Assessment of the Effect of Current Non-Uniformity on the ITER Nb3Sn Good Joint Short Sample DC Performance
ABSTRACT The DC performance of the so-called good joint Nb3Sn short sample conductor, measured in the SULTAN facility in 1999 with a progressively reduced (chopped) joint length, became worse as the joint became shorter. In this paper we present the analysis of those tests using the THELMA code. The results confirm quantitatively that the loss of performance was due to increasingly unbalanced current distribution. Once the unbalance due to the joint is properly modeled, the performance of the conductor can be fitted using the same extra longitudinal strain in the critical current scaling, proportional to the electromagnetic load but independent of the joint length.
[show abstract] [hide abstract]
ABSTRACT: A joint between superconducting cables is one of key elements in a large-scale magnet. Joint-resistance-induced nonuniform current distribution has been reported. The mechanism of this phenomenon is quite simple. The cable consists of the twisted superconducting strands. Therefore, in the DC condition, the current distribution is governed by the nonuniformity of individual sub-joint-resistances between twisted strands in different legs; those are mainly determined by the joint configuration. When one strand carries larger current and it saturates at the critical current, flux-flow resistance occurs. That nonlinear resistance functions as a current regulator. Once the current saturates in one strand, surplus current must go through other strands. Apparent critical current, n-value and current sharing temperature (Tcs) of the CICC are important parameters for magnet design. However these have been reported to be degraded from the expected values predicted from the strand performances. We analyzed the apparent evolution of flux-flow voltage along the cable considering the current nonuniformity due to the lap-joint qualityIEEE Transactions on Appiled Superconductivity 07/2006; · 1.04 Impact Factor
Article: Coupled mechanical–electromagnetic–thermal–hydraulic effects in Nb3Sn cable-in-conduit conductors for ITER[show abstract] [hide abstract]
ABSTRACT: The crucial multi-physics problem of how to extrapolate from the performance of an isolated Nb3Sn strand measured in the laboratory to the performance of a superconducting coil using multi-strand twisted cables is addressed here. We consider the particular case of the path going from the LMI strand to the international thermonuclear experimental reactor (ITER) toroidal field model coil (TFMC), through its associated Full Size Joint Sample, the TFMC-FSJS. Mechanical, electromagnetic and thermal–hydraulic conditions are simulated using the ANSYS, ENSIC and Mithrandir/M&M codes, respectively. At least in this case, the DC performance of the short sample turns out to be relatively close to (considering error bars) but not fully representative of that of the coil, showing higher (less compressive) effective thermal strain but also higher sensitivity to the electromechanical load.Superconductor Science and Technology 11/2005; 18(12):S376. · 2.66 Impact Factor
Article: From Short Sample to Coil DC Superconductor Performance: ITER Central Solenoid Model Coil (CSMC) vs. Good Joint (GJ) Sample[show abstract] [hide abstract]
ABSTRACT: The problem of how representative a short Nb<sub>3</sub>Sn conductor sample is for simulating conductor-in-coil conditions in the ITER magnets is addressed here by considering the particular case of the Central Solenoid Model Coil (CSMC), tested in 2001-2003 at JAERI Naka, Japan, and its associated Good Joint (GJ) sample (tested in 1999 in the SULTAN facility). While the basic thermal-hydraulic conditions are interpreted from experimental data by the M&M code, the sensitivity of the voltage-temperature characteristics to mechanical effects (due to the strain sensitivity of the Nb<sub>3</sub>Sn) is investigated by analysis. The results are used to assess the errors to be expected in predicting coil performance from measurements made on conductor samplesIEEE Transactions on Appiled Superconductivity 07/2006; · 1.04 Impact Factor
1382IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Assessment of the Effect of Current Non-Uniformity
on the ITER ????? Good Joint Short Sample DC
L. Savoldi Richard, P. Bruzzone, N. Mitchell, P. L. Ribani, and R. Zanino
Abstract—The DC performance of the so-called Good Joint
????? Short Sample conductor, measured in the SULTAN fa-
cility in 1999 with a progressively reduced (chopped) joint length,
the analysis of those tests using the THELMA code. The results
confirm quantitatively that the loss of performance was due to
increasingly unbalanced current distribution. Once the unbalance
due to the joint is properly modeled, the performance of the
conductor can be fitted using the same extra longitudinal strain
in the critical current scaling, proportional to the electromagnetic
load but independent of the joint length.
Index Terms—Fusion reactors, modeling, superconducting mag-
perimental Reactor (ITER), it is presently foreseen to test the
conductor performance in dedicated full-size short-sample tests
in the SULTAN facility. Several samples of this type, e.g., the
so-called Good Joint (GJ) short sample considered here ,
were already tested in the past , . For two of them, the GJ
and the Toroidal Field Model Coil Full Size Joint Sample ,
the test of DC performance of the corresponding long conduc-
tors wound in a coil was also performed , . Unfortunately,
of the short sample performance for the conductor-in-coil per-
formance , . Compared to expectations based on the iso-
lated (single) strand, both short samples and coils show indeed
degradation, which can be well fitted in a uniform current anal-
ysis by assuming an extra longitudinal strain
on the electromagnetic load. However,
ferent in the sample and in the coil , .
LONG the path towards the construction of the supercon-
ducting magnets for the International Thermonuclear Ex-
turns out to be dif-
Manuscript received August 29, 2006. This work, supported by the European
Communities under the contract of Association between EURATOM/ENEA,
carried out within the framework of the European Fusion Development Agree-
ment. The views and opinions expressed herein do not necessarily reflect those
of the European Commission.
R. Zanino and L. Savoldi Richard and are with Dipartimento di Energetica,
Politecnico, Torino, Italy (e-mail: email@example.com).
P. Bruzzone is with EPFL-CRPP, Villigen, Switzerland.
N. Mitchell is with ITER IT, Naka, Japan.
P. L. Ribani is with Dipartimento di Ingegneria Elettrica, Universita’ di
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TASC.2007.899039
For both sample and coil, the analysis performed so far con-
sidered. Among those assumptions, we concentrate here on the
effects of current non-uniformity on the GJ sample DC perfor-
mance. Concerning the simplifying assumptions behind
the need and possible scope of a more detailed thermo-mechan-
ical model of the
cable should also be considered, as
already albeit preliminarily discussed elsewhere .
The GJ sample was tested with progressively reduced
(chopped) joint length. In  the analysis of the GJ DC tests
with the original (full) joint length was performed assuming
a uniform current distribution on the cross section. Here we
analyse quantitatively the GJ conductor DC performance,
measured at different joint lengths, using the THELMA code
, which can model current non-uniformity.
II. EXPERIMENTAL SETUP
The GJ short sample was assembled with two
cable-in-conduit conductors (CICC), leftover from the winding
of the fourth layer of the ITER CSMC , using the VAC
strand and an Incoloy 908 jacket. The GJ conductor was tested
for DC performance in the SULTAN facility at Villigen PSI,
Switzerland, in 1999. Three different test campaigns were
performed, with a progressively reduced joint length (from the
, down to
) , to investigate the effect of
current distribution on the conductor performance.
The setup of the experiment is schematically reproduced in
Fig. 1. The sample was tested in vertical position, with He inlet
1 MPa and 4.5 K) at the bottom. The two conductor sec-
tions (“legs”) came from the same cable length, but while leg A
was simply a straight section, leg B was bent and re- straight-
ened to simulate the mechanical loads applied during the react-
and-transfer coil manufacturing process.
The joint and the upper terminations are manufactured in the
wraps from the sides to be connected, the compacted cables are
soldered to the Cu saddle modular elements. The joint is then
closed into a steel box.
The experimental results show that the conductor DC per-
formance was strongly affected by joint length (the shorter the
joint, the worse the performance) ,  and anyway lower
than expected from the strand performance. Both issues were
qualitatively explained at the time of the test as an effect of
which could not be effectively redistributed because of sub-
1051-8223/$25.00 © 2007 IEEE
RICHARD et al.: EFFECT OF CURRENT NON-UNIFORMITY ON ITERGOOD JOINT SHORT SAMPLE DC1383
Fig. 1. Schematic view of the GJ sample: (a) longitudinal view, (b) cross sec-
tion. Tx=thermometer, Vx=voltage tap. Lengths quoted in mm.
cable wraps and of the short distance between the joint and the
contribution to performance degradation related to the electro-
magnetic load on the conductor will also be included.
III. THELMA SIMULATION SETUP
The electromagnetic model of the cable, which is imple-
mented in the THELMA code, is described in . The current
distribution among the strands is calculated by means of a
distributed parameter model. In the present study, we model six
cable elements (CE), corresponding to the last-but-one cabling
stage (petals), so that all the strands in a petal are supposed
to carry the same current, which is a function of the axial
coordinate (z) and of time
of the cable are taken from , except for the petal twist
pitch, which was assumed equal to 500 mm instead of the
nominal 420 mm in view of the experimental evidence from
. The transverse conductance per unit length between two
. The geometrical parameters
adjacent petals is
. The transverse conductance between two non-adjacent
petals is considered negligible. The usual power law relation
is utilized for the
the superconducting (SC) material (
the SC material,
interpolative scaling law and the n-value depend on the
, on the modulus of the magnetic field
the longitudinal uniaxial strain
VAC strand we compute
zero strain, fully consistent with the average
sample conductor 
For the generic (i-th) CE, the uniaxial strain
depend on the local transverse electromagnetic load , 
, taken from the measurements
is the current density in
). The critical current density
as shown in , . For the
at 4.2 K, 12 T and
of the short
is supposed to
magnetic field in the CE, respectively.
determined, which is used to fit the measured critical current
inal (long) joint , which was carried out under the hypothesis
of uniform current distribution, we derive
. While in  (1) was based on
the average magnetic field computed on the cable cross section,
here we apply (1) locally to each petal. Thus the magnetic field
is computed on the respective petal axis, while the current
is that of each CE (because of this,
of 6 with respect to the value in )
is the thermal strain,and are the current and
is a constant to be
is multiplied by a factor
B. Joint and Termination
The complete model of the termination/joint which is imple-
mented in the THELMA code is described in . The distribu-
tion of the current density in the termination/joint region is cal-
the present study, only resistive effects are considered. The con-
the geometry of the CEs, assuming a value of the distributed
contact resistance between CE and saddle, which roughly re-
produces the measured joint resistance of
Consistently with , we model here only the current dis-
tribution in Leg A of the sample, assuming an equipotential
surface at the joint mid-plane (and at the upper termination
boundary as well); the contribution of Leg B to the magnetic
field is included.
at 10 T and
ramp have been selected, which have
tests at the background field of 10 T and temper-
–7.3 K (see Fig. 1), at the beginning of the
the same Lorentz load:
), E0604009 (chopped
), E1905003 (chopped).
The thermal-hydraulic boundary conditions for our analysis are
fixed He inlet temperature (assumed equal to the measured
value) and pressure, and fixed outlet pressure, such as to re-
produce a mass flow rate of
3.5 g/s. The central channel was
blocked in the shortest joint test
and in the
1384IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Fig. 2. Experimental (symbols) and computed average (solid) voltage evolu-
tion V5V7 for the different joint lengths. The computed maximum (dashed) and
minimum (dash-dotted) voltage are also reported, see text.
respective simulation. The total transport current at the equipo-
tential joint/termination surfaces is imposed.
IV. SIMULATION RESULTS AND COMPARISON WITH THE
The computed results are reported in Fig. 2 in terms of
voltage-current (V-I) characteristics. Different CEs show dif-
ferent voltage evolutions, because they carry different currents
and redistribution is hindered by the sub-cable wraps (see
below). For the purpose of the comparison with the experiment,
we consider the computed resistive voltage between V5 and V7
(see Fig. 1), averaged over the 6 petals. In some cases the full
V-I characteristic was not recorded, so that the voltage offset
has been chosen somewhat arbitrarily. The agreement of the
simulations with the measured voltage is very good (within
1 kA) for all joint lengths. The slope is somewhat overes-
timated, but this is due to the assumption
Since the strain recipe (1) is the same for the three simulations,
the degradation in conductor performance with the progressive
joint chopping (computed
and 47 kA, respectively) is confirmed to be due only to the
increasing current non-uniformity induced by the joint.
The computed evolution of the current unbalance among the
petals (more-or-less uniform along the conductor, because of
the low inter-petal conductance) is reported in Fig. 3 for the
different joint lengths. It is shown that the current unbalance
is in the range 70–130% in the case of the shortest
, 52.6 kA
Fig. 3. Computedcurrent unbalancein the petals for the different joint lengths.
joint, while the current is almost uniform in the case of the orig-
inal (unchopped) joint.
Again due to the low value of the transverse conductance
between the CEs, the redistribution of the current takes place in
the joint/termination region. Before the current sharing regime
is reached, the current repartition among the CEs, develops
towards the resistive distribution due to the termination/joint
contact resistances with the petals. The current sharing regime
starts in this case before the resistive distribution is reached. In
Fig. 3(c) the mechanism of current redistribution to adjacent
petals can be well observed: the petal #5 is the first to approach
the critical condition, because it carries the highest current in
view of the longest contact (lowest resistance) with the joint
saddle, see Fig. 4.
redistributes to the adjacent petals # 4
and 6 and petals # 1 and 3 are involved only eventually, while
the farthest petal (#2) is the slowest to react. (Note that, in
Fig. 3(b), petal #3 follows this time petal #2, which is again a
consequence of contact distribution, see Fig. 4). The current
redistribution to adjacent petals causes also a change of slope
in the computed V-I characteristic, see Fig. 2(c), which is
unfortunately impossible to confirm experimentally, because
data acquisition was interrupted early in this case. This could
also be related, however, to the assumed values for inter-petal
V. CONCLUSIONS AND PERSPECTIVE
The THELMA analysis of the effects of current non-unifor-
mity on the DC performance of the GJ conductor has quanti-
tatively confirmed the previous qualitative suggestion that the
reduction of the performance with the chopped joint is an effect
RICHARD et al.: EFFECT OF CURRENT NON-UNIFORMITY ON ITERGOOD JOINT SHORT SAMPLE DC 1385
Fig. 4. Cable geometry in the joint as modeled by THELMA: cross sections at different axial locations z, with the respective position of the different petals (#1
to #6). The dark grey section indicates the joint saddle. The joint ends at ? ? ??? ?? where the conductor starts.
of the current unbalance in the cable. The V-I characteristics
of Leg A measured at the same field and total Lorentz force,
but for different joint lengths, have been well fitted using lo-
cally the same longitudinal strain recipe and suitably modeling
the joint length reduction. This confirms the results of previous
analysis based on the uniform current assumption , showing
that the short sample performance degradation with respect to
the strand is not related to current non-uniformity but can be
correlated with the transverse electromagnetic load (and also
with cycling effects—to be discussed elsewhere). This analysis
additionally indicates that the discrepancy between the sample
case at least, to current non-uniformity effects in the sample. A
thermo-mechanical model of the cable, more physically based
than (1), is being developed  to address this remaining open
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