#  The measuring systems of the wire tension for the MEG II Drift Chamber by
means of the resonant frequency technique

A. M. Baldini  H. Benmansour  G. Cavoto  F. Cei<EMAIL_ADDRESS>M.
Chiappini  G. Chiarello  C. Chiri  G. Cocciolo  A. Corvaglia  F. Cuna  M.
Francesconi  L. Galli  F. Grancagnolo  M. Grassi  M. Meucci  A. Miccoli  D.
Nicoló  M. Panareo  A. Papa  C. Pinto  F. Raffaelli  F. Renga  G. Signorelli
G.F. Tassielli  A. Venturini  B. Vitali  C. Voena  Dipartimento di Fisica
dell’Università “La Sapienza”, Piazzale A. Moro, 00185 Roma, Italy  INFN
Sezione di Roma, Piazzale A. Moro, 00185 Roma, Italy  Dipartimento di
Matematica e Fisica ”Ennio De Giorgi” - Università del Salento, Via Arnesano,
Lecce, Italy  INFN Sezione di Lecce, Via Arnesano, Lecce, Italy  INFN Sezione
di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy  Dipartimento di Scienze
Fisiche, della Terra e dellAmbiente dell,Università, Via Roma 56, 53100,
Siena, Italy  Dipartimento di Fisica dellUniversità di Pisa, Largo B.
Pontecorvo 3, 56127 Pisa, Italy  Dipartimento di Fisica dellUniversità di
Bari, Campus Universitario, Via Amendola 173, 70125 Bari, Italy  Paul Scherrer
Institut PSI, 5232 Villigen, Switzerland

###### Abstract

The ultra-low mass Cylindrical Drift Chamber designed for the MEG experiment
upgrade is a challenging apparatus made of 1728 $\phi=20~{}\mu{\rm m}$ gold
plated tungsten sense wires, 7680 $\phi=40~{}\mu{\rm m}$ and 2496
$\phi=50~{}\mu{\rm m}$ silver plated aluminum field wires. Because of
electrostatic stability requirements all the wires have to be stretched at
mechanical tensions of $\approx 25$, $\approx 19$ and $\approx 29~{}{\rm g}$
respectively which must be controlled at a level better than $0.5~{}{\rm g}$.
This chamber is presently in acquisition, but during its construction $\sim
100$ field wires broke, because of chemical corrosion induced by the
atmospheric humidity.

On the basis of the experience gained with this chamber we decided to build a
new one, equipped with a different type of wires less sensitive to corrosion.
The choice of the new wire required a deep inspection of its characteristics
and one of the main tools for doing this is a system for measuring the wire
tension by means of the resonant frequency technique, which is described in
this paper. The system forces the wires to oscillate by applying a sinusoidal
signal at a known frequency, and then measures the variation of the
capacitance between a wire and a common ground plane as a function of the
external signal frequency. We present the details of the measuring system and
the results obtained by scanning the mechanical tensions of two samples of MEG
II CDCH wires and discuss the possible improvements of the experimental
apparatus and of the measuring technique.

##  1 Introduction

The Cylindrical Drift Chamber (from now on: CDCH) [1, 2, 3] is the most
innovative part of the MEG II experiment [4], an upgraded version of the MEG
experiment [5] at Paul Scherrer Institute [6] of Villigen (Switzerland), which
established the world most stringent upper limit on the
$\mu^{+}\rightarrow{\rm e}^{+}\gamma$ [7] and a significant upper limit on the
$\mu\rightarrow{\rm e}^{+}\gamma\gamma$ decay too [8]. This new chamber is a
unique volume detector, of $1.93~{}{\rm m}$ length and $34~{}{\rm cm}$ inner
diameter, equipped with $1728$ $\phi=20~{}\mu{\rm m}$111$\phi$ is the
international symbol standing for “diameter”. gold plated tungsten sense
wires, $7680$ $\phi=40~{}\mu{\rm m}$ and $2496$ $\phi=50~{}\mu{\rm m}$ silver
plated aluminum wires, used to define the electric field configuration within
the gaseous volume and at its boundaries. This huge number of wires forms a
dense matrix of approximately squared drift cells, whose size ranges from
$\approx 5.8~{}{\rm mm}$ at the chamber center to $\approx 8.7~{}{\rm mm}$
close to the chamber ends. The detector is immersed in a longitudinally
varying solenoidal magnetic field produced by a superconducting magnet (COBRA,
COnstant Bending RAdius), arranged to rapidly sweep away from the chamber
region the positrons emitted with small longitudinal momenta; the maximum
value of the magnetic field is $1.26~{}{\rm T}$ at the detector center and is
reduced by about a factor two at the longitudinal ends of the chamber. The
chamber and the other subdetectors of the MEG II experiment are equipped with
an innovative integrated trigger and acquisition system and with a custom made
high performance readout electronics, extensively described in [9, 10].

A positron emitted in a $\mu^{+}\rightarrow{\rm e}^{+}\gamma$ decay, whose
energy is $52.83~{}{\rm MeV}$, crosses on average an amount of material
equivalent to $1.6\times 10^{-3}$ radiation lengths $X_{0}$; the expected
momentum and angular resolutions at that energy are $\sim 100~{}{\rm keV}$ and
$\sim 6~{}{\rm mrad}$ respectively.

The use of very thin wires is mandatory to reduce as much as possible the
energy resolution degradation due to energy loss and multiple scattering. On
the other hand, particular care must be put during the handling and assembly
operations of such wires: the wiring operation is automatically performed by a
computer-controlled wiring robot [11] which solders the wires on metallic pads
deposited on printed circuit boards (from now on: PCBs) and builds several
multi-wire layers; then the layers are extracted, placed in storage and
transport frames, moved to the assembly site and finally installed on the
chamber end plate supports. The silver coating on aluminum wires was used to
protect the wire aluminum core and to make the soldering easier and more
stable.

Since the potential difference between anode and cathode wires in the chamber
is $\sim 1.5~{}{\rm kV}$, wires with charges of opposite sign are subject to a
strong electrostatic attraction, which can cause geometrical modifications and
short circuits. An appropriate mechanical tension is therefore needed to
counterbalance the electrostatic force and prevent the wires to collapse.

A very critical point is the possible chemical corrosion of the wires, due to
the exposure to room humidity, which can induce wire breakings when the wires
are stretched. During the chamber construction this problem arised and caused
the breakage of $\sim 100$ cathode wires, almost all with $\phi=40~{}\mu{\rm
m}$. Because of the huge number of cathode wires ($\sim 8000$), the effect of
few tens of broken cathode wires on the CDCH performances is absolutely
negligible; however, the presence of wire fragments within the chamber is
dangerous because of the strong electric fields inside it. Therefore all the
broken wires were carefully removed, the chamber construction was completed
and it is now in acquisition at PSI. However, in case of further breakages we
would be forced to stop the acquisition, open the chamber in a controlled
atmosphere, remove all fragments and close and seal the chamber again. This
operation is delicate and requires several weeks. We studied the corrosion
problem in deep details, both experimentally and phenomenologically, as
discussed in a previous paper [12] and developed a strategy to minimise the
risk of new breakages. Our detailed analysis shows that the chemical corrosion
of the wires was originated by the formation of cracks in the silver coating,
mainly during the last phase of the wire production, the so-called
“ultrafinishing” procedure, and that the breakage probability is much smaller
for the thicker $\phi=50~{}\mu{\rm m}$ wires. Therefore, we decided to build a
new chamber (while the old one is in acquisition) equipped with a different
type of cathode wires, less sensitive to chemical corrosion. Several
possibilities were explored and our present preference, not yet a final
choice, is in favour of $\phi=50~{}\mu{\rm m}$ silver plated aluminum wires,
without ultrafinishing procedure, which is unavoidable for a
$\phi=40~{}\mu{\rm m}$, but not strictly needed for a $\phi=50~{}\mu{\rm m}$
wire. The motivations for this choice and the constraints which must be
satisfied by the selected wire are discussed in [12], one of the most
important being the long-term mechanical stability of the wire when it is
stretched to compensate the electrostatic attractant force. The wire length
and tension must remain stable on time scales of at least several months,
avoiding significant deformations of the wire and maintaning a good electrical
contact with the electronic boards.

In this paper we show a technique for measuring the mechanical tension of the
wires based on the relationship between the tension itself and the resonant
frequency of an elastic string. We describe the experimental apparatus, the
acquisition and analysis software and the results of the measurements on two
samples of wires made by different aluminum alloys. We discuss the evolution
of the wire mechanical tension of these two samples, the offline corrections
to be applied and the possibility of using them in the new CDCH. We discuss
also how the performances of the measuring device can be improved by using a
new electronics, less sensitive to room temperature, or by moving the
apparatus in a controlled environment.

##  2 Characteristics of the wires used in the MEG II drift chamber

In the MEG II CDCH, three kinds of wires are used:

  * 1.

the anode (sense) wires, which collect the ionization electrons generated by
the charged particles traversing the drift chamber gas;

  * 2.

the cathode (field) wires, which define the drift cells of the chamber;

  * 3.

the guard wires, which define the electric field configuration near the edges
of the active volume.

Several wire types, manufactured by different companies (Alloy Wire
International [13], California Fine Wire Company (from now on: CFW) [14] and
Luma Metall Fine Wire Products [15]) were considered, taking into account
multiple requirements, as density, radiation length $X_{0}$, equivalent
radiation length of all wires and of wires and CDCH filling gas, and multiple
scattering angular deflection $\Theta_{MSC}$ for a $52.83~{}{\rm MeV}$
positron track. The best performance for field and guard wires was obtained
with the aluminum ${\rm Al}5056$ alloy from the CFW company, composed by
aluminum (94.6%), magnesium (5.01%), iron (0.14%), silicon (0.1%) and traces
of other elements. The wires are produced in different 4-inch spools by using
an initial wire drawing procedure which decreases the wire diameter to
$55~{}\mu{\rm m}$ in different phases; then a ultra-finishing procedure is
applied to reach the design diameter of $40~{}\mu{\rm m}$ or $50~{}\mu{\rm
m}$. The silver coating is performed by electrochemical deposition before the
ultra-finishing stage; therefore this coating is exposed to a mechanical
stress which can produce defects on the wire surface.

The density and the resistivity of the ${\rm Al}5056$ alloy are
$\delta=2.9~{}{\rm g/cm^{3}}$ and $\rho\simeq 20~{}\Omega\times{\rm m}$
respectively. An example of a stress-strain222“Stress” indicates the
longitudinal tension force acting on a mechanical wire, sometimes divided by
its the cross section; “Strain” indicates the elongation of the wire when it
is exposed to the tension force. curve for a $\phi=50~{}\mu{\rm m}$ aluminum
wire is shown in figure 1.

Figure 1: A stress-strain curve for a Al5056-silver plated $\phi=50~{}\mu{\rm
m}$ wire.

Pure gold plated tungsten is used for anode wires, whose diameter is
$20~{}\mu{\rm m}$. The anode wire material has a density $\delta=19.27~{}{\rm
g/cm^{3}}$ and a resistivity $\rho=175~{}\Omega\times{\rm m}$. This type of
wire allows us to use a readout electronics with lower gain and bandwidth (and
hence lower noise) compared to other wires considered in order to be able to
use the cluster counting technique [16].

The mechanical parameters of the silver plated Al$5056$ and gold plated
tungsten wires selected for the CDCH are summarized in table 1.

Table 1: Mechanical parameters of the MEG II CDCH wires. | Elastic limit | Breaking point | Elastic Modulus
---|---|---|---
Wire type | Elongation | Tension | Elongation | Tension | $\left({\rm g/mm/m}\right)$
| $\left({\rm mm/m}\right)$ | $\left({\rm g}\right)$ | $\left({\rm mm/m}\right)$ | $\left({\rm g}\right)$ |
20 $\mu$m W | $5.30\pm 0.05$ | $62.0\pm 0.7$ | $19.7\pm 0.3$ | $86.0\pm 2.5$ | $11.92\pm 0.091$
40 $\mu$m Al | $4.81\pm 0.14$ | $44.3\pm 0.8$ | $5.82\pm 0.33$ | $50.0\pm 2.5$ | $9.20\pm 0.13$
50 $\mu$m Al | $4.90\pm 0.04$ | $69.5\pm 0.5$ | $5.58\pm 0.31$ | $75.3\pm 3.9$ | $14.17\pm 0.20$

The operating point was chosen at an absolute elongation of $5.2~{}{\rm mm}$
with respect to the rest length, corresponding to about $60~{}\%$ of the
elastic limit of all wires. This value was obtained by means of detailed
Garfield [17] based simulations of the electrostatic stability of the whole
chamber and confirmed experimentally with the chamber in operation.

##  3 Wire tension measurement theory

The mechanical tension of the wires is one of the fundamental parameters that
determines the correct operation of a drift chamber since it avoids wire
deformations and short circuits between anode and cathode wires due to their
potential difference. Performing a measurement of the mechanical tension of
the wires before and during the chamber construction is crucial in order to
understand the operation capabilities of the drift chamber and to figure out
possible weak points in its construction. The wire mechanical tension needs to
be monitored also after the installation on the chamber and when the wires
have been stretched to the elongation needed to ensure the electrostatic
stability and kept stable at a level $<0.5~{}{\rm g}$. A precise measurement
of the chamber dimensions is performed periodically at PSI by means of an
optical survey.

The indirect measurement of the wire mechanical tension is based on the method
of the resonant oscillation induced on the wires [18], already used by other
high energy physics experiments [19, 20]. The nominal resonant frequency of a
wire is given by:

$\nu_{r}=\frac{1}{2L}\sqrt{\frac{T}{\mu}}$ (1)

where $L$ is the wire length, $T$ is the wire tension and $\mu$ is the wire
linear mass density.

The nominal resonance frequencies for the three different wires used in the
MEG II drift chamber and their working tensions are reported in table 2; all
wires have a nominal resonance frequency $\approx\left(50\div 55\right)~{}{\rm
Hz}$.

Table 2: Nominal resonance frequencies for the three types of wires. The linear density values take into account the different alloy compositions and coatings. Wire type | $\mu~{}\left(10^{-6}~{}{\rm g/m}\right)$ | $T~{}\left({\rm g}\right)$ | $f~{}\left({\rm Hz}\right)$
---|---|---|---
$20~{}\mu$m W (Au) | 6.04 | 24.51 | 51.74
$40~{}\mu$m Al (Ag) | 4.38 | 19.25 | 53.83
$50~{}\mu$m Al (Ag) | 6.53 | 29.64 | 54.74

The technique for measuring the effective resonant frequency of a wire is
based on the effects induced by an external harmonic electric field on the
capacitance $C_{wg}$ of a system formed by a wire and a ground plane. The
capacitance $C_{wg}$ is given by the formula:

$C_{wg}=\frac{2\pi\varepsilon L}{\ln\left(\frac{4H}{d}-1\right)}$ (2)

where $H$ is the distance between the wire and the ground plane, $d$ is the
wire diameter, $L$ is the wire length and $\varepsilon$ is the dielectric
constant of the material in-between the wire and the ground plane.

The ground plane is kept at a fixed position, while the wire is suspended on
its ends and is free to oscillate as a violin chord. When a sinusoidal signal
is applied to the wire, the wire is forced to oscillate and the distance
between the wire and the ground plane changes with time, depending on the
frequency of the external signal. Then, also the capacitance $C_{wg}$ varies
with time and can be measured by using an auto oscillator circuit. When the
distance between the wire and the ground plane increases, the capacitance
becomes smaller (formula 2) with respect to the situation when the wire is at
rest, while when the distance decreases, the capacitance becomes larger. Then,
the asymmetry between the capacitance measured when the wire is at the maximum
and at the minimum distance from the ground plane is sensitive to the
frequency of the external signal and is expected to reach its maximum value
when this frequency matches the resonant frequency of the wire.

##  4 The measurement system

The measurement system is shown in figure 2 and is formed by the following
elements:

  * 1.

A sinusoidal High Voltage (from now on: HV) generator circuit with a A7505P
CAEN chip;

  * 2.

A sinusoidal Low Voltage (from now on: LV) generator (not shown in the
figure), interfaced by means of a jack connector with the HV generator;

  * 3.

a Ring type auto oscillator circuit for the measurement of the frequency
variations;

  * 4.

a Xilinx Spartan-3E FPGA to process the signals of the auto oscillator and of
the LV generator and to handle the data;

  * 5.

a group of HV switches to select the wires to measure;

  * 6.

a USB port to interface the system with the DAQ computer;

  * 7.

a group of connectors for power lines and test signals.

Figure 2: The measurement system.

The sinusoidal LV generator, controlled by the DAQ computer through an
Ethernet connection, produces a $\left(0\div 4\right)$ V amplitude and $\sim
50~{}{\rm Hz}$ frequency signal, which is used to modulate a high frequency
($\approx 40~{}{\rm MHz}$) signal, generated by means of an inverter chain.
The LV signal is amplified from few V to $\sim 1~{}{\rm kV}$ in the HV
generator and sent to the wire; the wire is then excited by a signal at the
desired frequency of some tens of Hz and starts to oscillate, modifying the
distance between the wire itself and the ground plane. The Ring type
oscillator is connected to the wire under measurement; the combination between
the oscillator, the wire and the ground plane is equivalent to a RC circuit,
with two capacitances in series, that intrinsic of the oscillator and
$C_{wg}$, as shown in figure 3.

Figure 3: Electric scheme of the inverter chain of the Ring oscillator and
equivalent circuit of the combination between the Ring oscillator, the wire
under measurement and the ground plane. C$2$ and R$1$ are the intrinsic
capacitance and the resistance of the Ring oscillator, while C$1$ is the
variable capacitance $C_{wg}$ between the wire under measurement and the
ground plane. The effective value of $C_{wg}$ depends on the real distance
between the wire and the ground plane, so that the value ${\rm C}_{1}\approx
1~{}{\rm pF}$ is simply an indication of its expected order-of-magnitude.

The low frequency signal is also sent, before to be amplified, to a pair of
comparators, interfaced with the FPGA chip, to form two square wave pulses and
two synchronous gates. One of the square waves is inverted and shifted by
$90^{\circ}$ in order to enhance the frequency asymmetry (see later) when one
crosses the resonance condition. Since the two waves are inverted, one of the
two gates is opened when the leading edge of the oscillating signal exceeds
the discrimination threshold and is closed when the trailing edge goes under
this threshold, while for the other gate the opposite situation takes place;
then, one gate (from now on: gate $A$) is opened when the external pulse makes
the distance between the wire and the ground plane to increase, and the other
(from now on: gate $B$) when the external pulse makes this distance to
decrease.

Since a variation of the distance between the wire and the ground plane
corresponds to a variation of their capacitance $C_{wg}$, when gate $A$ is
open $C_{wg}$ is at its minimum value and when gate $B$ is open $C_{wg}$ is at
its maximum value. Referring to the equivalent circuit in figure 3 one can
deduce that the Ring oscillator frequency is different during the opening
times of gates $A$ and $B$. Note that the distance between the wire and the
ground plane is a critical parameter of the measurement and must be carefully
chosen: a too large distance would make the capacitance variations too small
for a reliable measurement, while in case of a too small distance a large
oscillation could cause a contact between the wire and the ground plane. We
used an average distance of $\approx 1.5$ cm; at this distance the capacitance
$C_{wg}$ when the wire is at the rest position is $\approx 18~{}{\rm pF}$,
when the wire and the ground plane are at the maximum distance is $\approx
16~{}{\rm pF}$ and when they are at the minimum distance is $\approx 30~{}{\rm
pF}$, so that the expected variation of the capacitance is $<14~{}{\rm pF}$.

The two gates have the same duration: $T_{A}=T_{B}=T=1/\nu$, where $\nu$ is
the frequency of the slow modulation signal ($\sim 50~{}{\rm Hz}$), so that
the number of Ring oscillations $N_{A}$ and $N_{B}$ measured during gates $A$
and $B$ is proportional to the frequencies $f_{A}$ and $f_{B}$ of the Ring
oscillator at the opening times of the two gates. The frequency aysmmetry
$\Delta f=f_{A}-f_{B}$ is therefore a measurement of the wire oscillation
amplitude as a function of $\nu$. Because of the $90^{\circ}$ phase shift, the
maximum $\Delta f$ occurs when $\nu=\nu_{r}$, i.e. in resonance conditions.
The resonant frequency of the wire is therefore identified by searching for
the maximum value of $\Delta
f\left(\nu\right)=f_{A}\left(\nu\right)-f_{B}\left(\nu\right)$ as a function
of $\nu$ by a frequency scan in a suitable range. Each $\Delta f$ measurement
is repeated over several periods of the LV oscillating signal and the number
of repetitions is chosen according to the required precision of the
measurement. It is interesting to note that the typical value is $\Delta f\sim
1~{}{\rm kHz}$, corresponding to a $\sim 10^{-5}$ relative effect on a $\sim
40~{}{\rm MHz}$ signal.

Figure 4 shows a block diagram of the measurement system.

Figure 4: Block diagram of the measuring system

##  5 DAQ and analysis software

The DAQ code, originally written in Labview and then rewritten in C to ensure
higher flexibility, drives the low frequency generator and all interfaces
between the measuring system and the acquisition computer.

The DAQ software sends the excitation pulses to the wires in an adjustable
frequency range, which can be tuned according to the expected region-of-
interest for the resonance frequency. Since the resonant frequency is expected
between $50$ and $55~{}{\rm Hz}$, the excitation frequency scan is performed
in the range $\left(40\div 60\right)~{}{\rm Hz}$, at $0.25~{}{\rm Hz}$ steps.
Fifty excitation pulses are sent for each measurement point and $<2$ minutes
are needed to perform all measurements on a single wire. All data are
automatically written and saved on disks, together with room information on
temperature and humidity, needed to perform offline corrections. The analysis
chain is largely automated and based on C codes working under ROOT
environment; the data acquisition and the full analysis on a representative
sample of six wires require less than $15$ minutes and can be easily performed
on a day-by-day basis also on much larger samples.

For each wire, the Ring oscillator frequency asymmetries333We remind that the
frequency asymmetry of the Ring oscillator is a measurement of the amplitude
of wire oscillations induced by the excitation signal. of the fifty pulses
corresponding to a given excitation frequency $\nu$ are averaged and their
standard deviation is computed; then, the pairs $\left(\nu,\langle\Delta
f\left(\nu\right)\rangle\right)$, where $\langle\Delta
f\left(\nu\right)\rangle$ is the average frequency aysmmetry, are fit with a
Breit-Wigner type curve plus a polynomial background:

$\langle\Delta
f\left(\nu\right)\rangle=\frac{A_{r}}{\left(1-\left(\frac{\nu}{\nu_{r}}\right)^{2}\right)^{2}+\left(\frac{\nu}{\Gamma_{r}}\right)^{2}}+\sum_{i=1}^{6}c_{i}\left(\nu-\bar{\nu}\right)^{i}$
(3)

In this formula $A_{r}$ is proportional to the frequency asymmetry at the
resonance, $\nu_{r}$ is the resonant frequency, $\Gamma_{r}$ is the resonance
width, $\bar{\nu}$ is fixed at the center of the scan frequency range
($50~{}{\rm Hz}$) and $c_{i}$ are phenomenological coefficients. An example of
a fit to an excitation curve is shown in figure 5.

Figure 5: Example of the excitation curve of a MEG II CDCH wire. The Breit-
Wigner behaviour close to the resonance at about $53~{}{\rm Hz}$ is clearly
visible.

The mechanical tension of the wire is computed from the resonance frequency by
inverting Equation 1.

##  6 Measurements and results

The measuring system was in operation for more than one year in an INFN-Pisa
laboratory. Despite the laboratory hadn’t any temperature or humidity control
infrastructure, the system operated in good conditions, with limited human
interventions; however, as we will show later, the room conditions were
monitored and a calibration of the temperature dependence of the resonant
frequency was needed to obtain a reliable relationship between this frequency
and the operation time of the instrument.

Here we show the results of two series of measurements which provided
important information for the choice of the wire type for the new chamber. The
wires were lodged in an Aluminum frame and mechanically aligned with a
$<0.3^{\circ}$ relative precision. In the former series we tested the short
term mechanical behaviour of a group of pure aluminum wires when they are
glued on the PCBs instead of soldered and in the latter we measured the
creeping and the long term stability of an other group of wires, made of a
different aluminum alloy, fixed on the PCBs by means of the usual soldering.

###  6.1 Measurements on glued wires

As discussed in the introduction section, the formation of cracks in the
silver coating facilitates the onset of the chemical corrosion. Therefore, one
of the possible options for the wire in the new chamber is a
$\phi=50~{}\mu{\rm m}$ aluminum wire without silver coating. Since the
material of CDCH field wires is Al$5056$ alloy, we started our tests on a
sample of Al$5056$ uncoated wires. However, the soldering of extremely thin
pure aluminum wires is problematic and despite various attempts with different
solder pastes and techniques we couldn’t obtain enough robust solderings to
prevent the wires slipping. Then, we explored the possibility of strengthening
the connection of Al$5056$ uncoated wires to the PCBs by using a glue (Loctite
$401$). A group of six $\phi=50~{}\mu{\rm m}$ wires was mounted and glued on a
PCB and stretched at equivalent tensions $T\approx\left(27\div
30\right)~{}{\rm g}$.

Figure 6 shows the mechanical tension of these wires as a function of time
starting from February, $28^{th}$, $2020$, when the wires were connected to
the PCB.

Figure 6: Mechanical tension of six uncoated Al$5056$ wires as a function of
time from the glueing date on a PCB; each colour corresponds to a different
wire. The interpolation is the combination of a constant and an exponential
decreasing function.

Each colour corresponds to a different wire and the curves are interpolated by
an exponentially decreasing function and a constant term. The unstable
behaviour of the wires corresponding to the blue (and less frequently to the
green) dots is due to accidental contacts between the wires and the ground
plane which were eliminated after the first weeks of measurements by a more
accurate control of the ground plane position. The tension of all wires is
continuously decreasing, with a $\approx 13~{}\%$ loss in three months,
clearly unacceptable. The conclusion of this set of measurements is that this
glue does not guarantee the required mechanical stability and cannot be the
right solution for mounting pure aluminum wires on PCBs. Other types of glue
are under testing and one of them (3M-DP 100) is giving promising results; we
will discuss this hypothesis in the final section.

###  6.2 Measurements on soldered wires

The second set of measurements was performed on soldered $\phi=50~{}\mu{\rm
m}$ aluminum wires. Because of the soldering difficulties with the uncoated
Al$5056$ wires, we examined unplated wires made by a different alloy,
Al$2024$, which has a lower percentage of magnesium and is easier to solder.
Indeed we were able to solder a sample of six Al$2024$ wires on a PCB by using
a TAMURA ELSOLD Al-S soldering paste and we could test their long term
mechanical stability after stretching. The purpose of this set of measurements
was to check if, after an initial decrease of the tension due to the creeping,
the wire tension reaches a saturation value, which remains stable within few
tenths of gram, as needed. The wires were soldered at the half of June $2020$
and the first data acquisition was performed on June, $15^{th}$, $2020$. The
measuring sample was formed by six wires, but one of them is not shown in the
following figures because its signal was too low for a reliable measurement of
the resonant frequency.

Figure 7 shows the resonance frequency of the five $\phi=50~{}\mu{\rm m}$
Al$2024$ wires as a function of time, starting from June, $15^{th}$, $2020$
(day $0$).

Figure 7: Resonance frequency of five Al$2024$ wires as a function of time;
each colour corresponds to a different wire and the origin of the time axis is
June, $15^{th}$, $2020$. Data collected in the first $34$ days are not
reliable and are not shown here. Because of its unstable behaviour after day
$160$, the “yellow wire” was excluded from the global analysis.

Each colour corresponds to a different wire; the “yellow wire” exhibited an
unstable behaviour after day $160$ and was excluded by the global analysis
which will be discussed later. The data of the first $34$ days are not
reliable because of an imperfect setting of the ground plane and are not
reported here; then, the effective starting time of the data acquisition is
day $34$, around the half of July $2020$. There was also a data taking
interruption of about $25$ days because of a problem on the electric lines
which happened in August $2020$ during one of the most severe phases of the
Covid-19 pandemic and was solved at the end of the month. Starting from day
$34$, we observed an initial decrease of the resonance frequency with time,
with a timing constant $\tau\sim 20$ days, followed by an increase starting at
day $\sim 100$. The first decrease is not unexpected, since wire creeping
phenomena are frequently observed when an elastic wire is stretched; however,
after a relaxation time of several days one expects that the resonance
frequency reaches a stable saturation value; then, the increase is totally
unexpected. Finally, after day $\sim 240$ the resonant frequency looks to
saturate at an almost stable value, within few tenths of Hz, corresponding to
relative fluctuations of $<1~{}\%$ with respect to the saturation level.

Figure 8 shows the room temperature in the laboratory, recorded during the
data acquisition of all wires, as a function of time. The measured
temperatures were, day by day, pretty stable during the acquisition time of
all the six wires; however, the values recorded during the data acquisition of
each individual wire are shown shifted by $0.25^{\circ}$ on the $y$ axis for
clarity444The true temperature values are shown in the black curve. Without
the shift, all points corresponding to a single day would be totally
superimposed..

Figure 8: Temperature versus time in the laboratory where the measuring system
was located starting from June, $15^{th}$, $2020$. The temperatures recorded
during the data acquisition of each individual wire are shown separately with
the same colours used in figure 7 and are shown shifted by $0.25^{\circ}$ on
the $y$ axis for clarity.

As expected, the temperature changes by several degrees according to the
different seasons; there is an almost linear decrease with time in Summer,
Autumn and Winter $2020$, from day $34$ to day $\sim 250$, followed by an
increase at the end of Winter and in Spring $2021$.

The correlation between the resonant frequency on five wires and the
temperature is shown in figure 9.

Figure 9: Resonant frequency versus temperature in the laboratory starting
from June, $15^{th}$, $2020$ for five wires, identified by the same colour
code used in the previous plots.

In this plot one can observe three different patterns, well visible on the
purple dots:

  * 1.

an isolated group of points for temperatures $>24^{\circ}$;

  * 2.

a decreasing trend in the temperature range $\left(20\div 24\right)^{\circ}$;

  * 3.

a slowly increasing trend of the frequency for temperatures between $\approx
21.5^{\circ}$ and $\approx 22.5^{\circ}$; the frequency appears to saturate at
a value of $\approx 53.6~{}{\rm Hz}$ for the purple dots for $T\geq
22.5^{\circ}$.

These three groups of points correspond to three different periods of data
taking: Summer $2020$, days between $34$ and $60$, before the interruption due
to the problem on the electric lines, from now on: period a); Autumn and
Winter $2020-2021$, days between $90$ and $250$, from now on: period b); and
Spring $2021$, day $>250$, from now on: period c). Since the initial decrease
of the resonant frequency with time is expected to be complete at the time of
period b)555The starting day of period b) is day $90$, more than three times
larger than the timing constant of the initial decrease., we decided to
introduce a frequency versus temperature correction function by using data
collected in this period, where a $\approx 4^{\circ}$ thermal excursion was
observed. After performing the calibration procedure, inserting the
corrections and obtaining the complete frequency versus time curve, we will
check that the timing dependence of the resonant frequency in period b) is
really negligible.

Figure 10 shows the resonant frequency versus temperature curves for four
wires666The “yellow wire” was excluded from this global analysis, as already
observed.; the data were collected in timing period b) and interpolated with
the following function:

$\nu_{r}\left(T\right)=\nu_{r,0}+\nu_{r,1}\exp{\left[-\left(\frac{T-T_{min}}{T_{ref}}\right)\right]}$
(4)

where $T_{min}$ is kept fixed at $20^{\circ}$ and $\nu_{r,0}$, $\nu_{r,1}$ and
$T_{ref}$ are free fitting parameters. $\nu_{r,0}$ is the resonant frequency
when its dependence on temperature becomes negligible and
$\left(\nu_{r,0}+\nu_{r,1}\right)$ is the resonant frequency at $T=T_{min}$,
the lower edge of the temperature range measured in period b). All the wires
exhibit the same behaviour, with $T_{ref}=\left(0.9\div 1.2\right)^{\circ}$
and $\left(\nu_{r,0}+\nu_{r,1}\right)=\left(52.5\div 53.5\right)~{}{\rm Hz}$.

Figure 10: Resonant frequency versus temperature in the laboratory during
period b) interpolated with calibration function 4.

The main difference between the wires is the saturation value of the resonant
frequency $\left(\nu_{r,0}+\nu_{r,1}\right)$. In figure 11 we show the
difference between the measured frequency and the function
$\nu_{r}\left(T\right)$ computed according to Equation 4 as a function of time
for all wires superimposed.

Figure 11: Difference between the measured resonant frequency and the
temperature correction function, Equation 4, for all the wires superimposed.
After subtracting the saturation values the behaviours of all the wires as a
function of time are very similar.

We used the coefficients deduced from the fits shown in figure 10 to calculate
the temperature dependence of the frequency in period a) according to Equation
4, while for period c), even if the average temperature was higher than
$T_{min}$, we replaced the function $\nu_{r}\left(T\right)$ with the
saturation constant $\left(\nu_{r,0}+\nu_{r,1}\right)$, according to the
experimental distributions in figure 9. The effect of introducing the
temperature corrections is to recover the expected behaviour of the resonant
frequency of all wires with time: an initial, exponential decrease due to the
wire creeping, followed by an almost stable resonant frequency. Note that
points corresponding to individual wires superimpose very well, confirming
that different wires have a different saturation value, i.e. each one has its
own resonant frequency, but the same relaxation time. In figure 11 one can
observe a possible modulation with time of the resonant frequency. This can
suggest that temperature corrections need to be refined or that other effects
should be taken into account. We checked if the possible modulation pattern is
correlated with the room humidity which is monitored together with the
temperature, but no signs of correlations were observed. Nevertheless, the
maximum amplitude of resonant frequency oscillations is at level of
$0.3~{}{\rm Hz}$. Table 2 shows that a $0.3~{}{\rm Hz}$ uncertainty on the
resonant frequency corresponds to a $\left(0.1\div 0.2\right)~{}{\rm g}$
uncertainty on the wire tension, which matches very well our requirement of an
uncertainty $<0.5~{}{\rm g}$, as explained in section $3$.

Since the evolution of the resonant frequency with time is very similar for
all wires, we summed and averaged the experimental points reported in figure
11 and fitted the average resonant frequency versus time relationship with the
combination of an exponential shape, a saturation constant and an oscillating
pattern. The results are shown in figure 12.

Figure 12: Difference between the measured resonant frequency and the
temperature correction function, Equation 4, summed and averaged over all
wires, as a function of time. The fit function is a combination of a
decreasing exponential shape, a saturation constant and an oscillating
pattern.

The fit parameters (exponential time constant, saturation constant, amplitude
and period of the oscillating pattern) are reported in table 3.

Table 3: Fit parameters for the interpolation shown in figure 12. Parameter | Parameter value | Units
---|---|---
Exponential time constant | $21.0\pm 0.5$ | days
Saturation constant | $\left(-25\pm 30\right)\times 10^{-3}$ | Hz
Modulation amplitude | $\left(57\pm 3\right)\times 10^{-3}$ | Hz
Modulation period | $51\pm 5$ | days

At the beginning of period b) (day $90$) the contribution of the exponential
term is $\approx 0.06~{}{\rm Hz}$, confirming our assumption that the timing
dependence of the resonant frequency in the timing interval used to determine
the temperature correction was marginal with respect to the temperature
dependence. The saturation constant is consistent with zero within one sigma,
showing that the temperature corrections are adequate, at least on average. If
one converts the modulation amplitude from frequency to tension the fitted
value corresponds to $\left(0.03\div 0.04\right)~{}{\rm g}$, largely within
our precision requirements on the knowledge of the wire tension. The origin of
the modulation is not yet explained but, as already noted, it has no
significant effects on the accuracy of the measurement. We tried also a
simpler fit without the modulation term; the results for the exponential time
constant and the saturation constant are in good agreement with that reported
in table 3. Including the modulation term in the fit has the advantage of
providing a quantitative estimate of the resonant frequency (and then of the
wire tension) stability; the resonant frequency looks pretty stable within
small fluctuations on a timing scale of (at least) several months.

###  6.3 Comments on the choice of the wire material for the new CDCH

On the basis of the measurements shown in the previous subsection the Al$2024$
uncoated wires appear to have good mechanical properties to be used for the
new CDCH. However, this kind of wires didn’t pass a corrosion test, since some
Al$2024$ wires were immersed in distilled water and broke in many small pieces
in less than two days, without need of stretching. The alloy Al$2024$ was then
rejected as a possible building material for the wires of the new CDCH and we
came back to the silver plated Al$5056$ wires, whose mechanical properties
were already tested during the assembly phase of the old CDCH. Since the
breaking probability of the $\phi=50~{}\mu{\rm m}$ wires was much smaller than
that of $\phi=40~{}\mu{\rm m}$ wires, we deciced to use only the more robust
thicker diameter wires and after discussions with the manifacturers they
agreed to avoid the ultrafinishing stage in the wire production and started
the fabrication of non-ultrafinished spools which are under testing.

##  7 Conclusions

The measurement system of the resonant oscillation frequency of thin metallic
wires developed for the MEG II experiment measures a small variation (few pF)
of the capacitance of a wire with respect to a ground plane induced by a
sinusoidal HV signal. An oscillation amplitude versus frequency curve is
obtained by means of a frequency scan and is fitted by a Breit-Wigner shape to
extract the resonance frequency; the measured wire frequency can be converted
into the wire tension and the corresponding elongation.

After the wire breakage problems due to chemical corrosion observed in the MEG
II CDCH, the construction of a new chamber was approved. The original chamber
was in any case completed after removing all fragments of broken wires and it
is taking data at PSI; nevertheless, the project of the new chamber went on
and the fundamental point to be addressed before the start of its constructon
is the type of wire to be chosen for replacing the too fragile
$\phi=40~{}\mu{\rm m}$ silver plated aluminum wires. Several possibilities
were explored and the measuring system described in this paper was a very
useful tool to check the reliability of some of the possible solutions.

First of all, the possibility of using uncoated Al$5056$ aluminum wires was
tested, but it appeared problematic because of the difficulty of soldering
these wires on PCBs and because the backup solution of ensuring the mechanical
connection between the wires and the PCBs by means of a glue was not
satisfactory: we observed a continuous loosening of the wire tension,
corresponding to a $13~{}\%$ loss in less than three months, without any
indication of reaching a stable value.

Secondly, we examined the possibility of a different aluminum alloy, Al$2024$,
easier to solder even without silver coating. After soldering a group of
Al$2024$ $\phi=50~{}\mu{\rm m}$ wires on a PCB, we studied the timing
behaviour of their resonant frequency and mechanical tension on a time scale
of about one year. We observed an initial tension loosening due to the
creeping, as usual when a thin mechanical string is stretched, followed by a
long term stability, with some (probably artificial) residual oscillations,
whose amplitude is well within our tolerance. However, the Al$2024$ wires were
rejected because of their weak resistance to the humidity induced corrosion
and we reverted to $\phi=50~{}\mu{\rm m}$ silver plated wires made with the
original Al$5056$ alloy, but avoiding the ultrafinishing stage which produces
a strong mechanical stress on the silver coating.

Despite the impossibility of using Al$2024$ wires, the long time measurements
on this kind of wires and on the glued Al$5056$ wires showed the
potentialities and the performances of our measuring system. The resonant
frequency of the wires can be measured with a precision of few tenths of Hz,
corresponding to a precision on the knowledge of the mechanical tension $\sim
0.1~{}{\rm g}$, well within our requirements. The measuring system operates
with very small human interventions, can be controlled remotely (an important
“quality factor” during the Covid-19 pandemic) and a complete set of
measurements requires $\sim\left(15\div 20\right)$ minutes per day of data
acquisition; also the analysis chain is largely automated, very fast and based
on standard packages. The recording of environment conditions, room
temperature and humidity, simultaneuously to the data acquisition, allows to
correct for the dependence of the resonant frequency on the room temperature,
a crucial step to obtain reliable frequency versus time curves. The origin of
the dependence of the measured resonant frequency on the room temperature is
probably the inverter chain of the Ring oscillator, which is highly sensitive
to the temperature. A redesign of the Ring oscillator circuit would be
necessary to correct this dependence at hardware level; presently this
solution is under discussion. Another simpler strategy for improving the
measurement quality is to move the experimental apparatus in a temperature and
humidity controlled room.

The final decision of the wire type for the new chamber was not yet taken. The
main option is to use non ultrafinished silver coated Al$5056$ wires, but we
found recently an efficient way of soldering pure aluminum wires of Al$5056$
type with the TAMURA ELSOLD Al-S soldering paste which is able to sustain a
tension up to $60~{}{\rm g}$ without wire slipping. In this case it is safer
to reinforce the wire mechanical connection by means of a glue; we are testing
the mechanical strength and the chemical properties of the 3M DP100 glue,
which seems a good candidate for our purposes.

The measuring system discussed in this paper will be used for long time
stability tests of these and other possible choices of wire types and
connections with PCBs.

##  8 Acknowledgements

We are very grateful to several technicians of our universities and INFN
Sections: G.Balestri, A.Bianucci, M.D’Elia, A.Innocente, A.Miccoli, C.Pinto,
G.Petragnani and A.Tazzioli who were deeply involved in the CDCH wiring and
mounting procedures.

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