A novel electrical method to measure wire tensions for time projection chambers

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A Novel Electrical Method to Measure Wire Tensions for Time Projection Chambers
Diego Garcia-Gameza,∗, Vincent Basquea , Thomas G. Brooksa,1 , Justin J. Evansa , Michael Perrya , Stefan Söldner-Rembolda , Fabio
Spagliardia,2 , Andrzej M. Szelca
a School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom

arXiv:1804.05941v2 [physics.ins-det] 24 Sep 2018

Abstract
We present a novel electrical technique to measure the tension of wires in multi-wire drift chambers. We create alternating electric
fields by biasing adjacent wires on both sides of a test wire with a superposition of positive and negative DC voltages on an AC
signal (VAC ± VDC ). The resulting oscillations of the wire will display a resonance at its natural frequency, and the corresponding
change of the capacitance will lead to a measurable current. This scheme is scalable to multiple wires and therefore enables us
to precisely measure the tension of a large number of wires in a short time. This technique can also be applied at cryogenic
temperatures making it an attractive solution for future large time-projection chambers such as the DUNE detector. We present the
concept, an example implementation and its performance in a real-world scenario and discuss the limitations of the sensitivity of
the system in terms of voltage and wire length.
Keywords: LArTPC; APA; Wire tension; Electrical

1. Introduction
The next generation of neutrino experiments will use LiquidArgon Time-Projection Chambers (LArTPCs) as detector technology [1]. In these detectors, the ionization electrons produced
in the passage of a charged particle drift from their production
points towards planes of anode wires, called Anode Plane Assemblies (APAs). The wires are strung or wrapped at different orientations along the length of a metallic frame. A minimum of two planes is required for three-dimensional reconstruction of the events in the liquid argon. The pitch between
wire planes and between wires in a plane is typically a few millimeters (3–5 mm), which defines the spatial resolution of the
LArTPC. With the increasing size of these detectors, ranging
from a few hundred tons for the short-baseline neutrino (SBN)
experiments [2] to 10 kt for a single DUNE module [3], the
numbers of wires can go from tens of thousands to hundreds of
thousands.
When these detectors cool down to liquid-argon temperatures, the thermal contraction in the thin wires can occur faster
than in the steel frame. For that reason, the nominal tension requirement chosen for the wires must be small enough to prevent
breaking of wires during cool down, while being strong enough
to ensure even the longest wires do not sag, as this could introduce readout noise [4]. To prevent wire breakage or sagging,
the completed wire planes need to be surveyed to ensure the
wire tension is within specifications. Currently, this is the most
time consuming step in the production of APAs. The standard
∗ Corresponding Author

Email address: diego.garciagamez@manchester.ac.uk (Diego
Garcia-Gamez)
1 now at the University of Sheffield
2 now at the University of Oxford
Preprint submitted to Elsevier

method used to measure the tension employs a laser-based optical setup that measures the fundamental frequency of the wire,
which is related to the wire tension T through
T = 4µL2 f02 ,

(1)

where µ is the wire’s linear mass density, L its length, and f0
its fundamental frequency in Hz. To perform the laser measurement, the wires have to be mechanically excited by, for example, strumming [5] or compressed air [6, 7]. The usage of this
mechanical method in large-scale detector production is difficult to envision due to how time consuming it can become and
the difficulty of replicating the automated positioning system at
the final assembly site. To mitigate sagging and breakage, wires
are split into segments by using holders or combs, similar to
capodasters, at intervals along the wire length. This can result
in different tensions in each of the segments, requiring separate
measurements for each segment, thus further complicating the
procedure.
Different electromagnetic-based techniques of measuring
wire tensions in wire chambers have been described in the literature [8, 9, 10, 11, 12]. Here, we present a novel method
using an electric-based system which resolves most of the difficulties of the laser-based setup. This technique has the ability
to measure multiple wires simultaneously, does not require a
mechanical disturbance of the wires and permits measurements
of tension at cryogenic temperature, even when the cryostat of
the detector is closed. In this work we have demonstrated our
method in a stable environment of cooled down gaseous nitrogen, at a temperature comparable to that of liquid argon. This
last feature has never been available in LArTPC detectors and
could be used to monitor the tension change during cooling in
situ and identify any problems arising from the cooling process,
providing the possibility to correct them immediately.
September 25, 2018

space between PCB tracks making it even harder to apply the
needed high voltage bias. Our method’s need for significantly
smaller bias voltages across each component makes it immediately applicable to modern LArTPC detectors.
For simplicity, we use a two wire model in order to describe
the signals that will be obtained. If the wires are in air (or gas
nitrogen as in Section 5), we can assume that the system is underdamped, and the amplitude a(ω) of the driven oscillation for
a given angular frequency ω of the driving force will factorize
as
a(ω) = ae (ω) + aconst ,

(2)

where

Figure 1: Schematic of the electrical tension measurement system. The ground
wire is denoted by a dashed line; it is the wire under measurement. Wires
denoted with a solid line are biased with a combination of AC and DC voltages,
the latter with a changing sign. This results in an enhanced electric force on the
wire under test.

ae (ω) ∝ VAC VDC

ω20 − ω2
(ω20 − ω2 )2 + (2Γω)2

= VAC VDC f (ω) (3)

and
aconst ∝

2. Description of the system
Each pair of wires in a multi-wire chamber acts as a capacitor. As proposed in Ref. [8] an electric force is created by applying AC and DC electric fields, which causes oscillating movements of the wires. The displacements of the wires change the
capacitance of the two-wire system. When the AC frequency
corresponds to the natural frequency of either wire the system
encounters a resonance, making the displacement particularly
large and the change in capacitance measurable through the
change in current flowing between the wires. If the driving
force has the form F ∝ sin(ωt), the wires will move as a driven
damped harmonic oscillator.
In the setup discussed here we employ a system of three wires
(see Figure 1). The wire under test is kept at ground potential,
while the two adjacent wires in a wire plane are biased by an
AC voltage with added or subtracted DC voltages (VAC ± VDC )
on either side. At the resonance frequency, the wires will oscillate as in a two-wire system. For the ground wires, the opposite
electric fields on each side will enhance the resultant electric
force responsible for the movement. This novelty carries with
it two major improvements: (i) it breaks the ambiguity introduced by the technique using two wires [8] and (ii) it requires
relatively low voltages, of the order of a few hundred volts.
The need for this low bias voltage is driven by the design of
modern TPC detectors where wires are usually held by termination boards built to apply the plane bias voltage, which is on
the order of few hundred volts. Since in normal TPC operation the wires are never exposed to large potential differences,
the electric components and PCB tracks on these boards are
typically not designed to work at high voltages, limiting the
maximum bias voltage that can be applied between adjacent
wires in a plane. Previously proposed electrical tension measurement methods [8] require placing a large bias voltage, as
large as 1.7 kV, across the wires to obtain a reasonable signal.
Using such a method in LArTPC detectors would thus require
installing appropriately rated resistors and capacitors to accommodate this voltage, which would be prohibitively expensive.
In addition, the wire pitch itself might also limit the maximum

2
VDC

ω20

,

(4)

where Γ is the damping coefficient of the system and ω0 = 2π f0
the natural angular frequency of the wire. We have folded the
resonant behaviour into f (ω). The expected current read out
from the circuit, assuming a(ω)  wire pitch, can then be described as
I(t) = c1 VAC ω cos(ωt) − c2 VDC ωae (ω) cos(ωt)+
+ O(VAC ae (ω))
h
i
2
≈ c1 VAC ω − c2 VDC
VAC ω f (ω) cos(ωt) ,

(5)

with constants c1 and c2 that depend on the system. Equation 5
shows that if VAC  VDC , then the amplitude of the output
current in the frequency domain will have the form shown in
Figure 2. The term proportional to c1 gives the underlying linear rise in amplitude, proportional to the driving frequency. The
term proportional to c2 introduces a bipolar resonance that centers on the natural frequency of the wire, and scales with the
2
voltages as VAC × VDC
. The amplitude of the signal at resonance also scales with 1/(4Γ(ω0 − Γ)) in the maximum and
−1/(4Γ(ω0 + Γ)) in the minimum. This means that√for a given
tension n × T 0 , the amplitude ratio changes as 1/ n. In Section 4.2 we compare the behaviour of a system composed of
three wires to this prediction. In a realistic system, additional
effects may play a role, such as the presence of the other wire
planes which could also affect the amplitude. These will be
tested in a future work.
A tension measurement becomes a scan over frequencies of
the driving AC voltage, and a search for the bipolar signature
of the resonance in the amplitude of resulting current (read out
as voltage). For each frequency value we measure the peak-topeak amplitude of the signal five times. This value results in a
precise measurement and more iterations add time to the acquisition without significantly improving the precision. The points
and the uncertainties are the mean and the standard deviation
of the different measurements, respectively. Figure 2 shows a
typical frequency scan observed in our setup. The bipolar resonance is clearly visible. We fit Equation 5 to this data to obtain
2

Signal Amplitude [V]

0.2
0.195
0.19
0.185
0.18
0.175
0.17
0.165
32

33

34

35

36

37

38

AC Frequency [Hz]

Figure 2: Frequency scan of a wire with the bipolar resonance peak of the data
points fitted with the model described by Equation 5 (red line).

ω0 , from which we calculate the wire tension using Equation 1.
The parameters c1 , c2 and Γ are also allowed to vary in the fit.
3. Implementation of the Setup
Figure 3: Simplified schematic of the measurement system.

A schematic of the measurement system is shown in Figure 3.
The main components are:
under test to instrumentation amplifiers that buffer the signals
and remove interference by subtracting the noise signal provided by the antenna wire.
The wires under test and the antenna wire are connected to
the interface box via a cable harness comprising a screened ribbon cable to minimize coupling of the bias AC component between the wires. The bias voltages are connected using hookup wire. The buffered signals from the wires under test are then
fed to the digitizer and onto the PC. A LabVIEW program running on the PC sweeps the injected AC signal through a defined
range of frequencies and logs an average of the amplitude of
the acquired signals for each frequency step.
One of the attractive features of this novel method is the option of measuring the tension of multiple wires at the same time.
The number of wires that can be measured at once is only limited by the hardware cost per channel. The multi-channel system we have developed can read out 32 wires at a time whilst
connected to 65 wires (every other wire has an AC±DC bias).
This can easily be scaled up to any multiple of 32 (or 64 if using the VME version of the digitizer). With the described setup,
our measurement time is about 1 s for a scanning range of 1 Hz.

• Two high voltage power supplies to provide the ± DC signal.
• A standard sine wave generator with remote control interface (Keithley model 3390).
• A linear AC high voltage amplifier to increase the sine
wave amplitude above the 10 V maximum value provided
by the signal generator (Falco Systems model WMA-02).
• A 24–30 V DC power supply to power the AC amplifier
(< 150 mA).
• A bespoke interface box.
• A DC power supply (±12 V) to power the instrumentation
amplifiers in the interface box.
• A CAEN DT5740 Digitizer.
• A PC running LabVIEW acquisition software.
The measurements described in this article are made using
a custom stainless steel frame with anchored FR-4 boards at
each end, which is similar to currently used wire plane designs,
e.g., in the SBND detector [2]. Copper-beryllium wires with
a diameter of 0.15 mm are soldered to metallic pads at a 3 mm
pitch. The wires are connected to the electrical system through
a bespoke interface box.
Within the interface box, the positive and negative DC voltages from the two high voltage power supplies are each combined with the amplified AC voltage from the signal generator
to form the two bias voltages (VAC + VDC and VAC − VDC ). An
extra wire is connected without bias as an antenna to subtract
ambient noise from the measured voltages. The interface box
connects the bias voltages to the adjacent wires and the wires

4. Performance of the system
4.1. The signal features
The novelty of the approach described here is the capability to measure the tension of multiple wires without ambiguity.
During a frequency scan, the fundamental frequency of each
of the wires involved in the measurement should be observed
through a resonant signal. If all the wires are at the same or very
similar tensions, which is a typical feature in real-life detectors,
the signal frequencies will lie very close together or overlap.
The method using only two wires, proposed in Ref. [8], makes
3

it very complicated or even impossible to distinguish between
the wires in the frequency scan as the resulting amplitudes are
of comparable size.

VDC [V]

280
7.07

Amplitude
[V]
Signal Amplitude
[V]

260

0.96

Wires à (1::2::3)
0.94

Wires 2 & 1

6.12

12.16

5.02

10.08

15.67

4.09

8.34

12.43

16.21

3.35

6.45

9.67

13.20

15.58

2.61

4.79

7.80

10.02

11.92

12.48

1.79

3.32

5.09

7.02

8.83

8.78

20

40

60

80

100

120

240

0.92

220
0.9

200

0.88
0.86

180
0.84

Wire 3

0.82

160

0.8
62

64

66

68

140

70
Frequency [Hz]

12.16

140

VAC [V]
0.88

Wires à (2::3::4)

(a)

0.86
0.84

Signal Amplitude relative to (20V, 150V)

Amplitude
[V]
Signal Amplitude
[V]

60

0.82

10

0.8
0.78

Wire 4

0.76
0.74
60

62

64

66

68

70
Frequency [Hz]

AC Frequency [Hz]

Figure 4: An illustration of the principle of decoupling the frequency of the
wire under measurement from the biased wire frequencies. In the top panel
wire 2 is measured and the large dip corresponds to its natural frequency. In the
bottom panel wire 3 is being measured, making its dip significantly larger and
the dip corresponding to wires 2 and 4 significantly smaller.

model prediction
8

6

4

2

0
0

In the setup presented here, multiple wires are biased and
grounded in parallel, see Figure 3, but each individual measurement uses three wires (VAC + VDC , ground, VAC − VDC ), as
illustrated in Figure 1. The wire in the center of the three-wire
configuration will produce a significantly higher signal than the
other two, because of the opposite-sign electric fields applied on
both sides of the wire. This feature makes possible to discriminate between the inner and outer wires and resolve degeneracies
between the fundamental frequencies of adjacent wires. To illustrate this point, we built a system with four wires of 1.3 m
length each (typical length of wire segments in the ProtoDUNE
single phase and SBND detectors). In order to demonstrate the
central wire enhancement we prepared the wires with slightly
varied tensions: (1) 5 N, (2) 5 N, (3) 4.8 N, and (4) 4.6 N. These
tensions correspond to frequencies of 66.8 Hz, 66.8 Hz, 66 Hz,
and 64 Hz, respectively which are visibly separate in a frequency scan.
For this illustration we use relatively high voltages of 40 V
for the AC amplitude and ±350 V for the DC voltage, to increase the amplitude of the signals. As a result the signal of
the adjacent, non-grounded, wires is clearly visible. In the first
case, shown in the top panel of Figure 4 we bias wire (1) and
wire (3) at AC±DC and leave wire (2) at ground. As a result we observe two distinct signals where the larger peak, at

data

10

20

30

40

50

60

6
3.5
VAC × V2.5
]
DC × 10 [ V

(b)
Figure 5: (a) Signal amplitudes (in mV) measured in bins of (VAC , VDC ) and (b)
2.5 . All measurements are quoted relative to the value
as a function of VAC × VDC
in the bin (20 V, 150 V). Measurements are compared to the function defined by
Equation 5 (dashed line).

higher frequency and thus higher tension, is the combined signal of wires (1) and (2), which are at the same tension (5 N).
The smaller peak is the signal of wire (3). In the second case,
shown in the bottom panel of Figure 4, we instead bias wire (2)
and wire (4) applying AC±DC voltages while leaving wire (3)
at ground, enhancing the signal from that wire. As expected,
the large signal of wire (3) in the bottom panel appears at the
same frequency of the smaller signal in the top panel. In the
bottom panel we observe two small peaks from the adjacent
wire (2) and wire (4), as they have different tensions. In both
cases, the signal of the wire at ground is significantly larger
than for the other wires. The disambiguation becomes even
easier when using smaller voltages, because the signals of the
adjacent stimulation wires become negligible leaving only the
signal of the wire under evaluation. This can be observed in the
signals shown in Figure 2 and Figures 6–7.
4

4.2. Dependence on VAC and VDC
Signal Amplitude [V]

The c2 term of the model described in Equation 5, derived
assuming a simple two wire system, predicts that the amplitude
of the output signal is proportional to the product of VAC and
2
VDC
. To test if this assumption holds for our three wire system,
we measure the amplitude in wires of 1 m length under different
bias conditions. We choose VAC = 20 V and VDC = 150 V as
a reference-point, which corresponds to an amplitude of about
1.8 mV in our setup, and we increase the values of VAC and VDC
in steps of 20 V whilst keeping (VAC + VDC ) < 300 V.
The results are shown in Figure 5(a), where the signal amplitudes measured for different values of VAC and VDC are shown.
This data set and the structure of Equation 5 allow us to evaluate
2
whether the signal amplitude depends on the product VAC ×VDC
,
as predicted by the two wire simplified model, or whether the
power dependency of either term is different. To test this we
considered the rows (constant VDC ) and columns (constant VAC )
of Figure 5(a) as separate data sets and fit a power law behaviour to VAC and VDC , respectively. We found a linear dependency on VAC and that VDC prefers a slightly steeper de2.5
pendence than expected, namely VDC
. This is demonstrated in
Figure 5(b) where for simplicity we have normalized the signal
amplitudes to the value at the reference point (20 V, 150 V). The
data show good agreement with the prediction of Equation 5,
2.5
where we change the c2 term to depend on VAC × VDC
. We can
use this updated semi-empirical model to predict the signal size
and to design a setup of the type proposed here given a particular performance requirement. This will be further explored in
Section 4.6.

0.19

0.18

0.17

0.16
28

29

30

31

AC Frequency [Hz]

Signal Amplitude [V]

(a)

0.87

0.86

0.85

0.84

4.3. Dependence on wire length
115

The signals shown in Figures 6(a) and (b) are the peak-topeak voltage in the circuit at different frequencies for wires
with a length of 3 m and 0.75 m, respectively, at voltages of
VAC =40 V and VDC =150 V. As predicted by Equation 1, the
resonances occur at different frequencies, and produce a distinguishable signal in both cases. The signal amplitude is significantly larger for the longer wire. In Equation 5, the factors c2 ,
ω0 and f (ω) depend on the wire length. The dependency of the
f (ω) factor is canceled by the dependency of ω0 , leaving the c2
term to govern the dependence of the resonance’s amplitude on
the wire length. The dependency of c2 on the wire length arises
due to the capacitance of the system: the capacitance between
two adjacent wires is proportional to their lengths, hence we
expect the dependence of the resonance amplitude on the wire
length to be linear.
To test this assumption, we study the effect of the wire length
on the signal amplitude. Figure 6(c) shows the measured amplitudes for wires at the same tension and with lengths in the range
of 0.75–3 m using the voltages VAC = 40 V and VDC = 150 V.
The amplitude is given relative to the operating point of 1 m.
We observe the expected linear relationship between amplitude
and wire length, and we also see that measurements can be
made for wires as short as 0.75 m. In Section 4.6, we will extrapolate this dependence to determine the shortest wire length
measurable at these voltages.

116

117

118

AC Frequency [Hz]

Signal Amplitude relative to 1m

(b)
4
3.5
3
2.5
2
1.5
1
0.5
0
0

0.5

1

1.5

2

2.5

3

3.5

4

wire length [m]

(c)
Figure 6: Examples of peak-to-peak amplitudes of signals as a function of frequency measured at a wire length of (a) 3 m and (b) 0.75 m. The wires are
biased with VAC ± VDC = (40 ± 150) V. (c) Measured signal amplitudes as a
function of the wire lengths. Measurements are given relative to the value at a
wire length of 1 m.

5

Tmeasured - Tnominal [N]

Signal Amplitude [V]

0.48

0.47

0.46

0.45

0.4
0.2

0

−0.2

0.44

0.43

−0.4
62

63

64

65

66

67

68

69

70

AC Frequency [Hz]

−0.6

Figure 7: Signals in wires that have been split up into three segments of about
1.3 m length each. The resonant signal from each segment is clearly visible.
The wires were biased with VAC = 40 V and VDC = 250 V.

−0.8
0.5

1

1.5

2

2.5

3

3.5

wire length [m]

(a)

4.4. Multi-segment wires
Number of measurements

The design of large-scale TPCs requires long wires with
lengths of 5 m in the MicroBooNE detector [13] or 6 m in the
protoDUNE single-phase detector [14]. Wires of this length
could be prone to mechanical deflection due to gravity, electrostatic forces, or even movement induced by argon flow. To
reduce such effects, a support structure is introduced at regular intervals along the length of the wire plane. An example of
such a structure is a series of plastic combs mounted on crossbraces that divide the long wires into segments. This minimizes
any sagging and, should a wire break, mitigates the impact of
broken wires by restricting the impact to a smaller region.
The effect of such combs on the tension measurements is that
each wire is split into multiple shorter wires with lengths determined by the spacings between the combs. These wires can be
at different tensions if they are glued to the combs. A setup using the laser method would need to measure each segment separately. The electrical measurement method is sensitive to the
fundamental frequency of all the individual segments connected
electrically. We have tested this effect using a setup where wires
of 4 m length are segmented into three units of about 1.3 m using dielectric combs. Figure 7 shows the signal obtained for a
segmented wire with well separated resonance peaks for each
segment. This demonstrates that the electrical method can be
used to measure the tension of all segments of wires divided by
combs with a single measurement.

500

Entries

900

Mean

−0.07

Std Dev

0.03

400

300

200

100

0

−0.25

−0.2

−0.15

−0.1 −0.05

(T

measured

0

0.05

- Tnominal)/T

0.1
nominal

(b)
Figure 8: (a) Difference between the measured and nominal tension for different
wire lengths. (b) Fit of a Gaussian function to the relative tension bias for wire
lengths between 0.75 m and 3 m.

in Figure 8. We observe a small reconstruction bias that depends weakly on wire length. The method systematically underestimates wire tensions by 0.2–0.3 N, or 7%. A Gaussian fit
to the measurements, shown in Figure 8b, yields a spread of the
measurements, and therefore a resolution of the technique, of
≈ 3%.

4.5. Resolution of the method
We determine the resolution of our method for different wire
lengths by repeatedly measuring the tensions of a sample of ten
wires of the same length. The tension is chosen to be 5 N as
this value is typical for the nominal tension of wires in LArTPCs [13, 14]. The tension of the wires is set by soldering the
wire to the wire-bonding-board at one end whilst it is strung
with weights attached to the other end. We assume the uncertainty on such setting of the tension to be negligible. The
wires are biased with VAC = 40 V and VDC = 150 V. We repeat this measurement at different lengths of the sets of wires:
0.75 m, 1 m, 1.5 m, 2 m, 2.5 m, and 3 m. The results are shown

4.6. Limits of Applicability
The results from Sections 4.2 and 4.3 allow us to extrapolate
the model to find the limits of the applicability of our system.
We determine the lowest combination of AC and DC voltages
and the shortest wire length at which the electrical method can
be applied. To ensure the validity of the method, we require that
95% of all measurements return a tension measurement within
5% of the true tension. The success rate of such a measurement
would depend on the amplitude of the signal and the noise.
6

Tension [N]

We use a toy Monte Carlo code to generate signals as would
be observed by the electronic setup. The amplitude is calculated using the dependencies presented in Figures 5 and 6.
The noise is modeled using measurements in our system. We
find that the noise depends weakly on the AC amplitude as
RMS/mV= (0.45 + 0.0025VAC /V). The dependence on frequency and wire length can be neglected. We shift the position of the signal resonance peak in the simulation within the
measurement interval of 0.1 Hz by a random phase.
To determine the shortest wire length, we chose the operating voltages of VAC = 40 V and VDC = 150 V as in Section 4.3.
Using the model we determine that the method should be applicable down to a wire length of 50 cm. Measuring shorter wire
lengths is possible, but would require applying higher bias voltages. We use wires of 1 m length and the dependence of the
amplitude on voltage observed in Section 4.2 to find that the
minimum values of VAC = 20 V and VDC = 150 V are close to
the sensitivity limit of the technique, corresponding to a signal
amplitude of about 1.8 mV. The electrical setup presented here
is tested with a wire pitch of 3 mm, a decrease of the signal
amplitude is expected for a larger wire pitch.

6

5.5

5

4.5

4

3.5

3

−200

−150

−100

−50

0

Average temperature [C degrees]

Figure 9: Wire tension values as function of temperature measured during the
cold test.

The equilibrium condition is satisfied at around −120◦ C and
−190◦ C. At these temperatures the tension of the wires, compared to room temperature, increases by about 6% and 20%,
respectively. This is a larger increase than expected from the
change in length of the wire caused by the thermal contraction
derived using Equation 1.

5. Cryogenic Operation
The electrical technique can be applied within a closed cryostat and at cryogenic temperatures, which is a novel feature and
important advantage. The possibility of performing a measurement under such conditions, e.g., during the cool down of the
liquid argon allows us to track the tension in real time. If the
thermal contraction of the different materials significantly alters
the tension of the wires, risking the integrity of the system and
potentially modifying the performance of a detector, we could
perform an intervention to mitigate the effect.
To demonstrate this capability, we tested our setup down to
a temperature comparable with that of liquid argon (−186◦ C)
by creating a stable environment of cooled down gaseous nitrogen. A sample of CuBe wires are soldered to FR-4 boards
anchored at the two ends of a stainless steel frame defining a
length of 72 cm for the wires. The coefficients of thermal expansion of CuBe alloy, FR-4 and stainless steel are similar. The
materials in this setup were chosen to minimize the potential
wire tension increment during the cool-down. The system is
immersed inside a vacuum-jacketed dewar which is filled with
a cold gas atmosphere. Liquid nitrogen was added to the system in controlled amounts to slowly decrease the temperature.
The dewar is equipped with four Pt1000 temperature sensors
uniformly distributed between the bottom and the top of the
steel frame to monitor the temperature along the full length of
the wires. During the cool down we maintain a gaseous atmosphere, keeping the liquid at all times at a level below the
wires, to avoid additional damping from the viscosity of the
liquid. We perform tension measurements in regions of relative equilibrium where the temperature difference between the
lowest and highest Pt1000 sensors is less then 30◦ C.
Figure 9 shows the first results of the tension measurements
at cryogenic temperatures. The data points and error bars represent the mean and standard deviations of our measurements.

6. Conclusions
We have designed and developed an electrical method to precisely measure the tensions of multiple wires simultaneously
with a resolution of about 3% applying voltages of a few hundred volts. The method uses a frequency scan of biased wires of
alternating potential and allows a measurement to be completed
within minutes, significantly reducing cost and time compared
to wire-by-wire measurements using lasers. The method also
removes the need for a physical disturbance of the wires. These
features make this procedure advantageous for the measurements of tensions of wires in large wire chambers, with thousands of wires. We study the behaviour of our system with
respect to the bias voltages applied and the wire length and we
develop a model that allows us to predict the amplitude of the
signal. We show that a measurement can be made down to wires
as short as 50 cm. Finally, we demonstrate that this technique
can be used to measure wire tension at cryogenic temperatures,
which has not been feasible before and should be applicable
during cool down of large liquid-argon TPCs.

Acknowledgements
This work was in part funded by the Royal Society and
the Science and Technology Facilities Council (STFC). V.B. is
funded by a Presidential Doctoral Scholarship at the University
of Manchester. We thank Claire Fuzipeg for the development of
the LabVIEW DAQ software. We thank Dr. Roxanne Guenette
for her insightful comments on the manuscript.
7

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