*Index Terms*---Accelerator, superconducting magnet, superconducting
cable, Nb~3~Sn.

# I. Introduction

[Recently]{.smallcaps}, a number of Nb~3~Sn dipole magnets have been
built and tested in order to demonstrate the feasibility of using a
brittle superconductor with a \"cosine theta\" winding approach \[1\].
The small bending diameters associated with the poles of cosine theta
cross section dipoles require that the cable be wound in the unreacted
condition in order to prevent damage to the Nb~3~Sn superconductor. An
alternative design concept, the common coil design \[2\], utilizes flat
pancake coils with large bending radii, and allows the consideration of
a react and wind technique for fabrication of coils from Nb~3~Sn or
other brittle superconductors. Several designs for 11 T common coil
dipoles were developed at FNAL in the past year \[3\]. All designs
utilize Nb~3~Sn wire, with a J~c~ (12 T, 4.2 K)=2000 A/mm^2^. The key
feature of these magnets is the cable, which must be designed to bend
around a 90 mm radius with a low degradation of the critical current
(\<15%). If the wire is reacted on a spool with twice the minimum coil
bending radius, the maximum bending strain in the conductor will be
equal in the straight section and in the ends of the magnet. The bending
strain depends on the strand diameter used for the cable. In addition,
the bending strain can be smaller or larger, depending on whether the
layers of strands in the cable stick together or slide during cable
bending. A R&D program \[4\] was launched to develop the optimal cable
design for a react and wind common coil dipole. The strand chosen for
the program was left-over ITER type wire manufactured by IGC. To keep
bending strain below acceptable levels the strand diameter was
restricted to ≤0.7 mm. The material was drawn to the nominal wire sizes
and sent to LBNL for cabling. With the high current requirement for the
magnet (15-20 kA) a high aspect ratio cable design was pursued. The
cables produced for the test program are described next.

# II. Prototype cable fabrication and reaction

Three cables with width 15 mm were chosen for evaluation: (1) a 41
strand cable with 0.7 mm diameter strands, (2) a 57 strand cable with
0.5 mm strands, and (3) a 259 strand cable with 0.3 mm strands. The 259
strand cable is made in two steps\--a first stage 6-around-1 cable and a
second stage consisting of 37 first stage elements cabled into the
standard flat Rutherford-type cable (Fig. 1).

![](media/image1.wmf){width="4.2347222222222225in"
height="3.05in"}Fig. 1. 0.3 mm strand cable made from 37, 6-around-1,
sub-elements.

TABLE I

Cables for the react and wind cable r&d -- dimensions in mm

  --------- ------- ------- -------------- --------------- ----------------
  Cable No. Wire∅   Str. No Cable          Core dimension  Min/max
                            dimension                      strain^1^

  *A1*      0.7     41      15.04x1.22     none            0.170 / 0.365

  *A5*      0.7     41      15.04x1.24     0.013x12.7      -\|\|-

  *B1*      0.5     57      15.01x0.86     none            0.122/0.260

  *B2*      0.5     57      15.04x1.35     0.025x12.7      -\|\|-

  *C1*      0.3     7x36    15.05x1.53     0.013x12.7      0.196 / 0.421^2^

  *C2*      0.3     7x36    15.05x1.51     none            -\|\|-

  *D*       0.7     60      22.22x1.25     none            0.170 / 0.365
  --------- ------- ------- -------------- --------------- ----------------

> All ITER type strands have a copper to non-copper ratio of 0.85. (1)
> Min/max strain refers to strand alone or 2 strand inter-layer bonding
> for a magnet with a minimum bending radius of 90 mm. (2) strains in
> cable C calculated for the 0.8 mm diameter sub-element.

This, being the only way to produce a high current cable from 0.3 mm
strands for our common coil magnet. In addition, a very wide (22 mm)
cable, made from 60 0.7 mm strands was successfully made in view of a
one-layer magnet design. Two versions of each cable were attempted (one
with no core, and the other with a core of 316-L stainless steel). In
addition several cable parameters were explored for each type of cable,
including number of strands, amount of compaction, and strand tension.
Once these parameters were optimized, cables of acceptable quality were
produced for each type (listed in Table I). However, the cables with a
core were somewhat problematic, and cores of varying thickness were
tried before successful cables could be made. It was found that cables
should either be core-dominated (thick core) or strand dominated (thin
core), the intermediate region of core vs. cable thickness resulting in
strand-popping or core-buckling after release of the cabling tension. At
least 10 m of each type of cable were produced for testing and
evaluation. Long lengths of cable B1 (260 m) and A5 (70 m) were produced
for coil winding experiments.

In the react and wind approach, the strain at all stages of coil
construction and operation must be considered. The first step is
reaction on a metal spool. The important considerations here are (1)
strand surface preparation so that the strands do not sinter together
during reaction, (2) method of winding onto the reaction spool, i.e.
layer or pancake winding, and (3) spool diameter. Coating the strands
with a

![](media/image2.png)

Fig. 2. Practice coil winding with cable B1.

synthetic lubricant (5% Mobil I in Naptha*)* during cabling was chosen
as method for preventing the strands from sintering, since this method
has been shown effective in previous studies \[5\]. Additionally the
cross-contact resistance in cables with bonded strands would be very
small, resulting in high loss and multipole hysteresis during ramping of
the magnet. A pancake winding for heat treatment was chosen to avoid the
hard way bend that is associated with the cable during layer winding.
Heat treatments for all cables were successful. The synthetic oil
lubricant proved to be an effective measure to prevent the sintering of
the strands within the cable for all samples. After reaction, the cored
cables, generated a noise during first time bending. The noise could be
related to cracking or stick-slide motion of the core.

The change of cable dimensions during reaction is still being
investigated. Recent measurements \[6\] on ITER type cables showed that
in the "free" case the cable width and thickness increase by 3% and 5%
and that the cable contracts longitudinally by 0.45 %. The cables listed
in Table I partly confirmed these findings. However, the effect of
reaction tooling on the dimensional changes of the cables is under
investigation. An important result from the first heat treatment
campaigns was that the cable dimensions remain uniform over the whole
length of the cable.

First winding tests for the common coil magnet have started recently. An
insulation procedure for pre-reacted cables was developed. The
insulation is wrapped around the cable with a low wrapping tension, so
that the cable is not excessively bent. The cable is supported along all
the way from the spools to the insulation device to avoid bending under
its own weight. As insulation an E-glass tape (60 µm) with 12.5% overlap
has been chosen as the lowest cost option. A picture of the first
practice coil winding is shown in Fig. 2.

# III. Measurement of the cabling degradation

The cabling degradation was obtained via the comparison of critical
current measurements on virgin strands and strands extracted from a
cable. The measurements (Fig. 3) indicate, that the cabling degradation
at 10 T in 0.5 and 0.7 mm diameter strands is 1-4% and 6-8%
respectively. The 6-around-1 sub-cable was not degraded prior to
cabling. After cabling the degradation of the 6-around-1 sub-cable is
16%!

![](media/image3.wmf)

Fig. 3. Cabling degradation measurements on 0.3, 0.5 & 0.7 mm strands.

![](media/image4.wmf)

Fig. 4. Degradation of 1 mm (triangles) and 0.7 mm (squares & circles)
ITER type strands due to a maximum bending strain of 0.15, 0.21 and
0.4%, compared to calculations (dashed) according to Ekin's deviatory
strain model, assuming an intrinsic filament pre-compression of 0.2%.

It was found that the cabling degradation is partly caused by a
cross-sectional surface reduction of the strand during cabling \[7\]. It
increases with magnetic field. Indications were found that the field
dependent part of the cabling degradation can be described with Ekin's
deviatory strain model \[8\], assuming an additional compressive strain
after reaction due to cabling of the order of 0.01%. Further
investigation is required to support this hypothesis.

# IV. Measurement of the bending degradation

Measurements of the degradation due to bending in 0.7 and 1 mm diameter
ITER strands, are shown in Fig. 4. The degradation is obtained by
normalizing the critical current of a bent strand on the critical
current of a similar un-bent strand. The measurement procedure and the
sample-holder design are described elsewhere \[4\]. It can be seen in
the plot that the agreement with Ekin's model (in the short twist pitch
limit) \[8\] is good, especially at low levels of maximum strain.

A series of similar measurements on cables was started recently. To
measure the critical current degradation of cables due to bending strain
the following procedure was developed:

![](media/image5.wmf){width="3.44375in" height="2.5875in"}

Fig. 5. Cable critical current sample-holder before insertion into
test-station.

![](media/image6.wmf)

Fig. 6. Critical currents of samples of cables A5 (here with a on virgin
strand measurement extrapolated to the cable level) for different
fields.

The cables were reacted bent and straightened before measurement in the
cable test facility at NHMFL \[9\]. Results were compared with those of
unbent samples. Fig. 5 shows a sample-holder\[10\] before insertion into
the test-rig. The first test results on a series of cables of type A5
(made from 0.7 mm strands), reacted straight and bent (reaction spool
diameter 290 mm), are shown in Fig. 6 \[11,12\]. Four samples reacted in
the straight condition gave similar critical currents. Four samples,
reacted in the bent condition, gave varying results. The calculated
maximum strain in the "bent" samples was 0.18 or 0.42%, according to
whether the two layers of strands in the cable were bending
independently, or not. Fig. 7 shows these results normalized to the
critical current of a virgin strand (hence free of cabling degradation),
extrapolated to the cable (the strand was reacted with the cables). In
addition, the measured cabling and bending degradation (see Fig. 3&4)
are indicated as lines. As expected, the straight samples have only
cabling degradation. The best performing bent sample of this series has
only a small bending degradation, indicative of a bending strain
determined by a single strand diameter rather than the cable thickness.
The worst performing sample is degraded by \~25%, which, is more than
the bending degradation found on strands for a max

![](media/image7.wmf)

Fig. 7. Normalized Critical Current of 0.7 mm strand cables (A5) reacted
straight and bent, compared to cabling and bending degradation
measurements performed on strands (see Fig. 3 & 4). Upper line: cabling
degradation only; 2^nd^ and 3^rd^ line from top: cabling plus bending
degradation at 0.2% and 0.41% maximum bending strain; bottom line
(dashed): bending degradation calculated^\[8\]^ with max bending of
0.4%.

![](media/image8.wmf)

Fig. 8. Effect of transverse pressure on critical current (here
normalized on its value at 20 MPa) for different fields. Sample A5 --
with bending strain (full symbols), without bending degradation (open
symbols). Dashed lines are calculated with Ekin's model.

bending strain of 0.4%. However a calculated prediction of the bending
degradation at that maximum strain (indicated in Fig. 7) level using
Ekin's model predicts an even larger degradation.

Similar measurements on a cable of type C2 revealed (not shown here) a
small bending degradation, indicative of a strain determined by the
strand diameter (0.3 mm). Unfortunately, due to a large cabling
degradation (see Fig. 3) this cable type presently is not optimal.
Further samples with lower packing factors will be measured next.

The n-values were 40 and higher for "straight samples" (in agreement
with the n-values on the virgin strand), while in the bent samples they
were \~ 20.

# V. Measurement of the transverse pressure effect

Lorentz-force and vertical pre-stress, result in a large vertical
pressure on the cables in a magnet. Fig. 8 shows the effect of pressure
on the cable broad face on the critical current of an A5 sample (reacted
bent). The pressure is applied with a hydraulic piston, provided in the
magnet system of the NHMFL test station \[9\]. Fig. 8 shows that the
critical current linearly decreases with pressure and that a degradation
of \~10 % is found at 100 MPa at 11 T. The sensitivity to pressure
increases with magnetic field, in agreement with Ekin's formula for the
strain sensitivity of H~c2~ (dashed lines in Fig. 8). The calculated
results according to Ekin were obtained with an intrinsic
pre-compression in the strands of 0.2% (as before in the calculation of
the bending degradation in strands) and an "average" bending strain of
0.3%. The pressure in the model had to be three times the nominal
(average) pressure indicated in the plot. This can be explained by
stress-concentration effects (e.g.) at the cable-edges. The labels in
Fig. 8 indicate the measurement sequence, showing the reversibility of
the pressure degradation effect. The n-values were not affected by
pressure. Although only limited data were taken, there are hints that
the pressure effect is similar in samples with and without bending
strain (see open symbols in Fig. 8).

# VI. Conclusion

Fermilab and LBNL are exploring the react and wind technique with
Nb~3~Sn superconductor for a common coil accelerator magnet. To this end
the critical current degradation of Nb~3~Sn cables subject to cabling,
bending and transverse pressure was measured. Procedures for the cable
fabrication, reaction and insulation were developed. LBNL produced
prototype cables made from 0.3, 0.5 and 0.7 mm strands with and without
core. The cables were reacted on a spool using synthetic oil to keep
strands from sintering. The degradation due to cabling was measured: it
varies between 5-7%. First measurements of the degradation due to
bending agree well with predictions from literature. The cable results
correlate well with separate strand measurements of cabling and bending
degradation. The doubly transposed cable has a too large cabling
degradation and its design has to be improved. Hints were found, that
the use of a core can result in high degradation. More measurements are
required for a better understanding of this behavior. The critical
current degradation due to pressure on the cable broad face after cable
bending was found to be linear (\~1% per 10 MPa) and reversible. The
next milestones for the react and wind R&D are the completion of cable
and winding tests and the test of a set of racetrack coils in a common
coil configuration.

# References {#references .Reference-Head}

1.  S. Gourlay et al., "Fabrication and Test of Nb~3~Sn Racetrack Coils
    at High Field", presented at this conference.

2.  R. Gupta, "A Common Coil Design for High-Field 2-in-1 Accelerator
    Magnets", 1997 Particle Accelerator Conference, May 1997.

3.  G. Ambrosio et al., "Development of a React & Wind Common Coil
    Dipole for VLHC", presented at this conference.

4.  G. Ambrosio et al., "Study of the React and Wind Technique for a
    Nb~3~Sn Common Coil Dipole", ", IEEE Trans. on Appl.
    Superconductivity, v. 10, No 1, March 2000.

5.  T.A. Painter et al., "Progress in the Manufacture of the Cable in
    Conduit Nb~3~Sn Outsert Coils for the 45 T Hybrid Magnet", IEEE
    Transactions on Magnetics 30, July 1994.

6.  D. Chichili, T. Arkan, I. Terechkine, "Mechanical Properties of
    Niobium Tin Composites", Fermilab Conf --99/052.

7.  E. Barzi et al., "Strand Critical Current Degradation in Nb~3~Sn
    Rutherford Cables", submitted for publication to this conference.

8.  J.W. Ekin, "Strain Scaling Law and Prediction of Uniaxial and
    Bending Strain effects in Multifilamentary Superconductors", in
    Filamentary A15 Superconductors, M. Suenaga and A.F. Clark, Editors,
    New York, Plenum Press, 1980.

9.  P. Bauer, D. Dietderich, "Critical Current Measurements of
    Superconducting Cables at the National High Magnetic Field
    Laboratory -- Documentation/User Guide Version 1", Fermilab,
    Technical Division Note, TD-99-039, Aug., 1999.

10. J. Ozelis, P. Bauer, K. Ewald, "Design of a Sample Holder for
    Measurements of Nb~3~Sn Cable Critical Current under Transverse
    Loading Conditions", Fermilab, Technical Division Note, TD-99-051,
    Nov., 1999.

11. P. Bauer, G. Ambrosio, J. Ozelis, E. Barzi, D. Dietderich, K.
    Ewald, G. Miller "Results of the first series of Measurements of the
    Critical Currents of Cables for the React&Wind Cable Development
    Program", Fermilab, Technical Division Note, TD-00-049, May, 2000.

12. P. Bauer, G. Ambrosio, J. Ozelis, E. Barzi, D. Dietderich, K.
    Ewald, M. Fratini, G. Miller "Results of the second series of
    Measurements of the Critical Currents of Cables for the React&Wind
    Cable Development Program", Fermilab, Technical Division Note,
    TD-00-074, Nov, 2000.

[^1]: ^^Manuscript received Sept 17, 2000.

    This work was supported by the U.S. Depart­ment of Energy.

    P. Bauer, G. Ambrosio, N. Andreev E. Barzi, K. Ewald, M. Fratini,
    S.W. Kim are with Fermilab, Batavia, IL 60510 USA (telephone:
    630-840-5409, e-mail: pbauer@fnal.gov).

    D. Dietderich, H.C. Higley, R. Scanlan are with Lawrence Berkeley
    Lab, Berkeley, CA 94720 USA.

    G. Miller, J. Miller are with the National High Magnetic Field Lab,
    Tallahassee, FL 32310 USA.

    A.K. Ghosh is with Brookhaven National Lab, Upton, NY 11973 USA.

    J. Ozelis is with Jefferson Lab, Newport News, VA 23606 USA.