Plasma-based intelligent reflecting surfaces (IRSs) have been recently proposed to reconfigure the radiation environment between transmitting and receiving antennas. Plasma-based IRSs rely on elements whose electromagnetic response is electronically controlled by varying the plasma density. Here, for the first time, the numerical design of an IRS is based on plasma discharges at the state-of-the-art. First, a cylindrical discharge has been realized and tested to identify realistic plasma parameters and geometries. Second, the design of a plasma-based IRS is proposed, accounting for practical constraints, such as the presence of the glass vessels needed to confine the plasma, the metal electrodes used to sustain the discharge, and the non-uniformity of the plasma parameters (e.g., density). Remarkably, at a central frequency of 10 GHz, a fractional bandwidth larger than 10% is feasible.

Gaseous plasma antennas (GPAs)1,2 are devices in which electromagnetic (EM) signals are transmitted and received via an ionized gas, namely, plasma. As a result, GPAs have unique advantages over their metallic counterpart.3,4 First, when the plasma is not energized, the main conductive medium is missing; therefore, the antenna's radar cross section (RCS) drops.5 This aspect is advantageous to minimize the mutual interference between GPAs stacked into arrays6 or if stealth is required.7 Second, it is possible to control the EM response of the plasma electronically, e.g., by varying its density.8,9 Thus, the GPA's radiation pattern10,11 and operation frequency12,13 are reconfigurable.

Intelligent reflecting surfaces (IRSs)14 have been proposed to enable the smart reconfigurability of the radiation environment.15 Specifically, IRSs increase communications' data rate and energy efficiency with a disruptive impact on the emerging B5G/6G technologies.16 IRSs are planar structures capable of controlling a reflected signal in amplitude, phase, polarization, and frequency.17 Regarding the hardware, IRSs are implemented via metasurfaces or phased arrays.18 The smart reconfigurability of IRSs is obtained by integrating active components (e.g., positive-intrinsic-negative diodes—PIN)19 into the surface elements. Recent studies have demonstrated the feasibility of plasma-based IRSs.20,21 This technology exploits plasma elements whose EM response can be varied by controlling the plasma density electronically.12 Early results relying on rectangular plasma blocks20,21 show that the main advantage of plasma-based IRSs is the possibility to control the phase of the reflected signal over approximately 360° while ensuring a modulus of the reflection coefficient close to the unit. In classical IRSs, the latter parameter drops drastically correspondingly to the 0° phase shift14,22 due to the enhanced losses associated with the in-phase reflection condition.23 

This is the first study in which the numerical design of an IRS is based on plasma discharges at the state-of-the-art (see Fig. 1). To this end, a cylindrical discharge has been realized and tested to identify realistic plasma parameters and geometries. These data are employed to formulate the design of an IRS that, relying on a digital control strategy,24 steers the reflected signal in the azimuth (xz plane). The numerical design accounts for practical constraints, such as the need for a glass vessel to confine the plasma,3 metal electrodes to energize the discharge,4 and the non-uniformity of the plasma parameters.12 The relation between plasma parameters and the IRS's bandwidth, as well as the reflection in the case of a non-normal incidence, are investigated. To sum up, the new plasma physics effects investigated in this work are related to the reflection of EM waves through cylindrical plasma discharges. In particular, the relation between the plasma density and the phase of the reflected wave, which drives the capability of an IRS to accomplish beam-steering, has been studied. The analysis accounts for realistic plasma parameters both in terms of average values25 and local profiles.12,26

FIG. 1.

Schematic of the plasma-based IRS operated at f = 10 GHz. The square ground plane side is L = 5 λ = 150 mm. The discharges have external diameter D = 0.25 λ = 7.5 mm, and the glass thickness is tgl = 0.75 mm. The electrodes have diameter Dele = 6 mm and length Lele = 7.5 mm. The color identifies the different plasma density discharges; n 0 = 5 × 10 22 m−3 ( p 0 = 2.0 mbar), and ν = 1.6 × 10 9 Hz.

FIG. 1.

Schematic of the plasma-based IRS operated at f = 10 GHz. The square ground plane side is L = 5 λ = 150 mm. The discharges have external diameter D = 0.25 λ = 7.5 mm, and the glass thickness is tgl = 0.75 mm. The electrodes have diameter Dele = 6 mm and length Lele = 7.5 mm. The color identifies the different plasma density discharges; n 0 = 5 × 10 22 m−3 ( p 0 = 2.0 mbar), and ν = 1.6 × 10 9 Hz.

Close modal
The EM response of the plasma is determined by the relative electric permittivity ε p l that reads27,
ε p l = 1 ω p l 2 ω 2 + ν 2 + j ν ω ω p l 2 ω 2 + ν 2 ,
(1)
where ω is the wave frequency in rad/s, ωpl is the plasma frequency in rad/s, and ν is the collision frequency in Hz. The plasma frequency reads ω p l = q 2 n e / m ε 0, where ne is the plasma density, q is the elementary charge, m is the electron mass, and ε 0 is the vacuum permittivity.27 The collision frequency reads ν = n 0 K ( T e ), where n0 is the neutral gas density in m−3, and K is a rate constant that depends on the electron temperature Te, whose expression is reported in Lieberman and Lichtenberg.28 Notably, neutral density and pressure are related via p 0 = k B T 0 n 0, where kB is the Boltzmann constant, and T0 is the gas temperature. The critical density n e c r reads20 
n e c r = m ε 0 ( 2 π f q ) 2 ,
(2)
where f is the wave frequency in Hz. For n e < n e c r, waves can propagate within plasma being Re ( ε p l ) > 0, whereas for n e n e c r, only evanescent waves may occur. The former case is referred to as the dielectric regime, and the latter as the conductor regime.

Numerical analyses are accomplished with the software CST Microwave Studio®. Maxwell's equations are solved in the frequency domain using an unstructured tetrahedral mesh. A linearly polarized plane wave is supposed to impinge the IRS. The performance indicators that characterize the proposed design are the RCS29 and the reflection coefficient Γ = E ρ / E ι, where E ρ and E ι are the complex amplitudes of the reflected and incident electric fields, respectively.

The plasma discharge depicted in Fig. 2 has been realized to evaluate realistic plasma parameters and geometries. The glass vessel, 150 mm long, has a thickness and internal diameter of 0.75 and 6 mm, respectively. It contains argon gas at a pressure of 2 mbar, which is turned into plasma and energized by two metal electrodes at the vessel ends. The plasma density is measured using a microwave interferometer designed to handle cylindrical plasma discharges.25 The effect of the refraction in plasma discharges smaller than the measurement beam ( 8 mm) has been accounted for using the ray-tracing technique.25 Thus, a law to relate phase shift and plasma density is available for diameters as small as 5 mm.25 The plasma density can be measured in the range from 4 × 10 16 to 7 × 10 19 m−3.

FIG. 2.

Plasma discharge realized to evaluate realistic plasma parameters.

FIG. 2.

Plasma discharge realized to evaluate realistic plasma parameters.

Close modal

The parameters ne and p0 are fundamental to be measured since they are directly related to ωp and ν, respectively, and in turn to the EM response of the plasma. The measured plasma density is n e 10 19 m−3 with a current supplied to the discharge I 250 mA. According to previous works,12 there is a linear correlation between plasma density and current, i.e., the plasma density can be controlled30,31 in the range of 0–1019 m−3 with a fine resolution of about 1017 m−3. It is worth mentioning that the plasma discharge is operated in the abnormal glow regime for I 50 mA.28,32 Indeed, the potential difference between the electrodes rises from 100 to 200 V increasing I from 50 to 250 mA. For I < 50 mA, the potential difference between the electrodes is almost constant and approximately equal to 100 V, namely, the discharge is in the glow regime.28,32

Working in the glow/abnormal glow regime, avoiding the transition to an arc32 is of paramount importance for the exploitation of plasma-based IRSs. In fact, the realized discharge can be operated cumulatively for tens of hours before electrodes are so degraded to fail the plasma ignition. At the same time, once at steady state (i.e., after a few minutes of operation), the temperature of the vessel reaches 400–500 K, a value that does not significantly affect the mechanical rigidity of the glass.5 Moreover, the transition to an arc discharge, with the consequent enhancement of the thermionic emission and electrode degradation, is not of practical interest in the field of plasma-based IRSs, provided the excessive power consumption and complexity of the power supplies associated with currents that are expected to be in the range of several Ampères.32 

The reflection coefficient Γ is computed to evaluate the feasibility of an IRS based on cylindrical plasma discharges (see Fig. 3). An operation frequency f = 10 GHz is assumed, and open boundary conditions are imposed along the z-direction and Floquet conditions along the other directions. Because of the Floquet boundary conditions, the geometries depicted in Fig. 3 are the constitutive elements of an infinite periodic structure extending along the x- and y-directions.33 The open boundary conditions, instead, constrain the waves exiting the computational domain to continue propagating in the free space. Open boundary conditions are imposed at a quarter wavelength from the geometry to ease the numerical treatment.33 This set of boundary conditions is useful to preliminary evaluate the reflection properties of the cylindrical plasma discharges rather than to compute the RCS of the IRS. According to these premises, the element depicted in Fig. 3(a) is equivalent to a uniform plasma slab placed on top of an infinite perfect electric conductor (PEC) that acts as ground plane (from now on, referred to as “theoretical”).20 This element is taken as a reference as its behavior is well known thanks to the analytical and numerical models discussed in Magarotto et al.20 The thickness of the theoretical plasma slab is half wavelength zpl = 15 mm since this value is expected to enable both 1-Bit and 2-Bit digital implementations (i.e., phase of the reflected wave controllable over 180° and 270°, respectively).24 Subsequently, a double layer of “cylindrical” discharges has been analyzed [see Fig. 3(b)]. This configuration has been simulated assuming a uniform plasma and a more realistic non-uniform radial density profile. The latter is imposed according to the power law reported in Ref. 26 (Eq. 3). Notably, with a diameter of the plasma column Dele = 6 mm and the vessel filled with argon gas at p 0 = 2 mbar, the edge-to-center density ratio is h R 0.07, and the average density ne is 40% of the peak one. The effect of the glass vessel has been subsequently included [see Fig. 3(c)]. The latter is described by a relative permittivity ε g l = 4.82 and loss tangent tan δ = 5.4 × 10 3. The overall thickness along the z-direction of the “cylindrical” element, glass included, is zpl = 15 mm to emulate the uniform plasma slab and consistently with the geometry of the realized plasma discharge.

FIG. 3.

Elements simulated to compute the reflection coefficient: (a) “theoretical” plasma slab, (b) “cylindrical” discharges, and (c) “cylindrical” discharges, including the glass vessel.

FIG. 3.

Elements simulated to compute the reflection coefficient: (a) “theoretical” plasma slab, (b) “cylindrical” discharges, and (c) “cylindrical” discharges, including the glass vessel.

Close modal

The theoretical configuration presents a minimum of | Γ | at n e n e c r (see Fig. 4) with the phase of the reflected wave ranging more than 270° over the considered plasma density values (i.e., n e 10 19 m−3). This trend is related to the EM response of the plasma: For n e 10 19 m−3, it behaves as a good conductor, as the incident wave is reflected on the edge of the plasma element. For n e 0, the wave is reflected on the ground plane since the plasma behaves as a dielectric.20 The results generally depend on the plasma density's effect on the distance traveled by waves within the plasma and the associated Ohmic losses. Similar trends are obtained with cylindrical plasma discharges; this was expected since all the elements have the same thickness zpl along the direction in which the waves propagate, i.e., the z-axis.20 Moreover, higher values of ne are required to reproduce the “theoretical” features consistently with previous studies dealing with elements in which propagation paths outside the plasma medium occur.20,21 Notably, assuming a non-uniform radial density profile has a mild effect on the EM response of the plasma: | Γ | is almost unaffected, while the phase changes are less than 5°. The largest differences are registered for n e > n e c r since the plasma in the proximity of the edge of the column is in the dielectric regime, while, in the center, it is in the conductor regime. Nonetheless, given the mild differences registered, the radial density profile has been assumed uniform in the following. When the glass vessel is added, a slight decrease in | Γ | is observed for n e 0 because tan δ 0, and ang ( Γ ) 0 being ε g l 1. Moreover, the glass vessel modifies the value of Γ because multiple reflections are generated at the air/glass and glass/plasma interfaces.34 Consequently, longer paths traveled by waves within plasma cause a decrease in the minimum of | Γ | 2 dB and the possibility of controlling ang ( Γ ) over 360°. These outcomes are a promising starting point for designing an IRS that can be controlled relying on a set of discrete plasma density values.

FIG. 4.

(a) Magnitude and (b) phase of the reflection coefficient Γ in function of the plasma density ne. Comparison between theoretical and cylindrical plasma elements. The non-uniform radial density profile and the presence of a glass vessel are analyzed in the “cylindrical” configuration. The yellow and white backgrounds indicate the dielectric and the conductor regime, respectively.

FIG. 4.

(a) Magnitude and (b) phase of the reflection coefficient Γ in function of the plasma density ne. Comparison between theoretical and cylindrical plasma elements. The non-uniform radial density profile and the presence of a glass vessel are analyzed in the “cylindrical” configuration. The yellow and white backgrounds indicate the dielectric and the conductor regime, respectively.

Close modal

The proposed plasma-based IRS is depicted in Fig. 1. It relies on 40 cylindrical discharges whose geometry and plasma parameters are consistent with the prototype presented in Sec. II B. For simplicity, a 1-Bit coding implementation is investigated.24 Nonetheless, a 2-Bit strategy might be implemented too, since the phase of the reflected wave is proven to be reconfigurable over 360° (see Sec. III).24 A linearly polarized plane wave is assumed to impinge the IRS orthogonally with the electric field directed along the y-axis. The RCS is numerically evaluated in the azimuth plane (xz) with the broadside direction at θ = 0°. Open boundary conditions are imposed along all the directions, namely, the structure analyzed in this section is not repeated in an infinite periodic lattice. Thus, this configuration is suitable to evaluate the RCS and, in turn, the capability of the IRS to produce beam-steering. It is worth noting that the proposed IRS allows for steering the reflected signal on the azimuth but not on the elevation plane since all the plasma discharges are aligned along the x-axis. Moreover, provided the slenderness of the cylindrical plasma discharges, the electric field shall be aligned along the y-axis to avoid poor polarization efficiency.29 

First, the IRS is characterized by evaluating the effect of the glass vessel while ignoring the metal electrodes and for different values of the plasma parameters; see Table I and Fig. 5. It is worth stressing that, both whether the presence of the glass vessel is considered or not, the position and the diameter of the plasma columns (Dele) are kept constant. Preliminarily, it is assumed to implement the 1-Bit coding by switching the plasma discharges “on” or “off” (ne = 0);20 this strategy is referred to as “plasma–vacuum.” The plasma density in the “on” state (green columns in Fig. 1) produces a 180° phase shift with respect to the “off” state in which the plasma is missing, namely, ne = 0 (magenta columns in Fig. 1).24 In this framework, the glass vessel affects the intensity of the side lobes rather than the mainlobe, whose position is generally correct (i.e., | θ | 30 °).24 Another implementation referred to as “plasma–plasma,” is chosen to enhance the difference between the main and side lobes: The two states (green and magenta columns in Fig. 1, respectively) are still 180° out of phase, but for none of them ne = 0. This solution is effective since the two plasma configurations, both in the conductor regime, produce a diffraction pattern otherwise not achievable by a medium in the dielectric regime.35 Correspondingly, the relative sidelobe level is −10 dB.

TABLE I.

Plasma parameters assumed to study the IRS neglecting the electrodes. The notation “plasma–vacuum” is used if n e 0 in one state (green columns in Fig. 1) and ne = 0 in the other (magenta columns in Fig. 1); “plasma–plasma” if n e 0 in both states.

Configuration ne (m–3) ωp (rad/s) | Γ | (dB) ang ( Γ ) (deg)
No glass  180 
Plasma-vacuum  1.9 × 10 18  7.9 × 10 10  −0.45 
Glass  −2 
Plasma-vacuum  3.4 × 10 18  1.0 × 10 11  −1.6  178 
Glass  3.4 × 10 18  1.0 × 10 11  −1.59  178 
Plasma-plasma  5.9 × 10 18  1.4 × 10 11  −0.81  −2 
Configuration ne (m–3) ωp (rad/s) | Γ | (dB) ang ( Γ ) (deg)
No glass  180 
Plasma-vacuum  1.9 × 10 18  7.9 × 10 10  −0.45 
Glass  −2 
Plasma-vacuum  3.4 × 10 18  1.0 × 10 11  −1.6  178 
Glass  3.4 × 10 18  1.0 × 10 11  −1.59  178 
Plasma-plasma  5.9 × 10 18  1.4 × 10 11  −0.81  −2 
FIG. 5.

Radar cross section vs azimuth angle θ (xz plane) of the plasma-based IRS of Fig. 1, evaluated: (i) neglecting the electrodes, (ii) with and without the glass vessels, and for different values of the plasma density ne (see Table I).

FIG. 5.

Radar cross section vs azimuth angle θ (xz plane) of the plasma-based IRS of Fig. 1, evaluated: (i) neglecting the electrodes, (ii) with and without the glass vessels, and for different values of the plasma density ne (see Table I).

Close modal

A second analysis evaluates how metal electrodes and a non-uniform axial density profile affect the performance of the IRS (see Fig. 6). Electrodes produce a negligible effect on the RCS. This is consistent with their lengths (Lele = 7.5 mm) being significantly shorter than the discharges (L = 150 mm). It is worth noting that the presence of metallic wires needed to feed electrical power to the plasma discharges has been neglected. In fact, their contribution is proven to be very mild if the power supplies that sustain the plasma are placed behind the ground plane and, consequently, the cables are bent at the edges of the metal electrodes.11 According to the model presented in Magarotto et al.12 and the measures reported in Melazzi et al.,36 a plasma density variation up to 20% is expected in the region between the two electrodes. Moreover, plasma profiles within the hollow electrodes are irrelevant regarding EM response provided that waves are reflected by metal.29 At the same time, the sheath occurring around the electrode is negligible in terms of EM response since the wavelength is 30 mm at f = 10 GHz, while the Debye length28,32 is in the micrometric range. Thus, assuming the axial density profile proposed by Magarotto et al.,12 it is possible to verify that also this effect is negligible in terms of RCS. For the sake of simplicity, only uniform plasma columns have been studied in the following.

FIG. 6.

Radar cross section vs azimuth angle θ (xz plane) of the plasma-based IRS depicted in Fig. 1: (i) with and without the electrodes and (ii) assuming a non-uniform axial density profile.

FIG. 6.

Radar cross section vs azimuth angle θ (xz plane) of the plasma-based IRS depicted in Fig. 1: (i) with and without the electrodes and (ii) assuming a non-uniform axial density profile.

Close modal

The selection of proper ne pairs to implement the 1-Bit coding strategy is analyzed in terms of bandwidth. Three cases are compared depending on the phase difference between the two states Δ: decreasing with f (case #1), almost independent of f (case #2), and increasing with f (case #3); see Table II and Fig. 7. In all cases, the relative bandwidth is larger than 10% provided the mild dependency of Δ from f. Remarkably, Δ varies by less than ±10° for f ranging between 9.5 and 10.5 GHz in case #2.

TABLE II.

Plasma parameters assumed to study the IRS depicted in Fig. 1 (electrodes included).

Case No. ne (m–3) ωp (rad/s)
1.0 × 10 18  3.9 × 10 18  5.6 × 10 10  1.1 × 10 11 
2.5 × 10 18  4.7 × 10 18  8.9 × 10 10  1.2 × 10 11 
3.4 × 10 18  5.9 × 10 18  1.0 × 10 11  1.4 × 10 11 
Case No. ne (m–3) ωp (rad/s)
1.0 × 10 18  3.9 × 10 18  5.6 × 10 10  1.1 × 10 11 
2.5 × 10 18  4.7 × 10 18  8.9 × 10 10  1.2 × 10 11 
3.4 × 10 18  5.9 × 10 18  1.0 × 10 11  1.4 × 10 11 
FIG. 7.

Phase difference Δ between high-density and low-density states as a function of the frequency f for the design cases of Table II.

FIG. 7.

Phase difference Δ between high-density and low-density states as a function of the frequency f for the design cases of Table II.

Close modal

The three cases are also analyzed in terms of RCS (see Fig. 8). Case #1 is the less performing since the main lobes are located at | θ | 30 ° only for f = 9.5 GHz, and the relative sidelobe level is about −5 dB. This modest performance is reasonable as the low-density state is in the dielectric regime. In case #2, the main lobes are located at | θ | 30 ° for f 10 GHz, and the relative sidelobe level is −5 dB. Finally, the main lobes of case #3 are properly steered over the entire frequency range, and if f 10 GHz, the relative sidelobe level is –10 dB. In general, the implementations where the plasma behaves as a conductor in both states perform better.35 

FIG. 8.

Radar cross section vs azimuth angle θ (xz plane) for the plasma parameters reported in Table II: (a) “case 1,” (b) “case 2,” and (c) “case 3.” Different operation frequencies f are considered.

FIG. 8.

Radar cross section vs azimuth angle θ (xz plane) for the plasma parameters reported in Table II: (a) “case 1,” (b) “case 2,” and (c) “case 3.” Different operation frequencies f are considered.

Close modal

The case #3 discussed in Sec. IV A is further analyzed in terms of non-normal wave incidence. A linearly polarized plane wave is still assumed to impinge the IRS propagating along the z-axis. Still, the broadside direction is at θ = 30°, namely, the plasma-based IRS is rotated of 30° with respect to previous analyses. The electric field is directed along the y-axis. The impinging wave is expected to be reflected along the broadside direction for reciprocity.29 This is exactly the behavior reported in Fig. 9. Indeed, the mainlobe is directed to θ = 30°, and the relative sidelobe level is approximately −10 dB.

FIG. 9.

Plasma-based IRS rotated of 30° with respect to the incident wave. Three-dimensional polar plot of the radar cross section included.

FIG. 9.

Plasma-based IRS rotated of 30° with respect to the incident wave. Three-dimensional polar plot of the radar cross section included.

Close modal

This proves that operating the proposed plasma-based IRS is possible in the case of non-normal incidence. Clearly, to enable a generic steering angle, a 1-Bit digital implementation is not sufficient.24 As previously mentioned, with the proposed design, a much more flexible 2-Bit coding implementation is feasible (see Sec. III), but its analysis is out of the scope of the present work.

An IRS based on plasma discharges at the state-of-the-art has been proposed for the first time. A cylindrical discharge has been realized and tested to identify realistic plasma parameters and geometries. Plasma density can be regulated up to 1019 m−3, provided the neutral background pressure is 2 mbar. Subsequently, a 1-Bit coding implementation24 has been numerically demonstrated, relying on 40 cylindrical plasma discharges. The proposed design presents a bandwidth larger than 1 GHz with a central frequency f = 10 GHz. This is a remarkable achievement considering that other systems operating at similar frequencies have a bandwidth of 0.1–0.2 GHz.14,37 The reflection coefficient presents a modulus above −2 dB: This also holds for realistic plasma parameters and geometries and the presence of glass vessels and electrodes. At the same time, the overall thickness of the proposed plasma-based IRS is 15 mm, only a few millimeters larger than more standard IRSs.20 

Future work will be focused on the realization of a proof-of-concept of the proposed design. To this end, a few challenges must be faced. First, the electronics for plasma production shall be optimized and miniaturized given that the solutions employed in the field of GPAs are usually power-consuming and bulky.3 Nonetheless, this problem has been tackled in space propulsion, where miniaturized solutions are available.30,31 Second, an “intelligent” control system shall be implemented to trigger the plasma discharge. Remarkably, the latter task has been partially solved in plasma display panels where strategies to control the ignition of multiple plasma elements are available.38 Another important aspect that shall be handled to realize plasma-based IRSs appealing for practical purposes is extending the discharges' lifetime up to thousands of hours. To this end, the material selection and the manufacturing processes to realize the electrodes are critical.39 Finally, it is worth stressing that the proposed design, which relies on plasma discharges at state of the art, allows controlling the reflected signal only in one plane and for a fixed polarization of the electric field. To enable reconfigurability of the IRS both in azimuth and elevation, it may be required to utilize plasma elements (e.g., miniaturized discharges40) arranged in a rectangular grid.20 To handle a generic polarization instead, it is necessary to develop isotropic plasma elements as square blocks.21,41 Thus, future developments will first focus on realizing a proof of concept based on the present design. The possibility of realizing a prototype of plasma-based IRS with beam steering capabilities in two planes and ability to handle a generic polarization will be analyzed subsequently.

This work was partially supported by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on “Telecommunications of the Future” (Grant No. PE0000001—program “RESTART”).

The authors have no conflicts to disclose.

Mirko Magarotto: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Luca Schenato: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Paola De Carlo: Data curation (equal); Methodology (equal); Writing – review & editing (equal). Marco Santagiustina: Methodology (equal); Resources (equal); Writing – review & editing (equal). Andrea Galtarossa: Methodology (equal); Resources (equal); Writing – review & editing (equal). Antonio-Daniele Capobianco: Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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