# Performance study of a $3\times 1\times 1\mbox{ m}^{3}$ dual phase liquid
Argon Time Projection Chamber exposed to cosmic rays

B. Aimard  L. Aizawa  C. Alt  J. Asaadi  M. Auger  V. Aushev  D. Autiero  A.
Balaceanu  G. Balik  L. Balleyguier  E. Bechetoille  D. Belver  A.M. Blebea-
Apostu  S. Bolognesi  S. Bordoni  N. Bourgeois  B. Bourguille  J. Bremer  G.
Brown  L. Brunetti  G. Brunetti  D. Caiulo  M. Calin  E. Calvo  M.
Campanelli11footnotetext: corresponding author K. Cankocak  C. Cantini  B.
Carlus  B.M. Cautisanu  M. Chalifour  A. Chappuis  N. Charitonidis  A.
Chatterjee  A. Chiriacescuf  P. Chiu  T. Coan  S. Conforti  P. Cotte  P.
Crivelli  C. Cuesta  J. Dawson  I. De Bonis  C. De La Taille  A. Delbart  S.
Di Luise  F. Doizon  C. Drancourt  D. Duchesneau  F. Dulucq  F. Duval  S.
Emery  A. Ereditato  A. Falcone  K. Fusshoeller  A. Gallego-Ros  V. Galymov
N. Geffroy  A. Gendotti  A. Gherghel-Lascu  I. Gil-Botella  C. Girerd  M.C.
Gomoiu  P. Gorodetzky  E. Hamada  R. Hanni  T. Hasegawa  A. Holin  S. Horikawa
M. Ikeno  S. Jiménez  A. Jipa  M. Karolak  Y. Karyotakis  S. Kasai  K. Kasami
T. Kishishita  H. Konari  I. Kreslo  D. Kryn  P. Kunzé  M. Kurokawa  Y.
Kuromori  C. Lastoria  I. Lazanu  G. Lehmann-Miotto  M. Leyton  N. Lira  M.
Liubarska  K. Loo  D. Lorca  P. Lutz  T. Lux  J. Maalampi  G. Maire  M. Maki
L. Manenti  R.M. Margineanu  J. Marteau  G. Martin-Chassard  H. Mathez  E.
Mazzucato  G. Misitano  D. Mladenov  L. Molina Bueno  T.S. Mosu  W. Mu  S.
Murphy  K. Nakayoshi  S. Narita  D. Navas-Nicolás  K. Negishi  M. Nessi  M.
Niculescu-Oglinzanu  F. Noto  A. Noury  Y. Onishchuk  C. Palomares  M. Parvu
T. Patzak  Y. Penichot  E. Pennacchio  L. Periale  H. Pessard  F. Pietropaolo
D. Pugnere  B. Radics  D. Redondo  C. Regenfus  A. Remoto  F. Resnati  O.
Ristea  A. Rubbia  A. Saftoiu  K. Sakashita  F. Sanchez  C. Santos  A.
Scarpelli  C. Schloesser  K. Sendai  F. Sergiampietri  S. Shahsavarani  M.
Shoji  J. Sinclair  J. Soto-Oton  D.I. Stanca  D. Stefan  R. Sulej  M. Tanaka
V. Toboaru  A. Tonazzo  W. Tromeur  W.H. Trzaska  T. Uchida  L. Urda  F.
Vannucci  G. Vasseur  A. Verdugo  T. Viant  S. Vihonen  S. Vilalte  M. Weber
S. Wu  J. Yu  L. Zambelli  M. Zito

###### Abstract

We report the results of the analyses of the cosmic ray data collected with a
4 tonne (3$\times$1$\times$1 m3) active mass (volume) Liquid Argon Time-
Projection Chamber (TPC) operated in a dual-phase mode. We present a detailed
study of the TPC’s response, its main detector parameters and performance. The
results are important for the understanding and further developments of the
dual-phase technology, thanks to the verification of key aspects, such as the
extraction of electrons from liquid to gas and their amplification through the
entire one square metre readout plain, gain stability, purity and charge
sharing between readout views.

##  1 Introduction

Dual phase (DP) Liquid Argon TPCs (LAr TPC) have been under development for
more than a decade [1, 2, 3, 4, 5]. They combine the properties of the liquid
argon as the tracking medium with the charge amplification in the gaseous
argon phase above the liquid at the top of the detector, after extracting
drift electrons from the liquid into the gas. This provides a full 3D imaging
of charged particle interactions with high resolution and low energy
threshold. As such, they can be a potent tool to study neutrino interactions
and other rare phenomena [6]. DP LAr TPCs at the 10 kt scale, located
underground and coupled to powerful neutrino beams offer a rich scientific
portfolio, that includes the study of leptonic Charge-Parity (CP) violation
and the determination of the neutrino mass ordering. Thanks to the VUV
scintillation of the liquid argon, they can operate in self-triggering mode to
study atmospheric and astrophysical neutrinos with very high statistics and
extend the sensitivity to proton decay.

The possibility to deploy and operate large scale DP LAr TPCs underground has
been studied in detail in the context of LAGUNA-LBNO [7] and subsequently in
DUNE [8]. Two prototype LAr TPCs (known as Dual Phase and Single Phase
ProtoDUNE) with about 300 tonnes in active mass each have been constructed and
operated at CERN [9] by the DUNE collaboration. In 2017, a 4 tonne ($3\times
1\times 1\mbox{ m}^{3}$) DP LAr TPC was operated, collecting over 300,000
cosmic ray interactions. A first look at this data presented in Ref. [10]
clearly demonstrates the excellent imaging capabilities of the detector and
provides a proof of principle of the DP technology at the tonne scale. Follow
up studies performed with the scintillation light in the detector have been
published in [11].

A more detailed analysis of the ionisation charge signals produced in the
pilot detector is the subject of this paper. Based on the acquired cosmic ray
data, we evaluate the impact and the relative importance of various parameters
on quantities such as signal-to-noise ratio, hit finding efficiency and the
uniformity of the response on a $3\times 1$ m2 area. The $3\times 1\times
1\mbox{ m}^{3}\mbox{ demonstrator}$ is the first large scale prototype of a DP
LAr TPC and a reduced scale replica of upcoming larger detectors. In this
context, a detailed study of its response and imaging capabilities is of
utmost importance to better gauge the performance and provide more accurate
simulations of large scale DP LAr TPCs.

In Section 2, we briefly present the overview of the detector along with the
response to the charge readout system. We also describe the key detector
parameters that can have the largest impact on the quality of the data. In
Section 3, we present some details on the Monte Carlo and data samples, and
the algorithms used for track reconstruction. Finally, we evaluate the
detector response and performance in Section 4.

##  2 Overview of the $3\times 1\times 1\mbox{ m}^{3}$ demonstrator detector

###  2.1 Experimental setup

The $3\times 1\times 1\mbox{ m}^{3}$ demonstrator detector is described in
detail in Ref. [10]. It consists of a $3\times 1\times 1\mbox{ m}^{3}$ liquid
argon active volume, defined by a cathode at the bottom, a field cage, and the
readout plane at the top. A charge amplification and anode readout stage is
positioned in the gas phase a few millimetres above the liquid argon surface.
Figure 1 shows several reconstructed cosmic muon track candidates from
different events superimposed, along with a schematic of the signal
amplification region in the right panel.

Figure 1: Left: The $3\times 1\times 1\mbox{ m}^{3}$ geometry with several
reconstructed cosmic muon tracks from different events superimposed. Only
reconstructed hits from one of the views after the 3D track matching are shown
and the colour scale represents the acquired hit charge integral in fC. Right:
Nominal electric field settings of the detector.

At the passage of an ionising particle inside the liquid, electron-ion pairs
are created. The electrons drift towards the surface at a velocity of about
$1.6\text{\,}\mathrm{m}\mathrm{m}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{s}$,
thanks to the nominal electric field of
$500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ provided by the cathode
and drift cage system. Scintillation photons with wavelengths peaked at
$128\text{\,}\mathrm{nm}$ are also produced and detected by five PMTs placed
in line at the bottom of the cryostat. They can provide the trigger and the
reference time for the event with an accuracy of a few nanoseconds [11]. The
produced charge is free to drift in the ultra pure liquid argon up to the
surface where it is extracted to the gas phase. Once in the gas, the drifting
electrons are multiplied by twelve $50\times 50$ cm2 Large Electron
Multipliers (LEMs) and collected on a two-dimensional and finely segmented
anode. The amplification in the LEMs allows to produce signals with amplitudes
which are significantly above the level of the ambient noise, resulting in a
high quality and good resolution image of the interacting particles.

The electron extraction, amplification, and collection are performed inside a
$3\times 1$ m2 structure called Charge Readout Plane (CRP). The CRP is
electrically and mechanically independent from the drift cage and can be
remotely adjusted to the liquid level. The electrons are efficiently extracted
from the liquid to the vapour by applying an electric field in the liquid
above $2\text{\,}\mathrm{k}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ [12].
This electric field is provided by a $3\text{\,}\mathrm{mm}$ pitch extraction
grid positioned $5\text{\,}\mathrm{m}\mathrm{m}$ below the liquid argon
surface. Once amplified inside the LEM holes, the charge is collected on a
two-dimensional segmented anode which consists of a set of independent strips
that provide the $x$ and $y$ coordinates of an event with a
$3.125\text{\,}\mathrm{mm}$ pitch. The anodes are electrically bridged
together so as to provide two orthogonal sets of three and one metre long
readout strips called views. The anodes are carefully designed in such a way
that the amplified charge is equally shared and collected on both views [13].

View 0 (view 1) consists of 320 three metre-long (960 one metre-long) strips
running parallel to the x (y) coordinate axis. As an example, in Figure 2 a
typical raw cosmic track, recorded with the $3\times 1\times 1\mbox{
m}^{3}\mbox{ demonstrator}$ is shown.

Figure 2: 2D event display of a cosmic muon track candidate. The event is
shown without the application of any noise filtering algorithms.

For each view the charge recorded per channel number is plotted as a function
of the drift time, and the colour scale, proportional to the strength of the
signal, has been optimised for optimal track visualisation. The readout pitch
on the horizontal axis is 3.125 mm and the drift time acquisition window of
$667\text{\,}\mathrm{\SIUnitSymbolMicro s}$ is digitally sampled at
$2.5\text{\,}\mathrm{MHz}$ which results in 1667 time samples. At a
$500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ drift field, this leads
to a $\sim$$0.64\text{\,}\mathrm{mm}$ spatial resolution along the drift
coordinate. Each readout view therefore provides a high resolution digitised
image of the interaction products with a pixel unit size of $\sim 3.125\times
0.64$ mm2. A list of relevant parameters of the TPC charge readout section
along with properties of the liquid and gas argon is provided in Table 1.

Property |  Value |  Unit
---|---|---
TPC charge readout |  |
active area |  3 $\times$ 1 |  $\text{\,}{\mathrm{m}}^{2}$
N LEMs (anodes) |  12 |
readout strip width |  3.125 |  $\text{\,}\mathrm{mm}$
readout strip length View 0 (View 1) |  3 (1) |  $\text{\,}\mathrm{m}$
N channels View 0 (View 1) |  320 (960) |
drift length (time) |  1 (607) |  $\text{\,}\mathrm{m}$ ($\text{\,}\mathrm{\SIUnitSymbolMicro s}$)
drift time digital sample |  400 |  $\text{\,}\mathrm{ns}$
drift time acquisition window |  667 |  $\text{\,}\mathrm{\SIUnitSymbolMicro s}$
N drift time digital samples |  1667 |
N Pixels $N_{channel}^{charge}\times N_{sample}^{drift}$ View 0 (View 1) |  0.5 (1.6) |  MPixel
digital integral to charge conversion View 0 (View 1) |  55 (66) |  ADC$\times$tick/fC
$\tau_{1},\tau_{2}$ for View 0 (View 1) |  6.9, 0.5 (2.2,0.9) |  $\text{\,}\mathrm{\SIUnitSymbolMicro s}$
liquid and gas argon properties |  |
ionisation energy $W_{ion}$ [14] |  23.6${}^{+0.5}_{-0.3}$ |  $\text{\,}\mathrm{eV}$
electron drift velocity [15] |  1.648 |  $\text{\,}\mathrm{m}\mathrm{m}\mathrm{/}\mathrm{\SIUnitSymbolMicro}\mathrm{s}$
ion drift velocity ($E_{\mbox{\tiny{drift}}}<1$ kV/cm)) [16, 17] |  8 |  $\text{\,}\mathrm{m}\mathrm{m}\mathrm{/}\mathrm{s}$
average (most probable) energy loss for MIP |  2.1 (1.7) |  $\text{\,}\mathrm{M}\mathrm{eV}\mathrm{/}\mathrm{c}\mathrm{m}$
$\mathscr{W}_{Birk}$ for MIP |  71 |  %
$\sigma_{T}$ ($\sigma_{L}$) for 1 m drift [15] |  1.2 (0.9) |  $\text{\,}\mathrm{mm}$
$\mathscr{A}$ at 100 ppt (30 ppt) for 1 m drift |  82 (94) |  %
GAr temperature near LEMs during data taking [10] |  90$\pm 0.5$ |  $\text{\,}\mathrm{K}$
cryostat pressure during data taking [10] |  1000$\pm 1.4$ |  $\text{\,}\mathrm{mbar}$
First Townsend coeff. $\alpha$ for $E_{\mbox{\tiny{LEM}}}$ = 28 (33) $\text{\,}\mathrm{k}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ |  20.2 (44.1) |  $\text{\,}{\mathrm{cm}}^{-1}$
Table 1:  Some parameters related to the imaging of the TPC along with a
summary of coefficients used for the analysis in this paper. Unless otherwise
indicated, all values are taken from Ref. [18], computed for a liquid with
temperature of 87.3 K, pressure of 1 atm, and drift electric field of
$E_{\mbox{\tiny{drift}}}=$500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$$.
For the first Townsend coefficient we use the value given in [19] for a
pressure of 980 mbar and temperature of 87K.

###  2.2 Effective gain and signal-to-noise ratio

An ionising particle depositing an energy $\Delta E_{dep}$ in the liquid,
produces an ionisation charge, free to drift in the liquid, $Q_{0}=e(\Delta
E_{dep}/W_{ion})\cdot\mathscr{W}_{Birk}$ where $W_{ion}$ is the work needed to
obtain the ionisation and $\mathscr{W}_{Birk}$ denotes the remaining fraction
of produced electrons that do not immediately recombine with the ions. The
latter depends on the ionisation density and the drift field and is well
parametrised by Birk’s Law [20]. The values $W_{ion}$ and $\mathscr{W}_{Birk}$
are reported in Table 1. At a drift electric field $E_{\mbox{\tiny{drift}}}$
of $500\text{\,}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$, a minimal ionising
particle (MIP) produces a charge yield of about
$1\text{\,}\mathrm{f}\mathrm{C}\mathrm{/}\mathrm{m}\mathrm{m}$ after
recombination. The charges drift for a duration $t_{drift}$ and electron
attachment to impurities in the liquid attenuates the signal by a factor
$\mathscr{A}=e^{-t_{drift}/\tau_{e}}$ where $\tau_{e}$ is called the electron
lifetime. Its value is dependent on the performance of the cryogenic
purification and recirculation system. As shown in [10], a study of the data
for this detector suggests a lifetime $\tau_{e}$ better than 4 ms, or an
oxygen
equivalent222$\tau_{e}[\mbox{ms}]\approx$300/[O2]${}_{\mbox{\small{eq}}}$[ppt]
impurity level of $\sim$75 ppt [O2]${}_{\mbox{\small{eq}}}$.

The amount of charge from a MIP collected on an anode strip of view $i$ can
therefore be written as:

$Q_{i}^{mip}[\mbox{fC}]\approx
Q^{mip}_{proj}[\mbox{fC}]\cdot\mathscr{A}(\tau_{e})\cdot\mathscr{G}_{eff}\cdot\frac{1}{2},$
(2.1)

where the effect of transverse and longitudinal diffusion
($\sigma_{T}$,$\sigma_{L}$) is neglected for the relatively short 1 metre
drift distance (see Table 1). The space resolution values are below the
channel pitch. The factor 1/2 represents the fact that the charge yield is
equally split between both collection views of the anode. The projected charge
on one anode strip, $Q_{proj}^{mip}$, depends on the azimuthal and polar
angles of the track crossing the TPC fiducial volume.

$\mathscr{G}_{eff}$ is the effective gain of the dual phase chamber which
primarily relies on the multiplication factor of the electrons inside the LEM
holes but also depends on the overall electron transparency (${\cal T}\leq 1$)
of the extraction grid, LEM and anode inside the CRP. The effective gain can
be analytically decomposed as:

$\displaystyle\mathscr{G}_{eff}$ $\displaystyle=$ $\displaystyle{\cal
T}\cdot\mathscr{G}_{LEM}~{}$ (2.2) $\displaystyle\mathscr{G}_{LEM}$
$\displaystyle=$ $\displaystyle\exp\left[{\alpha\cdot x}\right]$ (2.3)
$\displaystyle\alpha$ $\displaystyle=$ $\displaystyle
A\rho\cdot\exp\left[{-B\rho/E_{\mbox{\tiny{LEM}}}}\right],$ (2.4)

where $\alpha$ is the first Townsend ionisation coefficient for an
amplification field $E_{\mbox{\tiny{LEM}}}$ inside the LEM hole and gas
density $\rho$; $x$ denotes the effective amplification length. $A$ and $B$
are parameters which depend on the gas properties and are obtained from
numerical calculations [21], [19]. The value of $\alpha$ along with the
nominal pressure and temperature of the gas argon during operation of the
detector are reported in Table 1.

Stable effective gains of around 20 have been reported inside litre-scale dual
phase TPCs [13, 22] by operating the CRP at the electric field settings shown
in Figure 1. The $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$ is
however limited in effective gain due to the high voltage issues on the grid
and LEMs reported in [10]. The results discussed in Section 4.3 show that data
has been collected at $\mathscr{G}_{eff}=1.9$. A MIP crossing the TPC at the
polar and azimuthal angles of ($\theta,\phi$)=($90^{\circ},45^{\circ}$) will
produce on average $Q_{i}^{MIP}\approx 2.1$ fC of charge on the 3 mm strips
(without amplification) and neglecting attenuation due to electron lifetime.
The effective gain drives the signal-to-noise ratio of the charge readout of
the TPC ($S/N$) which is defined as the ionisation charge collected on one
anode strip of view $i$ divided by the Equivalent Noise Charge (ENC), the RMS
of the noise of that channel.

$S/N_{i}=\frac{Q_{i}^{mip}\mbox{[fC]}}{\mbox{ENC
[fC]}}\equiv\frac{\mbox{ionisation charge collected on one anode
strip}}{\mbox{ENC}}.$ (2.5)

The ENC on a channel is the combination of the intrinsic noise due to the
input capacitance of the anode strips and all other sources of coherent or
incoherent noise which may be picked up. As shown in Section 3.1 an ENC of
around 2’000 electrons on view 1 and 2500 electrons on view 0 is reported at
the beginning of the TPC operation period, those values drop to around 1’000
electrons for each view after the application of coherent noise removal. We
note that the amount of collected charge per strip and hence the quoted value
of the $S/N$ is dependent on the track topology. For the rest of the paper, we
will quote the $S/N$ per view for the specific case of a MIP track crossing
the strips at ($\theta,\phi$)=($90^{\circ},45^{\circ}$) before noise filtering
algorithms are applied. This provides a conservative lower bound on the $S/N$
since in general, and especially for cosmic particles, tracks are inclined and
will thus have a larger polar angle.

The value of $\mathscr{G}_{eff}$, as well as its uniformity over the readout
surface, therefore directly impacts the imaging quality of the event and is
hence a fundamental quantity used to benchmark the detector performance. The
right side of Figure 3 illustrates the expected $S/N$ for a MIP crossing a
dual phase detector with the operational parameters specified on the figure as
a function of $\mathscr{G}_{eff}$ and drift distance.

Figure 3: Left: relative fluctuation of $\mathscr{G}_{LEM}$ around its nominal
value when varying the gas density and LEM thickness from Table 1. The
fluctuation is shown for two different values of $E_{\mbox{\tiny{LEM}}}$.
Right: $S/N$ from a MIP interaction collected per view on one anode strip as a
function of the effective gain and drift distance. The $S/N$ is computed for a
MIP at an angle $\varphi=45^{\circ}$, $\theta=90^{\circ}$, purity of 75 [O2]eq
ppt, drift field of 500 V/cm and noise of ENC = 2000 e$-$.

For the rather modest one metre drift of the $3\times 1\times 1\mbox{
m}^{3}\mbox{ demonstrator}$, a $S/N$ of 11.2 can be expected even at an
effective gain of 1.9. With similar assumptions for the values of purity and
ENC, operating with $\mathscr{G}_{eff}=10$ would correspond to obtaining $S/N$
= 59.3 for one metre drift and $S/N$ = 11.2 for a TPC with 12 metre drift.
Twelve metres is the drift distance of the proposed DUNE 10kt dual phase
detector [23]. The plot illustrates the importance of the effective gain
especially if the targets in terms of noise performance or LAr purity are not
met.

In order to have a uniform and stable effective gain, the electric field
across the LEM, its thickness as well as the density of the argon vapour must
be carefully controlled. This is illustrated on the left side of Figure 3: due
to the exponential nature of $\mathscr{G}_{eff}$, variations in the
$50\text{\times}50\text{\,}\mathrm{cm}$ LEM thickness or fluctuations in the
gas density may have a relatively large impact on its value. In the $3\times
1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$, the thickness uniformity of all
the $50\text{\times}50\text{\,}\mathrm{cm}$ LEM plates was carefully checked
and the gas argon density was maintained at a stable value. Both were uniform
within typically one percent (see Ref. [10] and Table 1). The obtained
uniformity of the effective gain in the $3\times 1\times 1\mbox{ m}^{3}\mbox{
demonstrator}$ is discussed in Section 4.3. In all these studies, diffusion is
not accounted for, since over these short drifts its effects are negligible
and not measurable. The effects of diffusion, however, should be properly
considered in large detectors.

###  2.3 Charge readout detector response

By design the dual phase TPC, and specifically the $3\times 1\times 1\mbox{
m}^{3}$, allows to place the front-end electronics close to the readout
strips, profiting from the cryogenic temperatures while at the same time
ensuring its accessibility during detector operation. The front end electronic
boards are described in [10]: they have a DC decoupling stage, high voltage
surge protection components and an ASIC chip which contains the CMOS pre-
amplifiers and signal shaping. The pre-amplifiers feature a double-slope
response with a linear gain for input charges of up to 400 fC and a
logarithmic response in the 400-1200 fC range. The double slope feature allows
to extend the dynamic range of the detector and acquire events with high
ionisation yield. The data presented in this publication is mainly collected
at effective gains of around 2 and therefore we only consider the linear
regime of the pre-amplifier response.

The current produced by the cloud of drifting charge is extracted and
multiplied in the LEMs, collected on the anode and pre-amplified. The recorded
signal to be digitised $V_{out}(t)$ is a convolution of the induced current
$I(t)$ on the anode strip and the response of the pre-amplifier after shaping
of the signal $S_{response}(t)$:

$V_{out}(t)=\int_{t_{0}}^{t}I(t^{\prime})\cdot
S_{response}(t-t^{\prime})~{}\mbox{d}t^{\prime}$ (2.6)

with the amplifiers response function:

$S_{response}(t)=\frac{\tau_{1}}{\tau_{1}-\tau_{2}}\cdot\left(e^{-t/\tau_{1}}-e^{-t/\tau_{2}}\right),$
(2.7)

where the values of $\tau_{1}$ and $\tau_{2}$ are reported in Table 1. The
signal, $V_{out}(t)$, after digitisation, called the waveform, features a
standard shape with a peaking and falling time given by the internal RC-CR
shaping performed in the ASIC. The waveform is characterised by its amplitude,
integral and width (defined as the peak full width at half maximum). The
integral is proportional to the amount of collected charge.

Typical waveforms recorded on one channel of view 1 and of view 0 for the same
amount of injected charge are shown on the left side of Figure 4.

Figure 4: Left: response of the pre-amplifiers to an injected pulse of 14 fC
on the three metre strips (view 0) and one metre strips (view 1). Right:
linearity of the pre-amplifiers response for both views. Ticks refer to time
ticks, or time to digital converter (tdc) counts, where each one corresponds
to 400 ns.

They are acquired with the system described in [10], which allows to inject
calibrated pulses on groups of 32 strips from each view separately. Since an
anode strip has a capacitance to ground of $\sim$160 pF/m [10, 13] the front
end pre-amplifiers connected to the channels of view 0 and view 1 have
different capacitive loads. This results in a non-identical pre-amplifier
response between both views: for an equal amount of injected charge the
waveforms from the channels connected to view 0 have smaller amplitudes,
larger widths and a $\sim$20% lower value of the integral. The linearity of
the response in terms of the waveform integral is shown on the right side of
Figure 4, where the values of integrals for both views are shown over an
extended range of injected charge. The fitted slope for each view is used as a
calibration constant to convert the digitised integral into fC. The values of
both calibration constants are reported in Table 1.

###  2.4 Charge extraction and electron transparency

For a given LEM amplification field, the electron transparency ${\cal T}\leq
1$ is defined as the product of the efficiencies in the extraction and
induction regions:

${\cal T}=\varepsilon_{trans}\times\varepsilon_{ind},$ (2.8)

where $\varepsilon_{trans}$ denotes the probability for a given charge to be
extracted from the liquid and transmitted inside the LEM holes, and
$\varepsilon_{ind}$ represents the efficiency of collecting the amplified
charges from the top of the LEMs on the anode strips. In this paper, we define
the transmission efficiency as
$\varepsilon_{trans}\equiv\varepsilon_{extr}^{liq}\times\varepsilon_{extr}^{LEM}$
which includes the contributions from the electron transmission from the
liquid to the gas phase ($\varepsilon_{extr}^{liq}$) and that of the
collection of the electrons entering the LEM from the bottom electrode
($\varepsilon_{extr}^{LEM}$). While the latter is estimated from simulations,
the former is taken from previous measurements performed under similar
conditions by Gushchin et al. [12], shown by the black data points on the left
plot of Figure 5.

Above 2 kV/cm of extraction field in the liquid (E${}_{extr}^{liq}$), most of
the charge is extracted within a timescale of less than 100 nanoseconds (“fast
extraction”, red markers in Figure 5), as the electric field decreases a
growing fraction of the charge is transmitted via thermionic emission [24],
with characteristic times at the tens of microseconds scale [5]. The impact of
the extraction field at which the TPC is operated is noticeable on the shape
of the signal as shown in the right panel of Figure 5, where waveforms from
data collected at different extraction fields with similar track topologies,
amplification and induction fields are shown. The increase of the width at
lower extraction fields due to the slow extraction is clearly visible.

Figure 5: Left: efficiency to extract the electrons from the liquid to gas
argon phase ($\varepsilon_{extr}^{liq}$) as a function of the applied
extraction field in the liquid, $E_{extr}^{liq}$, showing slow and fast
components of the signal. The data points are taken from measurements
described in [12]. Right: Waveforms recorded in the $3\times 1\times 1\mbox{
m}^{3}$ detector at three different values of the extraction field.

It is therefore important not only to operate the TPC at the maximal possible
effective gain but also to understand the interplay between the electric
fields and estimate the best possible settings in terms of detector
transparency. The optimal value of the transparency can be estimated from
simulations of electron amplification and transport in the vapour phase. In
Figure 6, we show an illustration of a simulated electron avalanche performed
with the Garfield++ software package [25]. The electric field maps are
imported from ANSYS [26], and the gas properties (argon vapour at 90 K) are
computed using MAGBOLTZ [21].

Figure 6: Cut view of a 3D Garfield++ simulation of the electron amplification
in the LEMs in argon gas. The green and orange rectangles correspond to the
electrodes. The LEM holes are illustrated as white spaces. The anode is
simplified as a plane of copper at ground potential. The orange lines
illustrate the trajectory of the electrons in the gas phase after being
extracted from the liquid.

The 3D simulation is performed over a 3$\times$3 mm2 area, corresponding to
one readout pixel. The charge avalanche in the LEM holes is clearly visible in
the figure as well as the small fraction of electrons which are collected
either on the bottom or top electrodes of the LEM.

Performing such simulations for multiple combinations of field settings allows
to generate maps of $\varepsilon_{trans}$ and $\varepsilon_{ind}$ as a
function of the amplification electric field ($E_{\mbox{\tiny{amp}}}$). The
results are shown in Figure 7.

Figure 7: Simulated values of $\varepsilon_{trans}$ (left) and
$\varepsilon_{ind}$ (right). The red dots correspond to the best operating
fields the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$ was operated
for the data taking run. The black dots indicate the field values at which the
previous dual phase TPC [13, 22, 19] was operated under stable conditions at
$\mathscr{G}_{eff}$ = 20.

The induction efficiency increases with the induction electric field
($E_{\mbox{\tiny{ind}}}$) and tends to plateau at values near 5 kV/cm. The
value of $E_{\mbox{\tiny{ind}}}$ at which this plateau is reached increases
with the amplification field. The optimal setting for the extraction electric
field in the liquid ($E_{\mbox{\tiny{extr}}}^{\mbox{\tiny{liq}}}$) is reached
at around 2 kV/cm. Above this value, the fraction of electrons extracted from
the liquid and entering the holes decreases, since more electrons are lost on
the bottom LEM electrode. Also shown in the figure are markers which indicate
the best operating points of the $3\times 1\times 1\mbox{ m}^{3}\mbox{
demonstrator}$ and a smaller prototype equipped with a $10\times 10$ cm2 LEM
referred to as the 3L TPC [13, 22, 19]. The latter was operated stably at
$\mathscr{G}_{eff}$ $\approx$ 20 with electric fields of 5, 2, 33 kV/cm for
$E_{\mbox{\tiny{ind}}}$, $E_{\mbox{\tiny{extr}}}^{\mbox{\tiny{liq}}}$ and
$E_{\mbox{\tiny{amp}}}$, respectively. These field settings are those reported
in Figure 1 and referred to as the nominal settings. The $3\times 1\times
1\mbox{ m}^{3}\mbox{ demonstrator}$ is operated at lower field settings of
1.5, 2.0, 28 kV/cm for $E_{\mbox{\tiny{ind}}}$,
$E_{\mbox{\tiny{extr}}}^{\mbox{\tiny{liq}}}$ and $E_{\mbox{\tiny{amp}}}$
which, according to the simulated maps, corresponds to a transparency of
0.4$\times$ 0.6 $=$24%.

##  3 Cosmic ray data and dual phase detector simulation

###  3.1 Summary of the collected data

The TPC operation ranged over a period of about 5 months. As detailed in [10],
technical issues on the absolute high voltage of the extraction grid and
limitations on the maximum applied voltage of the $50\times 50$ cm2 LEMs
prevented us from operating the TPC for a long duration and at the nominal
field settings. Therefore most of the run period was dedicated to detector
optimisation, and in this paper, we discuss the data from approximately 300k
triggered events. Results are shown for data collected at electric field
settings which optimise the $S/N$ (see Table 2 for details), taking into
account the above mentioned limitations. For the rest of this paper, the long
(about 5 hours) stable run used for detector performance studies under stable
conditions is referred to as Reference Run.

In Table 2, we show the settings and some properties of the analysed data-sets
along with that of the detector Monte Carlo (MC) simulation tuned to match the
effective gain and electron lifetime of Reference Run as well as the detector
acceptance.

|  |  |  |  |
---|---|---|---|---|---
| Reference Run |  | Field scans
|  data |  MC |  |  Extr. |  Amp.
Ind. field [kV/cm] |  1.5 |  - |  |  1.0 |  1.0
Amp. field [kV/cm] |  28.0333The four corner LEMs are operated at 24 kV/cm [10]. |  - |  |  28.0 |  24-27
Extr. field [kV/cm] |  2.0 |  - |  |  1.2-2.2 |  1.5
Effective gain $\mathscr{G}_{eff}$ |  1.9 |  2.0 |  |  0.9-1.5 |  0.5-1.2
Electron lifetime [ms] |  7.0 |  10 |  |  - |  -
$S/N_{MIP}$ |  12.0 |  13 |  |  5.7 – 9.5 |  3.2 – 7.6
N events ($\times 10^{3}$) |  40 |  16 |  |  22 |  213
N sel. tracks ($\times 10^{3}$) |  15 |  5.5 |  |  1.3 |  7
Table 2:  Summary of data taking conditions for the data-sets used in this
paper. The $S/N$ is given before the application of the coherent noise filter
(see text for definitions).

The values of $\mathscr{G}_{eff}$ in the table are calculated from the data as
explained in Section 4.3 and the $S/N$ ratio is computed according to the
definition of Equation (2.5) for a MIP crossing the detector at
($\theta,\phi$)=($90^{\circ},45^{\circ}$) at the quoted purity level.

The evolution of the RMS of the noise on the charge readout during the
operation period of the TPC is shown on the left side of Figure 8. The periods
corresponding to the acquisition of the data discussed in this paper are also
indicated. The dashed bars indicate the two shutdown periods of approximately
1 month when maintenance was performed on the LEM high-voltage power supplies.
As can be seen, the noise RMS level is significantly reduced (by more than a
factor of two) by the coherent noise filter to reach a stable value of around
1.1 ADC counts (1000 electrons) in both views over the entire operation period
of the chamber. The origin of the increase of the coherent noise after both
shutdown periods is not well understood. It is most likely due to ground loops
created during the maintenance periods on the CAEN HV supply and re-connection
of sets of slow control cables.

Detailed Fast Fourier analysis of the noise frequency discussed in [27], shows
a prominent peak at around 900 kHz. A good stability is nevertheless observed
for each period. The right side of Figure 8 shows the electron lifetime
measured at different dates. The measured purity was found to be stable
throughout the whole data-taking period. Further information how the value
given in Figure 8 is computed is given in section Section 4.3.

Figure 8: Left: evolution of the noise during the entire TPC operation period.
The four colours correspond to the noise on the two views, before and after
coherent noise removal. Right: evolution of the electron lifetime over the
same data-taking period.Uncertainties are statistical only, and the large
error bars on the plot are related to the different number of tracks selected
for the lifetime evaluation. The weighted average of the lifetime is
$\lambda=(7.0\pm 0.4)$ ms.

All the data are acquired with a trigger requiring a coincidence of all 5
PMTs. Their thresholds are set to maintain a data acquisition rate at the
level of 3 Hz [10, 11]. At those settings, our event sample predominantly
consists of electromagnetically or hadronically induced cascades (showers),
emitting large amounts of scintillation light, or MIPs, which cross most of
the fiducial volume at a relatively shallow angle.

###  3.2 Detector simulation

A detailed Monte Carlo simulation of the detector was developed to reproduce
the detector acceptance and track topologies. Typical events for both data and
MC at Reference Run settings are shown in Figure 9. These include a muon
decaying in the active volume where the Michel electron is clearly visible, a
hadronic and an electromagnetic shower. The data are shown with a colour scale
representing the hit amplitude while reconstructed MC hits are coloured
according to the particle species.

Figure 9: Event displays for the three categories of events at the Reference
Run settings. The images at the top correspond to the data, those at the
bottom to the Monte Carlo simulation. From left to right: a stopping muon, a
hadronic and an electromagnetic shower.

The simulation is used to check the energy range of the cosmic muon sample,
verify the muon selection purity and quantify the track reconstruction
efficiency, using a method explained in Section 3.4.

Since comparison with data requires a reproduction of the atmospheric flux and
simulation of the detector acceptance, an event sample simulating the
atmospheric flux was generated with the CORSIKA [28] package. Primary
particles from CORSIKA were uniformly generated on a plane, located 3 metres
above the top of the TPC fiducial volume to simulate events produced from the
interactions of these particles with the cryostat or detector materials.

The trigger was simulated to reproduce the event rate, event topologies and
the relative amount of tracks and showers observed in our data sample. The
detector was divided into cubic areas with a volume of $25\times 25\times
25\,\mathrm{cm}^{3}$ each. From the centre of each volume, a light map was
built simulating 100 million photons to compute the probability of and the
arrival time for a photon produced at the centre of that volume to reach each
photomultiplier. The probability and arrival time for each position in the
detector was obtained by a linear extrapolation from the simulated values at
the centre of each volume, as described [11]. A simplified trigger simulation
was applied, which required all five PMTs to measure at least 1750 photons in
a time window of 80 ns.

Figure 10 shows the momentum distribution of the generated particles entering
the TPC and those which pass the simulated trigger condition. The polar angle
distribution of the triggered muons is also shown.

Figure 10: Left: simulated rate of particles entering the fiducial volume of
the TPC, in terms of expected number of particles per unit time, as a function
of the log of the particle’s momentum. Empty histograms with dashed lines
represent the total flux, while histograms with full lines are the
distribution of particles passing the trigger. Right: polar angle distribution
of the muons which pass the trigger condition.

The particles are grouped according to the topology of events they produced
when interacting in the $3\,\mathrm{m}^{3}$ of liquid argon target. Given the
$15\,\mathrm{cm}$ radiation and $84\,\mathrm{cm}$ interaction lengths of LAr,
both electromagnetic (EM) and hadronic showers initiated by electrons/gammas
and hadrons, respectively, will generally be contained in the detector volume.
As seen in the figure, the triggered event sample consists of muons with a
broad momentum distribution peaking at around 10 GeV and with polar angles of
$\sim$120 degrees, and a quite substantial content of showering events in the
1-10 GeV range. Triggered muons in those energy ranges are MIPs and after
careful track selection can be used to characterise the TPC effective gain.

####  3.2.1 Waveform generation and noise simulation

The energy deposited in the liquid argon is converted into ionisation charge.
The fraction of charge lost due to electron-ion recombination is estimated
with Birk’s Law and the drift of the charge can be performed following an
electric field map which is extracted from electrostatic simulations of the
detector [29]. Charge attenuation due to electron attachment as well as the
spatial spread of the electron cloud from transverse and longitudinal
diffusion along the drift are also included in the simulation according to the
values shown in Table 1.

Once the electron cloud has reached the anode, the waveforms on each view are
generated by convoluting the corresponding current with the charge readout
detector response function described in Section 2.3. The effective gain is
taken into account by multiplying the number of electrons inside the cloud by
the desired number. In addition, the broadening of the signal width and
reduction of its amplitude at low extraction fields is included in the
simulation by smearing the arrival time of the electrons in the slow component
according to an exponential distribution, see Figure 5. The time constant of
the exponential is chosen so that the width of the generated waveform matches
those from the extraction field scan data.

A simulation of the coherent noise is also included. This is done by using an
Inverse Fourier Transformation to produce a waveform based on the frequency
spectra of the noise in data. An identical random phase is assigned to groups
of channels, following the same correlation scheme that is observed in the
data. Details on the waveform simulation at low extraction fields can be found
in [30], and on the simulation of the noise in [27]. In Figure 11 we show a
simulated muon event (view 1) and a MIP candidate from data at the settings of
the Reference Run. The noise pattern, the dead channels and the waveform are
well reproduced in the MC.

Figure 11: Event display showing a MIP candidate from data (left) and a
simulated muon in the data driven simulation (centre), in the time versus
channel number plane. The continuous line is due to a dead channel, while the
dashed line indicates the channel from view 1 of the waveform shown in the
right plot.

The detector simulation features a data-driven approach to describe the
waveform shape and the noise. This allows a simulation of the TPC response at
any field settings and an effective gain with good agreement to data. A
comparison of the reconstructed track level between MC and data for the
specific case of the Reference Run is provided in Section 4.

###  3.3 Cosmic track reconstruction

The off-line reconstruction of tracks from both simulation and acquired data
is performed within the LArSoft software package [31] with the same procedure
applied for data and MC events. The entire reconstruction procedure is
illustrated in Figure 12 for a muon track candidate.

Figure 12: Schematic example of the different reconstruction stages applied to
a cosmic muon track collected with the $3\times 1\times 1\mbox{ m}^{3}\mbox{
demonstrator}$. The raw data (a) is first preprocessed in order to remove the
noise (b) and to identify signal hits (c). Hits are grouped into 2D clusters
(d) and clusters are finally associated to form a 3D image of the event (e).

The first step of the event reconstruction procedure consists in identifying
so called regions of interest (ROIs) where the signal exceeds a certain
threshold above the baseline pedestal. This is performed by standard threshold
discrimination: the waveform is scanned for peaks above a certain average
pedestal. This initial pedestal is computed in order to optimise signal over
background discrimination, and the following iterative procedure guarantees
that its initial value has a very small effect on the final S/N ratio. To
avoid any bias due to physical signals, the ROIs are neglected during the
subsequent pedestal subtraction and noise filtering process. The absolute
value and slow fluctuations of the pedestal are subtracted by applying a
polynomial fit on the waveform. Noise with a periodic behaviour is removed by
the successive application of Fast Fourier transform algorithms. A coherent
noise filtering algorithm is also applied to reduce the amplitude of noise
patterns which are common to groups of channels at a given time. The entire
process is repeated in an iterative manner since at each step the image of the
event is improved and new ROIs may be identified.

At the end of this process the baseline has less fluctuations and physical
hits can be extracted from the waveforms by means of standard threshold
discrimination. Once hits have been identified on both views, neighbouring
hits are merged together to form 2-dimensional clusters. The clusters from
each view are then matched together, allowing to build 3D track objects by
assigning a trajectory to the corresponding group of hits. On some occasions,
clusters may be interrupted because of a malfunctioning or dead readout
channel. During the operation of the TPC, about 14 channels ($\sim$1% of the
total) were found to be problematic. In addition, each strip immediately above
the 2 mm of copper guard ring surrounding the LEM borders [10] does not
register a signal (four strips on view 0 and twelve on view 1). Those channels
are removed from the track reconstruction algorithm to ensure the missing hits
do not interrupt the track fitting procedure.

While this approach permits reconstructing straight tracks with high
efficiency, it is not designed to provide an accurate 3D representation of
showering events which most of the time will be reconstructed as multiple
small clusters. Since we have no a priori knowledge of the event topology, the
procedure described above is applied on all data and shower-like events are
separated from muon-track candidates by off-line tools (see Section 4.1). The
same procedure is applied to the MC sample where the noise and detector
response are simulated according to data raw events.

###  3.4 Track reconstruction efficiency

The efficiency to reconstruct tracks in 3D, $\varepsilon_{r}$, is estimated
with the use of the flat phase space MC where primary particles, referred to
as MC-Particles, are generated over the 4$\pi$ phase space. The noise and
electron lifetimes are set to the Reference Run settings shown in Table 2. The
quality of the reconstruction in the simulation is computed by associating the
reconstructed hits inside a track with the original energy deposit from the
related GEANT trajectory. This quantity is called completeness. Tracks with
completeness greater than 50% are considered well reconstructed. More details
on the method to compute the reconstruction efficiency are provided in [27].
The efficiency maps as a function of $\theta$ and $\varphi$ for a TPC operated
at $\mathscr{G}_{eff}$ of 2 and 1.5 are shown in Figure 13. The former
corresponds to the Reference Run setting, and for the latter the lower
effective gain is obtained by reducing the extraction field to 1.5 kV/cm.

Figure 13: Efficiency to reconstruct a track in 3D as a function of the polar
and azimuthal angles, estimated using simulations. The left plot corresponds
to the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$ TPC operated at
$\mathscr{G}_{eff}$ of 2 and the right plot to the TPC operated at
$\mathscr{G}_{eff}$ of 1.5.

As can be seen, $\varepsilon_{r}$ for a TPC operated at $\mathscr{G}_{eff}=2$
is in general close to 100%. Specific geometrical topologies of near vertical
tracks ($\theta=180^{\circ}$) or, to a lesser extent, tracks parallel to the
strips of one view ($\phi=180^{\circ},90^{\circ},0^{\circ},..$) are not
efficiently reconstructed in 3D because the matching of the 2D tracks fails
due to an insufficient number of hits on one or both of the views. This is a
purely geometrical effect for which the effective gain at which the TPC is
operated has a minimal impact. Since the 2D hits are identified, an
improvement in the 2D matching procedure could increase $\varepsilon_{r}$ in
those regions. A 25% reduction in the effective gain translates in the same
$S/N$ reduction. As a consequence the efficiency for near horizontal tracks is
greatly reduced as visible on the right map of Figure 13.

In the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$, even though
operated at a sub-optimal effective gain of around 2, cosmic tracks are
therefore reconstructed with high efficiency regardless of their topology. At
$\mathscr{G}_{eff}$ =1.5, the efficiency begins to drop for certain track
orientations but remains near 100% for the average polar angle of the MIPs
selected by the trigger ($\theta=120^{\circ}$). We note that those maps are
generated for the specific case of the $3\times 1\times 1\mbox{ m}^{3}\mbox{
demonstrator}$ and clearly higher effective gains are needed for larger TPCs
aiming to study neutrinos with longer drifts and possibly larger noise RMS. We
also do not discuss the impact of the gain on other fundamental features such
as particle identification or reconstruction of low energy neutrinos.

##  4 Detector performance studies

In this section the detector performance in terms of effective gain and charge
sharing from the Reference run is discussed, taking into account the technical
limitations encountered during data taking. Qualitative comparisons of data
collected at various LEM fields with data from the 3L TPC are also discussed.
As a reminder, the four corner LEMs of the TPC could only be operated stably
at the maximum electric field of
$24\text{\,}\mathrm{k}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$ [10]. Unless
otherwise specified, the hits belonging to channels of these LEMs are excluded
from the analyses.

###  4.1 Muon track selection

Through-going muons are MIPs which deposit a known $\langle
dE/dx\rangle\simeq$2.1\text{\,}\mathrm{M}\mathrm{eV}\mathrm{/}\mathrm{c}\mathrm{m}$$
in liquid argon and are used to characterise the performance of the TPC in
terms of effective gain. As explained in Section 3.3, showers will often be
reconstructed as many independent clusters which are subsequently fitted to
straight lines, producing multiple short tracks. The distribution of the
lengths of the reconstructed tracks are shown for both MC and data in the left
panel of Figure 14, where it is shown that most of the tracks associated to
showers have lengths in the tens of centimetre range. The MC sample is
subdivided into each particle type that belongs to the reconstructed cluster.
A selection based on the length of the reconstructed track is thus an
effective first step to distinguish showers from through-going muons. A cut on
the track length $L\geq 50$ cm is applied, to reflect the point where an
excess in data is observed over the main background due to (EM) showers.

Figure 14: Distribution of reconstructed track lengths and polar angles for
all triggered events and selected MIPs from data compared to the Monte Carlo
sample at the Reference run settings.

To further clean up the sample, a second cut based on the amount of charge
deposited transversely along the reconstructed 3D track is applied. While an
EM shower may occasionally be reconstructed as a single track, since its
Moliere radius in LAr is about $9\text{\,}\mathrm{cm}$ [16], the transverse
spread of the charge will be relatively large compared to a MIP track. In
order to take advantage of this property of an EM shower, a new variable
called the Charge Box Ratio ($CBR$) is defined using the fractional difference
between the charge deposit in two boxes around the reconstructed track.

The amount of charge contained in the large white box in Figure 15,
$Q_{out}^{i}$, and the charge in the orange dashed box immediate adjacent to
the reconstructed track, $Q_{in}^{i}$, are computed for each view, $i$.

Figure 15: Illustration of the algorithm which computes the charge box ratio
on an EM shower reconstructed as a single track (left) and a muon candidate
(right). The CBR is equal to 56$\%$ for the EM shower and $13\%$ for the muon
candidate. These event displays are from the Reference run and only view 0 is
shown. The inner dashed box has a transverse dimension of
$3.5\text{\,}\mathrm{cm}$ and the outer one $9\text{\,}\mathrm{cm}$.

The $CBR^{i}$ is then defined as the fractional difference between these two
quantities with respect to the amount in the adjacent box,
$CBR^{i}=(Q_{out}^{i}-Q_{in}^{i})/Q_{in}^{i}$. A cut of less than 20% on the
$CBR$ in both views is required to tag the cluster as a MIP track. This value
is based on detailed Monte Carlo simulation studies and verified through
visual scans of the event displays of candidate tracks to maximise the track
selection efficiency and the muon sample purity.

Table 3 shows the effect of the cuts on the track lengths and $CBR$ on a MC
sample that reproduces the fraction of event categories expected in data. Of
the total number of reconstructed tracks in the sample, only about 5.6% of
them are from muons before the selection criteria are applied. When the track
length cut of $L\geq 50$ cm is applied on the whole data set, about 93% of the
EM showers and 85% of hadronic showers are eliminated, while preserving over
93% of the MIP-like tracks.

When the cut on $CBR\leq 20\%$ is applied, only 0.4% and 1.9% of the tracks
from EM and hadronic showers are left, respectively. These correspond to only
6% and 5.5% of the remaining tracks resulting from EM and hadronic showers
respectively, and about 88.5% from MIP. This means that given the initial
sample composition shown in the table, the muon purity increases from 5.5% of
all tracks to 88.5% after the two selection cuts are applied. This also
corresponds to an overall selection efficiency of 61% for muons and over 99%
and 98% rejection efficiency to EM and hadronic showers, respectively, clearly
demonstrating the effectiveness of the selection criteria. As potential
improvement for future analyses, a more sophisticated alternative selection
method based on multivariate classifiers has also been developed to take
advantage of correlations between track and shower variables.

| EM shower | HAD shower | MIP | total
---|---|---|---|---
N events | 8595 | 1316 | 6750 | 16666
N reco tracks | 83269 | 14222 | 7029 | 126092
$L\geq 50$cm | 5481 | 2079 | 6549 | 14109
$CBR\leq 20\%$ | 293 | 265 | 4299 | 4857
Residual Fraction | 0.4 % | 1.9 % | 61.2% | 3.9%
Table 3:  The numbers of events and tracks corresponding to each category of
interaction in the Monte Carlo samples. Track refers to that associated to a
particle of the specified category. The residual fractions represent the
percentage of tracks left in each category after the two selection cuts are
applied.

The distribution of the selected MIP track candidates from data with the cut-
based method described above is also shown in yellow in Figure 14. As can be
seen, the distributions of all MC and data reconstructed tracks are in
relatively good agreement before and after the selection criteria are applied,
illustrating that the detector acceptance is well reproduced by the simulated
trigger. The distribution of selected MIP candidates in data is close to that
of the reconstructed muons in the MC.

###  4.2 Space Charge and Field Distortion

A non-uniform electric field applied on the active LAr volume of the detector
worsens the energy and position resolutions and makes straight tracks appear
bent and distorted. The drifting ionisation electrons would not travel upwards
along a straight line with a uniform speed and could gain a horizontal drift
component in a non-uniform field. In a LAr TPC, a non-uniform field could be
caused by positive argon ions produced in the ionisation by a traversing
charged track. Due to their large mass, the ionised argon atoms drift towards
the cathode with much lower speed than the ionisation electrons and remain in
the liquid for a much longer time. These positive ions can accumulate within
the detector active volume and create a non-uniform high charge distribution
that could locally distort the drift electric field.

In addition, in a DP LAr TPC, for every electron created in the LEM avalanche,
a corresponding argon ion is created. These ions drift towards the gas-liquid
boundary, and a fraction of them could enter the liquid, adding to the space
charge already residing in the active volume. The rest remains trapped on the
surface of the liquid, distorting the extraction field. We define the fraction
of ions crossing the liquid-gas boundary as the ion back-flow. It is important
to precisely estimate the ion back-flow, to understand how large of an impact
the ions created in the gas phase would have on the space charge effect in the
active liquid volume.

In order to estimate the magnitude of the space charge in the $3\times 1\times
1\mbox{ m}^{3}\mbox{ demonstrator}$, a MIP sample was selected using the cuts
described in Section 4.1 in the data. Along the reconstructed path of each
track, the local 3D distortion is computed as the distance with respect to a
straight line connecting the start and end points of the track, as illustrated
in Figure 16 top left. To determine the effect of the drift field distortions
due to space charge, drift field maps with various fractions of the ion back-
flow (from 0% to 90% in steps of 10%) are computed using the COMSOL software
[29] with the detector technical parameters given in [10]. The simulations
consider both the space charge effect of ions coming from the gas and of ions
produced in the liquid. From each of the obtained drift field computations,
the time and space displacements of drifting electrons throughout the active
volume are extracted and stored in a map used as an input to the GEANT4-based
simulation.

Figure 16: Averaged distortions of MIP-like tracks in data (bottom left) and
in simulations (right). Three hypotheses are shown for the Monte-Carlo case:
no space charge (top), 10% of ion back flow (middle) and 90% (bottom).

Figure 16 shows the average distortion of MIP-like tracks in data (bottom
left), which displays pattern similar to the shape of the butterfly wings,
compared to three different Monte Carlo simulations in the three plots on the
right. The top right plot shows the case in which no ions, produced either in
gas or in liquid, flow towards the cathode. Hence, only the multiple
scattering can affect the track path. As the resulting distortion averages at
zero, it implies that the multiple scattering alone cannot explain the
observation of bent tracks in the data. The two remaining plots show 10%
(middle right) and 90% (bottom right) ion back-flow fractions. As can be
clearly seen, the higher the ion-back flow fraction, the better the MC samples
mimic the field distortion observed in the data. While the 90% ion back-flow
fraction MC shows the clear emergence of the pattern similar to the data, the
degree of the distortion and the detailed features, observed in the data
cannot be fully described by the ion back-flow fraction alone. It is clear
from the data plot, additional factors such as geometry and fringe effects
need to be investigated to fully determine the impact of the space charge.

Since the space charge can affect the 3D reconstruction of tracks, impacting
adversely the imaging capability of the detector, this effect should be
further investigated, especially for large scale future detectors with long
drift distance and higher gains. In large volumes, ions will remain in the
liquid for an even longer time. Additionally the targeted LEM gain in future
detectors is an order of magnitude higher than the one achieved in the
$3\times 1\times 1\mbox{ m}^{3}$ detector. Thus a high ion back-flow will add
a significant amount of ions to the liquid. Both effects combined might
therefore lead to significant distortions to the electric drift field. Due to
lack of data statistics, however, only qualitative measurements of space
charge and ion back-flow effects could be done with the $3\times 1\times
1\mbox{ m}^{3}\mbox{ demonstrator}$. Therefore, in the following results, no
corrections due to the drift field non-uniformity are applied.

###  4.3 Effective gain, uniformity and charge sharing asymmetry

The quantity $\Delta Q_{i}/\Delta s_{i}$ is the energy locally deposited by
the track in liquid argon per unit length for each readout view and is used to
estimate the effective gain of the chamber. Figure 17 shows $\Delta
Q_{0}/\Delta s_{0}$ (left panel) and $\Delta Q_{1}/\Delta s_{1}$ (right panel)
for view 0 and view 1, respectively, from the sample of 3D reconstructed MIPs
collected during the Reference run.

Figure 17: The $\Delta Q_{0}/\Delta s_{0}$ and $\Delta Q_{1}/\Delta s_{1}$
distributions for both views, using all LEMs together, for selected tracks
from the run with electric field settings defined as the Reference run in
Table 2. The reconstructed charge in each hit is corrected for the purity
effects. A Landau function convoluted with a Gaussian is fitted to the
distributions and the resulting Most Probable Value (MPV) and width of the
Gaussian ($\sigma_{Gauss}$) are indicated. More imperfections in the
reconstruction of view 0 lead to a slightly larger width.

The effective gain is defined as the sum of the charge collected per unit
length in each view divided by the average charge deposit of a MIP predicted
by the Bethe-Bloch formula:

$\mathscr{G}_{eff}=\frac{\langle\Delta Q_{0}/\Delta s_{0}\rangle+\langle\Delta
Q_{1}/\Delta s_{1}\rangle}{\langle\Delta Q/\Delta s\rangle_{\text{MIP}}}$
(4.1)

Taking into account the electron-ion recombination, $\langle\Delta Q/\Delta
s\rangle_{\text{MIP}}\sim 10$ fC/cm. The distributions shown in Figure 17
correspond to a chamber operated at $\mathscr{G}_{eff}$ = 1.9 at the field
settings and purity conditions of the Reference run and lead to a $S/N=12.0$
on each view for MIPs at ($\theta,\phi$) = ($90^{\circ},45^{\circ}$). This
result improves our previous measurement presented in [10], thanks to the use
of the charge readout response function described in Sec. 2.3 and a more
accurate muon selection.

The CRP is composed of $50\text{\times}50\text{\,}\mathrm{cm}$ units, thus we
should ensure that the effective gain is uniform over the $3\times 1$ m2 area.
The uniformity of the effective gain is illustrated in Figure 18 that shows
the collected charge per unit length in both views ($\Delta Q/\Delta s$)
averaged over each LEM as a function of the $x,y$ coordinates of the
reconstructed MIPs.

Figure 18: Average $\Delta Q/\Delta s$ collected per LEM and per view along
the $x,y$ coordinates of the reconstructed tracks. The 4 corner LEMs are
operated at 24 kV/cm and are excluded from the analysis while the 8 central
ones at 28 kV/cm. The color scale indicates the $\Delta Q/\Delta s$ averaged
over the two views.

The fluctuation of the effective gain in the area corresponding to the 8
central LEMs is contained within 5% tolerance.

In addition to demonstrating a good uniformity of the charge readout on a
large area, it is important to verify the good charge sharing between the two
views. The charge sharing asymmetry coefficient is defined as:

$\mathcal{A}=\frac{\langle\Delta Q_{0}/\Delta s_{0}\rangle-\langle\Delta
Q_{1}/\Delta s_{1}\rangle}{\langle\Delta Q_{0}/\Delta
s_{0}\rangle+\langle\Delta Q_{1}/\Delta s_{1}\rangle}.$ (4.2)

This coefficient depends on the azimuthal angle $\phi$ and varies within $\pm
1$, as shown in Figure 19 right. In particular, when $\phi=\pm 45^{\circ}$,
$\pm 135^{\circ}$, the track unit length $\Delta s$ is the same in both views.
In this case, the collected charge in each view should be equivalent and
$\mathcal{A}$ should therefore be equal to 0 (see Figure 19 left).

Figure 19: Left: The charge sharing asymmetry distribution for tracks in the
azimuth angle range $\phi=45\pm 5^{\circ}$, Right: MPVs from the fit to the
charge deposit in view 0 and view 1 (in black)

Despite the selection operated by the trigger conditions and difficulties in
the reconstruction of tracks parallel to the strips, the asymmetry remains
within 15%. A more careful evaluation of the systematic uncertainties on the
effective gain measurement and its stability as well as on the uniformity of
the CRP response will be carried out in the ProtoDUNE-DP detector, to ensure
the good fitting of the LAr TPC dual phase technology within the requirements
set by the DUNE experiment.

###  4.4 Scans of extraction and LEM fields

Field scans enable the study of the detector response variations as a function
of the high-voltage settings and the interplay of the different fields in the
final effective gain described in Section 2.2. We consider here the scans of
the extraction and the amplification fields summarised in Table 2. The results
from these scans, even if performed at sub-optimal settings and in restricted
electric field ranges, can be used to qualitatively confirm the electron
transmission efficiency at the liquid-gas interface shown in Figure 5 and to
quantify $\mathscr{G}_{LEM}$ as a function of the amplification field. The
conditions of the field scans do not allow to study independently each of the
fields. The combination of the field scans together with the simulated maps
from Figure 7 allow us to extract the extraction efficiency and the
amplification inside the LEMs in the detector.

Figure 20: Left: liquid to gas transmission and extraction efficiencies as a
function of the extraction field in LAr measured in the $3\times 1\times
1\mbox{ m}^{3}\mbox{ demonstrator}$. The measured points at 28 kV/cm obtained
from the extraction scan are superimposed on the transmission prediction
(yellow band), the convolution of the extraction field and the LEM
transparency. Right: $\mathscr{G}_{LEM}$ as a function of the amplification
field (solid circles) measured in the $3\times 1\times 1\mbox{ m}^{3}\mbox{
demonstrator}$ is compared to the best fit of the 3L TPC data (dotted line)
which was equipped with a single $10\times 10$ cm2 LEM, both normalised to the
transparency of each detector.

The effective gain is defined as $\mathscr{G}_{eff}=\cal
T\cdot$$\mathscr{G}_{LEM}$ (see Eq. (2.2) in Section 2.2), where the
transparency is defined as in Eq. (2.8) by the product between transmission
and induction efficiencies. Due to the high voltage limitations, we could not
operate the detector at induction fields above 1.5 kV/cm. However, we were
able to study the transmission efficiency, the product between the extraction
efficiency of electrons from the liquid to the gas phase and the efficiency of
the electrons successfully passing through the LEM holes,
$\varepsilon_{extr}^{LEM}$. The blue region of Figure 20 left shows the
expected evolution of the extraction efficiency from the liquid to the gas,
$\varepsilon_{extr}^{liq}$, as a function of the extraction field in liquid
according to [12], as explained in Section 2.4. The yellow band is the product
of this efficiency ($\varepsilon_{extr}^{liq}$) with the
$\varepsilon_{extr}^{LEM}$ obtained from the simulated maps described in
Figure 7 for 28 kV/cm. Data from the extraction scan shows a good agreement
between the condition at which the demonstrator was operated and our
prediction.

A scan of the amplification field in the limited high voltage region available
was performed in order to study amplification inside the LEM holes and the
resulting $\mathscr{G}_{LEM}$. The right panel of Figure 20 shows
$\mathscr{G}_{LEM}$ as a function of the amplification field for the scan
performed in the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$ compared
to the results from the smaller 3L TPC scan in Ref. [19]. $\mathscr{G}_{LEM}$
is extracted by using Eq. (2.2). The transparency is computed from Figure 7 in
the case of the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$ data and
the value for the 3L TPC is obtained from [19]. The two results show the same
trend as a function of the amplification field. Since the two detectors were
operated at different pressures and temperature (the $3\times 1\times 1\mbox{
m}^{3}\mbox{ demonstrator}$ was operated at 1000 mbar, while the 3L TPC ran at
980 mbar), extraction and collection field, we do not expect the two fitted
curves for the LEM gains to fully overlap.

The relative gain difference between the two curves is $\approx 20\%~{}(40\%)$
at 28 kV/cm (33 kV/cm). It can be partially explained by a 2% residual
variation in density between the two detectors according to Figure 3. Another
contribution could come from charging up of the dielectric layer of the LEMs.
While the data from the 3L TPC scan was collected before the dielectric layer
of the LEM was fully charged up, we cannot conclude the same in the $3\times
1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$. The high voltage stability issues
prevented operating the $3\times 1\times 1\mbox{ m}^{3}\mbox{ demonstrator}$
for a sufficiently long time to study properly the charging up effect of
$50\text{\times}50\text{\,}\mathrm{cm}$ LEMs. It was observed in $10\times 10$
cm2 LEM modules that the effective gain reduces by a factor of about 3 after a
characteristic time of about 1.5 days when operated at
$\mathscr{G}_{eff}\approx 100$ [22, 32, 19].

The results from these scans suggest that the electron extraction from the
liquid to the gas is similar to previous measurements. The electron avalanche
in the LEMs appears to be similar to that measured with smaller $10\times 10$
cm2 devices. Additional field scans in future prototypes, such as ProtoDUNE DP
LAr TPC demonstrator, would bring the opportunity for a better evaluation of
the performance of the $50\text{\times}50\text{\,}\mathrm{cm}$ LEMs.

##  5 Conclusion

This paper presents the performance of the $3\times 1\times 1\mbox{
m}^{3}\mbox{ demonstrator}$ during its cosmic ray data taking operation in
summer 2017. While the high voltage limitations prevented reaching the optimal
expected amplification performance, many properties of the detector could be
studied.

A data driven detector simulation including a realistic trigger based on the
photo-detection system has been developed to reproduce the topology of the
recorded tracks. The simulation has been used to tune an algorithm for track-
shower separation, which is a crucial task to measure most critical
performance metrics of the detector. The algorithm is based on the fractional
charge difference deposited in two boxes surrounding the reconstructed track
with a muon purity selection with respect to the cosmic ray sample of around
$\sim$90%. Multivariate analysis techniques can be used in the future to
further improve the purity of the selected sample. A data-driven Monte Carlo
simulation was used to study the impact of both signal-to-noise and
geometrical effects on the efficiency of cosmic muon track reconstruction.

The study of the straight muon-like tracks allowed us to measure the drift
electron lifetime which is connected to the LAr purity. We obtain a weighted
average lifetime of 7 ms consistent to that in [10] and stable over time. From
the selected tracks, an effective gain of 1.9 was measured. The differences
with respect to the number quoted in [10] are due to the improved track
selection and the use of a different electronic response. The charge sharing
asymmetry between the two views has been studied as a function of the
azimuthal angle. In the case of $\phi=45^{\circ}$, the asymmetry is centered
in 0, highlighting equally charge sharing among the collection views.

As described in [10], we confirm the extraction of electrons from liquid to
the gas phase in large areas of 3 m2. Despite the lack of statistics, we
address qualitatively the interplay among the different fields involved in a
dual phase detector, especially between the extraction and amplification
fields.

The amplification gain in the LEMs has been measured and compared to the 3L
TPC. A similar trend in gain variation as a function of the amplification
field is observed. However, the $3\times 1\times 1\mbox{ m}^{3}$ results have
lower values, which could be explained by a 2% density variation between the
two setups.

Despite the limitations, the results shown in this paper seem to confirm
qualitatively the key aspects of the dual-phase technology such as the
extraction of the electrons from liquid to gas and their amplification though
the entire one-squared-metre CRP. Also the gain stability, purity and charge
sharing between readout views looks in reasonable agreement from design
expectations. However, an extensive study of the amplification process and its
stability over a large readout surface during an extended period of time is
still necessary to ensure the fulfilling of all the requirements for a multi-
kilotonne neutrino detector. Although these results have set another milestone
towards the understanding of the dual phase technology, future prototyping
efforts are expected to confirm them under more controlled experimental
conditions and with improved reconstruction techniques.

## Acknowledgments

We are truly grateful to the strong and continuous support of CERN for the
experimental infrastructure, the development of the cryogenic system and for
the detector operation. We are also thankful to the CERN IT department and the
IN2P3 Computing Center (CC-IN2P3) for the computing resources needed for data
storage, processing, analyses and simulations.
This work would not have been possible without the support of the Swiss
National Science Foundation, Switzerland; CEA and CNRS/IN2P3, France; KEK and
the JSPS program, Japan; Ministerio de Ciencia e Innovación in Spain under
grants FPA2016-77347-C2, SEV-2016-0588 and MdM-2015-0509, Comunidad de Madrid,
the CERCA program of the Generalitat de Catalunya and the fellowship
(LCF/BQ/DI18/11660043) from “La Caixa” Foundation (ID 100010434); the
Programme PNCDI III, CERN-RO, under Contract 2/2020, Romania; the U.S.
Department of Energy under Grant No. DE-SC0011686. This project has received
funding from the European Union’s Horizon 2020 Research and Innovation program
under Grant Agreement no. 654168. The authors are also grateful to the French
government operated by the National Research Agency (ANR) for the LABEX
Enigmass, LABEX Lyon Institute of Origins (ANR-10-LABX-0066) of the Université
de Lyon for its financial support within the program "Investissements
d’Avenir" (ANR-11-IDEX-0007).

## References

  * [1] A. Badertscher, L. Knecht, M. Laffranchi, A. Marchionni, G. Natterer, P. Otiougova et al., _Construction and operation of a Double Phase LAr Large Electron Multiplier Time Projection Chamber_ , in _2008 IEEE Nuclear Science Symposium and Medical Imaging Conference and 16th International Workshop on Room-Temperature Semiconductor X-Ray and Gamma-Ray Detectors_ , 10, 2008, DOI [0811.3384].
  * [2] A. Badertscher. et al., _Stable operation with gain of a double phase Liquid Argon LEM-TPC with a 1 mm thick segmented LEM_ , _J. Phys. Conf. Ser._ 308 (2011) 012016 [1010.2482].
  * [3] A. Badertscher, A. Curioni, U. Degunda, L. Epprecht, A. Gendotti et al., _First operation and performance of a 200 lt double phase LAr LEM-TPC with a 40 $\times$76 cm2 readout_, _JINST_ 8 (2013) P04012 [1301.4817].
  * [4] D. Lussi, _Study of the response of the novel LAr LEM-TPC detector exposed to cosmic rays_ , Ph.D. thesis, ETH Zurich, 2013.
  * [5] F. Resnati, _Modeling, design and first operation of the novel double phase LAr LEM-TPC detector_ , Ph.D. thesis, ETH Zurich, 2012.
  * [6] D. Gonzalez-Diaz, F. Monrabal and S. Murphy, _Gaseous and dual-phase time projection chambers for imaging rare processes_ , _Nucl. Instrum. Meth. A_ 878 (2018) 200 [1710.01018].
  * [7] A. Stahl et al., _Expression of Interest for a very long baseline neutrino oscillation experiment (LBNO)_ , Tech. Rep. CERN-SPSC-2012-021. SPSC-EOI-007, CERN, Geneva, Jun, 2012.
  * [8] DUNE collaboration, _The DUNE Far Detector Interim Design Report Volume 1: Physics, Technology and Strategies_ , 1807.10334.
  * [9] WA105 collaboration, _Technical Design Report for large-scale neutrino detectors prototyping and phased performance assessment in view of a long-baseline oscillation experiment_ , Tech. Rep. CERN-SPSC-2014-013. SPSC-TDR-004, Apr, 2014.
  * [10] B. Aimard et al., _A 4 tonne demonstrator for large-scale dual-phase liquid argon time projection chambers_ , _JINST_ 13 (2018) P11003 [1806.03317].
  * [11] B. Aimard et al., _Study of scintillation light collection, production and propagation in a 4 tonne dual-phase LArTPC_ , _JINST_ 16 (2021) P03007 [2010.08370].
  * [12] B. M. Gushchin et al., _Emission of hot electrons from liquid and solid argon and xenon_ , _Sov. Phys. JETP_ 55(5) (1982) 860.
  * [13] C. Cantini et al., _Long-term operation of a double phase LAr LEM Time Projection Chamber with a simplified anode and extraction-grid design_ , _JINST_ 9 (2014) P03017 [1312.6487].
  * [14] M. Miyajima, T. Takahashi, S. Konno, T. Hamada, S. Kubota, H. Shibamura et al., _Average energy expended per ion pair in liquid argon_ , _Phys. Rev. A_ 9 (1974) 1438.
  * [15] Y. Li et al., _Measurement of Longitudinal Electron Diffusion in Liquid Argon_ , _Nucl. Instrum. Meth._ A816 (2016) 160 [1508.07059].
  * [16] Particle Data Group collaboration, _Review of particle physics_ , _Phys. Rev. D_ 98 (2018) 030001.
  * [17] S. Palestini, _Space Charge Effects in Noble Liquid Calorimeters and Time Projection Chambers_ , _Instruments_ 5 (2021) 9 [2102.06082].
  * [18] “Thermophysical Properties of Fluid Systems.” http://webbook.nist.gov/chemistry/fluid/.
  * [19] S. Wu, _Study of an alternative double phase LAtTPC charge readout system_ , Ph.D. thesis, 2017.
  * [20] J. B. Birks, _The Theory and practice of scintillation counting_. 1964, http://doi.org/10.1016/B978-0-08-010472-0.50001-X.
  * [21] “Magboltz - transport of electrons in gas mixtures version 8.9.” http://consult.cern.ch/writeup/magboltz/.
  * [22] C. Cantini et al., _Performance study of the effective gain of the double phase liquid Argon LEM Time Projection Chamber_ , _JINST_ 10 (2015) P03017 [1412.4402].
  * [23] DUNE collaboration, _The DUNE Far Detector Interim Design Report, Volume 3: Dual-Phase Module_ , 1807.10340.
  * [24] A. Borghesani, G. Carugno, M. Cavenago and E. Conti, _Electron transmission through the ar liquid-vapor interface_ , _Physics Letters A_ 149 (1990) 481 .
  * [25] “Garfield.” https://garfieldpp.web.cern.ch/garfieldpp/.
  * [26] “Ansys.” http://www.ansys.com.
  * [27] A. Scarpelli, _Performance studies of the dual-phase Liquid Argon TPC for the DUNE experiment and analysis of the 4-tonne prototype detector data_ , Ph.D. thesis, 2019.
  * [28] D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz and T. Thouw, _CORSIKA: A Monte Carlo code to simulate extensive air showers_ , .
  * [29] “Comsol multiphysics v. 5.4. comsol ab, stockholm, sweden..” www.comsol.com.
  * [30] C. Alt, _Sensitivity study for proton decay using a 10 kiloton dual phase liquid argon time projection chamber at the Deep Underground Neutrino Experiment_ , Ph.D. thesis, Zurich, ETH, 2020.
  * [31] “The larsoft reconstruction code.” http://larsoft.org.
  * [32] C. Cantini et al., _First test of a high voltage feedthrough for liquid Argon TPCs connected to a 300 kV power supply_ , _JINST_ 12 (2017) P03021 [1611.02085].