,
IEEE
TRANSACTIONS
ON
MAGNETICS,
VOL.
28,
NO.
1,
JANUARY
1992
The critical current in
a
NbTi tape measured in different directions
of magnetic field and the current reduction due to the self field.
B.
ten Haken, L.J.M van de Klundert,
University
of
Twente,
A
plied superconductivity centre,
POB.
21f 7500
AE
Enschede, the Netherlands.
V.S. Vysotsky, V.R. Karasik,
P.N.
Lebedev Physical Institute
of
the Academy
of
Science
of
USSR,
Leninskyprosp.
53, 117333
Moscow,USSR.
755
Abstract
-
For
the application
of
NbTi
tape in a
superconducting thermal witch. the critical current of
a
20
micrometers thick
NbTi
tape
is
measured in several
directionm of the magnetic field.
The
critical current
is
found to behave strongly anisotropically, due to the
deformation of the
NbTi.
The
tape
is
extra sensitive for the component
of
the
magnetic field perpendicular to the surface. Without
external field this component of the self field reduces
the critical current
far
below its intrinsic value.
A
one dimensional rodel
can
describe the reduction of
critical current due to the self field in a thin tape.
-
I. INTRODUCTION
A bare NbTi tape conductor
is
an interesting alter-
,
native for the fabrication of a fast superconducting
thermal switch. In the next section an estimation
is
made for the critical current density necessary for a
tape conductor to compete with the best switches of
NbTi wire as made up to now
The anisotropic behaviour of the critical current in
the tape is investigated by changing the directions of
,
the magnetic field on the superconductor.
In that way
I
the three main directions for the lorentz force in the
,
tape are investigated, plus the situation with the
Lorentz force absent (field and current parallel). The
measured influence of the field direction on the
critical current for this NbTi tape
is
compared with
the behaviour of a Nb,Sn tape.
The influence of the self field on the overall
critical current of the tape
is
investigated by
changing the geometry of the sample. If two pieces of
tape are placed close to each other, the self field
is
dependent on the direction
of
the current (parallel or
antiparallel). Finally a one dimensional model to
calculate the influence of the self field on the
critical current of a single straight piece of tape
is
described.
11. APPLICATION IN A THERMAL SWITCH
In a thermal switch the temperature of the super-
conductor
is
swept between the superconducting and the
normal state. In practical applications the heat
capacity of the (thermal) insulation layer can be
negligibly small, compared to the capacity of the
heated
volume
containing the superconductor.
A.
Switching Efficiency
In the center of the switch a volume
(V)
of super-
conductor, plus eventually some epoxy material,
is
responsible for the heat capacity of the switch (C).
So
the enthalpy used to raise the temperature of the
switch to the normal state
(Tst)
is:
Manuscript
received
June
24,
1991.
AH
=
C
V
(Tst-To).
(To
=
Bath temp.
1
(1)
The maximum switching velocity is proportional to the
time constant
(T)
of the system defined as:
T
=
AH/PSt
.
(2)
Where Pat is the power dissipation necessary to
maintain the normal state. Therefore fast (small
T)
and
efficient (small
PSt)
switch design is a question of
minimizing the enthalpy.
It
is
clear that for a switch of a certain current
and desired resistance the amount of material is
determined by the critical current density and the
electrical resistivity of the superconductor:
AH
a
V
a
p
JC3
(3)
Taking into account all the relevant material
properties (J,,p,T,,,C)
it
appeared that NbTi is a good
material for applications in liquid helium
[ll.
I
B.
Critical Current in
a
Thermal Switch
I
Several types of fast switches have been investi-
1
gated mainly for the application in superconducting
~
rectifiers
[l].
For a high current
(2
kA) switch the
best results have been achieved with a multifilamentary
conductor of bare NbTi filaments impregnated in epoxy
resin
[21.
Two important factors limited the
performance of this switch:
I
~
1)
The
current densitz
in the bare filaments
is
2)
The
heat capacity
of the switch
is
increased with
approximate1y.a factor of
6,
due to the epoxy material.
If one considers to make a switch from NbTi tape the
amount of epoxy material necessary for mechanical
fixing and thermal contact can be negligibly small. In
a switch made of bare NbTi filaments the volume of the
epoxy material
is
responsible for the main part of the
heat capacity of the switch. According to
(3)
the
application of a NbTi tape in a switch
is
interesting
if the tape exceeds a critical current of:
1.7-10’
Ah2.
relatively poor:
3-10’
A/m
(without external field).
C. Magnetic Field in a Switch
The external magnetic field is small in most
of
the
switching applications. In such a case the self field
of the tape can be the largest contribution to the
magnetic field on the superconductor. Usually a switch
’
is
designed to have a low (se1f)inductance. in that way
the self field
is
also minimized. A low inductance
is
achieved by using a bifilar geometry (=antiparallel)
for the conductor inside the switch.
0018-9464/92$03.00
0
1992
IEEE
756
I11
CRITICAL CURRENT IN DIFFERENT FIELD DIRECTIONS
In the experiments described in the next sections
the critical current of a NbTi tape
is
investigated.
The magnetic field and the electrical current
is
applied in all the possible main directions, and
compared with a Nb,Sn tape. The self field in the NbTi
tape
is
changed by preparing samples of different
geometries.
A:
Experimental Conditions
The NbTi tape
is
produced by rolling a slab of NbTi
to a final thickness of
20
pn
between two copper
plates. In our case a high electrical resistivity
is
desired therefore the copper layers are etched away
from the superconductor except for the connecting
areas. After the rolling process one can expect an
anisotropic behaviour in the superconducting properties
of the NbTi, due to the deformation of the material.
The samples are placed into a superconducting magnet
and tested in a
4.2
K helium bath, with direct contact
to the liquid helium. The
length of the testing section
is
20
mm
and the voltage criterion used for all the
experiments
is
lO%m. The width
of
the samples varied
from
1
to
20
nun,
in this range the critical current
density appeared to independent of the width.
B.
Perpendicular Field and Current
To investigate the dependence of the field and
current direction dependence The samples are cut in two
directions from the tape and placed in two different
directions of the magnetic field.
As
a result the
Lorentz force is acting in all three possible main
directions of the tape,
as pointed out in figure
1.
For
practical applications only the samples with the
current flowing parallel to the rolling direction are
relevant.
In
the other direction the sample length
is
limited, in our case to approximately
80
min.
I
2
I
I
-
Rolling
dit
-
Jn
I/
Forces:
1
Ft
-5
Fig. 1: Definition of the directions for the electrical
current, magnetic field and Lorentz force
1)
Results: The critical current versus magnetic
field of the tape in the four situations described
above
Is
presented in figure
2.
The most striking
result is the extreme difference in the critical
current between the two directions of the magnetic
field on the tape. A relatively small difference
appears for the two different directions of the current
in the tape.
For both the directions of the current in the tape,
the critical current decreases rapidly if a magnetic
field
is
applied perpendicular to the surface of the
tape. In an external field of
1
tesla the critical
current
is
reduced with a factor of
100.
The first part
of this curve matches good with the kim relation:
I
m
l/(B+Bo)
for a value of
Bo
=
0.02
tesla (figure
3).
I
0
I
0.5
-
B
[TI
’
I
1.0
Fig.
2:
The critical current versus magnetic field, in
different directions of field and current.
0 0.1
-
B
IT1
Figure
3:
Test of the Kim relation for a magnetic field
perpendicular to the surface.
If the magnetic field
is
parallel to the tape
surface, but perpendicular to the current the behaviour
is
somewhat similar to as
it
is found in NbTi (multi-
filamentary) wires. Above
1
tesla the critical current
decreases, indicating an upper critical field near
10
tesla (see also figure
5).
Below
0.5
tesla the
critical current, in the two investigated directions,
deceases to a value of
0.95*109
and
0.58
Ah2
for a
vanishing field.
2)
Instabilities: Usually, e.g. in NbTi wires, a
decrease of the critical current for small fields
is
due to the instability of the conductor. In this
material there are no instabilities found. Clear
voltage current characteristics are measured in this
range for all the directions of current and magnetic
field. This is in agreement with the simple adiabatic
stability criterion which predicts no stability
problems for this combination of relatively low
critical current and thickness
[31.
3.
Pinning Forces:
It
is interesting to summarize,
the previous results in terms of pinning forces. Using
the direction definitions of figure
1,
the results are
presented in figure
4.
The shape of the curve for the
pinning force as a function of the field is completely
different for the investigated directions. Only if the
pinning force acts in the direction perpendicular to
the tape surface shows reasonable high values. In the
other directions the pining mechanism
is
several orders
of magnitude weaker.
do,
D9
1
1061
0.01
0.1
-B
Fig.
4:
The pinning forces
10
TI
in the NbTi tape.
C.
A
Comparison of NbTi
and
NbGn Tape.
After analyzing the results of the NbTi tape, for
the different directions of the magnetic field and
current,
it
is
concluded that the strong anisotropy of
the current in an external field is caused by the
production process. The deformation of the NbTi, after
rolling the tape, creates directionally dependent
pinning centers. To state this conclusion a comparison
is
made with Nb,Sn tape made by Horizont (USSR). This
tape
is
produced by reacting a
Nb
tape between two
tin
layers covered with a copper stabilizer.
The dimensions of the Nb3Sn tape are comparable to
the NbTi tape, the Nb,Sn layer
is
approximately
24
p
thick and the width of the tape
is
4.5
nun.
This
material
is
tested in the two directions
of
magnetic
field perpendicular to the current. The Nb,Sn tape
showed no detectable dependence for the direction of
this field, in the field range from
10
to
15
tesla.
D.
Critical current
and
Magnetic Field Parallel
The next situation to consider is the magnetic field
acting parallel to the electrical current,
so
the
Lorentz force is diminishing. The critical current in
this geometry is plotted in figure
5
together with the
two perpendicular directions of the magnetic field, for
the same samples, all with the current flowing parallel
to the rolling direction.
As
usual the critical current density shows the
highest values for a small magnetic field
(E
0.5
tesla)
in the parallel direction.
An
interesting phenomena is
that it
is
possible to measure a voltage near the
critical current for low field values, without any
stabilizing material (no current sharing)
or
perpen-
dicular field (flux flow). The only mechanism left for
a voltage rise is the flux flow due to the self field
in the superconductor.
E.
The Influence of the Self Field
A
simple method to change the self field inside the
conductor, is to put two tapes near to each other. If
the current
is
flowing in the opposite direction
(antiparallel) the field components perpendicular to
the surface cancel each other. Otherwise the self field
in this direction is doubled. The other component
of
the magnetic field will act in the opposite way, but
it
is
expected to have only a negligible influence on the
critical current.
The experimental results (table
1)
indicate that
indeed the perpendicular component of the self field
is
responsible for a decrease
of
the current in the
situation where one single piece of tape is used,
reducing this component of the self field in the
antiparallel situation increases the critical current
with a factor two, in the parallel case a decrease of
approximately
0.75
is
found. One can assume that in the
antiparallel geometry the critical current density
is
close to the intrinsic value.
TABLE
I
CRITICAL CURRENT IN SELF FIELD FOR THREE GEOMETRIES
Sample shape Critical current density
Two antiparallel
Single tape
0.95
*
0.05
,,
Two parallel
0.73
f:
0.04
2.00
f:
0.20
.io9
A/m2
IV CRITICAL STATE IN A THIN TAPE
In our case the tape's width
(U:
1
to
20
nun)
is
inthe order of
lo3
times of
its
thickness (d).
It
is
reasonable to reduce our problem to an infinite thin
thickness. Consider an infinitely long straight and
thin tape with a position(x) dependent current density
(J), flowing in the z-direction. The magnetic self
field (B), pointing in the y-direction, at a certain
position (x=a) inside the tape
is
calculated with the
integral form of amperes law:
51
[TI
Sample
r
I
2
L
6
0
-B
IT1
Fig.
5:
Critical current for parallel and perpendicular
directions of the magnetic field.
The assumption of a infinite thin tape reduces the
self field to one component inside the tape pointing in
the perpendicular (y) direction. In that way the
problem is restricted to the most important component
of the field as deduced from the experiments described
before. The second step
is
to assume that the entire
tape
is
in the critical state, making the current equal
to the critical value in the field along the
x-coordinat:
J(x)
=
J,( B(x)
1
.
(5)
It
is convenient to rewrite the J,(B) relation used
in
(5)
by normalizing
it
at B
=
0
(J,
=
Jo)
and B
=
B,,
(J
=
0):
J
=
1
-
f(b)
,
(6)
with
J
=
J/Jo, b
=
B/B. The normalized function f(b)
contains the information of the actual J,(B) relation.
Combining the previous relations
(4),(5)
and
(6).
an
integral equation of the Fredholm type is received:
\',epp:
1-Xln4
\
A:
0.01
defining the parameter
A
=
(hJod)/(2nBc2). This
equation
(7)
shows that the width of the tape (U)
is
not playing a role in our problem. Besides the
characteristic parameter
A
only the shape of the J,(B)
relation in the function f is important for the current
profile in the tape.
A.
Linear Approximation
Assuming a linear Jc(B) relation, with the
normalization function simplified to f(b)
=
lbl, and
using the symmetry at the center (x
=
0)
the integral
equation is simplified to a linear type. An analytical
solution, as an approximation for small values of
A,
is
found by integrating a constant current (j(x)
=
1):
(8)
With this approximation for the overall current density
the relative current in the self field is:
1
(J(x),)
dx
=
1
-A
In
4
s
1
-
1.4
A
(9)
Using a value of
10
tesla for the upper critical
field, and the critical current found in the
antiparallel geometry the characteristic parameter
is
approximately:
A
=
0.008,
according to
(9)
the
reduction of the critical current
is
negligible.
.
B.'Solutions for Large
A
So
far the strong decrease of the critical current
in the perpendicular field as found in the experiments
has not been taken into account. There are two ways of
improving the approximation mentioned above:
I)
Increasing
A:
Approximate the experimental J,(B)
curve by fitting it with a much smaller critical field.
2)
Changing
f(b): Another way to change the J,(B)
relation in the model is by changing the function f.
A numerical calculation is made for a wide range of
the characteristic parameter
A.
The integral equation
(5)
in its linear approximation
is
solved by building a
set of linear equations for the solution J(x). If an
equidistant distribution for the points at the x-axis
is
used the solution becomes unstable, except for
a specific range near
A
=
0.3.
These instabilities
appear on the edges (for smaller
A)
or
in the center
of the tape (for larger
A).
An improvement of the calculation is found by
adjusting the points along the x-axis to build an
equidistant distribution, along in the J-b plane. This
iterative produces a consistent and non oscillating
solution for J(b)
(
figure
6).
Again a simple integration completes the calculation
of the overall critical current in the tape. Together
with the analytical solution, only valid for A<<1, this
result
is
plotted in figure
7.
The calculated result
indicates that the critical current in the NbTi tape,
under self field conditions, can be described by a
A
value near unity. Reducing the current to
50%
in a
single tape and
35%
in a parallel tape were
A
is
doubled, as
it
is
proportional with the thickness.
i
0
1
-x
fig.
6:
Calculated profiles for the current in the tape
in self field, using a linear approximation
.
\
\
\
-,
1.
The critical current density in NbTi tape depends
on the direction of the magnetic field. A magnetic
field of
1
tesla perpendicular to the surface of the
tape reduces the critical current with a factor of
100.
A magnetic field in the other direction, perpendicular
to the current but along the surface of the tape, shows
a less pronounced critical current decrease.
2.
Without an external field the critical current
density in the tape
is
limited below the intrinsic
value, due to the self field component pointing
perpendicular through the surface.
3.
The current reduction caused by the self field
is
described in a one dimensional model, and appears to be
independent of the width of the tape as
it
was also
found experimentally.
4.
The highest value for the critical current in
self field appears when the tape is put in a bifilar
geometry. This is a favourable property for using this
tape in a superconducting switch.
5.
The maximum critical current density of
2.10' A/m2
is
Just enough to match the properties of
the best switches as known. In this case
it
is
necessary that the heat capacity of the switch
is
not
further increased with additional (stabilizing)
materials
REFERENCES
[ll
G.BJ.
Mulder, "Increasing the operating frequency
of
superconducting
rectifiers",
Thesis, University
of
Twenre, the
Nerherlands,
1988.
[2]
G.BJ.
Mulder et
al,
"Experimental
results
of
Thermally controlled
superconducting switches
for
high frequency operation",
Proc.
MT
10
Boston, Massachusetts,
Sept.
23-26, 1981.
131
R.
Hanwx.
"Calculation
of
AC
losses
in
a
type
I1
superconductor".
Proc.
IEEE,
no
113,
p.
1221,
1966.