Physica C 316 Ž1999. 229–233
Measurement of the transport current distribution
in a superconducting tape
P. Usak
ˇ´
)
Institute of Electrical Engineering, SloÕak Academy of Sciences, BratislaÕa, SloÕak Republic
Received 8 December 1998; received in revised form 1 April 1999; accepted 1 April 1999
Abstract
A non-destructive measurement method was applied to evaluate transport current distribution across the width of a
superconducting tape. The self-magnetic field over the tape was mapped at a small distance from it. This provided input data
for an inverse calculation process through which the current distribution was evaluated. The procedure was used to
determine the dynamics of the distribution of AC current in a WIT BSCCO 2223 tape at a zero external magnetic field. A
different behaviour was observed for the unsaturated and saturated regimes. The critical current distribution was also
determined for transport current I s Ic . The measurement on the WIT BSCCO 2223 tape showed that at the critical current,
the current capacity in the central section was higher than that at the edges. q 1999 Published by Elsevier Science B.V. All
rights reserved.
Keywords: Critical current; Inverse problem; Current distribution
1. Introduction
For practical reasons, it is interesting to know the
transport current distribution across the width of a
superconducting tape. The question arises whether it
is homogeneous or preference is given to central
parts with respect to the edges. Simple physical
models based on critical state model are used to
calculate current density distribution within the
cross-section of a tape w1x, i.e., the current distribution across the tape width. However, it is questionable whether these models can be employed to assess
real thin and broad tapes which exhibit intrinsic
inhomogeneities in jc . Moreover, the inhomo)
Tel.: q421-7-5477-5816; Fax: q421-7-5477-5826-2719;
E-mail: elekusak@savba.sk
geneities are influenced by local values of the selffield and by corresponding effects related to the
anisotropy as demonstrated not only in the windings
w2x but present even within the tape width.
There is a need to have a more direct and exact
way to determine the current distribution. Unfortunately, there is no direct way to measure a current
distribution in the tape itself. There have been attempts to cut mechanically the tape into longitudinal
parallel pieces and to measure the critical currents in
the individual pieces w3x. The results have been
interpreted in the form of histograms of the current
carrying capacity distributed within the width of the
original tape. But this approach does not answer the
question about the role of the strong perpendicular
component of the self-field within the edges in the
case of the local anisotropy resulting in a current
0921-4534r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 2 8 3 - X
230
P. Usak
ˇ´ r Physica C 316 (1999) 229–233
distribution favouring the central parts of the tape,
where the perpendicular component is much smaller.
Hence, the local anisotropy has profound influence
on the interpretation of measurement for the saturated regime, at which the overall transport current
reaches the critical current level. Thus, in this situation, the real current distribution of an original nondestroyed tape may give smaller values of the current at the edges compared with the critical current
of the individual pieces cut from the edge parts.
Moreover, this approach gives no information
about the current distribution at an unsaturated state,
in which the transport current is much smaller than
the critical current of the tape, e.g., at AC regime
when the transport current passes through the zero
current level. The interference of this destructive
method with the original parameters of the tape
cannot be neglected either.
2. The method of measurement
To avoid the destructive approach for the investigation of current distribution at the unsaturated
regime, it is necessary to use characteristic tape
geometry, and to relate a current density distribution
within the tape to its self-field distribution around
the tape. At first the distribution of the self-magnetic
field component perpendicular to the tape plane is
mapped across its width. The scanning is carried out
in a distance from the tape which is comparable with
the tape thickness. Then the inverse problem is
solved to determine the distribution of the longitudinal component of transport current within the tape
width. This procedure is reliable provided the tape
transport properties exhibit translational invariance.
However, it can also be applied locally with a rea-
sonable precision, as there is a rapid decrease in the
input of distant parts in the longitudinal direction.
The distance from the tape, at which the mapping
is realised, plays a crucial role. If it is too short, the
mapping is only sensitive to upper layers of the tape.
Short-distance mapping is employed in the
magneto-optical approach, in which the tape is covered with a magneto-optically sensitive layer. If it is
too large, the precision of current distribution determination decreases and the input of more distant
parts of conductor in longitudinal direction increases,
i.e., the effect of locality in current distribution is
disturbed.
In a discretization process Žsee Fig. 1., the tape
was virtually cut longitudinally Ž z . into a finite
number of k subtapes of the same width Ž x direction.. It was supposed that the current within each
subtape was homogeneous. The perpendicular component of the magnetic field was mapped in a finite
number of k points over Ž y . the tape plane along the
line Ž x ., which was perpendicular to the tape axis
Ž z .. The measured values of B y i Ž i s 1 to k . were
used to calculate the values of current in the subtapes
Iz i Ž i s 1 to k .. Details are in Ref. w4x. The transformation matrix which correlates the current in subtapes with the field values in measured points was ill
conditioned. A very small error in the localisation of
a field probe or in its read-out can lead to a very
large error in the calculation of a current distribution.
To avoid this problem in real measurements where
finite level of errors is inevitable, the Tichonov
method of regularization w5,6x had to be applied.
In DC regime the transport current through the
tape is constant. The current distribution across the
tape width as well as the self-field distribution around
it are constant as well. The mapping procedure can
be performed in a stepwise way from point to point
gathering all the B y i data Ž i s 1 to k .. Then, these
Fig. 1. Mutual position of the virtual subtapes and the mapping line. The direction of the current flow Ž z . is perpendicular to the xy plane.
P. Usak
ˇ´ r Physica C 316 (1999) 229–233
data can be used to calculate the current distribution
within the k subtapes.
In AC regime the transport current is time-dependent, repeatedly increasing from minus amplitude to
plus amplitude and vice versa. In general, a current
distribution within the tape can also change within
this cycle. In a steady regime with a constant AC
amplitude, the transport current and its distribution
should be the same for the same phase. Mapping the
self-field profile B y i Ž w . in k points for a given
phase w gives the opportunity to calculate the current distribution Iz i Ž w . in k virtual subtapes for this
phase. The one point x i y one data Bi measurement
obtained with a stepwise field mapping in DC mode
is replaced by the one point x i-one array Bi Ž w j . j s 1
to n stepwise measurement in AC regime. The finite
number of array data n cover the entire cycle for
every location x i . All the k arrays measured at
points x i are synchronised by triggering the array
measurement to buffer i at the same initial phase
point, e.g., at crossing the zero transport current level
from down to up. In this way for every phase w j , one
can obtain profiles B y i Ž w j . i s 1 to k and calculate
the corresponding current distribution Iz i Ž w j . i s 1
to k related to the corresponding overall transport
current I Ž w j . at phase w j . Thus, by gathering the
current distributions for all the phase values j s 1 to
n, the dynamics of the current density distribution
within the cycle can be visualised. If the amplitude
of the current is Ic , all the important levels of AC
transport current, e.g., crossing zero were self-field
level is small, up to saturated region close to Ic were
current distribution reflects the critical current density distribution including possible local anisotropy
are covered in this way.
3. Results
The method was applied to several measurements.
A low-temperature Hall probe was used for the
self-field mapping of different types of superconducting tape ŽNb 3 Sn, TBCCO, BSCCO., and the
current distributions were calculated. In all the tapes,
the measurements demonstrated that the self-field
plays a role in the history and local distribution of
current within the edges of the tapes. Symmetrical
longitudinal frozen current loops within both edges
of a tape were observed in a Nb 3 Sn tape after a
231
stepwise increase up to 800 A and a consecutive
decrease of transport current in a zero external field
at 4.2 K w4x.
In another experiment at 77 K we changed the
local value of the self-field at one edge of a TBCCO
tape with DC transport current I, superimposing an
additional external magnetic field with a locally steep
gradient on the level of the local perpendicular selffield component. This method was used to demonstrate the effect of a local field on a current redistribution in the vicinity of the edge of a tape w7x. A
double mapping method was used to extract the
modified self-field profile from the complex profile
of the superimposed fields. The evaluation of the DC
measurement of transport current distributions in a
BSCCO monocore tape also revealed the role of the
perpendicular component of the self-field on the
current distribution close to the tape edges.
With a BSCCO tape, it was also shown w8x that
even frozen longitudinal magnetisation current distributions at the central cross-section of the tape can be
determined using a stepwise increase and decrease of
the external magnetic field perpendicular to the tape
surface. The measurement w9x was made at the presence of a superimposed non-zero transport current or
with a zero overall transport current. As a check,
both the overall transport current in the entire tape
calculated from the self-field mapped data, published
in Ref. w9x, and the overall transport current, which
was measured directly, coincided within several percent.
It was interesting to investigate the current distribution in an Ag-BSCCO 2223 tape prepared by a
wire-in-tube technique ŽWIT.. The vicinity of the
silver cloth has a positive influence on the grain
alignment and critical current density increase. This
advantage is used in the edge parts as well as in
Fig. 2. Schematic cross-section of wire-in-tube configuration
ŽWIT. tape.
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P. Usak
ˇ´ r Physica C 316 (1999) 229–233
central parts of the tape, as the result of the inserted
central silver sheet shows Žsee Fig. 2.. If this idea is
correct, the current distribution at saturated regime,
in which the overall current is close to Ic and it
reflects the critical current distribution within the
tape width, should favour the central parts of the
tape.
The 77 K measurement can be made with a DC
transport current close to Ic . However, we were also
interested in the effect of the history and behaviour
of the current distribution for the current crossing the
zero level in AC regime.
For this purpose, the AC method of self-field
mapping and data evaluation was applied. The amplitude of 12 A close to critical current was used in the
WIT tape of 6 mm width and 0.15 mm thickness.
The frequency was 5 mHz.
Fig. 3 shows a sequence of current distributions
determined during a continual decrease of the overall
transport current across the zero level within a cycle.
The current in each subtape was divided by its width,
and it is expressed in the form of linear current
density in kiloampere per meter Ži.e., Armm.. The
overall decreasing I Ž w . transport currents selected
for the presentation were q1 A, 0 A and y1 A. For
all the three selected phases, the current change at
the edges is in advance and in central part it is in
retard. This was true for the unsaturated region
around the zero overall current. Fig. 4 depicts a
situation in which a further current decrease within
the cycle achieved a level of y5 A, i.e., somewhat
Fig. 3. Change in the current distribution during a continual
decrease of the AC transport current across a zero level. Change
in the current is in advance at the edges and in retard at the center.
Fig. 4. Current distribution in an Ag-BSCCO 2223 wire-in-tube
tape at decreasing current y5 A.
P. Usak
ˇ´ r Physica C 316 (1999) 229–233
233
an original tape should give higher measured critical
currents because of the absence of the self-field of
all the tape pronounced just at these edges.
4. Conclusions
Fig. 5. Saturated current distribution for overall current I ; Ic
reflecting the intrinsic critical current distribution at the self-magnetic field.
less than half of the critical current in this sample.
The current is distributed approximately homogeneously across the width of the tape. A further
decrease of current to the negative amplitude yIc
led to a gradual saturation of the current capacity. In
Fig. 5 the overall current is on the level of the
critical current Žy12 A. and the presented current
distribution reflects the critical current distribution.
As expected for the wire-in-tube tape, the most of
the current is flowing through the central part of the
tape. Another mechanism favouring the central portions of the tape may be larger local values of the
perpendicular component of the magnetic self-field
at the tape edges. The determined critical current
distribution represents both the distribution of the
critical current density as a material parameter and
the influence of the local value and the orientation of
the self-magnetic field. Based on this, the critical
currents of subtapes mechanically cut at the edges of
A non-destructive method was used to determine
transport current distributions in a superconducting
tape. The tape was virtually cut into a finite number
of parallel subtapes of the same width, and the
homogeneous current in the individual subtapes was
calculated using data from a self-magnetic field mapping procedure. DC current distributions for different
types of superconducting tape were thus achieved.
Furthermore, the dynamics of current distribution of
the AC transport current can be exactly followed
both in unsaturated and saturated regimes. The critical current distribution for I s Ic was also achieved
this way, including self-field effect on Ic distribution. In WIT BSCCO 2223 tape critical currents at
center of the tape were higher than at the edges.
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