e _Coresponding author:_<EMAIL_ADDRESS>11institutetext: LIBPhys;
Department of Physics; University of Coimbra; 3004-516 Coimbra; Portugal
22institutetext: Dipartimento di Matematica e Fisica; Università Roma TRE;
00146; Roma; Italy 33institutetext: Istituto Nazionale di Fisica Nucleare;
Sezione di Roma Tre; 00146; Rome; Italy 44institutetext: Gran Sasso Science
Institute; 67100; L’Aquila; Italy 55institutetext: Istituto Nazionale di
Fisica Nucleare; Laboratori Nazionali del Gran Sasso; 67100; Assergi; Italy
66institutetext: Istituto Nazionale di Fisica Nucleare; Laboratori Nazionali
di Frascati; 00044; Frascati; Italy 77institutetext: ENEA Centro Ricerche
Frascati; 00044; Frascati; Italy 88institutetext: Centro Brasileiro de
Pesquisas Físicas; Rio de Janeiro 22290-180; RJ; Brazil 99institutetext:
Universidade Federal de Juiz de Fora; Faculdade de Engenharia; 36036-900; Juiz
de Fora; MG; Brasil 1010institutetext: Dipartimento di Fisica; Sapienza
Università di Roma; 00185; Roma; Italy 1111institutetext: Istituto Nazionale
di Fisica Nucleare; Sezione di Roma; 00185; Rome; Italy 1212institutetext:
Universidade Estadual de Campinas (UNICAMP); Campinas 13083-859; SP; Brazil
1313institutetext: Department of Physics and Astronomy; University of
Sheffield; Sheffield; S3 7RH; UK 1414institutetext: Dipartimento di Ingegneria
Chimica; Materiali e Ambiente; Sapienza Università di Roma; 00185; Roma; Italy

# Enhancing the light yield of He:CF4 based gaseous detector

Fernando Domingues Amaro1  Rita Antonietti2,3  Elisabetta Baracchini4,5  Luigi
Benussi6  Stefano Bianco6  Roberto Campagnola6  Cesidio Capoccia6  Michele
Caponero6,7  Danilo Santos Cardoso8  Luan Gomes Mattosinhos de Carvalho9
Gianluca Cavoto10,11  Igor Abritta Costa6  Antonio Croce6  Emiliano Dané6
Giorgio Dho4,6,e  Flaminia Di Giambattista4,5  Emanuele Di Marco11  Melba
D’Astolfo4,5  Giulia D’Imperio11  Davide Fiorina4,5  Francesco Iacoangeli11
Zahoor ul Islam4,5  Herman Pessoa Lima Jùnior4,8  Ernesto Kemp4,12  Giovanni
Maccarrone6  Rui Daniel Passos Mano1  Robert Renz Marcelo Gregorio13  David
José Gaspar Marques4,5  Giovanni Mazzitelli6  Alasdair Gregor McLean13  Andrea
Messina10,11  Pietro Meloni2,3  Cristina Maria Bernardes Monteiro1  Rafael
Antunes Nobrega9  Igor Fonseca Pains9  Emiliano Paoletti6  Luciano Passamonti6
Fabrizio Petrucci2,3  Stefano Piacentini4,5  Davide Piccolo6  Daniele
Pierluigi6  Davide Pinci11  Atul Prajapati4,5  Francesco Renga11  Rita Joanna
da Cruz Roque1  Filippo Rosatelli6  Alessandro Russo6  Joaquim Marques
Ferreira dos Santos1  Giovanna Saviano6,14  Pedro Alberto Oliveira Costa
Silva1  Neil John Curwen Spooner13  Roberto Tesauro6  Sandro Tomassini6
Samuele Torelli4,5

(Internal v1: 2024-05-13)

###### Abstract

The CYGNO experiment aims to build a large ($\mathcal{O}(10)$ m3) directional
detector for rare event searches, such as nuclear recoils (NRs) induced by
dark matter (DM), such as weakly interactive massive particles (WIMPs). The
detector concept comprises a time projection chamber (TPC), filled with a
He:CF4 60/40 scintillating gas mixture at room temperature and atmospheric
pressure, equipped with an amplification stage made of a stack of three gas
electron multipliers (GEMs) which are coupled to an optical readout. The
latter consists in scientific CMOS (sCMOS) cameras and photomultipliers tubes
(PMTs). The maximisation of the light yield of the amplification stage plays a
major role in the determination of the energy threshold of the experiment. In
this paper, we simulate the effect of the addition of a strong electric field
below the last GEM plane on the GEM field structure and we experimentally test
it by means of a 10$\times$10 cm2 readout area prototype. The experimental
measurements analyse stacks of different GEMs and helium concentrations in the
gas mixture combined with this extra electric field, studying their
performances in terms of light yield, energy resolution and intrinsic
diffusion. It is found that the use of this additional electric field permits
large light yield increases without degrading intrinsic characteristics of the
amplification stage with respect to the regular use of GEMs.

###### Keywords:

Dark matter detectors Gaseous imaging and tracking detectors Time projection
Chambers GEM

###### pacs:

95.35.d+ Dark matter 29.40.Cs Gaseous detector 29.40.Gx Imaging and tracking

##  1 Introduction

Currently, the existence of large quantity of non-electromagnetic interacting
form of matter in the Universe, referred to as dark matter (DM), is an
established and yet puzzling paradigm Bertone:2004pz . Unveiling its nature is
one of the frontier studies of modern physics. A possible and well motivated
candidate, predicted both by an extension of the Standard Model and by the
leading cosmological model ($\Lambda$-CDM), is the weakly interactive massive
particle (WIMP), a neutral, stable particle with very low cross section for
interaction with standard matter, and a mass that can range between hundreds
of MeV/c2 to hundreds of GeV/c2. The measurements of the rotation velocity
curves of our Galaxy support the hypothesis of the Standard Halo model,
according to which a halo of DM envelopes our Galaxy. Due to the Earth’s
motion with respect to the centre of the Galaxy, an apparent wind of Dark
Matter particles is generated and can be used to experimentally detect them
through scattering against regular matter. The effort of the direct detection
experiments consists in the exposure of a large mass of sensitive volume in
order to be able to detect the very rare occurrences of interactions between
WIMPs and nuclei of the target, resulting in nuclear recoils.
Theoretically, from these nuclear recoils, it is possible to extract not only
the energetic information, as all the current experiments are capable of, but
also their direction and hence the angular and energy distribution of the
WIMPs. Determining the incoming direction of the WIMPs can provide a
correlation with an astrophysical source that can not be mimicked by any known
background Mayet_2016zxu , offering a unique key for a positive identification
of a DM signal.
The CYGNO experiment Amaro:2022gub  is following an innovative path for
directional DM searches by using a gaseous time projection chamber (TPC)
operated at atmospheric pressure and room temperature, coupled to an optical
readout through photomultiplier tubes (PMTs) and scientific CMOS cameras
(sCMOS) to measure energy and direction of low energy nuclear recoils. The
He:CF4 based gas mixture grants sensitivity to DM masses of O(1) GeV/c2 for
both Spin Independent and Dependent coupling, a parameter space still
partially uncharted and theoretically well motivated bib:zurek ; bib:petraki ;
bib:relic . In CYGNO, a stack of three 50 $\mu$m thick gas electron
multipliers (GEMs) is employed as amplification stage, in order to generate
electron avalanches that in turn produce light thanks to the scintillating
properties of CF4. The ratio of photon to electron produced during electron
avalanche in He:CF4 is about 0.1, depending on the gas fractions
bib:GEMoptical ; bib:Morozov_2012 , implying a reduction of available signal,
which in turn can affect the detection threshold. Moreover, while the optical
system coupled to the sCMOS allows to image large areas properly distancing a
single detector, it has the drawback of strongly reducing the solid angle
covered by sCMOS sensor, hence the amount of light collected. The geometrical
acceptance can be as low as 10-4 for an imaged area of 25.6 $\times$ 25.6 cm2
as in the LEMOn detector illustrated in Sec. 4. Thus, enhancing the production
of photons by the amplification stage is of uttermost importance for the CYGNO
experiment in particular and for any gaseous detector exploiting optical
readout in general. Increasing the voltage across the GEMs does not solve the
problem as one would eventually face breakdown effects in the gas, which
disrupts the operation. In addition, larger gain implies larger energy for the
avalanche electrons that would further diffuse in the gap between two GEMs,
worsening the detector position resolution.

In bib:EL_cygno  we demonstrated the possibility to enhance the light yield of
He:CF4-based gaseous detector by further accelerating the avalanche electrons
after the last GEM with a strong O(10) kV/cm electric induction field. In this
paper, we present an additional validation of the results of bib:EL_cygno  and
we extend our studies to larger applied fields, different GEM thicknesses and
stacking options and different He:CF4 ratio in the gas mixtures. The paper is
organised as following: in Sec. 2 we recall the scintillating properties of
He:CF4 gas mixtures, in Sec. 3 we present the simulation of the electric
fields between the GEMs and the induction gap further supporting our case
study, in Sec. 4 we illustrate a series of measurements performed with a 7 l
active volume detector aimed to further validate the results of bib:EL_cygno
thanks to a precise evaluation of the charges at play during the light
amplification beyond the last GEM, in Sec. 5 we expand the study of such
phenomenon to different GEM thicknesses and stacking options also varying the
He to CF4 ratio, and in Sec. 7 we discuss the results.

##  2 Scintillating properties of the He:CF4 gas

It is deemed relevant for a better comprehension of the paper to summarise the
main characteristics of the scintillating properties of He:CF4 gas mixtures.
These properties were studied in details in bib:Morozov_2012 ; bib:Kurihara ;
bib:Margato_2013 ; bib:Fraga:2003uu . The light emission spectrum comprises
two continua peaked around 290 nm and 620 nm, respectively. The emission in
the region centred on the 620 nm peak results from the de-excitation from a
Rydberg state of the neutral CF*3 originated from the fragmentation of CF4,
with an energy threshold of about 12.5 eV. The dissociative ionisation
threshold, on the other hand, is about 15.9 eV. Fig. 5b of Ref. bib:Kurihara
shows the rate coefficient of the momentum transfer and different excitations,
attachment, ionisation, dissociation for CF4 gas interaction with electrons as
a function of the reduced electric field. In particular, the process which
refers to the neutral fragmentation responsible for the production of visible
light possesses a smaller reduced field threshold than the ionisation ones.
This implies that it is theoretically possible to produce light from CF4
without generating charge. Those cross sections are of pure CF4, while the
standard CYGNO gas mixture contains large amounts of helium. The cross
sections for these mixtures are not found in literature, thus no conclusive
assessment on the nature of the light to charge ratio production can be done.
Yet, since the primary ionisation energy of He is nearly twice that of CF4, it
is fair to assume that the thresholds of ionisation and fragmentation of CF4
do not change significantly from this plot for the gas mixtures under study,
even in presence of electric field.

##  3 Maxwell simulation

Figure 1: Examples of the 2D electric field maps generated by the Ansys
Maxwell program. The vertical axis to the drift direction. The colour scale
represents the intensity of the field, with red being the highest one. On the
left, the detailed structure of the GEM holes for one thin GEM (50 $\mu$m GEM
with 70 $\mu$m radius holes and 140 $\mu$m pitch) with 400 V applied across
the GEM, 1000 V applied to a metallic electrode below the GEM and a transfer
field of 0 kV/cm above the GEM. On the right, the same for a thick one (125
$\mu$m GEM with 175 $\mu$m radius holes and 350 $\mu$m pitch) with 490 V
applied across the GEM, 1000 V applied to the metallic electrode and a
transfer field of 0 kV/cm above the GEM.

The possibility of enhancing the light yield without substantial production of
charge, hence possibly limiting the degradation of energy resolution and
diffusion, and the results of Ref. bib:EL_cygno  support the idea that a
strong electric field below the outermost GEM, henceforth called _induction_
field or Eind, can lead to considerable advantages to the CYGNO optical
readout.
In order to understand the effect of strong Eind on a GEM-based TPC detector,
the electric field characteristics inside, above and below the GEM holes are
investigated through simulation. The study is performed with Ansys Maxwell
15111https://www.ansys.com/products/electronics/ansys-maxwell, a commercial
software that allows to solve the electromagnetic equations and to obtain the
electric field configuration of a specific geometry, among other features.

Figure 2: Examples of the 2D electric field vector maps generated by the Ansys
Maxwell program. The vertical axis corresponds to the drift direction. The
line colour scale represents the intensity of the field, with red being the
highest one. On the left, the detailed structure of the GEM holes when no
induction field is applied, whilst on the right the same for 1 kV/cm of
induction field. It is clearly visible how the field vectors are much more
ordered and straight towards the induction gap (bottom of the plot) in the
right panel than in the left one, as a result of the induction field addition.
Figure 3: On the left, the profile of the electric field along the direction
orthogonal to the GEM plane which passes through a $t$ GEM hole. The x-axis
coordinate refers to the distance from the centre of the GEM hole, positive
for above the GEM hole, negative for below, i.e. towards the induction gap.
Three voltage configurations are depicted and described by the legend. Three
regions are highlighted in grey (E1), red (E2) and blue (E3), which are
described in the text. On the right, a detail of the schematics of the $t$ GEM
simulation with superimposed the same three regions E1, E2 and E3 described in
the text.

A generalised simulation of a generic TPC, identical to the internal structure
of our prototype MANGO (see Sec. 5), was initially performed with a coarse
granularity. A copper 10$\times$10 cm2 cathode encases with the amplification
stage the drift volume with a 0.8 cm drift gap. The amplification stage
comprises three GEMs, numbered 1 to 3 from the closest to the drift region to
the outermost. At a distance of 3 mm away from GEM3, a metallic electrode is
placed in order to provide the induction field. This simulation confirmed the
existence of a region few centimetres away from the borders where both the
drift and the induction fields are uniform, and that the electric fields close
to the holes of GEM3 are independent from the voltage configuration of GEM1
and GEM2. Therefore, to study in detail the influence of the induction field
in the nearby of the outer most GEM holes, only a single 10 $\times$ 10 cm2
GEM foil including all its holes with proper dimensions and conic shape,
together with the induction electrode is simulated in 2D (to minimise CPU time
and since the geometry can be assumed to possess a cylindrical symmetry) and
discussed in the following. The granularity and accuracy of the simulation
were increased up to a point where the electric field values reached an
asymptote, not to have the result influenced by numerical errors. Two types of
GEMs are simulated: a thin 50 $\mu$m GEM with 70 $\mu$m radius holes and 140
$\mu$m pitch (henceforth called _t_) and a thicker 125 $\mu$m GEM with 175
$\mu$m radius holes and 350 $\mu$m pitch (henceforth called _T_). The voltages
applied across these two types of GEM mirrors typical values these objects are
operated at in the CYGNO context (see Tab. 4 in Sec. 5).
Close to the GEM hole structure, the field exhibits non-uniform patterns both
above and below it. The spatial scale of these irregularities covers a region
of roughly 40 $\mu$m (100 $\mu$m) above and below a $t$ ($T$) GEM hole, as
shown in Fig. 1 on the left (right). From the field vectors evaluation, in the
example of the $t$ GEM, displayed in Fig. 2, it is possible to notice that the
presence of the induction field straightens the field vectors below the GEM.
Fig. 2 shows on the left the field vectors in case no induction field is
applied, whilst on the right a small 1 kV/cm induction field is present. The
straightening of the field vectors is clearly visible making the electric
field structure below each GEM more ordered.

Figure 4: The simulated electric field in the three regions next to the GEM
hole are displayed as a function of the induction field $E_{ind}$ on the left
and as a function of VGEM on the right for a $t$ GEM geometry.

Fit parameter $A_{t,E}$ [kV/cm] $B_{t,E}$ $A_{t,V}$ [kV/cm] $B_{t,V}$ [kV/V
cm] E1 region 13.28 $\pm$ 0.03 0.727 $\pm$ 0.003 0.043 $\pm$ 0.002 0.034 $\pm$
0.001 E2 region 44.18 $\pm$ 0.03 0.172 $\pm$ 0.003 0.042 $\pm$ 0.006 0.108
$\pm$ 0.001 E3 region 16.25 $\pm$ 0.06 0.004 $\pm$ 0.005 1.72 $\pm$ 0.01 0.035
$\pm$ 0.001

Table 1: Result of linear fits with the functions $A_{t,E}+B_{t,E}E_{ind}$ and
$A_{t,V}+B_{t,V}V_{GEM}$ to the electric fields in E1, E2 and E3 regions as
simulated with Maxwell for a $t$ GEM.

The profile of the electric field in the direction orthogonal to the GEM plane
which passes through a $t$ GEM hole is shown in Fig. 3 on the left panel. The
x-axis coordinate refers to the distance from the centre of the GEM hole,
positive for above the GEM hole, negative for below, i.e. towards the
induction gap. Three voltage configurations are shown: in blue 400 V across
the GEM and no induction field is present, in green the voltage across the GEM
is increased by 30 V, and finally in orange the voltage across the GEM is 400
but 14 kV/cm of induction field are present. When no induction field is
applied, the peak of the field is found at the zero coordinate, exactly at the
centre of the GEM. The field symmetrically drops as the distance increases.
Enlarging the voltage across the GEM affects the maximum field reached inside
the GEM, but leaves the shape of the field profile untouched. Instead, when a
strong induction field is added, not only the peak of the field inside the GEM
hole increases, but the structure of the profile towards the induction gap
changes. In particular, the decrease of the field has a milder slope,
resulting in a stronger field close to the centre and edge of the GEM hole. In
order to quantify this effect as a function of the voltage across the GEM and
the induction field, the average value of the electric field is calculated in
three different regions, highlighted in gray, red and blue in the left plot of
Fig. 3. The region E2 is a square of 50 $\times$ 50 $\mu$m2 centred in the
centre of the GEM foil, to characterise the field inside the GEM hole. The
regions E3 and E1 are taken adjacent to E2, with the same dimensions,
respectively above and below E2. Fig. 3 shows on the right panel the three
regions in the Maxwell schematics. The electric field in the three regions is
simulated as a function of the induction field with constant 400 V applied
across the GEM and as a function of VGEM with no induction field. The results
are displayed in Fig. 4 respectively on the left and right panel. For each
value of $E_{ind}$ or VGEM, the electric field simulated using Maxwell is
averaged inside each box and the obtained mean is further averaged over 20
adjacent holes. Linear fits are performed on the sets of data and are
summarised in Tab. 1 for the induction field dependence, as
$A_{t,E}+B_{t,E}E_{ind}$, and for the VGEM one, as $A_{t,V}+B_{t,V}V_{GEM}$,
where $A_{t,E},B_{t,E},A_{t,V},B_{t,V}$ are the fitting coefficients. The
results remark that increasing the voltage across the GEM modifies the field
in all the three regions, symmetrically in E1 and E3, and with larger
intensity in E2, as expected. Instead, the addition of the induction field
augments the field in E1 more strongly than in E2, while E3 is left
unaffected. This allows to conclude that it is impossible to increase the
scintillation output by a modification of the GEM transparency due to the
addition of an induction field underneath. The electric field inside the GEM
hole (E2 region) increases linearly with both the induction field and
$V_{GEM}$, with a much stronger dependence on $V_{GEM}$. Nevertheless, in the
E1 region, the fields reach values above 20 kV/cm, high enough to attain
further amplification. Taking two configurations exemplified in Fig. 3, namely
where $V_{GEM}=$ 400 V and $E_{ind}=$ 14.0 kV/cm and where $V_{GEM}=$ 430 V
and $E_{ind}=$ 0 kV/cm, a numerical comparison can be performed on the average
intensity of the fields displayed in Fig. 4. It can be observed that the
increase in the E1 field with respect to nominal operating conditions
($V_{GEM}=$ 400 V and $E_{ind}=$ 0 kV/cm) is a factor ten larger in the first
case compared with the second one. Conversely, the increase in E2 is only a
factor of 2 larger when $V_{GEM}$ is increased, with respect to a raise in
$E_{ind}$. It also has to be noted that while this is an average value of the
field, Fig. 3 shows that the closer one gets to the GEM, the larger the field
intensity. Both Fig. 3 and Fig. 4 also demonstrate that the high intensity of
the electric field in region E1 is peculiar to the introduction of the
induction field, thus it is not present in the regular operation of a GEM.

Figure 5: Profile of the electric field along the direction orthogonal to the
GEM plane which passes through a $T$ GEM hole. The x-axis coordinate refers to
the distance from the centre of the GEM hole, positive for above the GEM hole,
negative for below, i.e. towards the induction gap. Three voltage
configurations are shown as described by the legend. Three regions are
highlighted in grey (E1), red (E2) and blue (E3) which are described in the
text.

Figure 6: The simulated electric field in the three regions next to the GEM
hole are displayed as a function of the induction field $E_{ind}$ on the left
and as a function of VGEM on the right for a $T$ GEM geometry.

Fit parameter $A_{T,E}$ [kV/cm] $B_{T,E}$ $A_{T,V}$ [kV/cm] $B_{T,V}$ [kV/V
cm] E1 region 6.27 $\pm$ 0.02 0.785 $\pm$ 0.002 0.09 $\pm$ 0.06 0.0134 $\pm$
0.0005 E2 region 21.16 $\pm$ 0.03 0.210 $\pm$ 0.001 0.54 $\pm$ 0.06 0.042
$\pm$ 0.001 E3 region 8.66 $\pm$ 0.02 0.002 $\pm$ 0.006 2.00 $\pm$ 0.03 0.0136
$\pm$ 0.0005

Table 2: Result of linear fits with the functions $A_{T,E}+B_{T,E}E_{ind}$ and
$A_{T,V}+B_{T,V}V_{GEM}$ to the electric fields in E1, E2 and E3 regions as
simulated with Maxwell for a $T$ GEM.

The same type of simulation and analysis is performed on a $T$ GEM, with a
reference voltage across it taken as 490 V (see Tab. 4, Sec. 5). Fig. 5 shows
the profile of the electric field along the direction orthogonal to the GEM
plane which passes through a $T$ GEM hole. The modification of the electric
field structure, with respect to the reference 490 V applied across the GEM,
are obtained by raising the voltage of 30 V or by introducing 14 kV/cm in the
induction gap. Akin to the $t$ GEM, when the induction field is added, not
only the maximum field reached inside the GEM increases, but the variation of
the field intensity with the distance from the GEM has a harder slope with
respect to when only the GEM voltage is raised. Due to the geometry when
compared to the $t$ GEM case, the distortion induced by the induction field
acts on a wider area below the GEM hole and has a larger relative impact on
the field intensity. To quantify the influence of the variation of the
electric field as a function of the voltage across the GEM and the induction
field, three regions are defined in the 2D space of the simulation the average
value of the electric field is calculated from, exactly as for the $t$ GEM. In
order to adapt to a larger $T$ GEM the regions are selected with an area of
125 $\times$ 125 $\mu$m2.
The results of the average field in the E1, E2, and E3 regions as a function
of the induction field and VGEM are displayed in Fig. 6 respectively on the
left and right panel. Linear fits are performed on the sets of data and are
summarised in Tab. 2 for the induction field dependence, as
$A_{T,E}+B_{T,E}E_{ind}$, and for the VGEM one, as $A_{T,V}+B_{T,V}V_{GEM}$ \-
where $A_{T,E},B_{T,E}$ $,A_{T,V},B_{T,V}$ are the fitting coefficients.
The results for the $T$ GEM are coherent to the one attained for the $t$ GEM.
The electric fields are generally lower in the case of the $T$ GEM, as
expected from the geometry of the problem, and the values obtained in the
region E2 of $\sim$ 20 kV/cm confirm that these fields allow amplification
processes, as it will be seen in Tab. 4 (Sec. 5) and Fig. 14 (Sec. 6).
Nonetheless, it can be noted that the slope of the increase of the field is
larger for the $T$ GEM than the $t$ GEM one.

The results of these simulations show that an increase in light production is
possible due to a increase of the field inside the GEM holes. More
interestingly though, strong induction fields can generate a region towards
the bottom of the GEM hole and right below it where amplification and photon
creation is possible. Given the physical dimension of this region and field
intensity, it is possible that abundant excess of light is produced. In
particular, given the typical lower electric fields inside the holes and
because of the larger size and electric field influence region, a $T$ GEM is
expected to undergo stronger light enhancement with respect to a $t$ GEM. As a
consequence, an experimental detailed investigation of this process is worth
to be performed.

##  4 LEMOn experimental setup

In order to test the results of the simulation presented in the previous
Section, to further validate the findings we presented in bib:EL_cygno  as
well as to extend them to stronger applied electric fields, we employed a
larger detector, the Long Elliptical MOdule (LEMOn).
A sketch of the LEMOn detector is shown in Fig. 7 on the top panel. A 7 litres
active volume TPC with a 20 cm drift length and a 24 $\times$ 20 cm2 readout
area is enclosed in a gas-tight acrylic vessel and operated in continuous gas
flux mode. An ellipsoidal field cage comprised of silver wires held by 3D
printed plastic supports with 1 cm pitch guarantees drift field uniformity in
the 20 cm drift gap. The cathode is manufactured from an ATLAS MicroMegas mesh
bib:Micromegas  with 30 $\mu$m diameter metallic wires with a pitch of 70
$\mu$m. Three 24 $\times$ 20 cm2 GEMs, 50 $\mu$m thick, 70 $\mu$m hole
diameter and 140 $\mu$m pitch, spaced each other 2 mm, are employed to
generate electron avalanche at the amplification stage.

Figure 7: On the top, the LEMOn prototype bib:Antochi_2021 . The elliptical
sensitive volume (A), the fast photo-multiplier (B), the optical bellow (C)
and the sCMOS-based camera (D) are indicated. On the bottom, a sketch of the
internal structure of the TPC of the CYGNO prototypes employed in this study
where the addition of the ITO or a mesh below the last amplification GEM plane
can be appreciated.

The GEMs are numbered from 1 to 3 with GEM1 being the closest to the drift
region. At a distance $\Delta z$ of 3 mm below GEM3, an ITO glass electrode
with a transparency of 90$\%$ is placed in order to establish an additional
electric field in the region below the last GEM (GEM3) to enhance the light
yield of the detector. This region between GEM3 and the ITO glass is the
induction region. A sketch of the internal structure of the TPC is displayed
on the bottom panel of Fig. 7. LEMOn cathode and field cage base are powered
by a CAEN N1570222https://www.caen.it/products/n1570/ HV supply, while the
GEMs are biased by a CAEN A1526333https://www.caen.it/products/a1526/ power
supply with 6 independent HV channels up to 15 kV with a current sensitivity
of 10 nA. The latter provides a very precise tool of measurement of the charge
on each of the GEM electrodes for currents above tens of nA. The ITO electrode
is biased by a CAEN DT1470ET444https://www.caen.it/products/dt1470et/ power
supply with a high sensitivity current-meter ($\sim$ 5 nA) able to precisely
measure the continuous current signals.

The LEMOn detector is optically coupled to a Hamamatsu sCMOS camera
(C14440-20UP ORCA-Fusion) through a TEDLAR transparent window and an
adjustable plastic bellow. The camera is equipped with a Schneider Xenon lens
with 25.6 mm focal length and 0.95 aperture. The Orca Fusion is positioned at
$(50.6\pm 0.1)$ cm distance from GEM3 and reads out an area of 25.6 $\times$
25.6 cm2. Therefore, each of the 2304 $\times$ 2304 pixels of the sCMOS sensor
images an effective area of 111 $\times$ 111 um2. A more detailed description
of LEMOn and its performances can be found in bib:Antochi_2021 ; bib:fe55 .

In this setup LEMOn is operated with a 0.5 kV/cm drift field, 2.5 kV/cm
transfer fields between GEMs and 400 V applied across each of them, with a
He:CF4 60/40 gas mixture at 1000 mbar, as it is installed at Laboratori
Nazionali di Frascati (LNF). A $\sim$ 115 MBq 55Fe source is placed at 5 cm
distance from GEM1 in order to induce 5.9 keV energy deposits inside the
detector active gas volume. The large source activity provides a detectable
current signal on each of the 3 GEM electrodes and the ITO glass, given the
current sensitivity of the supply configuration. Conversely, the source
intensity does not allow to identify each 55Fe cluster separately because of
the large pileup. For this reason, and since the current on the electrodes
represents an integrated information of all the 55Fe clusters produced in the
gas and amplified by the GEMs, a 1 s exposure time on self-trigger pictures is
used for the sCMOS camera data acquisition in LEMOn to perform a consistent
light measurement. The light yield from the sCMOS camera and the charge
measured on each of the seven LEMOn amplification electrodes (one for the ITO
and two for each GEM, the upper (U) and the bottom (D) ones) are studied by
varying the induction field Eind from 0 to 17 kV/cm for a constant V across
each GEM and the results are reported in the following.

###  4.1 sCMOS images analysis

Figure 8: Example of 1 s exposure picture taken with the sCMOS camera with
superimposed three regions the total light was evaluated from, as described in
the text in Sec. 4.1.

An example of a 1 s exposure sCMOS image acquired by LEMOn exposed to the 55Fe
source is shown in Fig. 8 with highlighted four different regions (two
elliptical and two rectangular) in orange. The light yield in the LEMOn data
is evaluated by calculating the number of counts seen by all the sCMOS pixels
in each region, after having subtracted the noise pixel by pixel exploiting
images acquired in absence of source and with the GEM turned off. This number
is normalised to the measurement with null induction field and the relative
increase is averaged among the four regions. Fig. 9 shows the comparison of
the relative increase of the light output and the charge measured on the ITO
glass (see Sec. 4.2 for details on how the charge is evaluated) as a function
of the induction field in He:CF4 60/40 at 1000 mbar, explicitly demonstrating
the different rate of increase of the two quantities. The light enhancement
measured with LEMOn and shown in Fig. 9 is consistent with the results
reported in bib:EL_cygno  when one considers the errata corrige to the
induction gap dimension claimed in that paper (actual: 2.5 mm, instead of the
claimed 3 mm).

###  4.2 GEMs electrodes current analysis

During the amplification processes a large amount of electrons and ions are
generated close to the bottom of the holes of each GEM and drifted away in
opposite directions by the electric fields applied. Considering the Shockley-
Ramo theorem bib:Ramo ; bib:Shockley , the instantaneous current induced on
the GEM electrodes depends on the amount of charge in motion (both ions and
electrons), on their velocity and on a function of the electric field along
the charge path from its generation to the point of collection. The
significant difference in ion and electron drift velocity leads to an average
charge collection time of the order of $\mu$s for the former and few ns for
the latter. The signal is induced as soon as a charge gets in motion and lasts
until it is collected by an electrode. It is important to notice how a current
signal is induced also on electrodes not collecting any charge due to the
electron and ion motion. In this case, the signal is bipolar and its overall
integral sums to zero. As a consequence, an infinite integration of the
current signal allows to correctly measure a signal dependent solely on the
actual charge collected by an electrode.

Figure 9: Comparison of the relative increase of light and charge integral for
LEMOn in He:CF4 60/40 at 1000 mbar.

Since no charge needs to be collected with the optical readout approach, all
CYGNO prototypes are operated with the GEM3 bottom electrode at ground. In
this configuration, the absence of induction field Eind causes the field lines
to weakly and disorderly close on the bottom electrode of the GEM. Immediately
after the multiplication inside the holes of the last GEM, an electric signal
is induced on its electrodes. The upper electrode is responsible for the
collection of the majority of the ions coming from the last step of
multiplication, while the bottom one of the electrons. When the induction
field Eind is turned on, the field lines are straightened and begin to close
on the ITO glass rather than on the bottom GEM3 electrode. In this
configuration, the ions are expected to be mostly collected on the top of
GEM3, while the electrons will be shared between the bottom of GEM3 and the
ITO glass. When the electric field inside the induction gap is large enough to
generate charge amplification, these additional electrons are collected on the
ITO, while the newly generated ions are shared between the other electrodes,
with the large majority of them being collected by the top and bottom ones of
GEM3.

Figure 10: Currents measured in LEMOn as a function of the induction field
Eind for all the six electrodes of the amplification stage plus the ITO glass,
where _U_ and _D_ represent respectively the upper and the bottom electrode of
each GEM, and the total charge (in gray) is the sum of all the components. The
black line represents the exponential fit to the ITO curve described in
Equation 1.

Given the LEMOn setup, the currents measured in this context can be considered
as equivalent to an infinite integration, also considering the large 55Fe
source activity employed. Fig. 10 shows the continuous current measured in
LEMOn as a function of the induction field for all the six electrodes of the
amplification stage plus the ITO glass, and the total charge (in gray) is the
sum of all the components.

The sum of the charge of all electrodes is always consistent with zero and
mostly flat, as expected from general arguments by a well grounded electrical
circuit. Similarly, the ITO glass and GEM 3D split between them (with
proportions depending on the induction field) the current induced by the
charges generated in the last amplification stage and moving in the induction
gap. When no induction field is applied, the ITO sees a null current and all
the 250 nA are collected at GEM 3D. The current measured on the upper
electrode of the last GEM, GEM 3U, as a function of Eind displays a constant
behaviour up to about 10 kV/cm, where an increase starts. This _breaking_
point behaviour at 10 kV/cm is shared with the ITO and GEM 3D measurements,
which show an inflection point at the same value. In order to evaluate the
actual relative increment of measured charge with respect to null induction
field, the charge sharing between GEM 3D and the ITO glass needs to be
properly taken into account. To do this, the ITO current measured for
induction fields between 0 and 10 kV/cm is fitted with the function (black
line in Fig. 10):

$I_{ITO}=a+e^{b+cE_{ind}}.$ (1)

The following parameters are obtained: $a=(-240\pm 20)$ nA, $b=(5.47\pm 0.08)$
, $c=(-0.20\pm 0.05)$ cm/kV. The resulting parameter $a$, which represents the
asymptote of the exponential function, exhibits a good agreement with the -250
nA value measured on GEM 3D due to the collection of all the electrons
generated in the last GEM when no induction field is applied. In order to
properly evaluate the actual charge generated in the induction gap, the ITO
data are normalised to the value at 10 kV/cm after having subtracted the
fitted $I_{ITO}$ function. These data are shown as a function of the induction
field Eind in Fig. 9 in comparison to the light output relative enhancement
(illustrated in Sec. 4.1), explicitly displaying the different derivative in
increase of the two quantities. This increment above 10 kV/cm in the measured
charge is attributed to the generation of a small additional amount of charge
right below GEM3 holes, which, nonetheless, can not account for the entire
increase of the light output. This is coherent with the discussion of Sec. 2
and 3. If the enhancement of light is produced at high Eind in the region
underneath the GEM hole as suggested by the Maxwell simulations, the electric
fields involved have lower intensities than the ones within the GEM holes.
Thus, the light-producing process results favoured in terms of cross section
with respect to charge production.

##  5 MANGO Experimental setup

Figure 11: A simple representation of the MANGO setup with exemplified triple
GEM amplification.

Ampl stage Tag Gas mixture (He:CF4) Study 60/40 70/30 Gain Energy Res
Diffusion Eind Triple thin GEM ttt $\checkmark$ $\checkmark$ $\checkmark$
$\checkmark$ $\checkmark$ Double thick GEM TT $\checkmark$ $\checkmark$
$\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ 1 thick and 1 thin GEM Tt
$\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$ $\checkmark$

Table 3: Table summarising the gas mixtures and GEMs configurations explored
in this study.

Config $V_{GEM1}$ [V] $V_{GEM2}$ [V] $V_{GEM3}$ [V] $V_{GEM}$ for Eind studies
[V] ttt 60/40 400-435 400-435 400-435 400+400+400=1200 TT 60/40 770-780
470-520 n.a 775+490=1265 Tt 60/40 740-780 400-435 n.a 770+400=1170 TT 70/30
700-715 500 n.a 700+490=1190 Tt 70/30 660-720 350-395 n.a 700+385=1085

Table 4: Table summarising the voltages applied to the various combinations of
GEMs structure explored in this study. Each column shows the range of voltages
employed for each GEM.

In order to expand and extend the results we presented in bib:EL_cygno  and
validated in Sec. 4, and to further test the results of the Maxwell
simulations presented in Sec. 3, we employed a smaller detector, namely the
Multipurpose Apparatus for Negative ions studies with GEM Optically readout
(MANGO), to be able to modify the GEMs thicknesses and stacking option, in
addition to the gas mixture (since no 20 $\times$ 24 GEMs are available with
thickness different from the standard 50 $\mu$m).

A sketch of the MANGO prototype is shown in Fig. 11 and described in more
details in bib:EL_cygno , while the internal TPC structure used for these
measurement is similar to the one displayed in Fig. 7 on the right. The
amplification stage consists in a stack of multiple GEMs of 10 $\times$ 10
cm2, spaced 2 mm, with a transfer field of 2.5 kV/cm in between. The number
and type of GEMs used changed during the data taking to explore the
performances of different thickness and multiple stacking options. At a
distance $\Delta$z$=3$ mm a metallic mesh from an ATLAS MicroMegas
bib:Micromegas  (30 $\mu$m diameter metallic wires at 50 $\mu$m pitch,
resulting in a transparency of $\sim 0.55$) is placed in order to induce an
electric field below the electrode of the last GEM. A different configuration
was also tested, replacing the metallic mesh with an ITO glass, similar to the
one employed in LEMOn, with a larger transparency (0.9). This test showed that
the results do not depend on the structure employed to produce the additional
electric field after the last GEM amplification. As in LEMOn and in the
Maxwell simulations, we define the region between the last GEM amplification
plane and the mesh as the _induction_ region, and the electric field applied
inside it the _induction_ field (Eind).

The drift gap measures 0.8 cm and the detector is operated with 1 kV/cm drift
field, a configuration that guarantees a uniform electric field in the drift
region without the need for a field cage. The TPC structure is enclosed in a
3D printed black plastic light-tight box that contains a gas-tight acrylic
internal vessel. A thin window of highly transparent (> 0.9) Mylar® decouples
the gas detector from the optical readout, which consists in a PMT (Hamamatsu
H3164-10) and the same ORCA FusionsCMOS camera as in LEMOn detector (C in Fig.
11 left), placed at a distance of $(20.5\pm 0.3)$ cm and focused on the last
GEM ampilfication plane. The camera is equipped with the same lens as in the
LEMOn prototype. Within this scheme, the camera images an area of 11.3
$\times$ 11.3 cm2, resulting in an effective pixel size of 49 $\times$ 49
$\mu$m2. Various combinations of He:CF4 mixtures are used in this study,
always keeping the helium content above 60%. All of the mixtures used
scintillate with peaks at 620 nm as described in Sec. 2, where the quantum
efficiency of the camera sensor reaches 0.8 and the Schneider lens
transparency about 0.85.

###  5.1 Datasets

A $\sim$ 480 kBq 55Fe X-rays source is employed to generate 5.9 keV signals in
the MANGO active gas volume. The relative low source activity allows the
reconstruction of each single 55Fe signal in the sCMOS images (acquired with
0.5 s exposure), as discussed in Sec. 6 and shown in Fig. 12.

A systematic study of the performances of different He:CF4 ratios in the gas
mixtures, 60/40 and 70/30, and different GEM thicknesses and stacking options
is performed. The same two types of GEM described in the simulation Section
are employed: a thin 50 $\mu$m GEM with 70 $\mu$m radius holes and 140 $\mu$m
pitch ($t$) and a thicker 125 $\mu$m GEM with 175 $\mu$m radius holes and 350
$\mu$m pitch ($T$). All the measurements are performed at the atmospheric
pressure at Laboratori Nazionali del Gran Sasso (LNGS) - located at roughly
1000 m a.s.l. - which corresponds to (900 $\pm$ 7) mbar.

Tab. 3 shows a summary of the different gas mixtures and GEM configurations
explored with MANGO, and Tab. 4 the voltages applied to the various
combinations of GEM structures.

##  6 sCMOS images analysis

Fig. 12 top shows an example of 5.9 keV signals generated by the 55Fe X-ray
source in MANGO as seen by the sCMOS camera.

The images acquired are analysed with an iterative density based scanning
algorithm (IDBSCAN) developed by the CYGNO collaboration Baracchini:2020iwg ;
bib:cygnoIDBscan  that searches for pixel clusters representing tracks with
different energy deposition patterns, after having subtracted the camera noise
pixel by pixel. An X-Y selection is applied to the clusters recognised by the
algorithm removing events outside of a 2.94 $\times$ 2.94 cm2 region at the
center of the image, to avoid events at the border which may be compromised by
drift field distortion, as confirmed by simulation in Sec. 3, and optical
distortions due to the lens.

The distance travelled in the gas by the primary electrons created by the
interaction of the 55Fe X-rays in the gas target is of the order of
$\mathcal{O}$(100) $\mu$m. The 2D X-Y projection of the signal imaged by the
sCMOS camera hence appears round, being the shape dominated by diffusion and
not by the original topology of the track. For this reason, the ratio of the
minor over the major axis of an ellipse containing the cluster (defined as
_slimness_) is required to be larger than 0.7, to reject long straight tracks
from cosmic rays or short curly tracks from natural radioactivity.

Figure 12: Example of 55Fe signals: on the top, an image acquired by the sCMOS
camera in MANGO with a _Tt_ GEM configuration, He:CF4 60/40 gas mixture and 6
kV/cm induction field, where the 55Fe clusters are individually identified by
the CYGNO reconstruction algorithm Baracchini:2020iwg ; bib:cygnoIDBscan ; on
the bottom, example of 55Fe photon spectrum with superimposed the Gaussian fit
from the same configuration.

For each of the found clusters satisfying the selection requirement described
above, the energy deposited is calculated from the sum of the content of all
the pixels belonging to the track (Integral), after noise subtraction. In
addition, the dimension of the 55Fe round spot encodes the information of the
diffusion suffered by the electron track from its production to the detection
point. Due to the very small drift gap of 0.8 cm in MANGO and the value of
transverse diffusion of about 100 $\frac{\mu m}{\sqrt{cm}}$ at the drift field
of operation Amaro:2022gub , the spot dimension is dominated by the
contribution of the amplification stage rather than diffusion during drift.
Therefore, the analysis of the 55Fe spot dimension provides important
information on the intrinsic diffusion due to the GEMs employed and the choice
of stacking.

Figure 13: On the top, light integral of the selected 55Fe clusters versus the
number of pixels included in the cluster by the reconstruction algorithm. On
the bottom, X projection of the 55Fe centered clusters with a Double Gaussian
fit superimposed. All axes of both graphs are in arbitrary count units. Figure
14: Gain scan summarizing plot. The light integral obtained by the 55Fe
analysis are shown as a function of the total sum of the voltage applied
across the GEMs. Different colours represent the various amplification and gas
mixture combinations.

Ampl stage Color on plot A’ B’ [1/V] Avg B’ [1/V] ttt 60/40 Black -3.7 $\pm$
0.3 0.0107 $\pm$ 0.0003 0.0107 $\pm$ 0.0003 Tt 60/40 Green -8 $\pm$ 1 0.0140
$\pm$ 0.0009 Tt 70/30 Cyan -7.3 $\pm$ 0.7 0.0147 $\pm$ 0.0006 0.0139 $\pm$
0.0004 Tt 70/30 Dark Green -5.8 $\pm$ 0.6 0.0133 $\pm$ 0.0005 TT 60/40 Blue
-28 $\pm$ 10 0.029 $\pm$ 0.008 0.030 $\pm$ 0.004 TT 70/30 Red -27 $\pm$ 7
0.030 $\pm$ 0.006

Table 5: Table summarising the results of the fit with Eq.3 to the data sets
in Fig.14. All the blue data sets were fitted together.

In this respect, it is important to notice how a simplistic definition of the
spot dimension in terms of number of pixels identified as belonging to the
track by the reconstruction code Baracchini:2020iwg ; bib:cygnoIDBscan  would
result in a biased determination of the diffusion. The light integral and the
number of cluster pixels above threshold are in fact highly correlated, as can
be seen in the top panel of Fig. 13. In order to employ a variable independent
from the track energy to properly evaluate the track diffusion, the
distribution of the X and Y projections of the cluster is studied, since the
shape is expected to be preserved even if the cluster becomes more luminous.
With the goal of minimising any systematic effect and provide a robust
diffusion estimation, the 55Fe spot cluster projection distributions are
averaged after having aligned all their barycentres, where the barycentre is
defined as the average x and y pixel coordinate weighted on the pixel
intensity. An example of this is shown in the bottom panel of Fig. 13, with a
Double Gaussian fit with a common mean superimposed.

A Double Gaussian is used in order to properly include secondary tails in the
projection distributions, that anyway never account for a fraction larger than
20%. By reconstructing the 55Fe spots with an older version of the CYGNO
collaboration reconstruction code and comparing the two, we verified that the
observed tails in the projection distributions depend on the algorithm
definition of a cluster boundary rather than by misalignment of the
barycentres. The Gaussian function of the two which fits the core part of the
projection distributions is called primary. The diffusion is hence estimated
by averaging the primary sigma, also called Sigma1, of the X and the Y
projection of the 55Fe spot.

The light output, the energy resolution and the diffusion of 55Fe-induced
events are studied for each of the configurations illustrated in Tab. 3 both
as a function of the voltage applied across the GEMs VGEM (i.e. the charge
gain) and the intensity of the induction field after the last GEM
amplification plane Eind, and the results are illustrated in the following
Sections.

###  6.1 Light yield as a function of the charge gain

In this section we present the study of the dependence of the light yield on
the voltage applied across the GEM electrodes VGEM (that effectively defines
the charge gain of the detector) without adding any field to the induction
region. The values chosen for VGEM (and shown in Tab. 4) depend, on the lower
end, on the minimum voltage that allows the signal to be visible in the sCMOS
images, and, on the higher end, on the voltages that are stable enough to keep
the rate of sparks lower than 0.2 Hz.

The light spectrum of the selected events is modeled with a Gaussian function
and the fitted mean is taken as the light integral. An example of a fitted
55Fe light spectrum is shown in Fig. 12 bottom panel. The light integrals
obtained by the 55Fe analysis for all the configuration of Tab. 3 are shown as
a function of the total sum of the voltage applied across the GEMs in Fig. 14.

Since in this MANGO configuration the light is produced only in the electron
avalanche amplification process happening within the GEMs, it is possible to
interpret the results in Fig. 14 in terms of detector charge gain. From the
general description of the electron avalanche processes bib:tom ; bib:Aoyama ;
bib:Williams ; bib:Diethorn , the reduced gain $\Gamma$ can be expressed as:

$\Gamma=\frac{ln(G)}{n_{g}pt}=A\left(\frac{V_{GEM}}{n_{g}pt}\right)^{m}exp\left(-B\left(\frac{n_{g}pt}{V_{GEM}}\right)^{1-m}\right)$
(2)

with $G$ the gain, $n_{g}$ the number of GEMs used in the amplification stage,
$p$ the gas pressure, $t$ thickness of the GEM, $V_{GEM}$ total voltage
applied to the GEMs and $m$, $A$, $B$ free parameters. In particular, $m$ is
constrained between 0 and 1 and depends on the gas. For gain scans that do not
span over a large range of voltages, $m$ can be approximated to 1, resulting
in the more widely used expression of the gain in a gas detector:

$ln(G)=A^{\prime}+B^{\prime}V$ (3)

Equation 3 can then be used to fit all the data sets in Fig. 14, and the fit
results are listed in Tab. 5.

The fit results show how each group of GEM stacking configuration (i.e. _ttt_
, _Tt_ and _TT_) displays the same gain slope (B’ parameter) independent from
the gas mixture used. Conversely, the He to CF4 ratio influences the voltage
on the GEMs needed to attain the same gain, with larger helium content
requiring lower voltages. The total light output achievable is of the same
order of magnitude once the same amplification structure is put under
examination, with the only exception being the _TT_ at 60/40. While the
increase of helium results beneficial in terms of a lower amplification
voltage, it significantly increases the frequency of sparks and cascade
instabilities.

Config Colour $\eta$ $\left[\frac{1}{torr\cdot cm}\right]$ $\beta$
$\left[\frac{1}{torr\cdot cm\cdot V}\right]$ ttt 60/40 Black -0.36 $\pm$ 0.14
0.00106 $\pm$ 0.00011 Tt 60/40 Green -0.7 $\pm$ 0.2 0.0012 $\pm$ 0.0004 Tt
70/30 Cyan -0.6 $\pm$ 0.2 0.0012 $\pm$ 0.0003 Tt 70/30 Dark Green -0.49 $\pm$
0.19 0.0011 $\pm$ 0.0002 TT 60/40 Blue -1.6 $\pm$ 0.9 0.0017 $\pm$ 0.0007 TT
70/30 Red -1.6 $\pm$ 1.0 0.0018 $\pm$ 0.0006

Table 6: Table summarising the results of the linear fit of the reduced light
gain of all the configurations as a function of VGEM, following Equation 5.

The larger gain and light output is achieved with the three thin GEM
configuration _ttt_ , with integral values on average $\sim$ 3 times larger
than _Tt_ and up to $\sim$ 5 than _TT_. As expected, having more planes of
GEMs grants higher amplification. It is also interesting to notice that for
the _Tt_ sets at 70/30, the scans are taken varying the voltage of the thick
or the thin GEM alternatively. The light results of these sets are perfectly
consistent as the points overlap each other nicely. This is consistent with
the expectation of the gain dependence only on the total voltage applied
across the GEMs, other than the stability of the detector during the data
taking.
An interesting way to compare the different GEM amplification stacking options
is by analysing their reduced gain $\Gamma$ (see Eq. 2) as a function of
reduced field $\Sigma$, which is an approximation of the electric field inside
the GEM holes normalised by some parameters of the experimental configuration.
The latter is believed to effectively characterise the development of the
electron avalanche and is defined as:

$\Sigma=\frac{V_{GEM}}{n_{g}pt}$ (4)

As the assumption of the limited range of voltages utilised for the data
taking of each scan is still valid, $m$ can be approximated to 1 and the
reduced gain can be written as:

$\Gamma=A_{0}+B_{0}\Sigma=A_{0}+\frac{B_{0}}{pn_{g}t}V_{GEM}.$ (5)

This is a simple mathematical recombination of the terms in play in order to
highlight the dependence on the number of GEMs and the applied voltages.
Indeed, when comparing Eq. 3 with Eq. 5, it is valid that
$A^{\prime}n_{g}pt=A_{0}$ and $B_{0}=B^{\prime}$. The results of the fits of
the data presented in Fig. 14 with a function

$\Gamma=\eta+\beta V_{GEM},$

are summarised in Tab. 6.

Once the terms proportional to $V_{GEM}$ are adjusted for, the number and
thickness of GEMs, their fitted values result highly consistent among all the
configurations and gas mixtures employed.

###  6.2 Enhancing the light yield through the addition of strong induction
field

Given the importance of enhancing the light yield for optically readout TPCs
as discussed in Sec. 1 and the results of Sec. 3, the effect of the
introduction of a strong electric field in the induction region is studied in
details in this Section, expanding on the results present in bib:EL_cygno  and
in Sec. 4. Thus, an additional induction field Eind is applied to the
induction region below the last GEM electrode and this effect is studied for
all the GEM stacking configurations and gas mixtures illustrated in Tab. 3.

Figure 15: Relative increase of light integral for the _ttt_ configuration in
MANGO and LEMOn.The two data sets are manifestly highly consistent with each
other and with the measurements presented in bib:EL_cygno , robustly
confirming the results presented in Sec. 6.

In Fig. 15 the relative increase in light yield with respect to the absence of
induction field applied is shown in black for a _ttt_ configuration with
He:CF4 60/40 and 400 V applied across each GEM as a function of the induction
field Eind. The relative light increase measured with the LEMOn detector and
discussed in Sec. 4 is superimposed in blue. The two trends are strongly
consistent with each other and show the same features, demonstrating that the
light yield enhancement does not dependent on a single detector
characteristics, but instead, it may be more likely associated to a physical
phenomenon happening with the setup structure. This last argument gains
strength as we emphasise that the two detectors employ identical voltages
applied to the GEMs, but with different absolute gain, since LEMOn is located
at LNF at about 150 m a.s.l., while MANGO at the LNGS at 1000 m a.s.l.,
highlighting the independence of the relative light output growth from the
absolute gain of the detector. The two detectors moreover employ different
structures to apply the induction field Eind (a metallic mesh in MANGO and an
ITO glass in LEMOn) demonstrating that, once the transparency of these
structures is properly taken into account, the light yield amplification
results independent from this feature.

Figure 16: On the top, the reduced light gain as a function of VGEM with a
linear fit superimposed. On the bottom, the reduced light gain is expressed as
a function of $E_{ind}$ with a linear fit superimposed in the region blow 10
kV/cm.

The dependence of the light gain on the induction field is common to all the
stacking configurations and gas mixtures studied, and can be split into three
regions. Firstly, as soon as the field is turned on there is a boost in the
light output of about 10%. Afterwards, from 0.5 kV/cm up to breaking point
$E_{b}$ between 7 kV/cm and 10 kV/cm, the light grows linearly with Eind, and
beyond it, the light yield increase becomes exponential. This breaking point,
where the increase changes from linear to exponential, is observed to depend
on the gas mixture, being about $E_{b}$ = 10 kV/cm for 60/40, and $E_{b}$ = 8
kV/cm for 70/30. Despite the difference in the type of analysis of the two
data sets (see Sec. 4), this behaviour is consistently shared also between the
MANGO and the LEMOn data. The features of each of these regions is discussed
in detail in the following.

#### Region between 0 and 0.5 kV/cm

The enhancement generated by a field between 0 kV/cm and 0.5 kV/cm can be
explained by the fact that typical MANGO (and LEMOn and all CYGNO prototypes)
operation foresees the bottom of the last GEM electrode to be put to ground,
to minimise the overall HV needed to be applied since no charge needs to be
collected with an optical readout, as discussed in Sec. 4. This implies that
the field lines, typically showing an unordered closure on the lower electrode
of the GEM, get straightened and align more systematically with this
additional small electric field, resulting in a slight light yield increase.
This hypothesis is confirmed by the simulation discussed in Sec. 3.

Conf $\gamma$ $\left[\frac{1}{torr\cdot cm}\right]$ $\delta$
$\left[\frac{1}{torr\cdot kV}\right]$ Cond. C $\alpha$ ttt 60/40 0.912 $\pm$
0.005 0.0036 $\pm$ 0.0010 $\checkmark$ 0.23 $\pm$ 0.06 Tt 60/40 0.747 $\pm$
0.009 0.0010 $\pm$ 0.0009 $\checkmark$ 0.05 $\pm$ 0.04 Tt 70/30 0.704 $\pm$
0.007 0.0029 $\pm$ 0.0015 $\checkmark$ 0.14 $\pm$ 0.07 TT 60/40 0.48 $\pm$
0.01 0.0025 $\pm$ 0.0013 $\checkmark$ 0.06 $\pm$ 0.03 TT 70/30 0.505 $\pm$
0.004 0.0016 $\pm$ 0.0010 $\checkmark$ 0.04 $\pm$ 0.03

Table 7: Table summarising the results of the linear fit of the reduced light
gain as a function of the $E_{ind}$, when VGEM is fixed. Cond. C is marked
with a $\checkmark$ if that condition is fulfilled.

#### Linear region between 0.5 kV/cm and Eb

In the region between 0.5 kV/cm and a breaking point $E_{b}$, the light yield
increase appears linearly proportional to the raise in induction field Eind.
Starting from the arguments presented in Sec. 6.1 and the Maxwell simulations
of Sec. 3, it is reasonable to believe that the induction field effectively
enhances the reduced field $\Sigma$ inside the GEM holes with a linear
relation. To include a contribution from the $E_{ind}$, an additional term to
Eq. 5 can be added as:

$\Sigma=\frac{1}{p}\left(\frac{V_{GEM}}{n_{g}t}+\alpha E_{ind}\right),$ (6)

with $\alpha$ the coefficient of proportionality of $E_{ind}$. Therefore, the
dependence of the reduced gain $\Gamma$ on the VGEM and $E_{ind}$ when m = 1
can be expressed as:

$\Gamma=A_{0}+\frac{B_{0}}{pn_{g}t}V_{GEM}+\frac{B_{0}\alpha}{p}E_{ind}$ (7)

When $E_{ind}$ is zero, Eq. 5 is recovered. On the contrary, if VGEM is fixed
and the $E_{ind}$ is increased, a linear increase of $\Gamma$ is expected.
Fig. 16 shows the reduced gain $\Gamma$ for _ttt_ configuration with He:CF4
60/40 on the top as a function of the $V_{GEM}$, with $E_{ind}=0$, and on the
bottom as a function of $E_{ind}$ with $V_{GEM}=400$, fitted with Eq. 7 up to
$E_{b}$, display the linear dependence of the light yield on both quantities.

Figure 17: Relative increase of light output as a function of the induction
field for all the GEMs stacking configurations studied with MANGO.

Config $a$ $b$ $c$ [cm/kV] $d$ Eb [kV/cm] ttt 60/40 0.99 $\pm$ 0.02 0.04 $\pm$
0.02 0.8 $\pm$ 0.1 8.2 $\pm$ 0.6 $9.8$ $\pm$ $1.5$ TT 60/40 0.99 $\pm$ 0.03
0.09 $\pm$ 0.03 1.1 $\pm$ 0.1 10 $\pm$ 1 $9.5$ $\pm$ $1.2$ Tt 60/40 1.00 $\pm$
0.02 0.08 $\pm$ 0.03 0.8 $\pm$ 0.2 8 $\pm$ 1 $10$ $\pm$ $2$ Avg. 60/40 $9.7$
$\pm$ $0.8$ TT 70/30 1.00 $\pm$ 0.02 0.3 $\pm$ 0.2 1.2 $\pm$ 0.1 10 $\pm$ 2
$8.5$ $\pm$ $1.3$ Tt 70/30 0.99 $\pm$ 0.02 0.17 $\pm$ 0.08 0.86 $\pm$ 0.03 7.6
$\pm$ 0.9 $8.8$ $\pm$ $0.9$ Avg. 70/30 $8.7$ $\pm$ $0.7$

Table 8: Table summarising the result of the fit with Eq. 9 to the data of
Fig. 17, where the field Eb represents the value at which the exponential
light increase growth starts.

We can hence perform a linear fit to the reduced gain $\Gamma$ data as a
function of $E_{ind}$ with the function

$\Gamma=\gamma+\delta E_{ind}$ (8)

between 0.5 kV/cm and $E_{b}$ for each configuration under study, to verify
our assumption and measure the dependence on $E_{ind}$ of the light yield
enhancement. If the assumption that $E_{ind}$ contributes linearly to increase
the effective field inside the GEMs holes is correct, the fitted $\delta$ term
has to be equal to $A+\frac{B}{pn_{g}t}V_{GEM,0}$, where VGEM,0 is the sum of
the voltages applied to the GEMs. We define this _Condition C_. The first
order term $[1]$ of the linear fit allows to estimate the parameter $\alpha$,
that defines the proportionality of the light increase to $E_{ind}$. Tab. 7
shows the result of the fit with Eq.8 to all the configurations considered in
this study, together with _Condition C_ and the $\alpha$ proportionality
parameter. _Condition C_ is always verified, demonstrating a clear
comprehension of the contribution of $E_{ind}$ to the linear part of light
yield increase and consistency with the Maxwell simulations.

#### Exponential region above Eb

The light yield enhancement beyond $E_{b}$ clearly stops to be consistent with
a linear increase, allowing to conclude that above this value a new phenomenon
comes into play. In order to properly study this additional feature, the
fitted function from Eq. 8 is subtracted from the data in the entire range for
each configuration for the following discussion. The relative light yield
increase resulting after this subtraction is shown in Fig. 17.

All the curves display very similar behaviours, including the three different
light enhancement regions discussed above, where the differences between gas
mixtures and amplification structures is highlighted by the different breaking
points $E_{b}$ and different exponential rise. The subtraction of the linear
$E_{ind}$ enhancement enables direct comparison between the different
configurations in the entire range of the data by employing a modified
expression to describe the increase of the light yield as:

$a+b\cdot e^{cE_{ind}-d}$ (9)

where $a$ represents the normalisation with respect to operation with null
induction field Eind, $b$ is the intensity of the exponential component, $c$
determines how steeply the exponential grows, and $d$ is a shift in Eind
field. The ratio between $d$ and $c$ returns the field value Eb where the
exponential growth starts, highly consistent with assumption used to evaluate
the linear growth in the above discussion. Tab. 8 summarises the parameters
obtained by fitting the different data sets with Eq. 9.

The results obtained show how the larger the helium concentration in the
mixture, the smaller the Eind value required to initiate the exponential
growth of light. This is consistent with what was observed in Sec. 6.1 in
terms of lower voltage across the GEM needed to start the electron avalanche
responsible for the charge gain for higher helium fractions. For what concerns
the phenomenological origin of this exponential rise, it can be related to the
Maxwell simulation results (Sec. 3). Given the large Eind employed, the zone
below the GEM holes of the last amplification GEM provides a wide and intense
enough field to account for a strong increase in light yield. In addition, the
exponential steepness parameter $c$ of the _TT_ configurations appears to
represent a stronger boost of the light yield with respect to the other
configurations, which are characterised by a $t$ GEM next to the induction
gap. This is coherent with the expectations driven after the Maxwell
simulation as the Eind generates below the $T$ GEM a wider region where light
production can occur.

###  6.3 Energy resolution

Figure 18: Energy resolution for the different amplification stages as a
function of the sum of the voltages applied to the GEMs with a null induction
field. Different colours represent the various amplification and gas mixture
combinations.

The energy resolution at 5.9 keV is evaluated as the ratio of the sigma over
the mean value of the Gaussian fit of the 55Fe spectrum and presented in this
Section. The results as a function of the different GEM configurations and
voltages with a null induction field applied are shown in Fig. 18. The energy
resolution appears to strongly depend on the GEMs configuration used, spanning
from 15% up to 35%, but seems unaffected by the gas mixture used.

The energy resolution for the data sets as a function of the induction fields
Eind is shown in Fig. 19.

In this case, the energy resolution appears to remain constant independently
from the light yield increase induced by the Eind field. This is in line with
the hypothesis underlying this entire paper, that it is possible to amplify
the light output of a gas detector without relevant additional charge gain. In
fact, if the light yield enhancement were due to additional electron
avalanches generated in the induction gap within a reduced electric field much
lower than those present in the GEM holes, the gain fluctuations would
increase resulting in a worsening of the energy resolution bib:tom ;
bib:Alkhazov ; bib:Schlumbohm . This data further supports the idea that the
enhancement of light is related to the findings of the Maxwell simulations
presented in this paper. The exceptions to what has just been described are
the _TT_ configurations at high fields. In this case the energy resolution is
noticeably worsening with strong induction field, above the $E_{b}$, following
again an exponential growth.

Figure 19: Energy resolution for the data sets with applied induction fields
Eind as a function of Eind.

###  6.4 Diffusion within the amplification stage

As illustrated in Sec. 6, a proper analysis of the 55Fe spot size allows us to
measure the contribution to the original track diffusion caused by the
amplification stage. Fig. 20 shows the primary sigma (averaged from the X and
Y projections) as a function of the voltage applied to the GEMs for the
different setups of amplification. Most of the double GEM structures are
performing better than the triple GEM one, supporting the assumption that each
stage of amplification contributes with an independent term to the overall
diffusion. The _Tt_ stacking configurations perform better than the _TT_
within the same gas mixture, in line with the expectation that the granularity
of the GEM closer to the sCMOS sensor sets the maximum achievable space
resolution if larger than the camera pixels. Having a _t_ GEM a pitch of 140
$\mu$m with compared to 350 $\mu$m of the _T_ , the effective pixel size of
the MANGO setup of 49 $\times$ 49 $\mu$m2 results sensitive to this feature.
Another interesting feature is that, while the triple GEM configuration
diffusion linearly depends on the voltage applied to the GEM, the double ones
display a much less significant (in some cases nonexistent) increase. More
recent data acquired with MANGO (but not discussed in this paper) seems to
suggest that the very large charge gain achieved with _ttt_ , coupled with the
very small holes dimensions of these GEMs, are generating space charge effects
that could be further worsening the diffusion in the amplification stage. This
hypothesis is under study by the CYGNO collaboration and will be the subject
of an upcoming paper.

Figure 20: Amplification stage diffusion as a function of the sum of the
voltages across the GEMs. Different colours represent the various
amplification and gas mixture combinations.

The smaller diffusion measured with the _Tt_ configuration with respect to the
_TT_ further demonstrates that the method developed to evaluate the diffusion
within the GEMs and illustrated in Sec. 6 is independent of the light yield,
having the first configuration a larger light output than the second.

The diffusion at the amplification stage (where now this includes the
induction gap) is further investigated as a function of the $E_{ind}$ field
and shown in Fig. 21. These results corroborate the assumption that no large
amount of charge is generated by electrons travelling in the induction gap,
which would otherwise result also in a large spread of the additional light
generated. Since the sCMOS camera is focused on the last GEM electrode (and
could not anyway be focused on a volume, but only on a plane), the overall
final effect results in a modest blur only slightly affecting the 55Fe spot
size. Indeed, the _ttt_ diffusion at the maximum applied voltage on the GEMs
(light increase of a factor 3.0 with respect to 1200 V) is about 6% larger
than the diffusion at the maximum induction field Eind (light increase of a
factor 3.5 with respect to null induction field at 1200 V). The data show the
same type of trend as the energy resolution and light yield, with a general
change in behaviour after the Eb fields in Tab. 8 are applied. It can be noted
that the _TT_ configurations are again marked by most increase in the
diffusion among the tested amplification structures. The increase in dimension
is visible directly on the raw images as the example of the _TT_ 60/40 in Fig.
22. The _ttt_ and _Tt_ spot size dimensions are generally less affected by the
increment in induction field, with a growth of less than 20% at the largest
Eind values tested. As the latter configurations have in common a $t$ GEM
closer to the induction gap, this finding suggests that this phenomenon is
affecting the two kinds of GEM differently.

Figure 21: Amplification stage diffusion as a function of the $E_{ind}$
induction field.

(a)

(b)

Figure 22: Raw images of the 55Fe data taking with the _TT_ amplification
structure and 60/40 of He:CF4 gas mixture. On the top a picture with the
E${}_{ind}=0$ kV/cm, while on the bottom the field is 11 kV/cm.

##  7 Discussion

Integral E res (%) Diff [$\mu$m] ttt min 9510 $\pm$ 40 16.0 $\pm$ 0.3 320
$\pm$ 4 max VGEM 28400 $\pm$ 110 16.6 $\pm$ 0.3 412 $\pm$ 5 max $E_{ind}$
33500 $\pm$ 140 13.8 $\pm$ 0.3 388 $\pm$ 5 TT min 3410 $\pm$ 20 28.0 $\pm$ 1.5
260 $\pm$ 3 max VGEM 5090 $\pm$ 30 31.0 $\pm$ 0.6 255 $\pm$ 3 max $E_{ind}$
58800 $\pm$ 300 25.7 $\pm$ 0.5 356 $\pm$ 5 Tt min 4600 $\pm$ 30 25.2 $\pm$ 0.5
245 $\pm$ 3 max VGEM 7700 $\pm$ 40 27.8 $\pm$ 0.5 245 $\pm$ 3 max $E_{ind}$
11800 $\pm$ 50 26.8 $\pm$ 0.5 280 $\pm$ 4

Table 9: Summary for the three configurations at 60/40 (ttt, Tt and TT) of the
integral, the energy resolution and the intrinsic diffusion in three
scenarios: the minimum voltage applied to the GEMs with no induction field
("min"), the maximum voltages applied to the GEMs with no induction field
("max VGEM"), and finally the minimum voltage applied to the GEMs with the
maximum induction field ("max $E_{ind}$")

The combination of Maxwell simulations (Sec. 3) with the results obtained in
Sec. 4 and in Sec. 6 suggests that when the induction field is raised beyond
Eb, the reduced field in the bottom region of the GEM hole and few micrometers
below it is high enough to produce a simultaneous (but not directly
proportional) amplification of light and charge, effectively enlarging and
shifting the actual amplification region of this configuration. In the
simulated $T$ GEM in Sec. 3, $E_{ind}$ appears to generate a larger region of
additional amplification, with electric fields closer to the ones in the
centre of the GEM hole. Once a single gas mixture is considered, this is
consistent with the larger light output of the TT configuration visible in
Fig. 17 and characterised by a larger $c$ parameter in Tab. 8, which
represented the slope of the exponential in the relative light increase as a
function of $E_{ind}$. Moreover, the larger size is also compatible with the
faster degradation of the signal due to diffusion for the TT configurations
observed in Fig. 21 with respect to the ones with a $t$ on the bottom. This
result is suggesting that the innovative amplification strategy illustrated in
this study effectively enhances the light amplification potentialities of the
region below the GEM holes, while minimising the additional simultaneous
charge production.

In this study different combinations of GEMs and a varying amount of helium in
the gas mixture were analysed with respect to their light yield properties,
energy resolution and diffusion. The 70/30 mixture results in higher
probability of discharges which makes the detector unstable and prone to
failure while not providing any particular improvement with respect to the
standard 60/40. When only the voltage across the GEM is increased, the _ttt_
configuration returns the better energy resolution and light yield as
expected, but at the cost of a larger diffusion, which also depended on the
voltage applied. The _Tt_ configuration has a lower light yield, around 3
times less, and guarantees a lower diffusion, with a reduction of 30%. The
_TT_ behaves in the middle for what concerns the diffusion, but possesses a
light yield about 5 times lower than the ttt.

$E_{ind}$ [kV/cm] Integral E res (%) Diff [$\mu$m] $0$ ttt 0 $\pm$ 0 9510
$\pm$ 40 16.0 $\pm$ 0.3 320 $\pm$ 4 TT 12 $\pm$ 0.3 9420 $\pm$ 40 17.4 $\pm$
0.4 302 $\pm$ 4 Tt 11.1 $\pm$ 0.3 9360 $\pm$ 40 27 $\pm$ 0.5 264 $\pm$ 3 $1$
ttt 3 $\pm$ 0.3 11300 $\pm$ 50 15.5 $\pm$ 0.3 347 $\pm$ 5 TT 12.3 $\pm$ 0.4
11300 $\pm$ 50 17.9 $\pm$ 0.4 307 $\pm$ 4 Tt 12.3 $\pm$ 0.4 11300 $\pm$ 50
25.0 $\pm$ 0.5 273 $\pm$ 4 $2$ ttt 15 $\pm$ 0.3 33500 $\pm$ 140 13.8 $\pm$ 0.3
388 $\pm$ 5 TT 14 $\pm$ 0.3 58800 $\pm$ 300 25.7 $\pm$ 0.5 356 $\pm$ 5 Tt 12.8
$\pm$ 0.2 11830 $\pm$ 50 26.8 $\pm$ 0.5 280 $\pm$ 4

Table 10: Summary, for each configuration, of the induction field, the
integral, the energy resolution and intrinsic diffusion in three different
scenarios. Scenario "0" refers to when the three configurations have the same
light output and the ttt has $E_{ind}=0$. Scenario "1" refers to when the
three configurations have the highest light output equal to each other.
Finally, scenario "2" refers to when the maximum induction field is applied to
each configuration.

The introduction of a strong electric field below the last GEM amplification
plane enhances the light gain without affecting heavily the diffusion and the
energy resolution. This innovative way of utilising the GEM with this specific
gas mixture allows to improve the performances of the diverse GEM stacks
employed. Tab. 9 summarises for the three configurations at 60/40 (ttt, Tt and
TT) the integral (proportional to the light yield), the energy resolution and
the intrinsic diffusion in three scenarios: the minimum voltage applied to the
GEMs with no induction field ("min"), the maximum voltages applied to the GEMs
with no induction field ("max VGEM"), and finally the minimum voltage applied
to the GEMs with the maximum induction field ("max $E_{ind}$"). It can be
noted that the addition of the induction field always allows to reach a light
output larger than what is possible employing the GEMs in the standard way.
Moreover, the larger light yield is accompanied by a similar, if not better
energy resolution. For the ttt configuration the intrinsic diffusion is also
improved when the induction field is employed in place of the increase of the
voltage applied to the GEMs. Conversely, for the TT and Tt ones, the diffusion
worsens. This can be explained by the fact that the intrinsic diffusion of the
ttt was shown to be dependent on the applied voltage on the GEMs, differently
from the TT and Tt cases (see Fig. 19).
The performances of the different stacking options in the 60/40 gas mixture
can be compared among each other to find the best solution. Tab. 10
summarises, for each configuration, the induction field, the integral, the
energy resolution and intrinsic diffusion in three different scenarios.
Scenario $0$ refers to when the three configurations have the same light
output and the ttt has $E_{ind}=0$. Scenario $1$ refers to when the three
configurations have the highest light output equal to each other. Finally,
scenario $2$ refers to when the maximum induction field is applied to each
configuration.
Scenarios $0$ and $1$ represent similar setups for which it is possible to
demonstrate that the introduction of the induction field allows the 2 GEM
stacks to attain a light output identical to the 3 GEM stack with similar
energy resolution (only for the TT) and reduced intrinsic diffusion.
Scenario $2$ directly compares the maximum light output achievable by the
different configurations. The largest area generated under the $T$ GEMs thanks
to the strong induction field permits to reach light gain dramatically high,
maintaining a smaller intrinsic diffusion than the standard ttt. The light
output of TT exceeds by a factor 2 the maximum achievable with standard
operation of the ttt GEM stack, keeping the energy resolution at 5.9 keV below
30% and intrinsic diffusion around 350 $\mu$m.
The analyses performed stress that depending on the experimental need each
configuration excels in one of the variable studied. The ttt has an excellent
energy resolution thanks to the high gain and reduced field intensity, the Tt
always has the smallest intrinsic diffusion well below 300 $\mu$m, and finally
the TT allows to reach the largest light yields. In the context of a
directional DM experiment, the largest impact on the sensitivity comes from
the energy threshold Billard_2012 . CYGNO’s expected energy threshold of 0.5
keV Amaro:2022gub  could be further lowered by the increase in light yield
down to almost 0.25 keV, opening the possibility to search for DM around 0.5
GeV/c2 with the He target. At the same time, if more importance is given to
the directional capabilities, such as HT recognition and angular resolution,
the reduced diffusion of the Tt can help improving the topology of the data
for the imaging of the recoil tracks. For the above mentioned reasons, this
study is deemed extremely important for the development of future recoiling
imaging experiments.

##  8 Conclusions

In the context of a Dark Matter direct search, the CYGNO experiment is
following an innovative path for directional detection to surpass the
limitations of the current direct detection experiments. CYGNO is a gaseous
TPC operated with a gas mixture of He:CF4 mixture. The property of the gas
allows the production of light during the amplification processes which is
constituted by a stack of GEMs. The produced photons are readout optically
with a combination of sCMOS cameras and PMTs. The optical readout provides
advantages as the sensors can be placed far from the amplification stage to
reduce radioactivity in the sensitive volume and to image a large area with a
single sensor. The amount of photons generated per secondary electrons in the
gas and the solid angle covered by the sensor diminish the intensity of the
signal detected and could pose limitation of the energy threshold of the
experiment. In order to improve the photon yield and minimise the intrinsic
diffusion caused by the amplification stage itself, a study is performed to
analyse the potential of improvement of different amplification structures and
helium content in the gas mixture. Moreover, following previous studies, the
introduction of a strong electric field below the outermost GEM is also taken
into consideration for the light yield improvements. Two of the collaboration
prototypes, MANGO and LEMOn, were utilised for the analyses. Different
combination of GEMs were mounted ranging from the typical triple 50$\mu$m
thick ($t$) to a combination of GEMs including a thicker 125 $\mu$m thick
($T$). The largest light output is achieved with the triple layer which also
provides the best energy resolution, but returns a high diffusion that is also
dependent on the voltage applied across the GEMs. Using only two GEMs results
in a reduction of the diffusion and loss of light output and energy
resolution. The smallest diffusion is obtained with a combination of one thick
and one thin GEM. The standard 60/40 mixture of He:CF4 is the one that allows
the best stability in terms of spark occurrence. Increasing the amount of
helium does not bring any sizable advantage other than reduced voltage
required to bias the GEMs and smaller density (good for tracking but less for
exposure purposes).
The addition of the electric field in the induction region is analysed in
depth. By measuring the relative increase in light and charge output with
increasing induction field leads to the recognition of a region at high fields
wherein the light increase surpasses the one of the charge. The Ansys Maxwell
simulations of the electric fields suggest that the introduction of a strong
induction field modifies the profile of the electric field of the GEM so that
a small region few tens of $\mu$m below the GEM holes it becomes strong enough
to allow the multiplication and the neutral fragmentation of CF4. Since the
strength of the electric field is not at the level of the one inside the GEM
hole, the process favoured is the neutral fragmentation over the ionization,
which results in a larger amount of photons than electrons. When the geometry
of the GEM closest to the induction electrode is changed with a thicker GEM,
the larger dimension of the hole and the weaker difference of field intensity
between inside and outside, makes this effect more powerful causing a higher
light enhancement with a slightly faster degradation of energy resolution and
larger diffusion.
In terms of performances, the addition of this strong field below the GEM
combined with a different amplification structure can lead a two stack of GEMs
to yield an amount of light which recovers the one granted by a triple layer,
but with a smaller diffusion from the amplification stage itself. Careful
analyses of the light yield, diffusion and energy resolution permitted to
discover that each type of structure combined with a strong induction field
was found to excel in the measurement of a specific observable: a triple $t$
stack had the best energy resolution, a double $T$ one had the best light
yield, and a $Tt$ one had the lowest intrinsic diffusion. Therefore, depending
on the type of search and purpose, the best amplification structure can be
employed to maximise performances. For example, the possibility of improving
by a factor 2 the light yield of a CYGNO detector, coupled to the
technological advancements of CMOS-based optical devices, could lead to a
reduction of the energy threshold down to few hundreds of eV, firmly improving
the sensitivity to below GeV/c2 WIMP masses. Nonetheless, in applications
where the topology of the recoiling track is more important than the light
yield, a $Tt$ configuration could be foreseen in order to minimise diffusion.
This innovative way of employing the GEM amplification structure in a He:CF4
mixture results, therefore, extremely relevant for several optical TPC
applications, even beyond dark matter searches.

## Acknowledgement

This project has received funding under the European Union’s Horizon 2020
research and innovation programme from the European Research Council (ERC)
grant agreement No 818744.

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