Transient poloidal field effects in twisted multifilamentary superconductor for toroidal field windings of tokamaks Page: 2 of 8
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TRANSIENT POLOIDAL FIELD EFFECTS IN TWISTED MULTIFILAMENTARY
SUPERCONDUCTOR FOR TOROIDAL FIELD WINDINGS OF TUKAMAKS'
S. S. Shen and J. R. Miller
Oak Ridge National Laboratory
Oak Ridge, Tennessee 37830
In this paper a circuit mcdel is presented for
a twisted filamentary superconductor exposed to a
pulsed parallel external field. Experimental results
are also reported on the measurements of transient
loss voltage aini its change due to transport current.
The measurements are in reasonable agreement with
that predicted by the postulated model.
Tokamak fusion reactors are designed to operate
in a pulsed mode. At the start of each burn period,
the toroidal field windings will be subjected to a
rapidly changnur magneti- field with components both
parallel and perpindicular to the conductor. When
filac-ntary sitLrconductuxs carrying dc transport
current encountcr such r:sid external perturbation,
they will dissipate heat and may become unstable.
In time varyirg tran.verse magnetic fields, it
is well kaown that a twist of pitch length k P <,c
(where i is a Laracteristic length of the con-
ducror} can eliminate mosr of the coupling effects.1,2
In fc:. twistir.g as essential for the stable per-
for:4n.e of tl, filamenta-v superconductors, However,
when transient lvnitudiral fields are considered,
twisting is re snsible for flux linkages which
create coupling between filaments and may lead to
high ,c losses !nd instcbiiity. This effect has
been observed ly Jungst3 in magnetization measure-
ments. Jungst also defined a critical length at
which the outermost layer of filaments becomes
saturated. This analysis deals with the whole length
and cross section of the conductor. An equivalent
couplr.g circuit is presented and ac losses are
calculated. The effect of transport current on the
ac losses is also discussed and examined experiment-
In what is to follow it will be assumed that the
conductor has a large number of veiv fine filaments
and the magnetic field is uniform over the conductor.
It will also be assumed that the filaments are uni-
formly distributed in hexagonal array.
51 units are used, with the following notation:
B = longitudinal field change rate
J = filament critical current density
2L = conductor length
ro = condurtor outer radius
d= conductor outer diameter
i - twist pitch
x0 - 2ir /ip conductor twist parameter
r - length between twist pitch reversals
t . effective transverse matrix resistivity
d - filament diameter
)L - fractional portion of superconductor in
N - number of concentric layers of super-
w = distance between nearest points of
P - loss per unit volume
Figure 1 shows the equivalent coupling circuit
for a conductor in a weak longitudinal time-varying
magnetic field. Each single filament is considered
I I .CS IR .
Figure 1. Equivalent coupling circuit
to be a voltage generator with negligible internal
resistance. For filaments at radius r, the voltage
generator over the length -z to +z is given by
V(r) - irr2(22
where 2a/p is the number of twist turns over length
2z. The induced screening currents in the outermost
filaments tend to flow through the matrix into the
irier ones. Inevitably, these screening currents
must return down the inner filaments in the opposite
direction. Thus a current loop is formed as will
appear in the analysis below.
The coupling current AIt at r is expressed as
Research sponsored by the U. S. Energy Research and Development Administration under contract with the
Union Carbide Corporation.
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Shen, S.S. & Miller, J.R. Transient poloidal field effects in twisted multifilamentary superconductor for toroidal field windings of tokamaks, article, January 1, 1975; Tennessee. (digital.library.unt.edu/ark:/67531/metadc869002/m1/2/: accessed December 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.