[^1]

*Abstract*--- The strain in a high field Nb~3~Sn coil was measured
during magnet assembly, cool-down, excitation and spot heater quenches.
Strain was measured with a full bridge strain gauge mounted directly
over the turns and impregnated with the coil. Two such coils were placed
in a "common coil" fashion capable of reaching 11T at 4.2K. The measured
steady state strain in the coil is compared with results obtained using
the FEM code ANSYS. During quenches, the transient strain (due to
temperature rise) was also measured and compared with the calculated
mechanical time response to a quench.

*Index Terms*---Strain gage, Superconducting Magnet, Quench.

# Introduction

Pre-stress in superconducting magnets has always been considered a
necessary part in minimizing conductor motion and reduce "training".
Measuring pre-stress however required special consideration due to the
complex and none-linear nature of the assembly. Measuring sensors such
as strain gauges or capacitor gauges are usually placed on the coil
peripheral structure or collars in an attempt to determine the coil
stress \[1\], \[2\]. In the past measured strain during assembly, cool
down, excitation and warm up, suggested that coil stress may vary in
non-linear fashion that is also history and time dependent. A phenomenon
called "ratcheting", measured in different magnet structures, suggested
a possible connection between the behavior of coils under Lorentz
forces, pre-stress, and training. We proceeded to impregnate strain
gauges within the coil for the following reasons: 1) a simpler more
reliable way to determine the coil stress 2) make strain measurements
anywhere within coils 3) measure thermal and quench effects 4) shed
light on training and better understand what can be done to eliminate it
5) compare with ANSYS strain calculations during a quench \[3\]-\[5\].

The method of placing strain gauges directly onto coils takes full
advantage of the impregnation process typical in Nb~3~Sn coils. An
alternative method of attaching strain gauges to coils after
impregnation has been tried elsewhere \[6\], \[7\].

We describe the technique of mounting strain gauges (Section II),
discuss measured strain data during assembly, cool down, and excitation
(Section III) and report on transient strain during spot-heater induced
quenches (Section IV).

# Strain Gauges and Traces

## Superconducting Coils 

Winding small Nb~3~Sn racetrack coils (\~2kg each) is a good way of
testing new ideas before their use in large magnets. The small coils,
approximately 300mm long and 90mm wide, are wound as a double pancake
and reacted at 650 C. Two such coils, SC13 and SC14, each with a
surrounding stainless protection horseshoe, were placed facing each
other in a "common coil" fashion and assembled into a structure (Fig.
1). The assembly used keys and bladders, taking full advantage of the
difference in thermal expansion between the inner coils, iron yoke and
the external aluminum shell. Testing coils this way was sufficient to
withstand pre-stress requirements up to 11T (at approximately 10kA).

![](media/image1.jpeg){width="3.035416666666667in"
height="2.48125in"}Fig.1. Exposed racetrack coil surrounded by iron
pads, iron yoke laminations, and aluminum shell.

Attaching strain gauges to coils and securing their position was done
with a coil trace overlay. The trace, a ProE (CAD) drawing, included two
full-bridge strain gauges, a spot-heater, and several voltage-taps
(Fig.2). Drawn on vellum paper the trace was subjected to a photo etch
process that resulted in a 25μm thick stainless image over a 50μm thick
Kapton sheet. Micro-Measurements full bridge strain gauges (350Ω,
SK-13-120NB-350) where used to replace cutout marked squares on the
Kapton sheet. The gauges were aligned and soldered to the Kapton trace
using short copper wires (Fig. 3). The heater was partially detached
from the trace, folded side ways and tucked between two turns in the
center block of the straight section Voltage taps on both sides of the
heater were extended over a 100mm segment and attached to the trace as
well. The measured RRR of that segment was later used to determine the
average coil temperature near the spot heater. The gauges on coil SC13
were designated the nomenclature SG13heater for the one next to the
heater and SG13Lead for the one on the lead side of the coil, opposite
the heater. The second coil, SC14, had similar gauges. SC14Lead broke
off shortly after cool down and was not used.

![](media/image2.jpeg){width="3.4944444444444445in"
height="1.2479166666666666in"}

Fig. 2. Trace drawing of the strain gauges, voltage taps and heater.

![](media/image3.wmf)

Fig 3. Cut out in the Kapton sheet with attached strain gauge.

A 100μm thick fiberglass cloth was placed between the coil and the
trace. Because the gauges are wider than the turns, they measured the
averaged strain across 5 turns (8mm). After impregnation, the gauges,
trace, turns and island become transparent making them completely
visible through (Fig.4).

We assume the thermal expansion of the coil to be isotropic and the
bridge temperature to be self-compensating. The full bridge strain is
bidirectional (ε~p~ - ε~n~), measuring the strain difference between
that along the turns (ε~p~) and that across them (ε~n~). We expected
that in a short common coil configuration end forces to dominate the
measured axial strain ε~p~ compared with the transverse strain ε~n.~

The stainless steel shoes were also instrumented with strain gauges
measuring the bidirectional strain in the mid straight section of the
shoe. The shoe strain (ε~p~ - ε~n~) was that between the strain along
the shoe and the normal across the coil.

![](media/image4.jpeg){width="3.416535433070866in"
height="1.6590551181102362in"}

# Test Results

### Cool-Down and Warm-up

Strain was measured during assembly, cool-down and excitation. Only a
small pre-stress was required for assembly, since most of the pre-stress
occurred during cool-down. The measured change of strain (ε~p~ - ε~n~)
in the coil and shoe during cool-down and warm up is compared with
calculations.

TABLE I

Cool-down change in coil strain

  ----------- ------------------- -------------------- ------------------
              (ε~p~ - ε~n~) με    (ε~p~ - ε~n~) με     (ε~p~ - ε~n~) με
              ANSYS, mu=0         ANSYS,mu=0.3         measured

  COIL        1015                1277                 846±120

  Shoe        270                 906                  812±70
  ----------- ------------------- -------------------- ------------------

![](media/image5.jpeg){width="3.579861111111111in"
height="2.7152777777777777in"}Fig. 5. Measured excitation strain of coil
and shoe.

### Excitation and Spontaneous Quenches

The magnet performance was limited to 6.7kA as a result of flux-jump
instabilities (65% of short-sample). Up to that current the coil strain
gauges responded linearly with the current squared (Fig. 5). However a
zero friction ANSY model resulted in a much lower change in strain (a
factor of 6 lower). Attempts to improve the model with varying friction
factors and coil orthotropic properties made some improvement reducing
the difference by 50%. The change of strain in the shoe with excitation
was in good agreement with calculations (Fig.5).

### Excitation and Pulsed Heater Quenches

During the first six sequential spontaneous quenches around 6.7kA the
coil local strain was reduced by 20%. A series of spot-heater quenches
followed. All spot-heater quenches were triggered at a current of 1.5kA,
using a 100ms 1.5V heater pulse. The magnet power supply could maintain
the current level for about 0.5s before voltage limitations were
encountered. The current however was sufficiently high to raise the
temperature at the heater location up to a maximum of 350K (with a 3.5s
delay). After each power supply shut-off, a constant current of 20A was
sustained in the coil in order to monitor the segment resistivity and
record the temperature decay.

Two data acquisition systems were used. A fast data acquisition system
with a resolution of 2ms measured the strain history during a quench,
and a slower acquisition system took measurements at 1s intervals. A
typical time history for coil SC14 (case H11) is shown in Fig.6 (pre and
post quench), and Fig 7 (during the quench). Recorded are the current,
spot heater-pulse, strain, and segment temperature. The maximum
temperature attained in case H11 was room temperature and the local
change in strain was 2300με (compressive). As the current drops to zero
and superconductivity is recovered the strain near the heater location
does not return to its original +500με level but rather remains
suppressed at a temporary level of -600με.

Shown in Fig. 8 are three consecutive spot heater quenches (at 1.5kA
each) followed by a spontaneous quench, Q03, at 6.1kA. The fast changing
strain during a pulsed quench is negative (indicating compression)
resulting from the local rise in temperature. Cool-down to 4.3K
following the spot heater quench does not cause a return in the local
strain to its pre-quench level. Subsequent spot heater quenches, with
longer time durations before power shut off (higher temperatures),
successively increase the compressive strain and its departure from its
original strain level.

Raising the current to 6.1kA raises the strain from −1350με to +650με
due to Lorentz forces. Following the spontaneous quench (which does not
originate next to the spot heater) the local coil strain recovers most
of its original value. During the current increase Lorentz forces remove
most of the ratcheting that occurred during the previous 3 spot heater
tests. The recovery is therefore highly none linear. Figure 9 shows the
rise in strain as a function of the current square. The gauge recovers
most of its strain as the Lorentz forces increase, replacing its initial
none linear behavior with a linear one. The quench resets the coil and
recovers most of its original strain. The gauge in the second coil
(SC13), which didn't undergo a high temperature excursion, continues to
exhibit a linear dependence on Lorentz stress.

![](media/image6.jpeg){width="3.497916666666667in"
height="2.7152777777777777in"}Fig. 6. Measured strain and temperature
near the spot heater before and after a quench.

![](media/image7.jpeg){width="3.497916666666667in"
height="2.696527777777778in"}Fig. 7. Measured strain and temperature
near the spot heater during a quench.

![](media/image8.jpeg){width="3.579861111111111in"
height="2.6326388888888888in"}Fig. 8. Three spot-heater quenches,
followed by a spontaneous 6.1kA quench.

The temperature dependence of the same three spot heater quenches is
shown in Figure 10. Above 100K a linear behavior in the
strain-temperature curve suggests a linear integrated thermal behavior
for the coil in that range. The non-linear and hysteretic behavior of
coils between loading and unloading has been seen before in mechanical
stress-strain curves of coil samples \[8\].

![](media/image9.wmf)Fig. 9. Thermally induced compression is relaxing
during a training ramp to a quench. The degree of relaxation depends on
the local temperature reached during the thermally induced quench.

## Comparison with ANSYS 

A complete ANSY 3D electro-thermal-mechanical transient analysis has
been reported on a similar magnet \[3\]. Computations suggested that a
local heating causes the strain in the coil near that location to
undergo substantial compression as a result of local thermal expansion.
The measured strain in coil SC13 and SC14 as a function of local
temperatures is compared with ANSY results (Fig. 11). ANSYS strain
values are plotted at the heater location (Tmax) and the end of the
segment (Tmin= ±45mm away). The results are in fair agreement.

# Conclusions 

A technique of adding strain gauges to coils has been described.
Measuring coil strain during steady state and transient conditions
suggests a possible new way of studying magnet training and quench
propagation. Preliminary results suggest:

1\) Local high compressive strain during a quench.

2\) The coil stores strain energy.

3\) The stored strain energy is localized and temperature dependent.

4\) Stored strain energy can be "released" with Lorentz forces.

5\) No agreement between measured strain-Lorentz force relation and
calculations.

6\) Agreement between measured strain-temperature build up during a
quench and calculations.

Based on our analysis we suspect that the stored strain energy is due to
bending.

![](media/image10.wmf)Fig. 10. Change in coil strain as a function of
local temperature during and after three consecutive spot heater
quenches.

![](media/image11.jpeg){width="3.497916666666667in"
height="2.55625in"}Fig. 11. Comparing measured strain and ANSYS
calculations during a spot-heater quench.

# References {#references .Reference-Head}

1.  C.L. Goodzeit et al. "Measurement of internal forces in
    superconducting accelerator magnets with strain gauge transducers",
    *IEEE Trans.* on Magnetics, vol: 25, no. 2, pp.1463 -- 1468, Mar
    1989.

2.  T. Shintomi et al. "Design, fabrication, and test of a 5-cm
    aperture, 1-m long superconducting dipole prototype for high energy
    Hadron collider" *IEEE Trans.* on Magnetics, vol: 27, no. 2, pp.1743
    -- 1747, Mar 1991

3.  P. Ferracin et al. "Thermal, Electrical and Mechanical Response in
    Nb~3~Sn Superconducting Coils" *IEEE Trans. Appl. Superconduct*.,
    vol. 14, no. 2, pp. 361-364, June 2004.

4.  S. Caspi et al. "Calculating quench propagation with ANSYS", *IEEE
    Trans. Appl. Superconduct*., vol. 13, no. 2, pp. 1714-1717, June
    2003.

5.  L. Imbasciat et al. "Effect of thermo-mechanical stress during
    quench on Nb~3~Sn cable performance" *IEEE Trans. Appl.
    Superconduct*., vol. 13, no. 2, pp. 1718-1721, June 2003.

6.  J. Chikaba et al. "Instabilities due to mechanical strain energy in
    superconducting magnets" ", *IEEE Trans.* on Magnetics, vol: 23, no.
    2, pp.1600 -- 1603, Mar 1987.

7.  F. Broggi et al. "Mechanical measurements on the race-track
    prototype for the ATLAS B0 and barrel toroid magnet" *IEEE Trans.
    Appl. Superconduct*., vol. 10, no. 1, pp. 385-388, March 2000.

8.  D.R. Chichili et al. "Investigation of cable insulation and
    thermo-mechanical properties of epoxy impregnated Nb3Sn composite"
    *IEEE Trans. Appl. Superconduct*., vol. 10, no. 1, pp. 1317-1320,
    March 2000.

[^1]: ^^Manuscript received October 4, 2004. This work was supported
    under contract DE-AD03-76SF00098 by the Director, Office of Energy
    Research, Office of High Energy Physics, U.S. Depart­ment of Energy.

    All authors are with Lawrence Berkeley National Laboratory,
    Berkeley, CA 94720 (phone: 001 510 486 7244; fax: 001 510 486 5310;
    e-mail: s_caspi@lbl.gov).