / H
5
s
(b)
Figure 1. Flux penetration into a sample during a single 3.1 ms
pulse with peak field of about 3.9H S at 77 K, measured for different
radial distances (a); transient magnetization measured at the centre
of the sample and obtained for pulse durations of 32 ms and 3.1 ms
and for different peak fields; for comparison the profile for a
quasi-stationary process is also shown (b).
be fully magnetized by the applied pulses, the absolute
figures for saturation fields µ0 H S had to be extrapolated
from the trapped flux profiles for saturated samples at higher
temperatures and/or at shorter measurement distances. In
addition, degradations of the samples during the magnetization
tests present another source of error. Thus a realistic estimate
for error bars of absolute values is ±10% for the cylinder
samples and perhaps ±20% for the ring samples. Of course,
the error bars for relative comparisons of magnetizations are
much lower.
3. Transient magnetizations
Shielding effects can be directly observed in measurements
of transient magnetizations. Figure 1(a) shows how the flux
penetrates from the edge of a cylinder sample to the centre
during a 3.1 ms pulse with a peak field Hp of about 3.9H S at
77 K. Each curve for the local magnetic field represents values
averaged over different angular positions. In accordance with
[4, 10] the field doesn’t reach the centre of the sample until the
pulse has begun to decay again. The local magnetic fields at
the end of the pulse already reflect the radial dependence of the
trapped flux profiles. To compare the transient responses of a
sample to pulses of different peak fields Hp and different pulse
durations t, local magnetic fields B(t) were recorded above
the centre of the sample only. In figure 1(b) the corresponding
transient magnetizations M(t) = B(t) − µ0H(t) (neglecting
any geometrical effects) are plotted versus the time-dependent
applied magnetic fields H(t). In this presentation the pulse
process starts at the origin, reaches different Hp on the right side
and ends with H(t) returning to zero. A curve obtained by using
a superconducting magnet is presented as well: in accordance
with Bean’s model the sample can only be magnetized up
to about −H S in a quasi-stationary process. In dynamic
processes, however, the relaxation of the current density due
to the non-vanishing resistivity cannot prevent the transient
current densities to clearly exceed Jc: the resulting transient
magnetizations go well beyond −2H S , and, as expected, by
increasing Hp, they reach higher values for the shorter t. The
magnetization at the end of the pulse shows a flat maximum
for a certain range of Hp, which is about 0.5H S –1H S lower for
the longer pulses. For high Hp the effect of the increased flux
penetration to the centre of the sample is overcompensated
by the related resistive losses, which lead to stronger local
temperature rises [2, 7]. Due to this heating effect, a higher Hp
for shorter pulses cannot compensate the stronger shielding
during the rise time. The overall shape of the transient
magnetization curves distinguishes somewhat from the curves
shown earlier [7], also because the shape of the pulses is
somewhat different: here a half sine-wave pulse form is used,
whereas in similar experiments mostly pulses are used, which
show an aperiodic decay with a duration much longer than the
rise time [2, 3, 7].
For both t values and for Hp near the corresponding
magnetization maximum, the finally measured trapped flux is
about 50–70% of the magnetization obtained at the end of the
pulse. The latter can be more than 50% higher for the longer
t, if the same Hp is applied. Due to a stronger relaxation,
however, this substantial difference is obviously reduced in
the finally trapped flux. Figure 2 shows some examples of
749
the fast relaxation processes occurring immediately after an
applied 3 ms pulse P1. Roughly two phases can be identified,
lasting from a few milliseconds and up to a few seconds. The
major primary decrease of non-persistent currents is probably
related to local effects and may be less pronounced for pulse
forms with an aperiodic decay. The second phase may be
related to thermal relaxations over the sample. In the case of
a very high Hp the temperature rise during the pulse leads
to a rather low trapped flux. One also sees that the first
relaxation is reduced, if a second pulse P2 is applied to an
already partially magnetized sample. An increase in the final
magnetization of about 10% is achieved, which in this case is
only about 5% lower than the maximum trapped flux for single
30 ms pulses.
Magnetization M / µ0Hs
M Sander et al
3.3ms, 70K
0.8
750
s
0.6
MP 2.6H
s
0.4
MP 1.3H
0.2
s
0.0
-15
-10
-5
0
5
10
15
X-Axis [ mm ]
4. Role of inhomogeneities
(a)
15
0.30
10
0.27
0.23
Y Axis [ mm ]
Remanent magnetic flux profiles at LN2 temperatures resulting
from pulsed magnetization were already successfully used
as a sufficiently fast and still simple non-destructive quality
control for large-grain HTS samples [11]. Compared with
the use of standardized permanent magnets, the stronger
magnetic fields of copper coils offer a substantially increased
sensitivity to inhomogeneities of the material. However, with
regard to the potential use of HTS bulk materials as cryopermanent magnets, it is of crucial importance that currently
available materials with limited homogeneity can be pulsemagnetized with sufficient homogeneity. For ring structures,
which drastically reduce the complexity of flux penetrations
and percolation paths due to the simpler geometry, this could
be shown [13].
Figure 3(a) gives an example for a cylinder sample at 70 K
and pulse durations t = 3.3 ms. A multi-pulse (MP) process
consisting of nine pulses (P1–P9) with peak fields Hp of only
about 1.3H S is clearly not able to substantially magnetize the
sample. The dip in the middle of the trapped flux profile
results from the shielding properties of the sample. Another
series with a peak field of about 2.6H S leads to an increased
flux penetration to the centre of the sample, but a certain
asymmetry remains. For comparison the corresponding flux
profile for a multi-pulse process with stepwise cooling (MPSC)
is also shown and will be discussed in section 5. Figure 3(b)
shows the corresponding contour plot for the first pulse P1
with 1.3H S . In all cases the flux penetration essentially starts
from the right side, which obviously represents an area of
weaker superconducting (shielding) properties. By repeating
these experiments with the same Hp, but t = 30 ms, the
asymmetry of the contour patterns is reduced and the trapped
flux increased.
Figure 4(a) shows two 30 ms MP processes at 70 K for
another sample. As in the first case, flux penetration starts
from one weaker region, which can be identified from the
contour plot in figure 4(c ). In this case even peak fields of
about 3.3H S are not sufficient to homogeneously magnetize
the sample. The corresponding flux profile for an MPSC
process with 3.3H S (figures 4(a) and (d)) has a nearly perfect
symmetry. Figure 4(b) shows data for the same sample at 77 K
and for the same absolute peak fields of about 1.0 T and 1.9 T,
which due to the higher temperature and the correspondingly
reduced Jc are now in the range of 2.5H S and 4.7H S . Only
the 4.7H S pulses fully magnetize this sample.
MPSC 2.6H
5
0.20
0
0.17
-5
0.13
0.10
-10
0.07
-15
0.03
-15
-10
-5
0
5
10
15
0
X Axis [ mm ]
(b)
Figure 3. Trapped flux profiles for series of nine pulses (shown: P1,
P3, P5, P7, P9) with pulse duration of 3.3 ms and peak fields of
about 1.3H S and 2.6H S at 70 K in comparison with the profile
obtained for an MPSC process (a); contour plot for the trapped flux
profile obtained for the first pulse P1 with peak field of about
1.3H S (b).
Summarizing, even for slower MP processes, some
asymmetry remains except for very high peak fields Hp.
If Hp /H S is low, the shielding prohibits a significant flux
penetration, and already small deviations from a perfectly
homogeneous sample result in distorted flux patterns. On
the other hand for sufficiently high values Hp /H S , the field
can well penetrate to the centre. In both cases the influence
of additional pulses is limited, and thus the largest effects
seem to occur for the intermediate cases: only if the magnetic
field front can reach regions with weaker shielding properties,
additional pulses can significantly contribute to the trapped
flux. This could already be demonstrated for ring structures,
for which local defects provide the gate for flux penetration
into the middle of the ring [13].
5. Multi-pulse processes with stepwise cooling
(MPSC)
MPSC processes were already introduced in [11], and a first
qualitative understanding was presented in [12]. In brief, for
example, at 75 K three pulses are applied, which result in a
Comparison of pulsed magnetization processes for HTS bulk parts
1.0
MPSC 3.3H
0.8
s
Magnetization M / µ0Hs
Magnetization M / µ0Hs
1.0
30ms, 70K
0.6
MP 3.3H
s
0.4
0.2
MP 1.7H
s
0.0
30ms, 77K
0.8
MP 4.7H
0.6
0.4
MP 2.5H
s
0.2
0.0
-15
-10
-5
0
5
10
15
-15
-10
-5
(a)
5
0
-5
-10
-15
-5
0
5
X Axis [ mm ]
10
15
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0
10
15
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0
15
10
Y Axis [ mm ]
10
-10
5
(b)
15
-15
0
X-Axis [ mm ]
X-Axis [ mm ]
Y Axis [ mm ]
s
5
0
-5
-10
-15
-15
-10
-5
0
5
10
15
X Axis [ mm ]
(c)
(d)
Bean-like cone. The magnetized sample is then cooled to 70 K
and additional three pulses are applied. This procedure is then
repeated at 60 K and, if required, at even lower temperatures.
The flux profiles obtained for each pulse P1 and P3 of an MPSC
process are given in figure 5. Three pulses were found to be
the optimum for this case. Additional pulses would give only
marginal increases. As for MP processes, with decreasing
Hp /H S i.e. in this case with decreasing temperature, the effect
of P2 and P3 is somewhat reduced.
Some flux profiles obtained for MPSC processes were
already shown in figures 3(a) and 4(a). The comparison with
figure 4(a) shows that with moderate peak fields remarkable
magnetizations can be obtained for 60 K. A corresponding MP
process at 60 K would require peak fields, which would have to
be a factor of about 1.5 higher. Thus the temperature range, in
which a given peak field can saturate a certain cryo-permanent
magnet, can be extended to lower temperatures and thus higher
magnetizations, if an MPSC process is used.
The magnetization for a single 3.3 ms pulse at 75 K,
which is also shown in figure 5, is about 10% lower than the
corresponding P1 pulse for 30 ms. In figure 6 two MPSC
processes with the same Hp, but for t of 30 ms and 3.3 ms
are compared. Only the flux profiles for pulses P3 are shown.
Magnetization M / µ0Hs(70K)
Figure 4. Trapped flux profiles obtained for series of nine pulses (shown: P1, P3, P5, P7, P9) with pulse duration of 30 ms and peak fields
of about 1.7H S and 3.3H S at 70 K (a) and of 2.5H S and 4.7H S at 77 K (b); for comparison the profile for an MPSC process is also shown in
(a); contour plots for trapped flux profiles obtained at 70 K for the first pulse P1 with a peak field of about 1.7H S (c) and for the third pulse
P3 of an MPSC process (d).
1.0
60K
s
3.3 H (70K)
70K
0.8
0.6
75K
0.4
P3 MPSC 30ms
P1 MPSC 30ms
P1 3.3ms
0.2
0.0
-15
-10
-5
0
5
10
15
X-Axis [ mm ]
Figure 5. Trapped flux profiles for each first and third pulse (P1 and
P3) of an MPSC process with pulse duration of 30 ms and a peak
field of about 3.3H S (70 K); for comparison also a profile for a
single 3.3 ms pulse P1 at 75 K with the same peak field is included.
Again, for higher temperatures about 10% higher magnetizations are found for the longer pulses. The preliminary
751
1.2
1.0
50K
1.0
Magnetization M / M max
Magnetization M / µ0Hs (70K)
M Sander et al
60K
0.8
70K
0.6
75K
s
2.6 H (70K)
0.4
P3 MPSC 30ms
P3 MPSC 3.3ms
0.2
-10
-5
0
5
10
15
C
0.4
0.2
A
0.0
-1.0
X-Axis [ mm ]
0.8
0.6
0.4
MPSC:
MP:
Ring:
30ms
30ms
30ms
3ms
3ms
3ms
0.0
1
2
3
4
0.0
0.5
1.0
Figure 8. Comparison of the shape of trapped flux profiles
for cylinder samples (A: Bean-like cone for a homogeneously
magnetized sample; B: profile with currents only flowing
in the outermost region) and a ring sample C (inner radius
is 0.63R0).
1.0
0.2
-0.5
Outer Radius R / R0
Figure 6. Trapped flux profiles for each third pulse P3 of two
MPSC processes both with peak fields of about 2.6H S (70 K), but
with pulse durations of 30 ms and 3.3 ms.
Magnetization M / µ0Hs
B
0.6
0.0
-15
5
6
7
s
Peak Magnetic Field H p / H
Figure 7. Comparison of remanent magnetizations as a function of
the applied peak field; collected data are for different samples, pulse
durations, temperatures and geometries; for the dashed and dotted
lines see text.
result reported earlier [12], in which a shorter pulse duration
seemed to result in a higher trapped flux, was probably due
to calibration problems for measurement distances. With
decreasing temperature or decreasing Hp /H S the trapped flux
at the centre of the sample is less affected by the pulses and
only the outermost regions experience the field. Differences
between pulse durations are more and more wiped out.
6. Practical issues
Some preliminary data collection is given for our half
sine-wave pulses, which, compared with aperiodic pulse
forms, have a lower thermal load on the magnetizing
coil. In figure 7 the obtained surface magnetization, which
for practical purposes is the relevant figure of merit, is
plotted as a function of Hp: several single- or multi-pulse
processes employing different samples, pulse durations,
temperatures and geometries have been included in the
graph. The maximum magnetization was always taken, even
752
0.8
when the flux profile showed a dip in the middle. The
observed spread in the data may not only be due to the
error bars for the absolute saturation values H S (estimated
±10% for cylinder samples), but also due to sample
specific characteristics: spatially inhomogeneous current–
voltage characteristics result in microscopically or even
macroscopically different percolation paths and, therefore,
significantly influence the shape and peak value of the trapped
flux profiles. Nevertheless, a broad MP band with saturation
fields of around 3.2H S –4.5H S seems to exist for cylinder
samples. For an infinitely long cylinder Bean’s model predicts
values of only about twice the saturation magnetization.
However, for homogeneously magnetized samples with our
finite thicknesses, the surface magnetization measured above
the sample corresponds to only about 50–70% of the maximum
magnetization in the middle of the bulk. This is also
experimentally observed when the trapped field between two
pellets is compared with the surface field of a single pellet [1].
As a guide to the eye, a dotted (dashed) line for 60% pointing to
the corresponding saturation field Hp of 1.7H S (3.3H S ) under
(zero-) field-cooled conditions is included in figure 7. Taking
this effect into account, the region around 3.2H S –4.5H S is not
much above an estimate based on Bean’s model. According to
section 4, MPSC processes lie on top of the MP band. Starting
around 3H S –5H S they end up with magnetizations around
2H S , which are between the dashed and the dotted lines. Data
for rings [13] were included as well and seem to lie below the
broad MP band for cylinders. Whether this is only related to
the error bars for H S , which may be in the order of 20% for
the ring samples, or to the material’s qualities, is still an open
question. However, the different geometry and size resulting
in different shielding and flux penetration properties, may play
a role as well.
Apart from the maximum magnetization obtainable for
certain peak fields, the shape of the trapped flux profile is also
of importance for cryo-permanent magnets. Figure 8 gives
a comparison of essentially three different kinds of profiles:
a Bean-like cone, which indicates reasonably good pinning
properties for the considered Jc(H, T ) range (A), a rather flat
Comparison of pulsed magnetization processes for HTS bulk parts
trapped flux profile typical for an MPSC profile, when the
pulse field is by far not sufficient to saturate the sample and
currents are mainly flowing in the outer parts of the sample
[12] (B), and finally, the profile of a saturated thick ring [13]
(C), which is essentially between both. Clearly, for several
applications rather flat profiles over significant diameters are
required. In this respect, ring structures may turn out to be the
best solution.
7. Summary
Cryo-permanent magnets utilizing the excellent pinning properties of melt-textured 123-HTS require application-specific
in situ pulsed magnetization processes. Inhomogeneities
present in all real materials, play an important role for
the initial magnetic flux penetration, but do not necessarily
prohibit a sufficiently symmetric trapped flux profile. Multipulse processes with stepwise cooling appear to be the best
choice for reaching high magnetizations with moderate peak
fields. In these processes 3 ms pulses result in slightly
lower magnetizations compared with ten-fold longer pulses.
Increasingly, also geometrical effects have to be taken into
account.
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