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Die vorliegende XML-Version der Publikation "https://doi.org/10.1088/1361-6595/ae4d88" wird "wie es ist" bereitgestellt, ohne jegliche Gewährleistung oder Garantie, sei es ausdrücklich oder stillschweigend. Die TIB übernimmt keine Verantwortung für etwaige Fehler, Auslassungen oder Folgen, die aus der Nutzung dieser Datei resultieren. xml_created 28-08-2026 dc.identifier.uri https://doi.org/10.1088/1361-6595/ae4d88 dc.rights.license CC BY 4.0 International dc.relation.doi https://doi.org/10.34657/39517 Experimentally informed modelling of argon dielectric barrier discharge 24 03 2026 Experimentally informed modelling of argon dielectric barrier discharge, Redzikultsava, KatazhynaSanginés, RobertoAlavi, SeyedehZhao, JerryBilek, Marcela, , (2026-03-24). Low-pressure (1.3Torr) plasma breakdown in an asymmetric argon dielectric barrier discharge with a 10mm gap was investigated both numerically and experimentally. A one-dimensional fluid model was validated against the experimentally obtained optical emission spectroscopy (OES) spectra, high-speed imaging and plasma current measurements. The model predicts distinct spatio-temporal oscillations in charged particle densities preceding breakdown, these are confirmed experimentally. OES analysis supports a Druyvesteyn form of the electron energy distribution function, challenging the conventional assumption at low partial ionisations. The effects of varying the applied voltage frequency, pulse width and rise time were also systematically examined. IntroductionDielectric barrier discharges (DBDs) are highly reactive, non-thermal plasmas characterised by elevated electron temperatures and near-ambient gas temperatures. Unlike other discharge types, they can operate at relatively high pressures with low input power, making them suitable for a broad range of industrial applications (e.g. water purification, decontamination, textile treatment, catalysis and nanomaterial synthesis [1][2][3][4][5]) and biomedical uses (e.g. plasma medicine, surface sterilisation and tissue engineering [6][7][8]), with low-pressure DBD (0.2 − 10 Torr) being particularly suited to implant surface modification, osteoblast adhesion/proliferation/differentiation, surface activation and functionalisation [9][10][11].DBDs form when high-frequency alternating voltages are applied across electrodes, with at least one insulated by a dielectric layer to limit current and prevent arcing. Their plasma dynamics are highly sensitive to waveform parameters, including rise time, pulse width, and frequency [12][13][14][15][16][17][18]. For instance, sharper rise times enable higher discharge currents and promote homogeneous plasmas by suppressing filamentation through ion accumulation and surface charging, whereas longer rise times increase electron and ion densities [15,16]; pulse width variations induce complex breakdown regimes driven by residual charge pre-ionisation [17]; and higher frequencies enable earlier current onset via remnant charges, mimicking elevated voltages and improving energy efficiency [18].Achieving stable, non-thermal DBD operation, especially at low pressures, remains challenging due to pre-breakdown instabilities and uncertainties in electron kinetics [19]. Computational modelling provides an essential means to probe these processes, yielding spatio-temporally resolved insights into plasma behaviour and the underlying complex chemistry [20]. Such models enable rapid exploration of parameter spaces and facilitate the analysis of experimentally inaccessible quantities. When supported by experimental validation, these models gain particular predictive value [21].Many recent studies have developed experimentally validated DBD models [22][23][24][25][26][27][28][29]. However, investigations that combine multiple validation techniques such as optical emission spectroscopy (OES), highspeed imaging and current measurements remain limited, particularly for asymmetric configurations under low pressure. Moreover, simultaneous temporal and spatial analysis of plasma dynamics is essential for understanding breakdown mechanisms. While two-dimensional models can capture lateral effects, one-dimensional (1D) approaches are often better suited to isolating fundamental processes without the additional complexity of multidimensional geometries.Present work investigates plasma breakdown in a low-pressure (1.3 Torr) asymmetric argon DBD with a 10 mm gap, through both numerical simulation and experimental measurement. A 1D fluid model is validated against OES, high-speed imaging and plasma current measurements. Our validated model identifies distinct spatio-temporal oscillations in charged particle densities preceding breakdown (animation 1), which are confirmed experimentally through high-speed imaging (video 1). OES analysis supports a Druyvesteyn electron energy distribution function (EEDF), despite conventional assumptions for low partial ionisation discharges [19,30]. Parametric studies examine the effects of applied voltage frequency, pulse width and rise time on electron temperature. Methodology Model descriptionA 1D fluid model was developed using Comsol Multiphysics built-in plasma module [31]. Figure 1(top) depicts the flat cylindrical DBD experimental setup which serves as a reference for the computational model. Figure 1(bottom) illustrates a schematic cross-section of the experimental setup. The yellow line along the vertical axis of symmetry represents the modelled domain.The model obtains a time-dependent solution by solving coupled differential equations describing the conservation of mass, momentum and energy for various plasma species. The drift-diffusion approximation employed in this study is appropriate for the discharge under consideration: a weakly ionised plasma with gas pressure above 10 mTorr and a reduced electric field below 500 Townsends [32]. The plasma is collisional, with the mean free path between electrons and the background gas significantly smaller than the characteristic dimension of the system.The rate of change of plasma species density is described by the mass conservation equation:∂n i ∂t + ∇ • Γ i = R i ,where n i is the density of plasma species i, Γ i is the flux vector and R i is a source term resulting from the species' production or loss. The rate of change of the electron energy density is described by:∂n ε ∂t + ∇ • Γ ε + E • Γ e = R ε ,(1)where n ε is the electron energy density, Γ ε is the electron energy flux, E is the electric field, Γ e is the electron flux and R ε is the electron energy source term. The electron flux Γ e is derived from momentum conservation:Γ e = −n e (µ e • E) − ∇ (D e n e ) ,where n e is the electron number density, µ e is the electric mobility and D e is the electron diffusion coefficient. The first term describes the electric drift. The electron energy flux Γ ε is given by:Γ ε = −n ε (µ ε • E) − D ε • ∇n ε ,where µ ε is the energy mobility and D ε is the energy diffusivity. The electron density and electron energy density are computed by solving a pair of drift-diffusion equations, equation (1) and:∂n e ∂t + ∇ • [−n e (µ e • E) − D e • ∇n e ] = R e . (2)The mean electron energy is computed via The electron diffusivity, energy diffusivity and energy mobility are computed from the electron mobility as the following:ε = n ε n e .D e = µ e T e , D ε = µ ε T ε , µ ε = 5 3 µ e .The source terms R e and R ε in the drift-diffusion equations ( 2) and (1) are determined by the plasma chemistry. The electron source term is obtained by summing the production and loss of electrons across all relevant reactions:R e = M ∑ j =1x j k j N n n e , where x j is the mole fraction of the target species for reaction j, k j is the reaction rate coefficient for reaction j and N n is the total neutral number density. The energy loss term is obtained by summing the collisional energy loss across all reactions:R ε = P ∑ j =1 x j k j N n n e ∆ε j ,where ∆ε j is the energy loss from reaction j. The reaction rate coefficients are computed from the chemical reaction cross-sections using the following equation:k k = γ ˆ∞ 0 εσ k (ε) f (ε) dε,where ε is energy, σ k is the collision cross-section, f is the EEDF and γ is:γ = √ 2q m e ,where q is the electron charge and m e is the electron mass. The mass fraction of non-electron species is computed using the following:ρ m ∂ω k ∂t + ρ m (u • ∇) ω k = ∇ • j k + R k ,where ρ m is mixture density, ω k is the mass fraction of species k, u is the mass averaged fluid velocity vector, j k is the diffusive flux vector of species k and R k is the rate expression for species k. The electrostatic field is calculated by solving the Poisson equation:−∇ • ε 0 ε r ∇V = ρ c ,where ε 0 is the permittivity of vacuum, ε r the relative permittivity of the gas, V is the potential and ρ c is the space charge density. The boundary conditions for the electron flux at the reactor walls account for electron losses within a few mean free paths of the wall due to random motion, as well as electron gains from secondary electron (SE) emission induced by ion bombardment:n • Γ e = ( 1 2 ν e,th n e ) − γ s (Γ s • n) ,where n is the normal vector, ν e,th is the electron thermal velocity, γ s is the SE emission coefficient (SEEC) due to Ar + bombardment and Γ s is the SE flux. The second term describes the gain of electrons due to secondary emission. The SEEC is notoriously difficult to quantify and depends strongly on the surface oxidation, roughness and contamination, as well as on the incident ion energy; moreover, it can be unintentionally increased by up to 0.5 through standard procedures such as ultrasonic cleaning [33].In Comsol, SEEC is specified as a constant, whereas in reality it depends on the ion energy and is expected to vary considerably both temporally and spatially [34]. In this work, the SEEC values are taken as γ glass = 0.15 for the soda-lime glass dielectric [35] and γ Al = 0.02 for the aluminium ground electrode (GND) [36]. The boundary condition for the electron energy flux is:n • Γ ε = ( 5 6 ν e,th n ε ) − γ s εs (Γ s • n) ,where εs is the mean energy of the SEs. The second term is the SE energy flux. Mean SE energy was approximated using the maximum kinetic energy derived from Hagstrum's theory for electrons emitted through Auger neutralisation [37]:εs = ∆ε Z − 2W Al ,where ∆ε Z is the ionisation energy of Ar and W Al is the work function of aluminium. Recommended values for W Al range from 4.23-4.32 eV [38]. The resulting values for the electric field, electron temperature, electric potential and positive ion number density showed little sensitivity to work function variation, differing by no more than 1% for 4 eV ⩽ W Al ⩽ 5 eV (sensitivity analysis performed for γ Al = 0.07). The mean energy of SEs emitted from the glass is assumed to be constant at εs = 2.5 eV. The loss of heavy species due to surface reactions and the electric field is described by:n • J k = M k R k + M k c k z k µ k (E • n) [z k µ k (E • n) > 0] ,where n • J k is the normal component of the k species density at the wall, M k is its molecular weight, R k is the sum of species' surface reaction rates, c k is its molar concentration, z k is the species' charge number and µ k is its mobility. The second term describes additional flux contribution due to migration in the case when species k is an ion. Surface charge accumulation at the dielectric is described by the following equation:n • (D 1 − D 2 ) = ρ s ,where D 1 and D 2 are the displacement fields on both sides of the dielectric boundary and ρ s is the surface charge density which is computed by solving:∂ρ s ∂t = n • J i + n • J e ,in which the first and the second terms are the normal components of the total ion and total electron current density at the wall, respectively. The model equations were discretised using the finite element method with linear Lagrange shape functions (first-order spatial accuracy) and a logarithmic formulation for plasma transport equations. Time integration was performed using an implicit backward differentiation formula scheme with adaptive time stepping [31]. The advective gas flow was not included in the model due to the value of the Reynolds number Re < 1 × 10 −5 ≪ 2300 (the typical laminar/turbulent threshold) placing the system in the creeping (Stokes) flow regime where inertial and advective terms can safely be ignored [39]. The model discharge is initiated by applying a pulsed bipolar potential to the outer boundary of the dielectric plate with a function matching that of the experiment. The bipolar pulse is characterised by a rise/fall time of 0.25 µs, a pulse width of 20 µs, an amplitude V 0 , a repetition frequency f 0 and a small duty cycle (see supplementary figure A.1). Unless otherwise specified, the model parameters are set to match the experimental conditions: gas temperature T exp = 21 • C = 294.15 K, gas pressure P = 1.3 Torr, pulse frequency f 0 = 3 kHz and voltage amplitude V 0 = 255 V.The EEDF is assumed to be the Druyvesteyn distribution on the basis of our analysis of measured OES line ratios compared to the relevant electron excitation cross sections as detailed in section 4.4. A Bolsig+ [40] derived EEDF (cross section data set [41] used as input) produced no plasma across the simulated reactor. In contrast, the Druyvesteyn distribution produced a model plasma which closely resembled the behaviour observed experimentally in the reference reactor (see section 4). This may be due to the Bolsig+ assumption of a DC or an AC electric field, whereas the experiment employs a bipolar pulse with a small duty cycle. Plasma chemistryThe plasma chemistry is based on the works of Bogaerts et al [47] and Baldry et al [48]. The species interact with each other via particle collisions, volumetric reactions and surface reactions (table 1). The model considers 6 different plasma species (table 2). The often neglected resonant and higher excited states are included as they have been found to be essential for accurately capturing plasma dynamics [48].The cross-section data for elastic collisions and electronic excitations came from the IST-Lisbon database [43]; ionisation cross-section data were taken from the SIGLO database [49]; excitation of metastable argon to higher 2p states was taken from Hyman [44] and ionisation of metastable argon to Ar + was taken from Hyman [46]. As reported in the literature [45,50,51] the electronic excited states were grouped into the metastable term Ar m , the resonant term Ar r (1s 2 , 1s 4 ) and the higher excited term Ar p (2p 10 through 2p 1 ). The dimer states of argon Ar 2 * and Ar + 2 are expected to have a negligible impact on the plasma behaviour at the low pressures and powers considered in this study and are hence are omitted from the model [52,53]. Mesh independenceMesh independence was tested against electron density, ion density and electron temperature. The parameters were monitored for convergence at points in space and time when their gradients vary most steeply. The solution was considered mesh independent with a 823-element mesh, because the relative error fell below 0.005% for all specified parameters. The mesh spacing was linear across the dielectric domain (23 elements) and exponential across the discharge gap to capture the steep gradients near the walls (800 elements). Experimental setupThe DBD setup (figure 1, top) consisted of two disc-shaped aluminium electrodes with a 120 mm diameter separated by 13 mm. A sheet of 140 × 140 mm soda-lime glass with thickness of 3 mm acted as a dielectric barrier shielding the powered electrode surface leaving a 10 mm gap between the dielectric and the GND. The small DBD assembly was placed inside a large cylindrical chamber made of Pyrex with a diameter of 170 mm and a length of 1000 mm. The chamber was evacuated down to 3.5 mTorr using a scroll dry vacuum pump, EDWARDS nXDS6i and a turbo pump station, Alcatel Drytel 1025, each connected to the chamber through separate lines. After reaching base pressure, argon gas was injected into the chamber at 10 sccm through an Alicat mass flow controller. The turbo pump line was then inactivated and the working pressure of 1.3 ± 0.1 Torr was maintained by a valve on the pumping line connecting the chamber to the scroll pump. The measured leak rate is 0.8 sccm, corresponding to an air admixture level of 7.4%. A discussion of the effects of the atmospheric contamination on plasma properties can be found in section 5. The experiment was conducted at 21 • C. The pulsed voltage was generated by a RUP6-18bipv7 power supply. The bipolar pulse frequency was set to 3 kHz, otherwise specified, with both positive and negative pulse widths set to 20 µs, otherwise specified. The bipolar pulse peak to peak voltage was set to 588 V (+294 V and −294 V applied during the positive and negative phases, respectively) to initiate plasma breakdown and to 510 V thereafter. The pulse rise time for both positive and negative phases of the power cycle was 250 ns, otherwise specified.A control experiment with no plasma present in the gap was performed to determine the intrinsic ringing frequency of the current in the circuit. The current in both the control experiment and in the presence of a glow discharge was determined by measuring the voltage drop across a 100 Ohm resistor connected in series with the DBD cell and the GND. Both the waveform of the applied pulsed voltage and the voltage across the resistor were monitored and recorded using a Rigol MSO5104 oscilloscope. The sampling rate for all recorded waveforms in the oscilloscope was 10 MSa s −1 (mega sample per second). The applied pulsed voltage was recorded from the voltage monitoring outlet of the power supply. OES analysisThe time-integrated OES measurements were carried out using a 600 grooves mm −1 spectrometer (Ocean Optics, HR4000) with a spectral range from 200 to 1100 nm and a resolution of 0.3 nm. The plasma emission (see table 3) was collected by an optical fibre connected to the spectrometer and positioned at the chamber wall in the middle of the discharge gap between the dielectric layer and the GND of the DBD reactor. Considering the numerical aperture of the optical fibre, the light collected by the fibre may be emitted from any point between the two electrodes. Thus, the process of light collection can be regarded as spatially integrated. The recorded spectra were visualised using OceanView software and the spectral response was calibrated using a Princeton Instruments intensity calibration system, IntenlliCal 2.0. An average of 10 scans with an integration collection time of 10 s were recorded on each Table 3. Argon emission lines used for electron excitation temperature calculation by the modified Saha-Boltzmann method. The f and g values were obtained from the NIST Atomic Spectra Database [55]. experiment. The acquired spectra are hence the result of an accumulation of several thousand voltage pulses. The data underwent background subtraction, where a Gaussian function was fitted over a defined wavelength interval to determine the line intensity. The integral of each identified specie was calculated over a baseline y = 0 using the fitted Gaussian and substituted for the intensity.λ kl (nm) f lk g k E k (The time-resolved OES measurements were acquired by a high-resolution spectroscopy system. This system consists of a Princeton Instruments intensified CCD (ICCD) camera, PI-MAX4:1024i, attached to the exit plane of the Princeton Instrument Spectrograph, Acton SpectroPro 2750. A 1200 grooves mm −1 diffraction grating was used for the recorded spectra. The plasma emission was collected through an optical fibre bundle connected to the entrance slit of the spectrograph. The entrance slit was set on 20 µm and the connected optical fibre bundle was positioned on the exterior surface of the Pyrex chamber, in the middle of the gap between the dielectric layer and the GND of the DBD reactor. This setup enabled the fibre bundle to collect the plasma emission from the entire gap region of the DBD reactor. To eliminate the instrumental artefacts of the optical components of the spectroscopy system, the plasma spectra were intensity calibrated. The calibration was performed using Princeton Instrument IntenlliCal 2.0. system. A trigger pulse from the power supply of the DBD reactor was used to synchronise the ICCD camera with the applied voltage pulse for capturing the time resolved plasma spectra. The spectra were recorded with 200 ns exposure time at a frame interval of 250 ns. To maximise the signal-to-noise ratio the plasma emitted light was accumulated over 1000 consecutive pulses.For plasmas not in local thermodynamic equilibrium (LTE), the relationship between the electron excitation temperature and the ratio of emitted transition lines can be expressed using the modified Saha equation (equation (34) in [54]), which can be rearranged to:ln ( I + kl I mn λ 3 kl f nm g m λ 3 mn f lk g k ) = 1 4.09 (k B T) 2 ( E 2 k − E 2 m +2E k E ∞ + 1 2 E 2 ∞ ) + C (n e , T) ,where subscripts kl and mn denote the ion and neutral transition lines (free of metastable contributions, as per [54]), respectively. I is the line intensity at the emission wavelength λ, E the upper-level energy relative to the ground-state, f the oscillator strength and g the degeneracy for a given transition. E ∞ is the first ionisation energy, T the temperature in eV, k B the Boltzmann constant and C(n e , T) is the yintercept term, which can be expressed as:C (n e , T) = − ln ( 2π 3 2 m 3 e n e h 3 [ 2.86k B T m e 3 2 ] ×U 1 ( 0.699 E ∞ k B T )) , (3)where m e is the electron mass, h Planck's constant and U 1 the parabolic cylinder function of order 1 evaluated at ( 0.699 E∞ kBT ) . Equation (3) enables the construction of a modified Saha-Boltzmann plot, from which the electron excitation temperature can be obtained via an iterative process: an initial T is assumed, compared with the T estimated using the gradient of the linear fit and updated iteratively until convergence (typically within 2-3 steps). The electron density n e was taken from the model, however the resulting temperature was found to be insensitive to the order of magnitude of n e . A typical recorded spectrum with the corresponding plot are shown in figure 2. High-speed photographyThe time-resolved images of the plasma in the DBD reactor gap were captured using the Princeton Instrument camera, PI-MAX4:1024i, equipped with a Nikon AF NIKKOR 28-105 mm f/3.5-4.5D lens. The camera was synced with the pulsed voltage using a trigger pulse from the power supply. Images in the regions of interest (the rise time, the polarity reversal and the fall time) were recorded with 50 ns gate width and 0 frame interval (no delay between frames). Each frame is the result of an accumulation of 10 plasma pulses in order to improve the signal-to-noise ratio. Results and discussionA plasma is a quasineutral gas consisting of charged and neutral particles which exhibit collective behaviour [56]. Hence, the presence of plasma can be qualitatively determined by comparing the positive ion density to the electron density and observing the quasineutral bulk's response to an external electric field. See animation 1 for the spatio-temporal evolution of electron density, positive ion density and the electric field across the model reactor during a power cycle. See figure 3 for stills from animation 1 depicting the pivotal moments in a power cycle. For each figure, a time code (TC) for the corresponding frame in the animation is provided in the standard hour: minute: second: frame number format. The animation y-axes are linear and dynamic to show the variables' evolution across several orders of magnitude.The animation is compiled using power cycle 9. Cycle 9 is converged, meaning plasma variables do not change from cycle to cycle and they no longer bear the imprint of the initial conditions (the latter typically occurring after 1 power cycle). The plasma variables oscillate within 10% (ion density), 1.6% (electron density) and 10% (electric field) for a given time in a power cycle. This behaviour was tested on over 100 pulses. Plasma dynamicsShortly before the start of a new power cycle (figure 3(a), TC 01:00:04:02 in animation 1), the electron and ion densities reach their minimum (10 8 m −3 and 10 10 m −3 respectively) with the electric field on the order of 10 4 Vm −1 . The change in the electric field magnitude is only 2 Vm −1 with vector direction: glass ← GND. The densities are not changing and the electric field is slowly decaying. The dielectric wall has a negative potential with respect to GND.The rise in voltage from V = 0 to V = +V 0 brings about a disturbance (figure 3(b), TC 01:00:04:11 in animation 1). The electrons in the gap accelerate towards the dielectric, which is shielding the positive electrode and an electron density maximum is established at ∼0.3 mm from the glass, E direction: glass ← GND. The accelerated electrons which come into contact with the glass are absorbed, building up a negative charge at the dielectric wall. Ion density across the reactor increases sharply by an order of magnitude as accelerating electrons collide with neutral argon and release positive ions. The ion density peak moves towards the dielectric and stops 0.8 mm from the glass wall. The electron density also increases by an order of magnitude due to the release of electrons in the ionisation events.At the end of the voltage rise time (figure 3(c), TC 01:00:04:18 in animation 1) the ions and electrons stabilise in an area 0 − 2 mm from the dielectric, E direction: glass ← GND. When the voltage reaches V = +V 0 , the ion density peak begins to shift away from the dielectric. Then, 0.5 µs later, it changes direction and drifts back towards the dielectric. This behaviour can be explained by the following: the ions overshoot the negative charge on the dielectric, bombard the dielectric surface and release SEs. The SEs are attracted to the positive potential at the other end of the gap near the GND. When moving towards the GND, accelerated electrons collide with and ionise additional neutral atoms, producing more positive ions and electrons.The behaviour described in the previous paragraph is oscillatory (see animation 1, seconds 4-8). The ion density peak shifts a few mm towards the GND electrode before moving back towards the dielectric wall. This cycle repeats thrice, each time lasting approximately a microsecond. The electron density peak, located between 0-1 mm from the dielectric, undergoes corresponding, but vertical oscillations, changing magnitude with respect to the ion density instead of changing location in the gap. The electron density grows with respect to the ion density when the ion density peak moves towards the dielectric and falls when it moves away. Throughout these oscillations, which begin after the voltage reaches +V 0 , the ion and electron densities gain 4 orders of magnitude.The oscillatory behaviour can be explained by charge inertia. During the voltage rise time (V = 0 → +V 0 ), the electric field accelerates electrons towards the dielectric, leading to the build-up of a negative screening charge. Once the applied voltage reaches +V 0 and stops increasing, the accelerated electrons continue moving across the gap, colliding with and ionising neutral atoms before embedding into the dielectric, which further increases the negative charge on the glass surface. The resulting net negative potential attracts ions, which bombard the dielectric surface and release SEs. SEs are repelled by the negative charge and accelerate towards the more positive GND potential, ionising neutral argon in their path. The accumulation of ions and the release of SEs add positive charge to the dielectric surface. This emission overshoots the amount required for shielding and leaves a net positive potential at the dielectric surface which now attracts electrons, thus initiating the next cycle.The oscillations repeat until the ions begin to shift away from the dielectric for the third time at t ∼ 2 µs. This time, the electron density peak continues to grow both absolutely and with respect to the ion density until a quasineutral pocket of plasma appears between 1 − 4 mm from the dielectric (figure 3(d), TC 01:00:08:18 in animation 1), E direction: glass ← GND. This pocket decays after 0.3 µs.Around t ∼ 2 µs, the electric field in the sheath approaches 10 5 V m −1 , or E/N of 2000 Td. The SEs emitted into the high electric field in the sheath are expected to act as a beam. The model accounts for this phenomenon by including the SE emission into the sheath, and the subsequent SE acceleration by the electric field. Since the model electron temperature is taken as a time average across the gap over the duration of a power cycle (used for OES model validation, section 4.3), and the OES estimates experimental temperature using light collected across the gap over several power cycles, we expect the model and the experimental temperatures to capture the beam component.During the remainder of the positive phase of the power cycle the electron and ion densities across the reactor decrease in magnitude and gradually return to distributions similar to those before the voltage pulse, albeit with peak values approximately double those before the start of the power cycle.The polarity reversal from V = +V 0 to V = −V 0 creates a negative potential at the dielectric. The more mobile electrons accelerate towards the GND electrode and a positive charge accumulates on the dielectric. The ions in the bulk plasma follow the electrons' space charge, shifting the electron and ion density maxima closer to the GND electrode. The same oscillatory behaviour observed near the dielectric wall during the positive phase of the voltage pulse now appears near the GND electrode. The bulk of ions moves back and forth near the GND electrode while the electron density grows and falls relative to the ion density, with both densities increasing overall. However, this time the oscillation is twice as fast, lasting 0.5 µs and repeating only once. When the ion density peak moves away from the GND electrode for the second time, the electron density no longer decreases relative to the ion density as in previous oscillations, but instead continues to grow both absolutely and comparatively. Electron and ion densities rise by approximately six orders of magnitude within less than 1 µs from the start of the voltage polarity reversal (figure 3(e), TC 01:00:46:01 in animation 1), E direction: glass →← GND. This could be because of the increased ion bombardment due to the negative potential at the dielectric, which results in the emission of more SEs than in the positive half cycle.The plasma ignited by the voltage polarity reversal spreads across the reactor (as opposed to a localised plasma pocket which appears after the first rise time). Within 6 µs quasineutrality with nearly symmetrical electron and ion densities is established, E direction: glass →← GND (figure 3(f), TC 01:00:55:29 in animation 1), however but the mean electron energy has dropped to below 1 eV. The quasineutral bulk remains stable for the remainder of the negative voltage pulse (14 µs), with ion and electron density maxima decreasing by 20% (9 × 10 14 m −3 ) and the electric field at the sheaths decreasing by half (2 × 10 3 V m −1 ).The return of the voltage from V = −V 0 to 0 strips the electrons nearer to the GND electrode from the quasineutral plasma (figure 3(g), TC 01:01:24:00 in animation 1), E direction: glass → GND, as the residual positive charge on the dielectric reverses the potential difference so that the GND electrode strongly repels electrons. The mean electron energy in the no longer quasineutral, but dense (10 15 m −3 ) region rises to 3-4 eV as a result of the burst of electron acceleration, before decaying together with the densities. For the remainder of the power cycle, the electron and ion densities decay and redistribute themselves to maintain a negative charge on the dielectric and a much larger positive charge on the GND electrode. The net negative charge on the dielectric at this stage is due to the higher mobility of electrons relative to ions. Time-resolved ionisation and lossesModel reactor electron gain (G e ) through the three ionisation channels: ground-state (R g ), metastablestate (R m ) and metastable-metastable collisions (R mm ), as well as via SE emission from the dielectric and GND boundaries (SE Diel , SE GND ), together with electron loss (L e ) to these same boundaries, were analysed for their contribution to the net electron balance. R g dominates, accounting for more than 92% of electrons generated during a given power cycle, with SE Diel and SE GND contributing approximately 7% and 1%, respectively. Time-resolved analysis reveals a strong phase dependence on the voltage waveform. During the positive half-cycle, G e is overwhelmingly dominated by ground-state ionisation (R g > 97%), with negligible contributions from stepwise (R m ∼ 0.01%) and metastable-metastable (R mm ≪ 10 −5 %) channels. L e is primarily to the dielectric, which absorbs > 99% of the lost electrons. Ionisation is strongly timelocalised: nearly all electrons in the positive half-cycle are produced within ∼ 2 µs of the voltage rise.The bulk of the plasma is generated after the polarity reversal, with a short, 0.1 µs burst of electron generation producing over half of the electrons generated over the entire pulse, of which R g ∼ 95% and SE Diel ∼ 5%. In the subsequent negative voltage phase, SE Diel contribution grows to ∼ 35% of the total, making it a substantial mechanism for sustaining the high-energy (T e > 1 eV) afterglow as ionisation declines. Both high-and low-energy afterglow periods are strongly loss-dominated, with the net electron densities falling accordingly. Overall, the discharge alternates between short bursts of intense ground-state ionisation and sustained wall-driven losses, with the negative half-cycle producing the longlived, volume-filling plasma. A time-resolved comparison of ionisation, SE emission and electron losses, together with net charge evolution, is given in tables 7 and 8 of appendix C. Effects of polarity reversalTo assess the polarity effects, the model was run with the voltage half-cycle order reversed (negative half cycle followed by a positive half-cycle, hereafter −V 0 ↗ +V 0 ). In both the experimental polarity (+V 0 ↘ −V 0 ) and the reversed polarity (−V 0 ↗ +V 0 ) case, plasma ignition is determined primarily by the onset of the negative voltage phase. During the negative phase, the spatial distributions of electron density, ion density and electric field are similar in both the experimental and the reversed polarity, except that the experimental polarity produces a ∼70% higher peak density (1.2 × 10 16 m −3 versus 7 × 10 15 m −3 ).An initial positive phase produces a seed plasma (net electron gain G e = 3.05 × 10 13 m −2 with > 97% from ground-state ionisation-m −2 units explained in appendix C) with > 99% lost to the dielectric over the same time period, while a follow-up negative phase sustains the discharge and produces a G e ∼ 9.18 × 10 13 m −2 , again dominated by ground ionisation (R g > 90%) with a modest contribution from SE emission (SE Diel ∼ 9%). When the negative half-cycle occurs first, it again drives plasma production (G e = 6.54 × 10 13 m −2 , R g ∼ 90%, SE Diel ∼ 10%), while the subsequent positive phase is overwhelmingly loss-dominated. See tables 9 and 10 in appendix C for a summary of the voltage phase evolution of ionisation, SE emission and electron losses. Model validationModel results were validated against the experimental setup on which the computational model was based. When comparing experimental observations with model results, caution must be exercised, as absolute values may disagree due to the presence of difficult-to-establish constants stemming from initial conditions and material properties. These include the initial number of free electrons within the gap, which depends on solar activity on the day and the SEEC of the dielectric and electrode materials, which are influenced by surface roughness, oxidation and contamination.Due to these factors, combined with software limitations (e.g. Comsol currently inputs the SEEC as a constant, despite it being a highly energy-dependent parameter), absolute values should be treated with caution. Instead, observational trends provide a more reliable benchmark. The following discussion examines the trends observed via temporally resolved plasma current measurements, high-speed photography and time-averaged OES measurements under the experimental conditions listed in section 2.4 and assesses their degree of agreement with the model results. Hereafter 'plasma current' refers to the current measured in the presence of a glow discharge in the gap with the control experiment current (measured in the absence of plasma) subtracted. Plasma current validationThe experimental plasma current is detected close to the voltage pulse rise time, polarity reversal and fall time, and not at other times, which is in excellent agreement with the model results (figure 4). The frequency of the ringing seen in the measured plasma current during the voltage rise and fall times matches the intrinsic ringing frequency of the current in the circuit, which was determined in a control experiment without plasma in the gap (detailed in appendix D). Hence, the current ringing is assumed to originate from the power supply, rather than from the plasma transport processes. The short lead of the experimental plasma current over the voltage is only 1 data point (0.1 µs, see figure 4(a) and can be attributed to the limited temporal resolution of the experimental measurements.The experimental and model current trends track each other in terms of the times when they occur in the pulse, their direction, magnitude, and the level of peak broadening (see figure f.1 for the evolution of the experimentally recorded and modelled plasma currents vs time in the voltage pulse over the duration of the voltage duty cycle). Both the experimental and the model currents peak with a shorter time delay after the polarity reversal (figure 4(b)) than after the rise time. Both current peaks increase in magnitude and are more compressed after polarity reversal than after the rise time. This is likely due to the increase in the residual charges available for plasma ignition owing to the 'seed' breakdown generated by the voltage rise time. The experimental current peaks are spread out over a longer duration, however, and occur earlier in the pulse than the model prediction.The discrepancy in time delay between the voltage change and the observed current in the experiment and model at the voltage rise time and the polarity reversal can be explained by the model stabilising to a lower afterglow than the experiment. This may be due to some differences between the experiment and the model, such as the presence of impurities in the experiment, or a higher SEEC for the experimental surfaces, however the mechanism is not known. The time delay between the change to the applied voltage and breakdown is very sensitive to the afterglow, and an increase in afterglow density results in a reduction in delay between voltage change and breakdown generation [57].The experimental current signal detected at the voltage fall time (figure 4(c)) is in excellent agreement with the model in time, duration, direction, peak broadening, and magnitude. This is because no new breakdown is generated by the voltage returning to 0 V. Rather, the current is caused by charged particles moving out of the gap. Hence, there is no dependence on the afterglow and the model and experimental current signals match.The time delay discrepancy between the experiment and model at the rise time and polarity reversal questions the model's ability to capture afterglow behaviour during the long interval between voltage pulses. However, the agreement at the fall time shows that the model is capable of accurately capturing plasma behaviour on the scale of a duty cycle. High-speed photography validationTemporally resolved high-speed images show strong agreement with the model predictions, see figure 5 for a selection of static frames and video 1 for the full sequence.Rise time (figure 5, top row): 0.4 µs after the start of the pulse, the camera captures 3 weak flashes originating in the middle of the gap and creeping toward the GND electrode, each flash lasting between 0.2-0.25 µs. The flashes' duration and direction match the oscillatory movement predicted by the model (animation 1, TC 01:00:04:11), with the experimentally detected light corresponding to the ions moving towards the GND in the model reactor as their density increases.Polarity reversal (figure 5, middle row): 0.2 µs after the voltage polarity begins to reverse, a long (∼ 0.55 µs) bright flash is captured originating near the GND electrode and swiftly moving up towards the dielectric. This flash corresponds to the model's predicted movement of ions and electrons from the GND towards the dielectric in a state approaching plasma and with a rapidly increasing density, before a stable plasma forms across the reactor. The timescales of the movement match very well, with the flash movement and the movement of the ions and electrons across the model reactor lasting ∼0.15 µs and 0.2 µs, respectively.Fall time (figure 5, bottom row): at 37.85 µs a bright flash originates in the middle of the reactor and begins to creep towards the exposed GND electrode before extinguishing 0.2 µs later. After a 0.15 µs pause another, faint flash follows, lasting only 0.05 µs and extinguishing without movement. These flashes are captured prior to the change in voltage which begins at 39.75 µs. Both the rise time and the polarity reversal produce light after the voltage begins to change. This can be explained by the unintended voltage variations introduced by the RUP6-18bipv7 (discussed in appendix D). The model predicts the contents of the reactor to not at all resemble plasma pre-pulse or pre-polarity reversal, but to closely approximate plasma in the lead up to the fall time. Shortly before the voltage goes back to 0, the model predicts the electrons and ions to be in a state of quasineutrality, with densities on the order of 10 15 m −3 , with electrons and ions decaying together (TC 01:01:23:01 in animation 1). It is plausible, that a small ±5 V experimental voltage fluctuation could re-ignite a plasma such as that predicted by the model and cause the flashes which are seen experimentally. Time-integrated OES validationTime-integrated optical emission spectra were used to estimate the electron excitation temperature (T exc ) using two approaches: the modified Saha-Boltzmann method, suitable for non-LTE plasmas (as detailed in section 2.5), and the Boltzmann plot method, applicable to plasmas in partial LTE (as detailed in appendix E). The OES-derived T exc are compared with the model T e for various experimental conditions in figure 6.As the system is unlikely to be in LTE due to its rapid temporal variations, the concept of electron temperature is not strictly applicable. The T exc does not represent a true thermodynamic temperature, but rather reflects the average energies of electrons responsible for populating excited states. Nevertheless, T exc is expected to follow similar trends to the T e , since an increase in T e generally leads to stronger emission; thus, the T exc determined by OES should also increase.The voltage frequency variation in the range 0.3-3 kHz does not appear to influence either the experimental or model temperatures, indicating that the short voltage duty cycle causes the plasma to initiate each cycle with minimal influence from the preceding breakdown. Frequencies above 3 kHz resulted in arc discharges and hence could not be tested experimentally.Varying the voltage rise time does not significantly influence the temperature, which can be attributed to the self-sustaining nature of the plasma. Once ignited, the plasma density follows a similar temporal evolution for all rise times tested (table 4), with comparable times to reach and decay from peak density. While rise time might be expected to influence plasma behaviour by altering the total energy available to the plasma, the results suggest a threshold behaviour: the rise time either supplies sufficient energy to initiate the discharge, or it does not. For rise times above this threshold, the plasma dynamics remain essentially unchanged.Varying the voltage pulse width produces a nonlinear response in the model. Because the Druyvesteyn EEDF enforces a stationary, energy-independent cross section, the discharge becomes sensitive to small variations in pre-pulse potential. These offsets determine the strength and timing of the seed plasma generated during the rise time and the extent of charge relaxation before the polarity reversal. The result is a pronounced variation in the modelled electron temperature T e across pulse widths.Experimentally, no such strong dependence is observed. In the experimental discharge, the EEDF evolves dynamically during the rise time and polarity reversal, with suprathermal electrons generated by rapid field acceleration and secondary emission sustaining ionisation regardless of pulse duration. OES diagnostics, further weighted toward characteristic excitation energies, smooth out residual differences. Together with metastable pooling and circuit-plasma feedback, these processes suppress the nonlinear trends predicted by the Druyvesteyn model.Overall, the model captures the experimental trends in frequency and rise time, but diverges for pulse width, where the stationary Druyvesteyn assumption cannot reproduce the robustness of the experimental discharge. As expected, non-LTE analysis consistently yields higher apparent temperatures than partial-LTE estimates [54]. Time-resolved OES EEDF probeTime-resolved spectroscopy was employed to further probe the choice of the EEDF for the model. The emission peaks corresponding to the electronic transitions 3p 5 → 1s 4 (419.8 nm, hereafter Ar 419 ) and 3p 9 → 1s 5 (420.1 nm, hereafter Ar 420 ) were utilised to determine the ratio of their emission intensities, R 420 419 . This ratio serves as an optical diagnostic tool to verify the presence of high-energy electrons. When excitation proceeds from the 1s 5 metastable level, the Ar 420 line intensity exceeds that of Ar 419 throughout the entire electron energy range (figure G.1(a)). If all of the electrons have energies below 14.5 eV, excitation occurs solely via metastable levels, yielding R 420 419 ∼ 4. At higher electron energies, where ground-state excitation dominates, the ratio approaches unity (figure G.2(b)). When a substantial population of electrons exceeds 25 eV, R 420 419 may fall below 1 [58]. Comparing the ratios enables the evaluation of suitability of different EEDFs, thereby providing experimental support for the choice of the model EEDF.Figure 7 presents the EEDF fractions across various energy ranges. The mean electron energy values for each EEDF are based on the analysis of the time-integrated OES data, detailed in section 2.5 and appendix E. The Maxwellian distributions plotted for mean electron energies of 0.8 and 1.2 eV exhibit only a small population of high-energy electrons essential for excitation and ionisation. In contrast, Druyvesteyn distributions with mean electron energies of 7 eV or higher contain a substantial proportion of electrons in the 14-24 eV range, consistent with the electron energies inferred from the OES line ratios shown in figure 8. Moreover, when the mean electron energy exceeds 13.4 eV, the electron population above 24 eV becomes significant. These findings, when matched against the observed intensity ratios, indicate that the electrons in the experimental plasma likely follow a Druyvesteyn EEDF with mean energies between 7 and 10 eV.The intensities of Ar 419 and Ar 420 were determined during the pulse's polarity reversal, with three spectral acquisitions taken at t = 19.80, 20.05 and 20.30 µs from the pulse onset, when plasma emission was observed by the spectroscopic system. The spectral fittings and the evolution of R 420 419 are presented in figure 8. Based on the cross-section data, at the start of the polarity reversal (figure 8(a)), excitation of Ar 419 and Ar 420 occurs via the ground-state, with maximum electron energies below 25 eV. This is consistent with the absence of plasma emission immediately before the polarity reversal, as confirmed by both the model results and high-speed photography. The subsequent OES frame at t = 20.05 µs (figure 8(b)) indicates excitation proceeding through two mechanisms: ground-state excitation and excitation from the 1s 5 metastable level. This is reflected by the ratio R 420 419 being greater than 1 but less than 4, since the metastable state must first be populated via electron-atom collisions as the polarity reverses. These concurrent excitation mechanisms account for the elevated emissivity observed during this frame, as low-energy electrons contribute to the excitation process. In the final emission frame at t = 20.30 µs (figure 8(c)), a similar excitation pattern is observed, although the population of high-energy electrons has decreased, as evidenced by the reduced emission intensities of these transitions.These findings indicate, that on the timescale of the applied pulse with a short active phase and a relatively long passive phase, the Druyvesteyn distribution provides a physically consistent description of the electron energy distribution, which is at odds with what is commonly assumed of Argon DBD at low partial ionisations. Experimental limitationsThe observed 7.4% air admixture level is considered low for the plasma system under investigation. Admixture-contributed nitrogen emission lines are observed in all OES spectra collected; however, their intensity remains low across the tested experimental conditions (figure 2, top). For example, the nitrogen excitation line intensity registers approximately 300 counts at applied voltage pulse frequencies of 0.5 kHz, 1.5 kHz and 2 kHz. This uniformity indicates that any influence of nitrogen on the plasma characteristics is consistent across the tested conditions. The detected nitrogen excitation peaks correspond to transitions that require relatively low excitation energies. Notably, emission from ionised nitrogen at 391.4 nm is minimal, with observed intensities of just ∼ 60 counts. Some high-energy electrons are likely being consumed in the excitation of nitrogen species, thereby reducing the average electron temperature. Consequently, the average electron temperature predicted by the model assuming pure argon is likely to exceed the experimentally determined values, which inherently reflect the energy losses associated with nitrogen excitation.The HR4000 spectrometer's compact design facilitates rapid measurements across a wide wavelength range, making it particularly suited for studying fluctuating plasma. However, this advantage comes at the cost of reduced spectral resolution. Additionally, residual nitrogen is observed in the spectra, which can be attributed to the system's base pressure of 1 × 10 −3 mTorr. Identifying higher upper-level energies of argon (E k > 14 eV) typically found within 400-500 nm and lower upper energies found within 700-800 nm becomes challenging due to overlapping nitrogen peaks. This limits the selection of argon upperlevel energies available for constructing a Boltzmann plot for excitation electron temperature calculation. Consequently, the lines chosen for the Boltzmann plot were largely standalone argon lines, expressing a fitting range of R 2 = 0.78-0.83. This is expected in DBD systems, where the electron density does not satisfy the McWhirter criterion [59], collisional rates do not exceed radiative rates and particles are not equally thermalised, causing the plasma to deviate from the LTE and resemble a collisional radiative.The use of a manually operated isolation valve introduced pressure fluctuations, to which plasma ignition stability in low-temperature DBD systems exhibits high sensitivity. Increasing pressure leads to a reduction in the mean free path, necessitating higher energy input to sustain the plasma, potentially resulting in extinction. Conversely, decreasing pressure may enhance ionisation, potentially leading to inaccuracies in calculated T exc .The pulsed voltage generated by the power supply introduced uncertainty in the overall operating voltage across the plasma. The experimental voltage was measured using a Rigol MSO5104 oscilloscope and a 100 Ω resistor enabled current extraction measurements. To minimise the impact of the above limitations and improve consistency, the concurrent measurements of the modelated parameters were performed on the same day. ConclusionThis study developed a 1D fluid model for plasma breakdown in a low-pressure (1.3 Torr) asymmetric argon DBD with a 10 mm gap, validated against OES, high-speed imaging and plasma current measurements. The model provides a stable computational framework for exploring plasma dynamics under varied conditions, offering insights into quantities, which are currently difficult to access experimentally.Key findings include the identification of distinct spatio-temporal oscillations in charged particle densities preceding breakdown, confirmed experimentally through high-speed imaging. The dischargeemitted light aligns with the model's predictions in frequency and timescale. The simulated plasma behaviour matches the expected dynamics. The electron losses are dominated by surface interactions which alternate between electrodes based on polarity, and ground-state ionisation controlling the discharge in active voltage phases. Metastable-assisted processes emerge in the afterglow. Secondary electrons play an important role in sustaining the high-energy (T e > 1 eV) afterglow, contributing over a third of the electrons. The negative voltage phase proves to be essential for generating a long-lived plasma, enhanced by a preceding positive half-cycle, whereas reversing polarity leads to the positive phase quenching the discharge generated by a preceding negative half-cycle. Additionally, under the conditions examined, the Druyvesteyn approximation better describes the EEDF than the Maxwellian or the Bolsig+ calculated alternatives. The Druyvesteyn is supported by both the improved agreement with the model and, independently, through the time-resolved spectroscopy data.Parametric analysis shows that applied voltage frequency and rise time have a minimal impact on the electron temperature, T e , suggesting independent cycle initiation and threshold energy behaviour for discharge onset. For pulse width variation, the trends are consistent for pulse widths above 5 µs, and diverge for pulse widths below 5 µs, with the model T e increasing for shorter pulse widths and the experiment showing minimal change. The voltage current analysis suggests that the discrepancy between the delay time to discharge initiation is due to the model underestimating the afterglow density.The authors would like to underscore limitations in current modelling practices, such as representing the SEEC as a constant value, which inadequately accounts for its temporal and spatial dependence on ion energy. Future plasma modelling software should incorporate SEEC via lookup tables, similar to energy-dependent collision cross-sections, to improve simulation accuracy.These insights advance the optimisation of low-pressure DBDs. Future work should employ temporal resolution techniques to further detail plasma dynamics and provide spatially resolved spectra to map parameter variations across the discharge gap. Figure 1 . Figure 1. The experimental DBD assembly (top) and a schematic representation of the experimental setup (bottom) with the 1D modelled domain highlighted in yellow. Figure 2 . Figure 2. Top: a typical recorded spectrum. The light was collected and averaged over many voltage pulses. Blue shows presence of nitrogen lines. Bottom: typical modified Saha-Boltzmann plot used to estimate the electron excitation temperature from OES. Figure 3 . Figure 3. Spatial distributions of ion density, electron density, electric field and electron temperature across the discharge gap of the model reactor at different times t within a single power cycle. The schematic in the bottom right indicates the location of the plotted x-axis within the model. Note that the y-axis scales differ between panels to accommodate variable changes spanning multiple orders of magnitude. Figure 4 . Figure 4. Evolution of the experimentally recorded (Iexp) and modelled (I model ) plasma currents vs time in the voltage pulse for the (a) rise time, (b) polarity reversal and (c) fall time. Both currents are effectively zero outside of the times shown. Figure 5 . Figure 5. Temporally resolved high-speed images captured during the voltage rise time (top row), polarity reversal (middle row), voltage fall time (bottom row) and the reference image (bottom left). The times indicated correspond to the interval since the start of the voltage pulse and up to the beginning of the 0.05 µs acquisition window for each frame. Figure 6 . Figure 6. Effect of varying the applied pulse frequency, rise time and pulse width on the modelled Te compared with the experimental Texc values derived from OES via the modified Saha-Boltzmann and via the Boltzmann plot methods. Error bars represent uncertainties from the linear fits. Figure 7 . Figure 7. Fractions of electron energy populations for various Maxwellian (Mx) and Druyvesteyn (Dr) EEDFs. Figure 8 . Figure 8. Lorentzian fits for lines 420.1 nm and 419.8 nm around the time of the polarity reversal and the resulting intensity ratios. Table 1 . Table 1 . Argon collisions and reactions present in the model. DB indicates detailed balancing, σ(ε) refers to the cross-section data, ∆ε is the energy change, k is the forward rate constant. Calculation of the effective radiative rates for Arr and Arp are detailed in appendix B. Formula Description Rate expression ∆ε (eV) 1 e + Ar → e + Ar Elastic collision σρs(ε) m −2 - 2 e + Ar → 2e + Ar + Ionisation σρs(ε) m −2 15.78 [42] 3 e + Ar → e + Arm Excitation to metastable states σρs(ε) m −2 11.55 [43] Collisions 4 e + Arm → e + Ar 5 e + Ar → e + Arr De-excitation of metastables Excitation to resonant states σρs(ε) m −2 σρs(ε) m −2 −11.55 (DB) 11.62 [43] 6 e + Arm → e + Arp Metastable excitation to 2p states σρs(ε) m −2 3.2 [44] 7 e + Ar → e + Arp Direct excitation to 2p states σρs(ε) m −2 12.91 [42] 8 e + Arm → 2e + Ar + Ionisation of metastable states σρs(ε) m −2 4.21 [45, 46] 1 Arm + e → Arr + e Electron quenching k = 2 × 10 −1 m 3 s −1 - [32, 47] Volumetric reactions 2 2Arm → e + Ar + Ar + Metastable collision 3 Arm + Ar → 2Ar Two-body collision 4 Arr → Ar Radiative rate (1s2, 1s4) k = 6.4 × 10 −4 m 3 s −1 [47] -k = 2.3 × 10 −9 m 3 s −1 [47] -k = 3.12 × 10 3 s −1 - [appendix B] 5 Arp → Ar Radiative rate (2p10 − 2p1) k = 1.37 × 10 7 s −1 - [appendix B] 1 Ar + → Ar Argon ions bombarding dielectric - Surface reactions 2 Ar + → Ar 3 Arm → Ar 4 Arr → Ar Argon ions bombarding aluminium -De-excitation of metastable states -De-excitation of resonant states - --- 5 Arp → Ar De-excitation of higher 2p states - - Table 2 . Table 2 . Species present in the model plasma. Symbol Description e electron Ar neutral argon Arm metastable argon Arr resonant states 1s2, 1s4 Arp higher excited states 2p10 − 2p1 Ar + ionised argon Table 4 . Table 4 . Times ∆ta and ∆t b for the ion density to exceed and then fall to a) ρ ion = 4 × 10 15 m −3 and b) ρ ion = ×10 3 ×10 15 m −3 , together with the maximum average ion density ρmax, for each tested rise time. Peak density occurs ∼1 µs after the polarity reversal. Rt (ns) ∆ta (ns) ∆t b (ns) ρmax (m −3 ) 350 366 2522 5.46 × 10 15 550 360 2476 5.48 × 10 15 650 375 2671 5.49 × 10 15 AcknowledgmentsThis project has been funded through the Australian Research Council Laureate Fellowship FL190100216. R Sanginés would like to acknowledge his Sabbatical fellowship to University of Sydney and Mexico's Ministry of Science, Humanities, Technology and Innovation (SECIHTI) and his Research Grant SECIHTI-CF-2023-I-704. ORCID iDsKatazhyna Redzikultsava  0000-0001-8554-5648 Roberto Sanginés  0000-0003-2695-0955 Seyedeh KH Alavi  0000-0002-4721-3092 Jerry Zhao  0009-0003-3403-2406 Marcela M Bilek  0000-0003-3363-2664 Data availability statementThe data that support the findings of this study are available upon reasonable request from the authors.Animation Conflict of interestThe authors declare no financial or commercial conflict of interest. , Zille, AOliveira, FSouto, A PPlasma treatment in textile industry Plasma Process, 12, (2015). 10.1002/ppap.201400052 , White paper on the future of plasma science in environment, for gas conversion and agriculture Plasma Process. Polym, 16, 1700238 (2019). 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