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Dynamic Resistance Measurements in a GdBCO-Coated Conductor

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In this article, the authors present dynamic resistance measurements of a 5mm-wide Fujikura coated conductor wire at 77 K. They report experimental values obtained through varying the field angle (the angle between magnetic field and normal vector of the conductor wideface), the dc current levels, and the magnetic field amplitude, and frequency.
Abstract
Dynamic resistance is a phenomenon which occurs when a superconducting wire carries dc transport current whilst experiencing an alternating magnetic field. This situation occurs in a range of HTS machinery applications, where dynamic resistance can lead to large parasitic heat loads and potential quench events. Here, we present dynamic resistance measurements of a 5-mm-wide Fujikura coated conductor wire at 77 K. We report experimental values obtain through varying the field angle (the angle between magnetic field and normal vector of the conductor wide-face), the dc current levels, and the magnetic field amplitude, and frequency. We show that the dynamic resistance in perpendicular magnetic field can be predicted by using a simple analytical equation. We also show that across the range of field angles measured here the dynamic resistance is dominated by the perpendicular component of the applied magnetic field.

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Dynamic resistance measurements in a GdBCO-
coated conductor
Zhenan Jiang, Ryuki Toyomoto, Naoyuki Amemiya, Chris W. Bumby, Rodney A. Badcock, Nicholas J. Long
Abstract Dynamic resistance is a phenomenon which occurs
when a superconducting wire carries DC transport current whilst
experiencing an alternating magnetic field. This situation occurs
in a range of HTS machinery applications, where dynamic
resistance can lead to large parasitic heat loads and potential
quench events. Here, we present dynamic resistance
measurements of a 5 mm-wide Fujikura coated conductor wire at
77 K. We report experimental values obtain through varying the
field angle (the angle between magnetic field and normal vector of
the conductor wide-face), the DC current levels, and the magnetic
field amplitude, and frequency. We show that the dynamic
resistance in perpendicular magnetic field can be predicted using
a simple analytical equation. We also show that, across the range
of field angles measured here the dynamic resistance is dominated
by the perpendicular component of the applied magnetic field.
Index Terms Dynamic resistance, ReBCO, GdBCO, coated
conductor.
I. INTRODUCTION
ynamic resistance occurs when a superconducting wire
carries DC transport current whilst experiencing an
alternating magnetic field [1, 2]. In HTS applications such as
rotating machines, magnets, and SMES (Superconducting
Energy Storage Systems), dynamic resistance plays an
important role [3-6]. In HTS flux pumps, dynamic resistance
within the HTS stator determines the maximum available
output current [7-11]. In recent years, HTS coated conductors
have become the dominant wire choice for next generation
superconducting machines [12], and hence accurate prediction
of the dynamic resistance incurred within an HTS coated
conductor wire is a critical issue.
Oomen et al developed an analytical model for calculating
dynamic resistance in a superconducting slab in an AC parallel
magnetic field [2]. There have been some previous
experimental reports on dynamic resistance in coated
conductors in AC perpendicular magnetic fields [13, 14].
However, this previous work has only employed applied
magnetic field amplitudes of < 20 mT, and the wire I
c
value for
the measurements reported in [13] was much smaller than
todays wires.
Recently we have measured the dynamic resistance in a 4
mm-wide SuperPower coated conductor in AC perpendicular
magnetic field up to 100 mT, and have developed an equation
Manuscript submitted September 02, 2016. This work was partially
supported by the JSPS (Japan Society for the Promotion of Science).
Zhenan Jiang, Chris W. Bumby, Rodney A. Badcock, and Nicholas J. Long
are with the Robinson Research Institute, Victoria University of Wellington,
PO Box 33436, Lower Hutt 5046, New Zealand. (e-mail:
zhenan.jiang@vuw.ac.nz).
which can predict dynamic resistance in a superconducting strip
in perpendicular magnetic field. This approach employs a
formula adapted from the Oomen equation for a
superconducting slab in parallel magnetic fields [15].
Here, we present dynamic resistance measurement results in
a 5 mm-wide Fujikura GdBCO coated conductor at 77 K. This
Fujikura wire has a considerably higher self-field I
c
than the 4
mm-wide SuperPower wire previously reported, and hence
provides a test of the useful applicability of our developed
equation. In addition, in this work we examine the dependence
of dynamic resistance on the applied field angle (the angle
between magnetic field and normal vector of the conductor
wide-face,
, see Fig. 1).
FIG. 1 HERE
II. EXPERIMENTAL METHOD
Fig. 2(a) shows the experimental set-up used to make our
dynamic resistance measurements at 77 K [16]. The AC magnet
can generate up to 100 mT peak magnetic field at frequencies
up to 112.5 Hz. The sample can be rotated inside the magnet,
and the field angle,
can be varied from to 360°. A 300 A
DC power supply was used to supply DC current to the 15 cm-
long Fujikura sample wire (FYSC-SC05). The sample was
fabricated by IBAD/PLD method, and has a self-field I
c
of
266.0 A at the 1 V/cm criterion, 77 K. The specification of the
sample is shown in Table 1. The DC circuit was arranged in
order to reduce coupling with the AC magnet circuit. Fig. 2(b)
shows voltage taps attached on the sample. Two sets of voltage
taps were prepared as seen in Fig. 2(b): in the first set, two
voltage taps were attached on the center of the sample, and two
voltage signal wires run opposite along the sample axis and
meet in the center of the sample; in the second set, a spiral loop
was arranged around the sample as shown in the figure [17].
The spiral loop was introduced to cancel out the effect from
external magnetic field. The distance between the voltage-taps
is 5 cm. The voltage output from the voltage taps were
measured using a Keithley 2182 nano-voltage meter.
Appropriate filters were used to average the voltage from the
voltage taps [18]. Dynamic resistance values measured from the
two voltage pick-ups were exactly the same, and the first set of
Ryuki Toyomoto and Naoyuki Amemiya are with Graduate School of
Engineering, Kyoto University, Kyoto, Kyoto-Daigaku-Katsura, Nishikyo,
Kyoto 615-8510, Japan.
D

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voltage taps was used in this work.
FIG. 2 HERE
TABLE 1 HERE
III. EQUATION FOR DYNAMIC RESISTANCE IN A STRIP IN
PERPENDICULAR MAGNETIC FIELD
The dynamic resistance per unit length per cycle in a
superconducting strip, carrying DC current exposed to AC
perpendicular magnetic field, R
d,
, can be estimated using the
following equation [15],
(1)
where a is half-width of the coated conductor, B
a,
is the
amplitude of applied magnetic field, I
c0
(266.0 A) is the self-
field critical current of the conductor, I
t
is the DC transport
current, f is the frequency of the applied magnetic field, L is the
distance between the two voltage taps. The threshold magnetic
field, B
th,
is given by,
(2)
where (1- I
t
/I
c0
) is the DC current filling factor and B
p,
is
effective penetration field [19, 20], which can be evaluated by
finding B
a
value at the maxima of the
curve shown in Fig. 3.
In this figure
= Q
BI
/B
a
2
, where Q
BI
is the Brandt expression
for the theoretical magnetization loss in a superconducting
strip exposed to AC perpendicular magnetic field [21]. The
maxima of this curve can be obtained from straightforward
numerical methods to yield [15],
(3)
where J
c0
is defined as I
c0
/(2a × 2t). For the wire considered
here, we calculate that B
p,
=51.71 mT, as shown in Fig. 3.
FIG. 3 HERE
IV. EXPERIMENTAL RESULTS
Fig. 4 shows the measured R
d,
data obtained from the
sample at 3 different frequencies and 4 different values of the
reduced current, I
t
/I
c0
. In these plots R
d,
is normalized by f. The
R
d,
data for different frequencies show close agreement, which
indicates the hysteretic nature of the dynamic loss mechanism.
In all plots, R
d,
is zero until the threshold magnetic field, B
th,
, is exceeded. We have obtained experimental values for B
th,
from the x-axis intercept of linear fits of the composite dataset
using all frequencies measured for each value of I
t
/I
c0
. B
th,
values decrease as the reduced current, I
t
/I
c0
is increased which
is consistent with Eq. (2). In Fig. 4(d), the R
d,
data for f = 26.62
Hz deviate from the linear fit. We believe this is due to flux
flow loss which occurs as the I
c
(B) of the wire at the peak
applied field falls below the magnitude of the total driven DC
current [15]. Flux flow loss leads to a rapid increase in total
dissipated power with increasing field amplitude, and we burnt
out a sample during the measurement at I
t
/I
c0
= 0.9 and high B
a
due to this effect.
FIG. 4 HERE
The experimentally derived values of B
th,
from the Fujikura
sample are shown in Fig. 5(a) alongside calculated values based
on Eq. (2) [15]. The figure also shows calculated values
obtained using an alternative formula proposed by Ciszek et al,
which uses B
th
values in parallel fields in conjunction with a
calculated demagnetization factor [13]. It can be seen that the
experimentally obtained values of B
th,
have excellent
agreement with the values determined using Eq. (2), while the
Ciszek model only converges with our model and experiment
at high I
t
/I
c0
values.
Fig. 5(b) compares the gradient of the linear fits (dR
d
/dB
a
) in
Fig. 4 and the theoretical value of 4a/I
c0
expected from Eq. (1).
This is plotted as a function of the reduced current I
t
/I
c0
. In all
cases the experimentally obtained gradient is larger than the
theoretical value, although agreement improves slightly with
increasing I
t
/I
c0
. The difference ranges between 30 15 %.
There are several possible causes for this discrepancy,
including: possible non-uniform J
c
distributions in the sample
wire; possible contributions due to J
c
-B dependence of the wire;
or possible errors in measured I
c0
values and GDBCO film
dimensions used in the theoretical calculations.
In Fig. 6, R
d
data is plotted for measurements made at 3
different field angles,
= 0, 30, 60 , using 3 different I
t
/I
c0
values at 26.62 Hz. For a given I
t
/I
c0
, B
th
increases with
increasing field angle
while the gradient of the fitted linear
lines, dR
d
/dB
a
, and decreases with increasing field angle

These results can be explained by the fact that calculated
dynamic resistance in parallel magnetic field [2] is negligible
compared to our experimental results. For example, if we
consider B
a
= 100 mT, I
t
/I
c0
= 0.3 and f = 26.62 Hz, we find that
the experimentally measured R
d
at
= 60 is 1.19 /m/Hz.
This can be compared with a calculated value for the expected
dynamic resistance in parallel field of from the Oomen model
of 𝑅
d, ∥
= 5.76 x 10
-4
/m/Hz which is a factor of about 2000
smaller than the measured value. Fig. 7 shows calculated values
of 𝑅
d, ∥
for parallel field amplitudes up to 100 mT, and it is clear
that 𝑅
d, ∥
𝑅
d
throughout the experimental range reported
here. In light of this observation, it is reasonable to consider
whether the angular dependence of R
d
(α) can be explained
simply by the perpendicular component of B
a
which varies
according to B
a
cosα. Fig. 8 shows plots of B
a
cosα versus R
d
at
= 0, 30, 60. It is readily apparent that this simple
transformation leads to the data collapsing onto an
approximately common curve for all angles.
FIG. 6 HERE
FIG. 7 HERE
The apparent perpendicular threshold field, B
th,
(given by
( )
=
th, a,
c0
d,
4
BB
I
a
fL
R
=
c0
t
p, th,
1
I
I
BB
/9284.4
c00 p,
tJB =

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the x-axis intercept) now closely agree for the datasets collected
at each field angle. This is a result of the very high aspect ratio
of the coated conductor wire, which ensures that shielding
currents are restricted to flow only within the ~ 2.3 m GdBCO
film. This gives rise to a magnetization field which is always
perpendicular to the tape, and hence shields only the
perpendicular component of the applied field. This situation is
markedly different to that previously observed for BSCCO wire
[18], where the aspect ratio of the filamentary zone is normally
more than 100 times the aspect ratio (2a/2t) of a ReBCO wire.
FIG. 8 HERE
Fig. 8 also shows that the gradient dR
d
/dB
a
,
is also
approximately constant at
= 0, 30 and 60, although the
agreement at the largest field angle studied is not perfect, and
suggests the emergence of a further small contributing factor.
Nonetheless, Figure 8 provides strong evidence that R
d
(α)
of
the GdBCO coated conductor wire can be well described by
considering solely the contribution of the perpendicular field
component to Eq. (1).
V. CONCLUSION
We have measured dynamic resistance in a 5 mm-wide
Fujikura GaBCO coated conductor at 77 K when exposed to AC
external magnetic fields at various applied field angles and
amplitudes up to 100 mT.
The threshold field, B
th,
of the coated conductor in
perpendicular field can be accurately predicted from the
penetration field, B
p,
identified from the maxima of the Brandt
gamma curve, and the DC current filling factor (1- I
t
/I
c0
). The
measured dynamic resistance, R
d,
values in perpendicular
magnetic field, have reasonable agreement with the values
predicted from the Oomen equation for a superconducting slab
using the B
th,
values.
We have also shown that the dynamic resistance due to an a
magnetic field applied at angles up to 60 degrees from the
perpendicular field, can be accurately determined by
considering solely the contribution due to the perpendicular
field component. This situation is contrary to that previously
reported for BSCCO wire, and arises due to the very high aspect
ratio of the coated conductor wire, which restricts shielding
currents to flow solely in the plane of the ReBCO film.
ACKNOWLEDGMENT
The authors acknowledge Drs. N. Strickland and S. Wimbush
for I
c
(B,
) measurements of the sample at 77 K.
REFERENCES
[1] K. Ogasawara, K. Yasukochi, S. Nose, and H. Sekizawa, “Effective
resistance of current-carrying superconducting wire in oscillating
magnetic fields 1: Single core composite conductor,Cryoginics, vol. 16,
pp. 33-38, Jan. 1976.
[2] M. P. Oomen, J. Rieger, M. Leghissa, B. ten Haken, and H. H. J. ten Kate,
“Dynamic resistance in a slab-like superconductor with J
c
(B)
dependence,” Supercond. Sci. Technol., vol. 12, pp. 382-387, 1999.
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[6] E. Pardo, “Modeling of AC loss in coils made of thin tapes under DC bias
current”, IEEE Trans. Appl. Supercond. vol. 24, 2013, Art. ID 4700105.
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“Dynamic resistance of a high-T
c
superconducting flux pump,” Appl.
Phys. Lett, vol. 105, Sep. 2014, Art. ID 112601.
[8] Z. Jiang, C. W. Bumby, R. A. Badcock, H. J. Sung, N. J. Long, and N.
Amemiya, “Impact of flux gap upon dynamic resistance of a rotating HTS
flux pump,” Supercond. Sci. Technol., vol. 28, Sep. 2015, Art. ID 115008.
[9] J. Geng and T. A. Coombs, “Mechanism of a high-Tc superconducting
flux pump: Using alternating magnetic field to trigger flux flow”, Appl.
Phys. Lett. vol. 107, 2015, Art. ID 142601.
[10] C. W. Bumby, Z. Jiang, J. G. Storey, A. E. Pantoja, R. A. Badcock,
“Anomalous open-circuit voltage from a high-T
c
superconductor
dynamo”, Appl. Phys. Lett. vol. 108, 2016, Art. ID 122601.
[11] C. W. Bumby, R. A. Badcock, H. J. Sung, K. M. Kim, Z. Jiang, A. E.
Pantoja, P. Bernado, M. Park, and R. G. Buckley, “Development of a
brushless HTS exciter for a 10 kW HTS synchronous generator”,
Supercond. Sci. Technol. vol. 29, 2016, Art. ID 024008.
[12] V. Selvamanickam, A. Guevara, Y. Zhang, I. Kesgin, Y. Xie, G. Carota,
Y. Chen, J. Dackow, Y. Zhang, Y. Zuev, C. Cantoni, A. Goyal, J. Coulter,
and L. Civale, “Enhanced and uniform in-field performance in long (Gd,
Y)BaCuO tapes with zirconium doping fabricated by metalorganic
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ID 014014.
[13] M. Ciszek, O. Tsukamoto, J. Ogawa, and D. Miyagi, “Energy losses in
YBCO-123 coated conductors carrying transport current in perpendicular
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[14] R. C. Duckworth, Y. F. Zhang, T. Ha, and M. J. Gouge “Dynamic
resistance of YBCO-coated conductors in applied AC fields with DC
transport currents and DC background fields,” IEEE Trans. Appl.
Supercond., vol. 21, pp. 3251-3256, June 2011.
[15] Z. Jiang, R. Toyomoto, N. Amemiya, X. Zhang, and C. W. Bumby,
“Dynamic resistance of a high-T
c
superconducting strip in perpendicular
magnetic field at 77 K”, 2016 In Press, Supercond. Sci. Technol.,
https://doi.org/10.1088/1361-6668/aa54e5
[16] Z. Jiang and N. Amemiya, “An experimental method for total AC loss
measurement of high T
c
superconductors”, Supercond. Sci. Technol. vol.
17, pp. 371- 379, 2004.
[17] S. Fukui, Y. Kitoh, T. Numata, O. Tsukamoto, J. Fujikami, and K.
Hayashi, “Transport current AC losses of high-Tc superconducting tapes
exposed to AC magnetic field”, Advances in Cryogenic Engineering, vol.
44, pp. 723-730, 1998.
[18] M. Ciszek, H. G. Knoopers, J. J. Rabbers, B. ten Haken, and H. H. J. ten
Kate, “Angular dependence of the dynamic resistance and its relation to
the AC transport current loss in Bi-2223/Ag tape superconductors”
Supercond. Sci. Technol. vol. 15, pp. 1275- 1280, 2002.
[19] M. Iwakuma, K. Toyota, M. Nigo, T. Kiss, K. Funaki, Y. Iijima, T. Saitoh,
Y. Yamada, and Y. Shiohara, “AC loss properties of YBCO
superconducting tapes fabricated by IBAD-PLD technique,” Physica C,
vol. 412-414, pp. 983-991, May 2004.
[20] A. Palau, T. Puig, X. Obradors, E. Pardo, C. Navau, A. Sanchez, A.
Usoskin, H. C. Freyhardt, L. Fernández, B. Holzapfel, and R. Feenstra,
“Simultaneous inductive determination of grain and intergrain critical
current densities of YBa
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[21] E. H. Brandt and M. Indenbom, “Type-II-superconductor strip with
current in a perpendicular magnetic field,” Phys. Rew. B, vol. 48, pp.
12893-12906, Nov. 1993.
TABLE I
SAMPLE SPECIFICATIONS
Critical current at self-field, 77 K (A)
266
Width of conductor (mm)
5.07
Ag layer (m)
6.4
Thickness of YBCO layer
(m)
2.3
Sample length (mm)
150
Thickness of substrate (m)
100
Thickness of stabilizing layer (m)
100

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Fig. 1. Definition of field angle .
Fig. 2. (a) Experimental set-up for dynamic resistance measurement, (b)
voltage tap arrangement.
Fig. 3.
plot of calculated AC magnetization loss [21],
= Q
BI
/B
a
2
used to
define the effective penetration field, B
p
in the sample. The maxima of
plot
occurs when B
a
= B
p
, which in this work is found to be 51.71 mT.
Fig. 4. Measured dynamic resistance values for different frequencies plotted as
a function of the amplitude of the applied magnetic field (a) I
t
/I
c0
= 0.1, (b) I
t
/I
c0
= 0.3, (c) I
t
/I
c0
= 0.5, (d) I
t
/I
c0
= 0.7.
Fig. 5. (a) Threshold magnetic field in perpendicular magnetic field, B
th,
, vs.
reduced current [15], (b) the gradient of the linear fits, dR
d
/dB
a
vs. 4a/I
c0
from
Eq. (1).
10
-2
10
-1
10
0
10
1
1 10 100
AC loss (Jm
-1
cycle
-1
T
-2
)
Perpendicular magnetic field (mT)
51.71 mT
0
1
2
3
4
5
0 20 40 60 80 100
26.62 Hz
65.44 Hz
112.5 Hz
Fit
R
d,
(/m/Hz)
B
a,
(mT)
I
t
/I
c0
= 0.1
(a)
0
1
2
3
4
5
0 20 40 60 80 100
I
t
/I
c0
= 0.3
(b)
R
d,
(/m/Hz)
B
a,
(mT)
0
1
2
3
4
5
0 20 40 60 80 100
I
t
/I
c0
= 0.5
(c)
R
d,
(/m/Hz)
B
a,
(mT)
0
1
2
3
4
5
0 20 40 60 80 100
I
t
/I
c0
= 0.7
(d)
R
d,
(/m/Hz)
B
a,
(mT)
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8
Exp.
Eq. (2)
Ref. 13
B
th,
(mT)
I
t
/I
c0
(a)
0
0.05
0.1
0 0.2 0.4 0.6 0.8
4a/I
c0
(/m/Hz/mT)
I
t
/I
c0
Eq. (1)
(b)

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Fig. 6. Measured dynamic resistance in various field angles at 26.62 Hz, (a)
I
t
/Ic
0
= 0.3, (b) I
t
/Ic
0
= 0.5, (c) I
t
/Ic
0
= 0.7.
Fig. 7. Calculated dynamic resistance due to parallel magnetic field, B
a, //
.
Fig. 8. Dynamic resistance in different field angles at 26.62 Hz, (a) I
t
/Ic
0
= 0.1,
(b) I
t
/Ic
0
= 0.3, (c) I
t
/Ic
0
= 0.5, (d) I
t
/Ic
0
= 0.7.
0
1
2
3
4
5
0 20 40 60 80 100
0 deg
30 deg
60 deg
R
d
(/m/Hz)
B
a
(mT)
I
t
/I
c0
= 0.3
(a)
f = 26.62 Hz
0
1
2
3
4
5
0 20 40 60 80 100
B
a
(mT)
I
t
/I
c0
= 0.5
(b)
R
d
(/m/Hz)
0
1
2
3
4
5
0 20 40 60 80 100
B
a
(mT)
I
t
/I
c0
= 0.7
(c)
R
d
(/m/Hz)
0
5E-4
1E-3
0 20 40 60 80 100
I
t
/I
c0
= 0.7
I
t
/I
c0
= 0.5
I
t
/I
c0
= 0.3
R
d
(/m/Hz)
B
a, //
(mT)
f = 26.62 Hz
0
1
2
3
4
5
0 20 40 60 80 100
0 deg
30 deg
60 deg
R
d
(/m/Hz)
(a)
I
t
/I
c0
= 0.3
f = 26.62 Hz
B
a
cos(mT)
0
1
2
3
4
5
0 20 40 60 80 100
(b)
R
d
(/m/Hz)
I
t
/I
c0
= 0.5
B
a
cos(mT)
0
1
2
3
4
5
0 20 40 60 80 100
(c)
R
d
(/m/Hz)
I
t
/I
c0
= 0.7
B
a
cos(mT)
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Dependence of Dynamic Loss on Critical Current and n -Value of HTS Coated Conductors

TL;DR: In this article, the dependence of the ac loss in high-temperature superconductors (HTSs) on these properties has been well studied, but it is still unknown how the dynamic loss is affected.
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Journal ArticleDOI

Type-II-superconductor strip with current in a perpendicular magnetic field.

TL;DR: Analytical results are at variance with the critical-state model for longitudinal geometry and explain numerous experiments in a natural way without the assumption of a surface barrier.
Book

Applications of High Temperature Superconductors to Electric Power Equipment

TL;DR: In this paper, the authors present an overview of the properties of superconducting field windings and their application in the context of cooling and cooling of high-speed motors, as well as a discussion of the challenges involved in the design of such systems.
Journal ArticleDOI

Review of high power density superconducting generators: Present state and prospects for incorporating YBCO windings

TL;DR: In this paper, the development of high power density generators for airborne applications by bridging the chasm between generator and high temperature superconducting (HTS) wire developmental efforts is discussed.
Journal ArticleDOI

Dynamic resistance of a high-Tc superconducting flux pump

TL;DR: In this article, a mechanically rotating superconducting flux pump was used to excite an HTS double pancake coil at 77 K. This flux pump is found to possess an effective internal resistance, Reff, which varies linearly with frequency, and is two orders of magnitude larger than the measured series resistance of the soldered contacts within the circuit.
BookDOI

Applications of High Temperature Superconductors to Electric Power Equipment: Kalsi/Applications of High Temperature Superconductors

TL;DR: In this article, the authors present an overview of the properties of superconducting field windings and their application in the context of cooling and cooling of high-speed motors, as well as a discussion of the challenges involved in the design of such systems.
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Frequently Asked Questions (11)
Q1. What are the contributions mentioned in the paper "Dynamic resistance measurements in a gdbco- coated conductor" ?

Here, the authors present dynamic resistance measurements of a 5 mm-wide Fujikura coated conductor wire at 77 K. The authors report experimental values obtain through varying the field angle ( the angle between magnetic field and normal vector of the conductor wide-face ), the DC current levels, and the magnetic field amplitude, and frequency. The authors show that the dynamic resistance in perpendicular magnetic field can be predicted using a simple analytical equation. The authors also show that, across the range of field angles measured here the dynamic resistance is dominated by the perpendicular component of the applied magnetic field. 

Flux flow loss leads to a rapid increase in totaldissipated power with increasing field amplitude, and the authors burnt out a sample during the measurement at It/Ic0 = 0.9 and high Ba due to this effect. 

The authors believe this is due to flux flow loss which occurs as the Ic(B) of the wire at the peak applied field falls below the magnitude of the total driven DCcurrent [15]. 

There are several possible causes for this discrepancy, including: possible non-uniform Jc distributions in the sample wire; possible contributions due to Jc-B dependence of the wire; or possible errors in measured Ic0 values and GDBCO film dimensions used in the theoretical calculations. 

It is the DC transport current, f is the frequency of the applied magnetic field, L is the distance between the two voltage taps. 

The maxima of this curve can be obtained from straightforward numerical methods to yield [15],(3)where Jc0 is defined as Ic0/(2a × 2t). 

Two sets of voltage taps were prepared as seen in Fig. 2(b): in the first set, two voltage taps were attached on the center of the sample, and two voltage signal wires run opposite along the sample axis and meet in the center of the sample; in the second set, a spiral loop was arranged around the sample as shown in the figure [17]. 

The authors have measured dynamic resistance in a 5 mm-wide Fujikura GaBCO coated conductor at 77 K when exposed to ACexternal magnetic fields at various applied field angles and amplitudes up to 100 mT. 

The authors have obtained experimental values for Bth, ⊥ from the x-axis intercept of linear fits of the composite datasetusing all frequencies measured for each value of It/Ic0. 

This is a result of the very high aspect ratio of the coated conductor wire, which ensures that shieldingcurrents are restricted to flow only within the ~ 2.3 m GdBCO film. 

2 HERETABLE 1 HEREThe dynamic resistance per unit length per cycle in a superconducting strip, carrying DC current exposed to ACperpendicular magnetic field, Rd, ⊥, can be estimated using the following equation [15],(1)where a is half-width of the coated conductor, Ba, ⊥ is the amplitude of applied magnetic field, Ic0 (266.0 A) is the selffield critical current of the conductor,