11institutetext: Karlsruhe Institute of Technology, Karlsruhe, Germany
22institutetext: Instituto de TecnologÃas en DetecciÃn y AstropartÃculas,
CNEA-CONICET-UNSAM, Buenos Aires, Argentina 33institutetext: Pierre Auger
Observatory, MalargÃe, Argentina

# Preliminary results of the AMIGA engineering array at the Pierre Auger
Observatory

Alvaro Taboada 1122<EMAIL_ADDRESS>for the Pierre Auger Collaboration
<EMAIL_ADDRESS>33

###### Abstract

The Auger Muons and Infill for the Ground Array (AMIGA) aims to both extend
the detection range of the Pierre Auger Observatory down to energies $\sim
10^{16.5}\leavevmode\nobreak\ \mathrm{eV}$ and to measure the muon content of
extensive air showers. To accomplish these goals, its detection system is
composed of an array of coupled water-Cherenkov and scintillation detectors
deployed in a graded triangular grid of 433 and 750 m spacings. At each
position, the scintillation detector is buried $2.3\leavevmode\nobreak\
\mathrm{m}$ deep so as to shield it from the air shower electromagnetic
component and thus only measure the muon component. These muon detectors have
$30\leavevmode\nobreak\ \mathrm{m^{2}}$ area split into modules, each of them
highly segmented in 64 plastic-scintillator strips with an embedded
wavelength-shifter optical fiber to transport light to an optical sensor
located at the center of the module. During the engineering array phase
(finished in November 2017) two module areas ($5\leavevmode\nobreak\
\mathrm{m^{2}}$ and $10\leavevmode\nobreak\ \mathrm{m^{2}}$) and two optical
sensors (photo-multiplier tubes and silicon-photomultipliers) were tested. In
this work, we present the final performance of the muon detectors equipped
with silicon-photomultipliers which were thereafter selected as the baseline
design for the AMIGA production phase. Analyses and results are based both on
laboratory and field measurements.

##  1 The AMIGA array

The Pierre Auger Observatory completed its surface-detector array with
$1500\leavevmode\nobreak\ \mathrm{m}$ spacing (SD-1500) in 2008 to study
cosmic rays with energies above $10^{18.5}$ eV. An area of
$3000\leavevmode\nobreak\ \mathrm{km^{2}}$ was fully deployed with water-
Cherenkov detectors (WCD) Auger2015 . To extend the energy threshold down to
$\sim 10^{16.5}$ eV, the Auger Muons and Infill for the Ground Array (AMIGA)
AMIGA  proposed a smaller area of $23.5\leavevmode\nobreak\ \mathrm{km^{2}}$
which has already been completely equipped with WCDs spaced at
$750\leavevmode\nobreak\ \mathrm{m}$ (SD-750). More recently an even denser
array at a $433\leavevmode\nobreak\ \mathrm{m}$ spacing with an area of
$1.9\leavevmode\nobreak\ \mathrm{km^{2}}$ is being deployed (SD-433).

Figure 1: Layout of the AMIGA EA. In this prototype phase the
$30\leavevmode\nobreak\ \mathrm{m^{2}}$ UMDs were segmented in modules of
$5\leavevmode\nobreak\ \mathrm{m^{2}}$ and $10\leavevmode\nobreak\
\mathrm{m^{2}}$. Also, two positions were equipped with extra twin modules to
assess detector uncertainties. Two optical sensors were tested, multipixel and
silicon photomultipliers.

Still, AMIGA’s main and novel contribution to the Pierre Auger Observatory is
to provide direct muon measurements with dedicated underground muon detectors
(UMD) made of plastic scintillators. Each UMD is coupled to a WCD of both
SD-750 and SD-433 arrays. Between March 2015 and November 2017, an UMD
engineering array (EA) was operated in the SD-750 as a proof of concept, for
physics validation, and optimization of the detector design. The layout of
this EA is shown in fig. 1.

Figure 2: Left: Final layout of the AMIGA production-phase design: each WCD is
coupled to three $10\leavevmode\nobreak\ \mathrm{m^{2}}$ buried scintillator
modules. Right: Detector deployment in the field in which the tube that hosts
the electronics and the optical sensor can be seen.

Figure 3: Left: UMD fabrication and assembling. Each module is composed of 64
scintillator bars with a wavelength-shifter optical fiber glued to them.
Middle: Central $8\times 8$ optical connector to which light is transported by
the fibers. Right: The SiPMs array which is coupled to the connector.

The $30\leavevmode\nobreak\ \mathrm{m^{2}}$ of scintillators, buried
$2.3\leavevmode\nobreak\ \mathrm{m}$ deep close to a WCD, were segmented in
modules of 5 and 10 $\mathrm{m^{2}}$. In turns, each module consists of 64
extruded plastic-scintillator bars with a wavelength-shifter optical fiber
glued to transport light towards an optical connector located at the module
center Suarez . Two kinds of optical sensors were tested during the prototype
phase: a 64 pixel multi-anode photomultiplier tube (MPMT) and an array of 64
silicon photomultipliers (SiPM). After completion of these tests, the final
decision for the production phase was to only build $10\leavevmode\nobreak\
\mathrm{m^{2}}$ modules equipped with SiPMs. A schematic of the final layout
is shown in fig. 2 alongside a field deployment in which is seen the
inspection tube that hosts the electronics and the optical sensors.

In fig. 3, an example of a module fabrication and assembly is shown together
with the chosen SiPM array (Hamamatsu S13361-2050NE-08) and the optical
connector that couples the fibers onto it.

The electronics readout works simultaneously as a counter (counts number of
arriving muons) and as an integrator (integrates the total signal of the
arriving muons). The counter mode consists of 64 channels (one for each
scintillator strip in a module) made of a pre-amplifier, a fast-shaper and,
finally, a discriminator. These channels are integrated in two 32-pixel ASICs
(Application-Specific Integrated Circuits). The signals after the
discriminators are all identical in amplitude and only differ in their time
width depending on the time the input pulses are above a given threshold. All
signals from the 64 discriminators are sampled by a Field-Programmable Gate
Array (FPGA) with a sampling time of $3.125\leavevmode\nobreak\ \mathrm{ns}$
($320\leavevmode\nobreak\ \mathrm{MHz}$). At each sampling, the FPGA
associates a “1” if the discriminator pulse is present and a “0” otherwise. As
a result, the electronics for the counter mode outputs 64 binary traces where
individual muons, and their arrival time, can be easily measured by inspecting
the strings of “1s”.

Figure 4: Left: Oscilloscope capture of dark pulses from the AMIGA SiPM,
crosstalk pulses and afterpulses are clearly visible. Right: Gain, dark rate,
and crosstalk as a function of the over-voltage. Figure 5: Left: Dark-rate
curve as a function of the discriminator threshold (blue). The first plateau
(below 190 ADC counts) corresponds to the baseline while the followings
indicate an increasing number of PE amplitudes. The derivative of this rate
curve (green) readily identifies the PE amplitude spectrum. Middle: Dark-rate
curves at different $V_{\mathrm{br}}$. It is seen how the dark rates and PE
amplitudes shift towards higher values when rising the $V_{\mathrm{br}}$.
Right: Determination of the breakdown voltage ($V_{\mathrm{br}}$) for an
individual SiPM. The linear extrapolation to 0 amplitude indicates the
$V_{\mathrm{br}}$ value.

On the other hand, and complementary to the counter mode, the integrator mode
of the front-end electronics adds up analogically the 64 SiPM signals and
processes the result through a low-gain and a high-gain amplification channel.
The amplified signals are sampled with Analog-to-Digital Converters (ADCs)
with sample time of $6.25\leavevmode\nobreak\ \mathrm{ns}$
($180\leavevmode\nobreak\ \mathrm{MHz}$), resulting in two waveforms of 1024
samples from which the total charge of the signal may be calculated.

The counter mode is hardware limited by the segmentation of each module since
if two muons arrive simultaneously in any given strip (i.e. within a preset
time window AMIGA , typically of 35 ns), they will pile up and be counted as a
single muon111It is important to stress, that the time distribution of muons
within a shower certainly allows one to measure more than one muon per strip
in the counter mode, increasing noticeably the total number of non-
simultaneous particles that can be measured. The integrator mode solves this
issue and extends the dynamic range of the detector to measure higher muon
densities close to the shower core.

##  2 SiPM operation

Figure 6: Calibration: after breakdown voltages have been found, all SiPMs are
set to the same over-voltage to assure uniform gain. The dark-rate curves and
gain histograms are shown, before calibration (top) and after calibration
(bottom).

A single silicon photomultipier is an array of photodiodes (referred as micro-
cells) with densities that usually range from a hundred to several thousand
per $\mathrm{mm^{2}}$. The photodiodes are operated with a reverse voltage
($V_{\mathrm{bias}}$) which exceeds the breakdown voltage ($V_{\mathrm{br}}$)
of the silicon junction.

$V_{\mathrm{br}}$ is the minimum voltage needed for SiPMs to operate in Geiger
mode Renker . If $V_{\mathrm{bias}}>V_{\mathrm{br}}$, each electron-hole pair
created by the absorption of a photon produces a diverging avalanche of
multiplication of carriers resulting in a macroscopic current flow in a single
micro-cell. If the generated Geiger avalanche is not confined to the same
micro-cell it was initiated in, crosstalk is produced, and the SiPM outputs a
pulse with twice (or more) the amplitude and charge of a single photo-
equivalent (PE) pulse. As an illustration, in the left panel of fig. 4, the
oscilloscope capture of dark pulses of the AMIGA SiPM is shown. Therein, the
discrete nature of the crosstalk pulses (as well as those of the afterpulses)
is seen. Fig. 5 depicts the PE amplitude spectrum arising from the crosstalk.
The selected SiPM for AMIGA has 1584 micro-cells and, as already explained,
there are 64 SiPMs per muon module coupled to the fibers through an optical
connector (see fig. 3). It is known that SiPMs have a high dark rate so each
of these 64 pixels might produce muon overcounting during data taking. Their
dark rate (as well as crosstalk and gain) is proportional to the over-voltage
($\Delta V$), which is in turn determined by $\Delta
V=V_{\mathrm{bias}}-V_{\mathrm{br}}$. In the right panel of fig. 4, the gain,
dark rate, and crosstalk are shown as a function of $\Delta V$ while the
experimental measurement of $\Delta V$ is shown in the right-hand side of fig.
5.

The operating point of each AMIGA module is set by choosing a single $\Delta
V$ value for all its 64 SiPMs to assure a uniform gain for all of them. On top
of this and regarding the counter-mode operation of the front-end electronics,
a discriminator threshold has to be selected. During the EA phase, these two
parameters were optimized to enhance the detector performance. Note that
increasing $\Delta V$ increases both noise and efficiency while a higher
discrimination threshold reduces noise but may alongside reduce the detector
efficiency. Laboratory measurements Matias  have shown that both low
background noise and high efficiency are achieved for $\Delta V=3.5$ V with a
discriminator threshold set to $2.5\leavevmode\nobreak\ \mathrm{PE}$. A signal
equal or above this threshold is counted as a muon in the UMD counter mode.
This one-bit electronics makes muon identification fairly independent of
fluctuations (light production, amplitude of PE signals, fiber attenuation,
gain shifts).

###  2.1 Calibration

Contrary to MPMTs, SiPMs have a well-defined PE spectrum. Therefore, it is
possible to calibrate them using dark-rate pulses. The PE amplitude spectrum
can be obtained by measuring the dark rate as a function of the discrimination
threshold. The well-defined SiPM pulses result in turn in well-defined
plateaus as shown in the left panel of fig. 5. The transition from one plateau
to the following earmarks the corresponding PE amplitude that can be readily
identified via the curve derivative as also shown in the figure (green line).
To set the $V_{\mathrm{bias}}$ (sec. 2), it is necessary to first determine
the $V_{\mathrm{br}}$ of each SiPM. To do this, dark-rate curves are measured
at different $V_{\mathrm{bias}}$ as shown in the middle panel of fig. 5. It
can be seen how the PE amplitude, dark rate and crosstalk (ratio between two
plateaus) increase when $V_{\mathrm{br}}$ is increased. From these curves, the
single PE amplitude as a function of the $V_{\mathrm{bias}}$ is obtained, as
shown in the right panel of fig. 5. The extrapolation of this curve to 0 (in
amplitude) indicates the voltage corresponding to $V_{\mathrm{br}}$.

Once all 64 $V_{\mathrm{br}}$ are known for all 64 SiPMs, the
$V_{\mathrm{bias}}$ is roughly adjusted with a Hamamatsu C11204-01 high-
voltage source, which sets the same preliminary
$V_{\mathrm{bias}}^{\mathrm{prel}}$ to all SiPMs. This value is determined by
$V_{\mathrm{bias}}^{\mathrm{prel}}=\mathrm{max}\left\\{V_{\mathrm{br}}\right\\}+\Delta
V$, where $\mathrm{max}\left\\{V_{\mathrm{br}}\right\\}$ is the maximum value
of the array of 64 SiPMs and $\Delta V$ is the desired over-voltage. To
compensate for the $V_{\mathrm{br}}$ difference of each SiPM channel, a smooth
adjustment per channel is performed with the ASIC which allows setting an
individual voltage per channel to ensure the same $\Delta V$ for all SiPMs. As
an example of the impact of the above described procedure, the dark rate
curves and the corresponding $1\leavevmode\nobreak\ \mathrm{PE}$ amplitude
histograms are shown in fig. 6, before (top) and after (bottom) the
calibration run for $\Delta V=3.5\leavevmode\nobreak\ \mathrm{V}$ (sec. 2). It
can be seen that after calibration the curves show less fluctuations,
particularly the standard deviation in the $1\leavevmode\nobreak\ \mathrm{PE}$
amplitude is reduced by a factor of $\sim 2$ . Therefore the detector response
becomes more uniform.

###  2.2 Temperature compensation

The SiPM dark rate and its PE amplitude depend on temperature (see fig. 8).
The dark rate is accounted for by the muon-counting strategy and the time
duration of the air shower. In this section, we concentrate on characterizing
the temperature impact on the PE amplitude.

Dark-rate curves at different temperatures have been measured in the field
with temperature sensors close to the SiPMs (see fig. 7). There is a
noticeable shift in the $1\leavevmode\nobreak\ \mathrm{PE}$ amplitude due to
temperature variations since, when temperature increases, the
$\mathrm{V_{br}}$ increases accordingly and therefore $\mathrm{\Delta V}$
(along with the SiPM gain) decreases.

Field-temperature changes during the day and year and therefore it is crucial
to provide automatic control of $V_{\mathrm{bias}}$ so as to maintain $\Delta
V$ constant. By accomplishing this, the SiPM gain would remain stable over
time. For the AMIGA detector modules, a temperature compensation mechanism is
integrated into the Hamamatsu C11204-01 high voltage source. This mechanism
adjusts $V_{\mathrm{bias}}$ according to the temperature variation thus
compensating for any fluctuations in $V_{\mathrm{br}}$ and, therefore,
stabilizing $\Delta V$. To study the performance of a compensation mechanism,
the gain was estimated repeatedly for more than 8 months. Over periods lasting
for approximately one to two weeks, both SiPMs gain and temperature were
measured every two hours. The resulting dependence of gain on temperature is
displayed in fig. 8 where a temperature correspondence with seasonal changes
can be observed. The data points acquired during the coldest months (May and
June in the Southern hemisphere) cluster on the left-hand side while on the
right-hand side, are those corresponding to the warmest months (January and
February). Note that, since the UMC are buried 2.3 m deep, the overall
temperature variation is only $\sim 20^{\circ}\mathrm{C}$. The average gain
over the entire period was $\mathrm{(88.7\pm 1.6)}$ in DAC-counts units. The
corresponding gain variation was approximately $\mathrm{0.2\%/^{\circ}C}$.
Without the compensation, the variation would have been
$\mathrm{4.3\%/^{\circ}C}$ datasheet2 . Thus, the compensation mechanism is
reducing the gain variations by a factor of 20 (i.e. from $\sim 86$ to $4\%$).

##  3 Muon reconstruction performance

The two primary tasks of AMIGA UMDs are to count muons and to detect their
arrival time. Muon counting can be performed individually muon-by-muon in the
counter mode (one-bit electronics) and on a mean-value approach in the
integrator mode (charge integration). The counter mode of the read-out
electronics produces binary signals relying on the signal amplitude while the
integrator mode is based on the total-signal charge.

As SiPMs are located only at a single scintillator-strip edge, it is important
to characterize the attenuation of the signal along the scintillator fibers
and its impact on the muon-identification efficiency. In the following
section, the attenuation of both modes is quantified with laboratory
measurements. For this purpose, a dedicated setup was mounted on a test-bench
and the analog SiPM waveform pulses were directly acquired with an
oscilloscope. The event trigger was performed by a small movable muon
telescope and the whole length of the strips was swept in steps of 0.5 m.

Figure 7: Results for six different calibration runs at different
temperatures. The shift in the $1\leavevmode\nobreak\ \mathrm{PE}$ spectrum
can be observed. As a consequence of the temperature increase, the breakdown
voltage increases accordingly and, therefore, the gain decreases.  Figure 8:
$1\leavevmode\nobreak\ \mathrm{PE}$ amplitude as a function of field
temperature over an 8 month period with a temperature range of $\sim
10-30^{\circ}\mathrm{C}$. The colors indicate the months: greenish for the
coldest season and reddish to the warmest. The dotted-gray line shows the
temperature dependence of the $1\leavevmode\nobreak\ \mathrm{PE}$ amplitude
without any temperature compensation in the front-end electronics. As can be
seen, the almost constant $1\leavevmode\nobreak\ \mathrm{PE}$ amplitude shows
that the gain stabilization works at the level of $0.2\%/^{\circ}\mathrm{C}$.

###  3.1 Single-muon reconstruction

The number of PEs in the muon signals both in amplitude and charge as a
function of the distance to the SiPM is shown in the top panel of fig. 9. The
difference between amplitude and charge attenuations is related to the time
distribution of photons reaching the optical sensor: the processes involved in
the plastic scintillator as well as in the wavelength-shifter fiber spread
photons in time and thus they do not add to the total SiPM pulse amplitude.
Therefore, the final amplitude will not be the sum of the individual PE-signal
amplitudes (they may be reduced by a factor $\approx 2$, see fig. 9 top)
whereas the charge of the pulses will not be affected by this time spread
since it is integrated over the total pulse timespan. Note that the counter
mode is sensitive to the amplitude attenuation (as it implements an amplitude
threshold) whereas the integrator mode is sensitive to the charge attenuation.
The impact of the attenuation on efficiency to detect muons in the counter
mode is shown in the bottom panel of fig. 9. Typically, the SiPM dark rate
(with 3 or more PE) surpasses the discriminator threshold for less than 12.5
ns. For this reason, muons are identified when the signal above the
discriminator threshold lasts more than $12.5\leavevmode\nobreak\
\mathrm{ns}$. The efficiency loss at the end of the bar is the consequence of
the PE attenuation, as signals below the discriminator threshold
($2.5\leavevmode\nobreak\ \mathrm{PE}$) are lost. The total efficiency of the
$5\leavevmode\nobreak\ \mathrm{m^{2}}$ and $10\leavevmode\nobreak\
\mathrm{m^{2}}$ modules is $99.7\%$ and $98.5\%$ respectively (the efficiency
of the integrator mode has not yet been determined).

###  3.2 Array reconstruction

As an example of the performance of AMIGA as an array, the reconstruction of
the muon lateral distribution reconstruction  in an air shower with
reconstructed energy of $\left(9.54\pm 0.39\pm 0.18\right)\times
10^{17}\leavevmode\nobreak\ \mathrm{eV}$ and zenith angle of $\left(21.8\pm
0.4\right)^{\circ}$ is shown in fig. 10. Both air shower arrival geometry and
energy were obtained from the surface WCD array, SD-750 reconstructionSD .
Since the UMC integrator mode is yet to be fully calibrated, muon densities
were reconstructed in the counter mode alone. The measured muon densities
mueller  at each position are shown in the top panel of the figure while the
fit to their lateral distribution is seen in the bottom panel. The UMD array
of AMIGA is expected to be completed by 2020.

Figure 9: Top: Number of PE as a function of the distance from the SiPM both
in amplitude (sensitive to the counter mode) and in charge (sensitive to the
integrator mode). Bottom: Efficiency as a function of the distance from the
SiPM for the counter mode. The total efficiency of the 5 and 10
$\mathrm{m^{2}}$ modules is estimated by integrating the efficiency curve
between 1 m and 3 or 5 m respectively.

##  4 Conclusion

Preliminary results of the AMIGA engineering array have been analyzed and
shown. A final satisfactory assessment in regard to both UMD construction
(mechanics, telecommunications, optoelectronics, counter plus integrator
electronics) and data analyses (calibration, temperature compensation, muon
reconstruction performance) has been achieved. UMD production phase has
started.

Figure 10: A real event reconstructed with the counter mode alone for an event
with an energy of $\left(9.54\pm 0.39\pm 0.18\right)\times 10^{17}$ eV and
zenith angle of $\left(21.8\pm 0.4\right)^{\circ}$. Top: Footprint, core
position, and azimuth angle. Bottom: Lateral distribution of muon densities.

## References

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