# The formation of O and H radicals in a pulsed discharge in atmospheric pressure helium with water vapour admixtures

Alexandra Brisset, Matthew Bieniek, Laurent Invernizzi, Mohammad Hasan, James Walsh, Kari Niemi, Erik Wagenaars

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## To cite this version:

Alexandra Brisset, Matthew Bieniek, Laurent Invernizzi, Mohammad Hasan, James Walsh, et al. The formation of O and H radicals in a pulsed discharge in atmospheric pressure helium with water vapour admixtures. Plasma Sources Science and Technology, 2023, 32, 10.1088/1361-6595/acd57f hal-04917235

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Submitted on 28 Jan 2025

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# The formation of O and H radicals in a pulsed discharge in atmospheric pressure helium with water vapour admixtures

To cite this article: Alexandra Brisset et al 2023 *Plasma Sources Sci. Technol.* **32** 065004

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# The formation of O and H radicals in a pulsed discharge in atmospheric pressure helium with water vapour admixtures

Alexandra Brisset<fnref n="1" />, Matthew Bieniek<fnref n="2" />, Laurent Invernizzi<fnref n="1" />, Mohammad Hasan<fnref n="2" />, James Walsh<fnref n="2" />, Kari Niemi<fnref n="1" /> and Erik Wagenaars<fnref n="1" />,*

E-mail: erik.wagenaars@york.ac.uk

Received 6 October 2022, revised 19 April 2023

Accepted for publication 15 May 2023

Published 6 June 2023

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CrossMark

## Abstract

The spatio-temporal distribution of O and H radicals in a 90 ns pulsed discharge, generated in a pin-pin geometry with a 2.2 mm gap, in He + H₂O (0.1% and 0.25%), is studied both experimentally and by 1D fluid modelling. The density of O and H radicals as well as the effective lifetimes of their excited states are measured using picosecond resolution two-photon absorption laser induced fluorescence. Good agreement between experiments and modelling is obtained for the species densities. The density of O and H is found to be homogenous along the discharge axis. Even though the high voltage pulse is 90 ns long, the density of O peaks only about 1 µs after the end of the current pulse, reaching 2 × 10¹⁶ cm⁻³ at 0.1% H₂O. It then remains nearly constant over 10 µs before decaying. Modelling indicates that the electron temperature (T_e) in the centre of the vessel geometry ranges from 6 to 4 eV during the peak of discharge current, and after 90 ns, drops below 0.5 eV in about 50 ns. Consequently, during the discharge (<100 ns), O is predominantly produced by direct dissociation of O₂ by electron impact, and in the early afterglow (from 100 ns to 1 µs) O is produced by dissociative recombination of O₂⁺. The main loss mechanism of O is initially electron impact ionisation and once T_e has dropped, it becomes mainly Penning ionisation with He₂⁺ and He⁺ as well as three-body recombination with O⁺ and He. On time scales of 100–200 µs, O is mainly lost by radial diffusion. The production of H shows a similar behaviour, reaching 0.45 × 10¹⁶ cm⁻³ at 1 µs, due to direct dissociation of H₂O by electron impact (<100 ns) followed by electron–ion recombination processes (from 200 ns to 1.5 us). H is dominantly lost through Penning ionisation with He⁺ and He₂⁺ and by electron impact ionisation, and by charge exchange with O⁺. Increasing concentrations of water vapour, from 0.1% to 0.25%, have little effect on the nature of the processes of H formation but trigger a stronger initial production of O, which is not currently reproduced satisfactorily by the modelling. What emerges from this study is that the

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Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹York Plasma Institute, Department of Physics, University of York, York YO10 5DD, United Kingdom</footnote>

<footnote n="2">²Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, Merseyside, United Kingdom</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
built up of O and H densities in pulsed discharges continues after electron-impact dissociation processes with additional afterglow processes, not least through the dissociative recombination of $O_2^+$ and $H_2^+$.

Keywords: two-photon absorption laser induced fluorescence, nanosecond discharge, radical density/distribution, 1D fluid modelling

(Some figures may appear in colour only in the online journal)

# 1. Introduction

Pulsed non-thermal atmospheric pressure plasmas (NT-APPs) combine valuable features for industrial applications in fields as varied as surface processing, assisted combustion, or plasma medicine [1–5]. They have proven that they could be very stable even at atmospheric pressure and can even cover large diffuse volumes of activated gas when a very strong over-voltage is applied (voltage above breakdown voltage) [6–10]. More commonly, pulsed discharges can greatly improve the energy efficiency of the production of reactive species compared to the use of continuous or AC discharges [11]. The plasma chemistry and the pathways of production of the key reactive species can vary critically depending on the plasma parameters. Detailed knowledge of the plasma chemistry is usually required to control and optimise the use of plasma sources for applications. O and H are highly reactive and are key precursors of long-living species such as $NO_x$, $O_3$ and $H_2O_2$. Their quantification is therefore necessary to unravel the chemical pathways in pulsed APPs.

Pulsed APPs can be run both in noble gases (He, Ar, Xe, ... with or without admixtures or molecular gases) and in molecular gases (air, air and combustible admixtures (methane/ethane, ...), $CO_2$, ...) [12–16]. For biomedical purposes, discharges generated in Helium and Argon can be easily maintained at room temperature (in particular He) and ignited at lower voltages than for other feed gases. With an addition of up to a few percent of molecular species in the feed gas or by mixing with ambient air, NT-APPs produce significant concentrations of reactive oxygen and nitrogen species (RONS). Numerous studies were undertaken to unravel the very complex chemistry of APPs in He with molecular species admixing and ambient air mixing [17–26]. To efficiently produce oxygen containing species (e.g. O, $O(^1D)$, $O(^1S)$, $O_2(v)$, $O_2(a)$, $O_2(b)$, $O_3$, ...), molecular oxygen or air is often added to the feed gas. Other works focused on admixing water vapour which is quasi ubiquitous in plasma medicine and leads to the production of some of the most reactive species (OH, $H_2O_2$, $HO_2$, ...). Despite the additional complexity of the chemistry, numerical studies gave a hint of the evolution of major reactive species in mixtures of He + $O_2$ + $H_2O$ [13, 17, 27]. In [28], the ground state O density experimentally measured in the channel of a RF COST-like jet run in He + $H_2O$ was two orders of magnitude lower than that measured in a related configuration in He + $O_2$ [19] or in a cylindrical RF plasma jet in He + $O_2$ in [29]. This is because the production of O from $O_2$ is more efficient than from $H_2O$ in these discharges. In regard with this difference in production efficiency, the work of [28]

also highlighted that the common presence of impurities such as $O_2$ [20, 28], can play a significant or even dominant role in the production of O compared to the molecular species intentionally introduced like $H_2O$, when the later are introduced in low concentrations. In the effluent of APPJs, various processes can take place that consume or generate RONS downstream and even in the far effluent. In [30, 31], VUV radiation was detected far in the effluent region of two He + $O_2$ APPJs in a helium controlled atmosphere and is believed to maintain a relatively high O density in the far effluent (~1014 cm⁻³). In the channel, O is mainly produced by electron impact reactions and lost by heavy species particle recombination [31]. When water vapour is introduced, H-based reactive species are also produced. OH kinetics in He + $H_2O$ pin-pin pulsed discharges was studied by Verreycken et al in both a low electron density mode, as in this work, and a high density mode, for which the strong ionisation leads to important charge exchange and dissociative recombination processes in the highly ionised plasma core [32]. In He + $H_2O$, the role of secondary species such as $HO_2$ has also been studied in capacitively coupled discharges and plasma jets [19, 33]. In particular, $HO_2$ plays a role in the acidification of plasma treated liquids due to the low dissolution reaction of $HO_2$ in water ($HO_2 \rightarrow H^+ + O_2^-$). Its production is fostered by the presence of $O_2$ through: He + H + $O_2$ → He + $HO_2$. With increasing water vapour concentration, the impact on the production of reactive species is manifold since it also affects the electron properties and discharge development with competing effects. In the pin-pin negative pulse discharge studied in [34], it was observed that the discharge propagation is slower than in dry conditions probably due to a lower initial electron density left by the previous pulse, but the channel conductivity becomes higher at the instant of breakdown due to higher ionisation rates of water than He, leading to a faster return wave in the presence of water vapour and consequently leading to a faster current rise. The effect on electron properties also significantly affects reaction rates. In RF He + $H_2O$ discharges at atmospheric pressure, the electron density lowers with increasing water concentration, while the mean electron temperature increases, leading to complex behaviours of reactions by electronic impact with increasing water concentration (e.g. OH production by electron impact dissociation of water [18]). Consequently, the rise of the species density with increasing water vapour can be nonlinear. In [34], the electron density was shown to drop by a factor about 2 with the introduction of 0.25% $H_2O$ to a He feed gas and the electron recombination was much faster due to dissociative recombination with ions and water clusters ($O_2^+$, $H_2O_3^+$, etc). In [35], a nanosecond pulsed diffuse discharge
is generated over liquid water in He with or without O₂. nₑ and Tₑ were measured by incoherent Thomson scattering. The maximum electron density reached ~5 × 10¹⁴ cm⁻³ during the pulse. The electron temperature measured soon after at the beginning of the pulse was about 4 eV and dropped quickly with voltage down to less than 0.5 eV at the end of the pulse. In general, in streamer discharges, the mean electron temperature in the streamer head is about 4–10 eV [32, 36, 37], while the electron temperature during the conduction phase is down to 1–2 eV at most. At such electron densities and temperatures, in He + H₂O, it is expected that electron impact reactions dominate the production of ROS during the discharge and that recombination processes dominate in the early and late afterglow as will be demonstrated in this paper through comparison of experimental and numerical simulation.

The general objectives of this work are to study the kinetics of reactive species, in particular O and H, in a fast pulsed discharge (rise rate ~80 V ns⁻¹) generated at atmospheric pressure in an enclosed chamber wherein pure or humid Helium (up to 0.25% H₂O) is present. Densities of O and H are obtained experimentally by picosecond resolution two-photon absorption laser induced fluorescence (ps-TALIF) and are combined with 1D fluid modelling to investigate the reaction mechanisms for O and H production.

The measurement of the spatio-temporal evolution of atomic species in non-homogenous atmospheric plasmas requires spectroscopic or laser methods. TALIF is based on the measurement of the fluorescence emitted by a laser pulse excited state of the probed atomic species. The density of the atomic species in its ground state is related to the fluorescence signal through a system of rate equations that depend on the population/depopulation mechanisms of these states. This system of equations is valid under certain excitation conditions that will be discussed in this paper. Under these conditions, TALIF requires the precise knowledge of the fluorescence decay times but at atmospheric pressure, quenching is strong and these decay times are of the order of a few nanoseconds or less, while the quenching partners are largely unknown. Thus, quenching cannot be accurately calculated and the use of fs or ps laser pulses and detection systems are necessary to determine the decay time accurately. In this work, TALIF is performed in the unsaturated regime with a ps pulse to resolve the fluorescence decay times. Oxygen calibration is performed with a xenon source and hydrogen with a krypton source. This method has already been described in a number of sources [29, 38–44].

One-dimensional plasma fluid modelling was performed to better understand the reaction kinetics of O and H as measured in the experiments. The model and chemistry set used are described and discussed in section 3 and in the appendix respectively.

## 2. Experimental setup and method

### 2.1. The discharge system

The discharge is generated in a 2.2 mm gap pin-to-pin electrode geometry enclosed in a 0.3 l vessel. The electrodes are

both made of stainless steel, they are symmetric of conical shape with a tip which radius of curvature is around 500 µm. A positive high-voltage nanosecond pulse is applied to one of the pins by means of a high voltage DC supply coupled to a home-made switch box delivering a pulse of about 2 kV voltage, 35 ns rise time (10%–90%) and 90 ns duration FWHM at 0.1% H₂O (80 ns at 0.25% H₂O), see figure 1. The energy dissipated in the discharge is kept constant at 90 µJ by adjusting the voltage amplitude. The discharge is run at 5 kHz. The voltage is measured using a high bandwidth probe (Tektronix P5100A 500 MHz) and the current with a Rogowski coil probe—CM-100-L, 1.0 V A⁻¹ (Ion Physics). The applied voltage and the discharge current are recorded with a 1 GHz–10 Gs s⁻¹ digital oscilloscope (LeCroy wavesurfer 10). The discharge is generated in helium (99.996% purity) with a total controlled flow rate of 1 l min⁻¹, injected in the vessel sideways to the axis of the electrodes (about 3 cm from the discharge axis). Water vapour is admixed to the gas flow by guiding a fraction of the total helium flow through a glass bubbler filled with distilled water as in [18]. The amount of water vapour is calculated using the vapour pressure at room temperature and the flow rate through the bubbler. Most of the lines are made of stainless steel to limit the level of impurities in the gas. The output gas of the reactor is guided to an exhaust several metres downstream.

<figure><img src="image_9.png" /><figcaption>**Figure 1.** Typical voltage and current signals in He + 0.1% and 0.25% H₂O for a gap of 2.2 mm.</figcaption></figure>

### 2.2. The laser and fluorescence detection setup

The laser and detection setup are illustrated in figure 2. An Nd:YAG pumped picosecond laser at 1064 nm is coupled first to an amplifier (APL2100, Ekspla) and second to a system (PG411, Ekspla) made of (i) a parametric generator (OPO + OPA), (ii) a second harmonic generator (FSH/SSH) and (iii) a deep UV extension system. It enables to generate a 30 ps-laser pulse of up to a few hundreds of µJ that can be tuned in the range 193–2300 nm with a spectral bandwidth of about 4 cm⁻¹, at 10 Hz.
<figure><img src="image_10.png" /><figcaption>Figure 2. Laser and fluorescence detection setup adapted from [28]. Reproduced from [28]. © The Author(s). Published by IOP Publishing Ltd CC BY 4.0.</figcaption></figure>

The laser pulse energy is controlled over time with a pair of rotating attenuators coupled to an energy meter. At every laser shot, the energy is monitored and compared to the target energy value and the pair of attenuators is rotated accordingly by a stepper motor to increase or lower the laser beam energy of the next shot. A pair of attenuators is used to compensate for the laser beam deviation across each attenuator and keep a straight laser beam line. The attenuators are coated CaF₂ substrates (Layertec®). The standard deviation of the shot-to-shot fluctuations in the pulse energy is about 6%.

The laser beam is focused with a 30 cm focal length lens into the discharge gap plane, the focus point being a few centimetres after the discharge axis to get a laser beam diameter of 300 µm at the point of TALIF measurement, between the electrodes. The laser beam diameter is measured by sliding a razor blade across the laser beam while its energy is recorded. This beam diameter was chosen to get sufficient TALIF signal and spatial resolution while avoiding saturation of the two-photon transition or laser-plasma interactions (photo-ionisation and photo-dissociation, here) and to avoid any damage of the reactor windows and cuvette walls. The laser beam is then stopped by a beam dump.

The fluorescence emission of the laser pulse excited state is collected at 90° by a doublet of achromatic lenses (diameter 50 mm each, effective focal length 80 mm) and recorded with a 4Picos ICCD camera from Stanford Computer Optics (780 × 580 array, 8.3 µm² pixels, S25IR photocathode) equipped with an interference filter placed in front of the camera (central wavelengths λO = 844.5 ± 0.5 nm, λH = 656 nm ± 5 nm, λXe = 835 ± 5 nm, λKr = 825 ± 5 nm) to eliminate stray light and fluorescence at other wavelengths. To increase the signal to noise ratio, the fluorescence signal of 30–300 shots has been accumulated on the ICCD. The camera is triggered by a TTL output signal from the laser which has only 5 ps jitter with the laser pulse, and the internal camera jitter between the gate opening and the reception of the trigger signal is only 10 ps, allowing the measurement of sub-nanosecond fluorescence lifetimes (see table 1).

The TALIF technique is performed in the non-saturated regime using the noble-gas calibration technique [38–44].

In this regime, the density $n_x$ of the ground state species x is related to the density of the gas used for calibration $n_{cal}$ through:

$$ \frac{S_{F,x}}{S_{F,cal}} = \frac{\eta(\lambda_{F,x}) T_f(\lambda_{F,x}) T_w(\lambda_{F,x})}{\eta(\lambda_{F,cal}) T_f(\lambda_{F,cal}) T_c(\lambda_{F,cal})} \frac{a_{ik,x}}{a_{ik,cal}} \frac{\sigma_x^{(2)}}{\sigma_{cal}^{(2)}} \frac{n_x}{n_{cal}} \times \left( \frac{E_{L,x}}{E_{L,cal}} \frac{\lambda_{L,x}}{\lambda_{L,cal}} \right)^2 $$

where $S_F$ is the measured fluorescence signal that has been integrated spatially, temporally and spectrally, $\eta(\lambda_F)$ is the camera quantum efficiency at the fluorescence wavelength $\lambda_F$, $T_{f/w/c}$ are the transmission coefficients of the filter/reactor window/cuvette wall, $a_{ik}$ are the branching ratios of the transitions ($a_{ik} = \sum_k A_{ik} + \sum_q k'_q n_q$), where $A_{ik}$ is the Einstein coefficient of the transition from state i to k, $k'_q n_q$ is the quenching rate between state i and q), $\sigma^{(2)}$ are the cross sections for two-photon absorption, E is the laser energy at the position of TALIF measurement and $\lambda_{LiS}$ the laser wavelength.

The atomic species probed are oxygen and hydrogen and the associated calibration gases used for TALIF analysis are respectively xenon and krypton. The TALIF schemes for these species are as illustrated in figure 3 of [28]. The ground state of atomic oxygen O(2p⁴³P_J), as well as the excited states O(3p³P_J), are triplet states with $J = 0,1,2$. The laser wavelength for two-photon absorption of this transition from $J = 2$ is 225.6 nm. Relaxation of the triplet upper state happens through quenching and radiative emission at 844.6 nm. To get the total density of the ground triplet state of O, it is necessary to correct the density of the level $J = 2$ measured ($n_2$) with the Boltzmann factor: $n_O = \frac{n_2}{g_2} \sum_{J=0,1,2} g_J e^{-E_J/(k_B T_B)}$, where the spectral parameters can be found on the NIST database. The gas temperature was estimated from [34]. With a linearly polarised laser at 205.1 nm, the ground state of atomic hydrogen H(1s²S₁/₂) can be excited to the two sub-levels H(3s²S₁/₂)
<table><caption>**Table 1.** Parameters for TALIF analysis.</caption><thead><tr><th></th><th>Pressure</th><th>λ<sub>L</sub> (nm)</th><th>λ<sub>F</sub> (nm)</th><th>ratio of σ<sup>(2)</sup></th><th>A<sub>ik</sub> (s<sup>-1</sup>)</th><th>τ<sub>ik</sub> (ns)</th><th>E<sub>L</sub> (μJ)</th></tr></thead><tbody><tr><td><b>O</b></td><td>1 atm</td><td>225.6</td><td>844.6</td><td rowspan="2">σ<sub>Xe</sub><sup>(2)</sup> / Σ<sub>j'</sub> σ<sub>O<sub>0</sub>,j→j'</sub><sup>(2)</sup> = 1.02 ± 0.2</td><td>2.88 × 10<sup>7</sup></td><td>9 ± 0.5</td><td>19.6</td></tr><tr><td><b>Xe</b></td><td>200 Pa</td><td>224.3</td><td>834.9</td><td>3.08 × 10<sup>7</sup></td><td>13</td><td>0.64</td></tr><tr><td><b>H</b></td><td>1 atm</td><td>205.1</td><td>656.3</td><td rowspan="2">σ<sub>Kr</sub><sup>(2)</sup> / σ<sub>H</sub><sup>(2)</sup> = 0.62 ± 0.31</td><td>4.41 × 10<sup>7</sup></td><td>1.7 ± 0.1</td><td>7.9</td></tr><tr><td><b>Kr</b></td><td>200 Pa</td><td>204.1</td><td>826.3</td><td>2.79 × 10<sup>7</sup></td><td>14</td><td>0.55</td></tr></tbody></table>

Reference for $\sigma_{Xe}^{(2)}$ [1]:—reference for $\sigma_{O}^{(2)}$ [2]:—reference for $A_{ik}$ [3]. The uncertainty of the measured fluorescence lifetime of O and H is given by the standard deviation of repeated measurements.

and H(3d $^2$D$_{3/2,5/2}$) of 0.15 cm$^{-1}$ spectral separation, much lower than the laser spectral width. Relaxation of these three upper states happens mostly through quenching and radiative emission at 656.3 nm with a natural lifetime of the weighted combination of the 3s and 3d sublevels of 17.6 ns [45]. Selection rules prevent the sub-level 3p $^2$P$_{1/2,3/2}$ to be excited by the laser. However, L-mixing, i.e. the redistribution of the population in the three mentioned higher excited levels of atomic hydrogen, can lead to a loss of fluorescence signal. However, since the work of Preppernau et al [46], the significance of that process was not established clearly and the experimental measurement of the lifetime of H ($n = 3$) is used for calibration. The TALIF schemes considered for the rare gases are simpler. The ground state of Xenon Xe(5p$^6$ $^1$S$_0$) is excited to the single upper state Xe(6p' [3/2]$_2$). It relaxes through quenching and radiative emission to several lower states, in particular Xe(6s' [1/2]$_1$) at 834.91 nm, with an optical branching ratio of 0.733 [47]. The ground state of Krypton (Kr(4p$^6$ $^1$S$_0$) is excited to the single upper state Kr(5p' [3/2]$_2$), that radiates to the lower state Kr(5s' [1/2]$_1$) at 826.32 nm with an optical branching ratio of 0.953 [48].

The parameters used for the TALIF measurement of oxygen, hydrogen, xenon and krypton densities are given in table 1. In particular, it should be noted that the value of the two-photon cross section of Xenon used in this work is the recently measured value given in [49].

### 3. Modelling and numerics

A one-dimensional plasma fluid model was employed in this work, which is based on a system of differential equations, comprised of the equations of continuity of the flux density of electrons, electron energy, ions, and neutral species, and Poisson's equation (as in e.g. [50–52]):

$$ \frac{\partial n_e}{\partial t} + \nabla \cdot \mathbf{J}_e = S_e - \frac{\Gamma_e}{R}, \quad \mathbf{J}_e = -D_e \nabla n_e + n_e \mu_e \nabla \varphi; \quad (1) $$

$$ \frac{\partial n_{\varepsilon}}{\partial t} + \nabla \cdot \mathbf{J}_{\varepsilon} = e \mathbf{J}_{\varepsilon} \cdot \nabla \varphi - S_{\varepsilon}, \quad \mathbf{J}_{\varepsilon} = -D_{\varepsilon} \nabla n_{\varepsilon} + n_{\varepsilon} \mu_{\varepsilon} \nabla \varphi; \quad (2) $$

$$ \frac{\partial n_{\text{ip}}}{\partial t} + \nabla \cdot \mathbf{J}_{\text{ip}} = S_{\text{ip}} - \frac{\Gamma_{\text{ip}}}{R}, \quad \mathbf{J}_{\text{ip}} = -D_{\text{ip}} \nabla n_{\text{ip}} - n_{\text{ip}} \mu_{\text{ip}} \nabla \varphi; \quad (3) $$

$$ \frac{\partial n_{\text{in}}}{\partial t} + \nabla \cdot \mathbf{J}_{\text{in}} = S_{\text{in}} - \frac{\Gamma_{\text{in}}}{R}, \quad \mathbf{J}_{\text{in}} = -D_{\text{in}} \nabla n_{\text{in}} + n_{\text{in}} \mu_{\text{in}} \nabla \varphi; \quad (4) $$

$$ \frac{\partial n_n}{\partial t} + \nabla \cdot \mathbf{J}_n = S_n - n_n (D_n / \Lambda^2) + \frac{\chi_i Q_T}{M_j}, \quad \mathbf{J}_n = -D_n \nabla n_n; \quad (5) $$

$$ \varepsilon_0 \nabla^2 \varphi = -e(n_{\text{ip}} - n_{\text{in}} - n_e), \quad (6) $$

where $n$, $J$, $D$, $\mu$, $S$ are the number densities, transport fluxes, diffusion coefficients, mobility coefficients, and reaction source terms, respectively. The subscripts $e$, $\varepsilon$, $ip$, $in$, $n$ refer to electrons, electron energy density, positive ions, negative ions, and neutrally charged species, respectively. The electron energy density is defined as $n_{\varepsilon} = n_e \bar{\varepsilon}$ where $\bar{\varepsilon}$ is the average electron energy. $\varphi$ is the electrostatic potential; $\varepsilon_0$ is permittivity of free space; and $e$ is elementary charge. Neutral species are assumed to radially diffuse away from the discharge into the remaining vessel through a loss term $n_n(D_n/\Lambda^2)$, where $\Lambda$ is the characteristic diffusion length, with $(1/\Lambda)^2 = (2.4/R)^2 + (\pi/L)^2$, and $R$ is the discharge radius, consistent with optical emission spectroscopy as 0.25 mm, and $L$ is the inter-electrode gap length [53]. An ambipolar diffusion of charged species into the remaining vessel is assumed. The radial ambipolar flux of positive species, $-D_{\text{ip}}n_{\text{ip}}/R - n_{\text{ip}}\mu_{\text{ip}}E_r$, is set equal to the radial flux of negative species, $-D_{\text{ni,e}}n_{\text{ni,e}}/R + n_{\text{ni,e}}\mu_{\text{ni,e}}E_r$, along the discharge axis, with the ambipolar field, $E_r$, solved for in the course of the simulations. The loss term was added to the charged species continuity equations of $\Gamma/R$ where $\Gamma$ corresponds to a species ambipolar flux. The total mass flow rate of species radially diffusing away from the discharge is matched by a mass flow rate of species from the remaining vessel diffusing into the discharge. The species diffusing into the discharge are assumed to have the mass fraction corresponding to the initial conditions. The production term $\chi_j Q_T/M_j$ was added to the continuity equation of vessel species $j$ (O$_2$, H$_2$, H$_2$O, and He). Where $M_j$ is the mass of vessel species $j$, $Q_T$ is the total mass flow of all species diffusing away from the discharge, $\sum(D_n/\Lambda^2)n_nM_n + \sum(\Gamma/R)n_{\text{ni, np,e}}M_{\text{ni, np,e}}$, and $\chi_j$ being the fraction of the total mass flow rate into the discharge of species $j$, $(D_j/\Lambda^2)n_{ji}M_k/\sum(D_j/\Lambda^2)n_{ji}M_k$, where $n_{ji}$ corresponds with the initial densities of background species $j$.

The local mean energy approximation is used, where the macroscopic electron swarm characteristics vary only with the local average electron energy. Electron transport and reaction coefficients are determined by the solution of the local steady state two-term Boltzmann equation, parameterised over a range of average electron energies [54]. The validity of the
local mean energy approximation becomes imprecise at certain times in the discharge evolution. It was found in the modelling that for a short period of time, while the discharge channel spans from the cathode to the anode, and the applied voltage is still high, the sheath electrons become hot (up to 160 eV), and so would ‘run away’ [54]. Further, the fast time scales of the discharge lead to a greater significance of transient features in the EEDF. As a result of employing the steady state approximation when deriving the electron Boltzmann equation, these transient features of the EEDF were not modelled. It was shown that the rapidly varying electric fields in pulsed discharges, without space charge being considered, can lead to transient EEDF structures that, for example, alter the density of O by around 15% in comparable discharges [55]. Other time-dependent EEDF effects in atmospheric pressure pulsed discharges, for example, occurring as a result of electron-electron collisions, to the authors knowledge, remain uninvestigated in these conditions. The simulations performed here reveal excitation degrees for electronically excited species greater than $1 \times 10^{-4}$ during the pulse, which is sufficient to alter the EEDF by super-elastic collisions [54]. Finally, the Maxwellianisation of the electron energy distribution function by electron-electron collisions could have a quantitative effect on radical species densities produced during the pulse [53]. Solving the model self-consistently with a more general approach to the electron kinetics would improve the accuracy of the modelling in such discharges. Other considerations relevant to electron kinetics could include gas hydrodynamic effects, as well as a more detailed description of the electron emission from cathode, and the role of gas phase vibrational energy. However, we believe the basic plasma model employed in this work does qualitatively capture the dominant channels of production and losses of O and H.

The reaction kinetic scheme is presented in the appendix with the electron collision cross sections used to determine the transport and reaction coefficients for the electrons. Transport coefficients for ions and electrically neutral heavy species were obtained from [53, 56].

The computation domain used corresponds to the interelectrode dimension, with a length of 2.2 mm. Boundary conditions at the anode describe the absorption of a thermal flux of plasma species and the electron energy density, and a condition describing applied voltage pulses. The boundary conditions used for the plasma species (equations (7)–(9) and (11)–(13) were derived in [57], or can be derived from the same article assuming $D_e = 5/3 D_{en}$ [54]:

$$J_e = n \left(\frac{1}{2}\right) \sqrt{\frac{8k_B T_e}{\pi m_e}} n_e; \qquad (7)$$

$$J_e = n \left(\frac{5}{6}\right) \sqrt{\frac{8k_B T_e}{\pi m_e}} n_e; \qquad (8)$$

$$J_{ip,in,n} = n S_{ip,in,n} \frac{1}{4} \sqrt{\frac{8k_B T_g}{\pi m_{ip,in,n}}} n_{ip,in,n}; \qquad (9)$$

$$\varphi = 0.5 V_0 (\tanh(\nu_{\text{rise}}(t - P_{\text{start}})) - \tanh(\nu_{\text{fall}}(t - P_{\text{end}}))), \qquad (10)$$

where *m* is the species mass, *n* is the unit vector facing outwards of the vessel, $k_B$ is the Boltzmann constant, *S* is the sticking coefficient (with values from [13]). $T_e$ is the electron temperature defined as $2/3\bar{\epsilon}$, and $T_g$ is the gas temperature, set to 300 K. The voltage pulse waveform shape parameters ($V_0$, $\nu_{\text{rise}}$, $\nu_{\text{fall}}$, $P_{\text{start}}$, $P_{\text{end}}$) were chosen to fit the experimentally measured pulses, where $V_0$ is the voltage pulse amplitude, $\nu_{\text{rise}}$ is the pulse rise time rate, $\nu_f$ is the pulse fall time rate, $P_{\text{start}}$ is the pulse start time, and $P_{\text{end}}$ is the pulse end time.

The boundary conditions at the grounded electrode describes the absorption of a thermal flux of plasma species and electron energy density, secondary electron emission, and zero electrostatic potential:

$$J_e = n \left(\frac{1}{2}\right) \sqrt{\frac{8k_B T_e}{\pi m_e}} n_e - \gamma J_{ip}; \qquad (11)$$

$$J_e = n \left(\frac{5}{6}\right) \sqrt{\frac{8k_B T_e}{\pi m_e}} n_e - \gamma (I - 2W) J_{ip}; \qquad (12)$$

$$J_{ip,in,n} = n S_{ip,in,n} \frac{1}{4} \sqrt{\frac{8k_B T_g}{\pi m_{ip,in,n}}} n_{ip,in,n}; \qquad (13)$$

$$\varphi = 0, \qquad (14)$$

where the secondary emission coefficient, $\gamma$, is assumed to characterize all mechanisms of electron emission (due to ion, photon, and excited species bombardment), and was set to 0.25 (by matching modelling and experiment); *I* corresponds to the energy required for ionisation of a given ion, and *W* is the work function of the cathode material, set to 4.1 eV [58].

Modelling revealed the build-up of $O_2$ and $H_2$ over successive pulses until a quasi-steady state was reached. The steady state values of the presented results of $O_2$ and $H_2$ were found by changing the initial conditions of $O_2$ and $H_2$ such that the initial and final values of $O_2$ and $H_2$, measured in the centre of the discharge, were within 0.5% of each other after a voltage pulse. The initial conditions were 170 ppm of $O_2$, and 70 ppm of $H_2$, for 0.1% $H_2O$, and 190 ppm of $O_2$, and 75 ppm of $H_2$ for 0.25% $H_2O$. The remaining mole fraction was made up by Helium, with trace amounts of the other species. Ten pulses were modelled with the final pulse used in the results presented. The final pulse voltage pulse width was slightly altered in the last pulses (not by more than 3 ns), to achieve a pulse energy of 90 $\mu$J, to match the pulse energy from the experiment.

The plasma model was implemented using the commercial finite element analysis software COMSOL Multiphysics.

## 4. Spatial and temporal evolution of the density of O and H

The temporal evolution of the density of the ground states of O and H obtained by ps-TALIF and by 1D fluid modelling at mid-gap in He + 0.1% and 0.25% $H_2O$ are presented in figure 3. They demonstrate a reasonable agreement between experiment and modelling, within around a factor of 3 for O and H densities.
<figure><img src="image_11.png" /><figcaption>Figure 3. Experimental and numerical results of the temporal evolution of the density of O (left) and H (right) at mid-gap (U = 2 kV, P = 1 atm, gap = 2.2 mm). Experimental error is based on standard deviation determination only. The other major uncertainties come from the uncertainty of the TALIF cross sections of O and H which are 20% and 50% respectively and of the fluorescence lifetimes determination and the total experimental error is estimated to be 60% and 64% respectively.</figcaption></figure>

### 4.1. $He + 0.1\% H_2O$

Atomic oxygen is mainly produced during the early post discharge. In the experiments, the density builds up over the first 1–2 µs, then remains nearly constant at about $2 \times 10^{16}$ cm$^{-3}$ over 10 µs before decreasing on a time scale of 100 µs. The density of H shows a strong production during the discharge followed by a moderate decrease over 200 ns and then, similarly to O, remains constant at about $0.45 \times 10^{16}$ cm$^{-3}$, over 10 µs, before decreasing on a time scale of 100 µs. While the density evolution of H in the post discharge is well reproduced by modelling, the fast rise and fall of H during the discharge phase, between 0.1 and 0.4 µs, is underestimated by the model. The authors speculate the rotational and vibrational energy of $H_2O$, which is not captured by the model, may lead to an increased rate of dissociation of $H_2O$ by electron impact, leading to the faster rise of the H density than is currently predicted in the model.

At increased water vapour concentration, the production of O is enhanced during the pulse, which is reproduced to a lesser extent by modelling. The production processes governing the evolution of H density seem similar at increased water content, only the absolute density of H increases by nearly 40% from 0.1% to 0.25% $H_2O$.

The production and loss reaction rates of O and H in $He + 0.1\% H_2O$ according to the modelling are given in figure 4. They show that the four most significant kinetic processes happen during the discharge and in the early post discharge (<1 µs). Since the relative importance of these processes is quite similar at 0.25% $H_2O$ according to the model, only processes at 0.1% $H_2O$ are shown here. The temporal evolution of the electron temperature obtained by modelling is given in figure 5.

According to the simulation, at 0.1% $H_2O$, atomic oxygen is dominantly formed through two different processes. As the electron temperature remains high (4–6 eV) during the pulse

(up to ~100 ns), electron impact dissociation of $O_2$ dominates, with molecular oxygen being produced during the previous discharges (density of $O_2$ at the beginning of the pulse is around $4 \times 10^{21}$ m$^{-3}$). As the electron temperature drops down below 0.5 eV, O is then formed through a two-step process: formation of $O_2^+$ (during the discharge, mainly by charge transfer of $He_2^+$ and $H^+$ with $O_2$), followed by electron-ion dissociative recombination with $O_2^+$. This process lasts until $O_2^+$ is totally consumed and is responsible for most of the production of O. It was already pointed out in Bruggeman and Schram [59] that dissociative recombination was an important process for the production of radicals (in that case OH) in atmospheric pressure glow discharges where the electron temperature ranges in 1–2 eV at low gas temperature. The same applies here for O and H (see below for H), all the more as the electron temperature decays down below 0.5 eV since the rate for dissociative recombination is proportional to the inverse of the electron temperature.

The main loss mechanisms of O also vary with the electron temperature. As the latter is still high, 4–6 eV, O is ionised by electron impact to form $O^+$. Only few $O^+$ ions will recombine to atomic oxygen, most $O^+$ ions are lost in the formation of $O_2^+$. From 100 to 400 ns, charge transfer with $He^+$ and ionisation by excited Helium states dominate but the density of O still rises due to electron-ion recombination. After 400–600 ns, radial diffusion losses largely dominate and lead to the drop of O density after 1–2 µs when the production of O nearly stops. The situation is rather similar for H. During the discharge, H is mainly produced by electron impact dissociation of $H_2O$ and OH and by electron impact dissociation of $H_2^+$ (density of $H_2$ at the beginning of the pulse is around $1.7 \times 10^{21}$ m$^{-3}$ according to modelling). During the early post-discharge, H production is almost entirely due to electron-ion recombination with $H_2^+$ and $H^+$. Losses are mainly governed by Penning ionisation and charge transfer reactions with $O^+$, then by radial losses.
<figure><img src="image_12.png" /><figcaption>**Figure 4.** Temporal evolution of the four largest production and loss reaction rates for O (top) and H (bottom) in He + 0.1% H₂O, and rate of radial losses for O and H. HeS and He₂S represent the excited states of He and He₂, treated as an effective excited state in the chemistry set.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 5.** Temporal evolution of the mean electron temperature at mid gap obtained by 1D fluid modelling at 0.1% H₂O.</figcaption></figure>

Neutral kinetics involving O and H happen on longer time scales than radial diffusion. The fastest processes are recombination of O and H with OH, to form O₂ + H and H₂ + O

or H₂O, respectively. However, from 1 to 20 µs, the density of OH drops down from 5 × 10²⁰ to 2 × 10¹⁹ m⁻³ and the recombination time scale in these conditions is about
60 µs and 1500 µs, respectively. Therefore, once the ion chemistry is finished, the densities of O and H remain relatively constant until it drops due to radial diffusion. This large time window may therefore provide an opportunity to use O and H radicals to produce long-lived species tailored to specific applications. Increased repetition frequency up to 50 kHz would trigger the next discharge before the decrease of the density of O and H radicals, possibly fostering their production.

Finally, we can note that in the conditions presented here, the impact of impurities seems negligible on the formation of atomic oxygen. The concentration of water vapour is sufficient to form significantly more O₂ than what comes from impurities coming from the bottle and the gas lines. Similarly, effects of impurities on an RF atmospheric discharge in He + H₂O were shown to affect the density of O for water concentrations below 0.1% only [19].

## 4.2. He + 0.25% H₂O

As the water vapour concentration in the feed gas increases, both the discharge properties and the kinetics are affected. Competing effects due to the loss of electrons by attachment processes and increasing electron temperature due to energy losses in inelastic collisions with water molecules, can lead to a complex evolution of the discharge development and reaction rates of electron impact induced reaction. For instance, in He + H₂O RF discharges, changes in the electron properties induce the non-linear rise of OH density with increasing water content [18]. Also, in the negative ns-pulsed discharge studied in [34], humidity affects the discharge ignition due to a competition between a slower discharge propagation at lower initial electron density (left by the previous pulse), leading to a higher channel conductivity at breakdown and a faster return wave and consequently a faster current rise. A similar behaviour may characterise this work (see figure 1).

Figure 3 (left) shows a strong enhancement of the production of O during the discharge phase at 0.25% H₂O. It is reproduced to a lesser extent by modelling. The increased production of O during the discharge is consistent with the dissociation of O₂ by electron impact being the dominant production reaction of O, since the O₂ density produced by the previous pulses increases significantly with H₂O concentration (4.7 × 10²¹ m⁻³ according to modelling). Also, the modelling suggests an increased reaction rate for the dissociation of OH by electron impact relative to the other processes. The earlier rise of the density of O at 0.25% H₂O is only due to the earlier rise of the current as explained above.

The density of H increases by about 50% as the water concentration increases from 0.1% to 0.25%, while the temporal evolution of the density is unchanged. This could be explained by the fact that H is mainly produced by direct interaction of electrons with water molecules and by He* induced reactions with H, the density of He* being

<figure><img src="image_14.png" /><figcaption>**Figure 6.** Evolution of the O density along the discharge axis at 4 µs. Grey zones are impacted by loss of TALIF signal by interaction with the electrodes (solid angle of detection, beam profile truncation) and are not studied in detail here.</figcaption></figure>

weakly affected by the increase of humidity according to the modelling work of Murakami et al [60] in helium-oxygen plasmas with humid-air impurities at atmospheric pressure.

The build-up of O₂ over successive pulses occurs more quickly with increased H₂O water vapour. The reported modelling finds a factor of 1.2 increase in the average O₂ density at the start of the final pulse, with 0.25% H₂O as opposed to 0.1% H₂O. Given that direct electron impact of O₂ is the main source of O, the build-up O₂ is an important aspect when considering the controllability of O production.

The results and the analysis of the kinetics of O and H done at mid gap are valid along the discharge axis. Indeed, the experimental determination of the density of O along the axis of the discharge at 4.0 µs (done at 0.1% H₂O) is illustrated in figure 6. It demonstrates that the production of O is quasi homogenous within experimental error along the gap.

It should be noted that water clusters are not yet considered in the current model while they could allow for additional pathways to O and H production in the afterglow, similar in nature to the ones identified in this work [28]. This effort will be the topic of a future publication.

## 5. Conclusion

The spatio-temporal distribution of O and H radicals in a He + H₂O (0.1%-0.25%) nanosecond pulsed discharge was studied experimentally by ps-TALIF and by 1D fluid modelling. The model indicates which reaction pathways achieve the O and H production seen in the experiment, particularly in the afterglow. Most O and H radicals are produced in the early
afterglow (up to 1 µs) through recombination processes of O₂⁺ and H₂⁺. The accurate prediction and optimisation of these radical densities in pulsed discharges therefore requires the consideration of both electron-impact dissociation during the plasma pulse and the additional afterglow processes, mainly dissociative recombination.

## Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI: https://pure.york.ac.uk/portal/en/datasets/data-for-psst-paper-2023.

## Acknowledgments

The authors acknowledge the support of the Engineering and Physical Science Research Council (Project Nos. EP/S026584/1 and EP/S025790/1)

## Appendix

The kinetic scheme used in this work was based on [61], which had reactions involving nitrogen removed. The reactions that involved H₂ and H and the non-nitrogen species from [13], were also included.
<table><thead><tr><th>Reaction number</th><th>Reaction formula</th><th>Reaction coefficient</th><th>Energy cost (eV)</th><th>References</th></tr></thead><tbody><tr><td>R1</td><td>e + He → e + He</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>Calc.</td><td>[62]</td></tr><tr><td>R2</td><td>e + He → e + He<sup>*</sup></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>19.80</td><td>[62]</td></tr><tr><td>R3</td><td>e + He<sup>*</sup> → e + He</td><td>1.7633 × 10<sup>-16</sup> ε<sub>avg</sub><sup>0.31</sup></td><td>-19.80</td><td>[63]</td></tr><tr><td>R4</td><td>e + He → 2e + He<sup>+</sup></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>24.58</td><td>[62]</td></tr><tr><td>R5</td><td>e + He<sup>*</sup> → 2e + He<sup>+</sup></td><td>1 × 10<sup>-13</sup> ε<sub>avg</sub><sup>0.6</sup> exp(-7.175/ε<sub>avg</sub>)</td><td>4.78</td><td>[63]</td></tr><tr><td>R6</td><td>e + O<sub>2</sub> → e + O<sub>2</sub></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>Calc.</td><td>[64]</td></tr><tr><td>R7</td><td>e + O<sub>2</sub> → 2e + O<sub>2</sub><sup>+</sup></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>12.06</td><td>[64]</td></tr><tr><td>R8</td><td>e + He<sub>2</sub><sup>*</sup> → 2e + He<sub>2</sub><sup>+</sup></td><td>7.28 × 10<sup>-16</sup> ε<sub>avg</sub><sup>0.71</sup> exp(-5.1/ε<sub>avg</sub>)</td><td>3.4</td><td>[63]</td></tr><tr><td>R9</td><td>e + He<sub>2</sub><sup>+</sup> → He + He<sup>*</sup></td><td>6.1382 × 10<sup>-15</sup> ε<sub>avg</sub><sup>-0.5</sup></td><td></td><td>[63]</td></tr><tr><td>R10</td><td>2e + He<sup>+</sup> → e + He</td><td>7 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4.5</sup></td><td></td><td>[65]</td></tr><tr><td>R11</td><td>2e + He<sub>2</sub><sup>+</sup> → e + 2He</td><td>7 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4.5</sup></td><td></td><td>[65]</td></tr><tr><td>R12</td><td>e + He + He<sub>2</sub><sup>+</sup> → 3He</td><td>2 × 10<sup>-39</sup> T<sub>eg</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R13</td><td>e + He<sup>+</sup> → He</td><td>2 × 10<sup>-18</sup></td><td></td><td>[65]</td></tr><tr><td>R14</td><td>e + He<sub>2</sub><sup>+</sup> → 2He</td><td>1 × 10<sup>-14</sup></td><td></td><td>[65]</td></tr><tr><td>R15</td><td>e + O<sub>2</sub><sup>+</sup> → 2O</td><td>7.762 × 10<sup>-15</sup> ε<sub>avg</sub><sup>-1</sup></td><td>-6.91</td><td>[63]</td></tr><tr><td>R16</td><td>e + He + He<sup>+</sup> → He + He<sup>*</sup></td><td>1 × 10<sup>-39</sup></td><td></td><td>[65]</td></tr><tr><td>R17</td><td>e + He + He<sub>2</sub><sup>+</sup> → 2He + He<sup>*</sup></td><td>5 × 10<sup>-39</sup>/T<sub>eg</sub></td><td></td><td>[65]</td></tr><tr><td>R18</td><td>e + He + He<sub>2</sub><sup>+</sup> → He + He<sub>2</sub><sup>*</sup></td><td>1.5 × 10<sup>-39</sup></td><td></td><td>[65]</td></tr><tr><td>R19</td><td>2e + He<sup>+</sup> → e + He<sup>*</sup></td><td>6 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4</sup></td><td></td><td>[65]</td></tr><tr><td>R20</td><td>2e + He<sub>2</sub><sup>+</sup> → He + He<sup>*</sup> + e</td><td>1 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4</sup></td><td></td><td>[65]</td></tr><tr><td>R21</td><td>2e + He<sub>2</sub><sup>+</sup> → He<sub>2</sub><sup>*</sup> + e</td><td>3 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4</sup></td><td></td><td>[65]</td></tr><tr><td>R22</td><td>e + He<sup>+</sup> → He<sup>*</sup></td><td>6.76 × 10<sup>-19</sup> T<sub>e</sub><sup>-0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R23</td><td>e + He<sub>2</sub><sup>+</sup> → He + He<sup>*</sup></td><td>8.9 × 10<sup>-15</sup> T<sub>eg</sub><sup>-1.5</sup></td><td></td><td>[65]</td></tr><tr><td>R24</td><td>e + H<sub>2</sub>O → e + H<sub>2</sub>O</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>Calc.</td><td>[65]</td></tr><tr><td>R25</td><td>e + O<sub>2</sub> → O<sub>2</sub><sup>-</sup></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td></td><td>[65]</td></tr><tr><td>R26</td><td>e + H<sub>2</sub>O → e + H + OH</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>9</td><td>[65]</td></tr><tr><td>R27</td><td>e + H<sub>2</sub>O → O<sup>+</sup> + H<sub>2</sub> + 2e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>19</td><td>[66]</td></tr><tr><td>R28</td><td>e + H<sub>2</sub>O → OH + H<sup>+</sup> + 2e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>16.9</td><td>[66]</td></tr><tr><td>R29</td><td>e + H<sub>2</sub>O → O + H<sub>2</sub><sup>+</sup> + 2e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>20.7</td><td>[66]</td></tr><tr><td>R30</td><td>e + H<sub>2</sub>O → H + OH<sup>-</sup></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td></td><td>[13]</td></tr><tr><td>R31</td><td>e + H → H<sup>+</sup> + 2e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>13.6</td><td>[66]</td></tr><tr><td>R32</td><td>e + H<sub>2</sub> → H<sub>2</sub><sup>+</sup> + 2e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>15.96</td><td>[66]</td></tr><tr><td>R33</td><td>e + H<sub>2</sub> → 2H + e</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>14.68</td><td>[66]</td></tr><tr><td>R34</td><td>e + H<sub>2</sub><sup>+</sup> → e + H + H<sup>+</sup></td><td>1.89 × 10<sup>-7</sup> T<sub>e</sub><sup>0.5</sup> exp(-2.3/T<sub>e</sub>)</td><td></td><td>[66]</td></tr><tr><td>R35</td><td>e + H<sup>+</sup> → H</td><td>2.62 × 10<sup>-13</sup> T<sub>e</sub><sup>0.5</sup></td><td></td><td>[66]</td></tr><tr><td>R36</td><td>2e + H<sup>+</sup> → e + H</td><td>8.8 × 10<sup>-27</sup> T<sub>e</sub><sup>-4.5</sup></td><td></td><td>[66]</td></tr><tr><td>R37</td><td>e + H<sub>2</sub><sup>+</sup> → 2H</td><td>5.66 × 10<sup>-8</sup> T<sub>e</sub><sup>-0.6</sup></td><td></td><td>[66]</td></tr><tr><td>R38</td><td>e + OH → e + O + H</td><td>2.08 × 10<sup>-13</sup> T<sub>e</sub><sup>-0.76</sup> exp(-6.9/T<sub>e</sub>)</td><td>6.9</td><td>[65]</td></tr><tr><td>R39</td><td>2e + O<sub>2</sub><sup>+</sup> → e + O<sub>2</sub></td><td>7 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4.5</sup></td><td></td><td>[65]</td></tr><tr><td>R40</td><td>e + O<sub>2</sub> + O<sub>2</sub><sup>+</sup> → 2O<sub>2</sub></td><td>2.49 × 10<sup>-41</sup> T<sub>eg</sub><sup>-1.5</sup></td><td></td><td>[65]</td></tr><tr><td>R41</td><td>e + O<sub>3</sub> → O + O<sub>2</sub><sup>-</sup></td><td>5.87 × 10<sup>-15</sup> T<sub>e</sub><sup>-1.5</sup> exp(-1.59/T<sub>e</sub>)</td><td></td><td>[65]</td></tr><tr><td>R42</td><td>e + O<sub>3</sub> → O<sub>2</sub> + O<sup>-</sup></td><td>2.12 × 10<sup>-15</sup> T<sub>e</sub><sup>-1.06</sup> exp(-0.93/T<sub>e</sub>)</td><td></td><td>[65]</td></tr><tr><td>R43</td><td>e + O<sup>-</sup> → O + 2e</td><td>5.47 × 10<sup>-14</sup> T<sub>e</sub><sup>0.324</sup> exp(-2.98/T<sub>e</sub>)</td><td>2.98</td><td>[65]</td></tr><tr><td>R44</td><td>e + O<sub>2</sub> → 2O + e</td><td>1.41 × 10<sup>-15</sup> T<sub>e</sub><sup>0.22</sup> exp(-12.62/T<sub>e</sub>)</td><td>12.62</td><td>[65]</td></tr><tr><td>R45</td><td>e + O<sub>2</sub> → O + O<sup>-</sup></td><td>1.07 × 10<sup>-15</sup> T<sub>e</sub><sup>-1.39</sup> exp(-6.26/T<sub>e</sub>)</td><td>6.26</td><td>[65]</td></tr><tr><td>R46</td><td>e + O<sub>2</sub> + H<sub>2</sub>O → H<sub>2</sub>O + O<sub>2</sub><sup>-</sup></td><td>1.4 × 10<sup>-41</sup></td><td></td><td>[65]</td></tr><tr><td>R47</td><td>e + He + O → He + O<sup>-</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R48</td><td>e + He + O<sub>2</sub> → He + O<sub>2</sub><sup>-</sup></td><td>3.6 × 10<sup>-43</sup> T<sub>e</sub><sup>-0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R49</td><td>e + He + O<sub>3</sub> → He + O<sub>3</sub><sup>-</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R50</td><td>e + O + O<sub>2</sub> → O + O<sub>2</sub><sup>-</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R51</td><td>e + O + O<sub>2</sub> → O<sub>2</sub> + O<sup>-</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R52</td><td>e + 2O<sub>2</sub> → O<sub>2</sub> + O<sub>2</sub><sup>-</sup></td><td>3.6 × 10<sup>-43</sup> T<sub>e</sub><sup>-0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R53</td><td>e + O<sub>2</sub> + O<sub>3</sub> → O<sub>2</sub> + O<sub>3</sub><sup>-</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R54</td><td>e + O<sup>+</sup> → O</td><td>4 × 10<sup>-18</sup></td><td></td><td>[65]</td></tr></tbody></table>

(Continued.)
(Continued.)

<table><thead><tr><th>Reaction number</th><th>Reaction formula</th><th>Reaction coefficient</th><th>Energy cost (eV)</th><th>References</th></tr></thead><tbody><tr><td>R55</td><td>e + O<sub>2</sub><sup>+</sup> → O<sub>2</sub></td><td>4 × 10<sup>-18</sup></td><td></td><td>[65]</td></tr><tr><td>R56</td><td>2e + O<sup>+</sup> → O + e</td><td>7 × 10<sup>-32</sup> T<sub>eg</sub><sup>-4.5</sup></td><td></td><td>[65]</td></tr><tr><td>R57</td><td>e + He + O<sup>+</sup> → He + O</td><td>6 × 10<sup>-39</sup> T<sub>eg</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R58</td><td>e + O<sub>2</sub> + O<sup>+</sup> → O<sub>2</sub> + O</td><td>6 × 10<sup>-39</sup> T<sub>eg</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R59</td><td>e + O → 2e + O<sup>+</sup></td><td>9 × 10<sup>-14</sup> T<sub>e</sub><sup>0.7</sup> exp(-13.6/T<sub>e</sub>)</td><td>13.6</td><td>[65]</td></tr><tr><td>R60</td><td>e + O<sub>2</sub> → 2e + O + O<sup>+</sup></td><td>5.4 × 10<sup>-16</sup> T<sub>e</sub><sup>0.5</sup> exp(-17/T<sub>e</sub>)</td><td>17</td><td>[65]</td></tr><tr><td>R61</td><td>e + O<sub>2</sub> → O<sup>-</sup> + e + O<sup>+</sup></td><td>7.1 × 10<sup>-17</sup> T<sub>e</sub><sup>0.5</sup> exp(-17/T<sub>e</sub>)</td><td>17</td><td>[65]</td></tr><tr><td>R62</td><td>e + H → e + H</td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>Calc.</td><td>[66]</td></tr><tr><td>R63</td><td>e + H<sub>2</sub> → e + H<sub>2</sub></td><td>f(x<sub>gas</sub>, ε<sub>avg</sub>)</td><td>Calc.</td><td>[66]</td></tr><tr><td>R64</td><td>e + OH → OH<sup>-</sup></td><td>1 × 10<sup>-21</sup></td><td></td><td>[65]</td></tr><tr><td>R65</td><td>e + OH + He → He + OH<sup>-</sup></td><td>3 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R66</td><td>He<sup>*</sup> + 2He → He<sub>2</sub><sup>*</sup> + He</td><td>1.3 × 10<sup>-45</sup></td><td></td><td>[63]</td></tr><tr><td>R67</td><td>2He + He<sup>+</sup> → He + He<sub>2</sub><sup>+</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[63]</td></tr><tr><td>R68</td><td>2He<sup>*</sup> → He + e + He<sup>+</sup></td><td>2.7 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R69</td><td>O<sub>2</sub> + He<sup>+</sup> → He + O<sub>2</sub><sup>+</sup></td><td>3.3 × 10<sup>-17</sup> T<sub>g</sub><sup>0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R70</td><td>He<sup>*</sup> + He<sub>2</sub><sup>+</sup> → 2He + He<sup>+</sup></td><td>1 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R71</td><td>O<sub>2</sub> + He<sub>2</sub><sup>+</sup> → 2He + O<sub>2</sub><sup>+</sup></td><td>1 × 10<sup>-15</sup> T<sub>g</sub><sup>0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R72</td><td>2O<sub>2</sub> → 2O + O<sub>2</sub></td><td>6.6 × 10<sup>-15</sup> T<sub>0</sub><sup>-1.5</sup> exp(-59 000/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R73</td><td>He<sup>*</sup> + He + O<sub>2</sub> → 2He + e + O<sub>2</sub><sup>+</sup></td><td>1.6 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R74</td><td>He<sup>*</sup> + O<sub>2</sub> → He + e + O<sub>2</sub><sup>+</sup></td><td>2.6 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R75</td><td>2O → O<sub>2</sub></td><td>9.26 × 10<sup>-40</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R76</td><td>3O → O<sub>2</sub> + O</td><td>9.21 × 10<sup>-46</sup> T<sub>0</sub><sup>-0.63</sup></td><td></td><td>[65]</td></tr><tr><td>R77</td><td>2O + O<sub>2</sub> → 2O<sub>2</sub></td><td>2.56 × 10<sup>-46</sup> T<sub>0</sub><sup>-0.63</sup></td><td></td><td>[65]</td></tr><tr><td>R78</td><td>2O + H<sub>2</sub>O → O<sub>2</sub> + H<sub>2</sub>O</td><td>1.7 × 10<sup>-44</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R79</td><td>O<sub>2</sub><sup>-</sup> + He<sup>+</sup> → O<sub>2</sub> + He</td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R80</td><td>O<sub>2</sub><sup>-</sup> + He<sub>2</sub><sup>+</sup> → 2He + O<sub>2</sub></td><td>1 × 10<sup>-13</sup></td><td></td><td>[65]</td></tr><tr><td>R81</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub><sup>+</sup> → 2O + O<sub>2</sub></td><td>1 × 10<sup>-13</sup></td><td></td><td>[65]</td></tr><tr><td>R82</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub><sup>+</sup> → 2O<sub>2</sub></td><td>4.2 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R83</td><td>O<sub>2</sub><sup>-</sup> + He + He<sub>2</sub><sup>+</sup> → 3He + O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R84</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub> + He<sub>2</sub><sup>+</sup> → 2He + 2O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R85</td><td>He + O<sub>2</sub><sup>-</sup> → He + O<sub>2</sub> + e</td><td>3.9 × 10<sup>-16</sup> exp(-7400/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R86</td><td>He<sup>*</sup> + O<sub>2</sub><sup>-</sup> → He + O<sub>2</sub> + e</td><td>3 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R87</td><td>He<sub>2</sub><sup>*</sup> + O<sub>2</sub><sup>-</sup> → 2He + O<sub>2</sub> + e</td><td>3 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R88</td><td>O<sub>2</sub> + O<sub>2</sub><sup>-</sup> → 2O<sub>2</sub> + e</td><td>2.7 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup> exp(-5590/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R89</td><td>H<sub>2</sub>O + O<sub>2</sub><sup>-</sup> → H<sub>2</sub>O + O<sub>2</sub> + e</td><td>5 × 10<sup>-15</sup> exp(-5000/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R90</td><td>2He<sup>*</sup> → e + He<sub>2</sub><sup>+</sup></td><td>1.05 × 10<sup>-15</sup></td><td></td><td>[65]</td></tr><tr><td>R91</td><td>He<sub>2</sub><sup>*</sup> + He<sup>*</sup> → 2He + e + He<sup>+</sup></td><td>5 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R92</td><td>He<sub>2</sub><sup>*</sup> + He<sup>*</sup> → He + e + He<sub>2</sub><sup>+</sup></td><td>2 × 10<sup>-15</sup></td><td></td><td>[65]</td></tr><tr><td>R93</td><td>2He<sub>2</sub><sup>*</sup> → 3He + e + He<sup>+</sup></td><td>3 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R94</td><td>2He<sub>2</sub><sup>*</sup> → 2He + e + He<sub>2</sub><sup>+</sup></td><td>1.2 × 10<sup>-15</sup></td><td></td><td>[65]</td></tr><tr><td>R95</td><td>2He + He<sup>*</sup> → He + He<sub>2</sub><sup>*</sup></td><td>1.5 × 10<sup>-46</sup></td><td></td><td>[65]</td></tr><tr><td>R96</td><td>2O + He → O<sub>2</sub> + He</td><td>1 × 10<sup>-45</sup></td><td></td><td>[65]</td></tr><tr><td>R97</td><td>O<sub>2</sub><sup>-</sup> + He + O<sub>2</sub><sup>+</sup> → He + 2O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R98</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub> + O<sub>2</sub><sup>+</sup> → 3O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R99</td><td>He<sub>2</sub><sup>*</sup> + O<sub>2</sub> → 2He + e + O<sub>2</sub><sup>+</sup></td><td>3.6 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R100</td><td>OH + O → O<sub>2</sub> + H</td><td>2.2 × 10<sup>-17</sup> exp(120/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R101</td><td>O + H<sub>2</sub>O → 2OH</td><td>2.5 × 10<sup>-20</sup> T<sub>0</sub><sup>1.14</sup> exp(-8624/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R102</td><td>2OH → H<sub>2</sub>O + O</td><td>4.2 × 10<sup>-18</sup> exp(-240/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R103</td><td>H + OH + H<sub>2</sub>O → 2H<sub>2</sub>O</td><td>2.46 × 10<sup>-42</sup> T<sub>0</sub><sup>-2</sup></td><td></td><td>[65]</td></tr><tr><td>R104</td><td>H + OH + O<sub>2</sub> → H<sub>2</sub>O + O<sub>2</sub></td><td>6.88 × 10<sup>-43</sup> T<sub>0</sub><sup>-2</sup></td><td></td><td>[65]</td></tr><tr><td>R105</td><td>O + H + H<sub>2</sub>O → H<sub>2</sub>O + OH</td><td>2.76 × 10<sup>-44</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R106</td><td>H + OH + He → H<sub>2</sub>O + He</td><td>1.56 × 10<sup>-43</sup> T<sub>0</sub><sup>-2.6</sup></td><td></td><td>[65]</td></tr><tr><td>R107</td><td>O<sub>2</sub> + H → O + OH</td><td>3.7 × 10<sup>-16</sup> exp(-8455/T<sub>g</sub>)</td><td></td><td>[65]</td></tr><tr><td>R108</td><td>O<sup>-</sup> + He + O<sub>2</sub><sup>+</sup> → O + O<sub>2</sub> + He</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R109</td><td>O<sup>-</sup> + O<sub>2</sub> + O<sub>2</sub><sup>+</sup> → O + 2O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R110</td><td>O<sup>-</sup> + O<sub>2</sub> + O<sub>2</sub><sup>+</sup> → O<sub>2</sub> + O<sub>3</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr></tbody></table>

(Continued.)
(Continued.)

<table>
  <tbody>
    <tr>
      <td>R111</td>
      <td>2O<sub>3</sub> → O + O<sub>2</sub> + O<sub>3</sub></td>
      <td>1.6 × 10<sup>-15</sup> exp(-11400/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R112</td>
      <td>O<sub>3</sub> + H<sub>2</sub>O → O + O<sub>2</sub> + H<sub>2</sub>O</td>
      <td>1.6 × 10<sup>-15</sup> exp(-11400/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R113</td>
      <td>O<sub>3</sub> + H → O<sub>2</sub> + OH</td>
      <td>7.78 × 10<sup>-17</sup> T<sub>0</sub><sup>0.25</sup> exp(-327.8/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R114</td>
      <td>O<sub>3</sub> + O<sub>2</sub> → O + 2O<sub>2</sub></td>
      <td>1.6 × 10<sup>-15</sup> exp(-11400/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R115</td>
      <td>O<sub>3</sub> + O → 2O + O<sub>2</sub></td>
      <td>9.4 × 10<sup>-17</sup> exp(-11400/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R116</td>
      <td>O<sub>3</sub> + O → 2O<sub>2</sub></td>
      <td>8 × 10<sup>-18</sup> exp(-2060/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R117</td>
      <td>2O + O<sub>2</sub> → O<sub>3</sub> + O</td>
      <td>3.4 × 10<sup>-46</sup> T<sub>0</sub><sup>-1.2</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R118</td>
      <td>O + 2O<sub>2</sub> → O<sub>3</sub> + O<sub>2</sub></td>
      <td>6 × 10<sup>-46</sup> T<sub>0</sub><sup>-2.8</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R119</td>
      <td>O + O<sub>2</sub> + O<sub>3</sub> → 2O<sub>3</sub></td>
      <td>2.3 × 10<sup>-47</sup> exp(-1057/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R120</td>
      <td>O + O<sub>2</sub> + He → He + O<sub>3</sub></td>
      <td>3.4 × 10<sup>-46</sup> T<sub>0</sub><sup>-1.2</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R121</td>
      <td>O<sup>-</sup> + O<sub>2</sub><sup>+</sup> → 3O</td>
      <td>1 × 10<sup>-13</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R122</td>
      <td>O<sup>-</sup> + O<sub>2</sub><sup>+</sup> → O + O<sub>2</sub></td>
      <td>1 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R123</td>
      <td>O<sup>-</sup> + He<sup>+</sup> → O + He</td>
      <td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-1</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R124</td>
      <td>O<sup>-</sup> + He<sub>2</sub><sup>+</sup> → O + 2He</td>
      <td>1 × 10<sup>-13</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R125</td>
      <td>O<sup>-</sup> + He + He<sup>+</sup> → 2He + O</td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R126</td>
      <td>O<sup>-</sup> + O<sub>2</sub> + He<sup>+</sup> → He + O + O<sub>2</sub></td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R127</td>
      <td>O<sup>-</sup> + He + He<sub>2</sub><sup>+</sup> → 3He + O</td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R128</td>
      <td>O<sup>-</sup> + O<sub>2</sub> + He<sub>2</sub><sup>+</sup> → 2He + O + O<sub>2</sub></td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R129</td>
      <td>O<sup>-</sup> + He → He + O + e</td>
      <td>2.5 × 10<sup>-24</sup> T<sub>0</sub><sup>0.6</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R130</td>
      <td>O<sup>-</sup> + He<sup>*</sup> → He + O + e</td>
      <td>3 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R131</td>
      <td>O<sup>-</sup> + He<sub>2</sub><sup>*</sup> → 2He + O + e</td>
      <td>3 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R132</td>
      <td>O<sup>-</sup> + O → O<sub>2</sub> + e</td>
      <td>2 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R133</td>
      <td>O<sup>-</sup> + O<sub>2</sub> → O + O<sub>2</sub><sup>-</sup></td>
      <td>1.5 × 10<sup>-18</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R134</td>
      <td>O<sup>-</sup> + O<sub>2</sub> → O<sub>3</sub> + e</td>
      <td>5 × 10<sup>-21</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R135</td>
      <td>O<sup>-</sup> + O<sub>3</sub> → 2O<sub>2</sub> + e</td>
      <td>3.01 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R136</td>
      <td>O<sup>-</sup> + H → OH + e</td>
      <td>5 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R137</td>
      <td>O<sub>2</sub><sup>-</sup> + O → O<sub>2</sub> + O<sup>-</sup></td>
      <td>1.5 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R138</td>
      <td>O<sub>2</sub><sup>-</sup> + O → O<sub>3</sub> + e</td>
      <td>1.5 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R139</td>
      <td>He + O<sub>3</sub> → He + O + O<sub>2</sub></td>
      <td>1.56 × 10<sup>-15</sup> exp(-11400/T<sub>g</sub>)</td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R140</td>
      <td>He<sup>*</sup> + O<sub>3</sub> → He + O + e + O<sub>2</sub><sup>+</sup></td>
      <td>2.6 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R141</td>
      <td>He<sub>2</sub><sup>*</sup> + O<sub>3</sub> → 2He + O + e + O<sub>2</sub><sup>+</sup></td>
      <td>3.6 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R142</td>
      <td>O<sup>-</sup> + O<sub>3</sub> → O + O<sub>3</sub><sup>-</sup></td>
      <td>1.99 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R143</td>
      <td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub> → O + O<sub>3</sub><sup>-</sup></td>
      <td>3.5 × 10<sup>-21</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R144</td>
      <td>O<sub>2</sub><sup>-</sup> + O<sub>3</sub> → O<sub>2</sub> + O<sub>3</sub><sup>-</sup></td>
      <td>6 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R145</td>
      <td>O<sub>3</sub><sup>-</sup> + He → He + O + O<sub>2</sub> + e</td>
      <td>3 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R146</td>
      <td>O<sub>3</sub><sup>-</sup> + He<sup>*</sup> → He + O<sub>3</sub> + e</td>
      <td>3 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R147</td>
      <td>O<sub>3</sub><sup>-</sup> + He<sub>2</sub><sup>*</sup> → 2He + O + O<sub>2</sub> + e</td>
      <td>3 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R148</td>
      <td>O<sub>3</sub><sup>-</sup> + O → 2O<sub>2</sub> + e</td>
      <td>1 × 10<sup>-17</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R149</td>
      <td>O<sub>3</sub><sup>-</sup> + O → O<sub>2</sub> + O<sub>2</sub><sup>-</sup></td>
      <td>2.5 × 10<sup>-16</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R150</td>
      <td>O<sub>3</sub><sup>-</sup> + O<sub>2</sub><sup>+</sup> → 2O + O<sub>3</sub></td>
      <td>1 × 10<sup>-13</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R151</td>
      <td>O<sub>3</sub><sup>-</sup> + O<sub>2</sub><sup>+</sup> → O<sub>2</sub> + O<sub>3</sub></td>
      <td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-1</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R152</td>
      <td>O<sub>3</sub><sup>-</sup> + He + He<sub>2</sub><sup>+</sup> → 3He + O<sub>3</sub></td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R153</td>
      <td>O<sub>3</sub><sup>-</sup> + O<sub>2</sub> + He<sub>2</sub><sup>+</sup> → 2He + O<sub>3</sub> + O<sub>2</sub></td>
      <td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R154</td>
      <td>O<sub>3</sub><sup>-</sup> + O<sub>3</sub> → 3O<sub>2</sub> + e</td>
      <td>1 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R155</td>
      <td>O<sup>-</sup> + 2O<sub>2</sub> → O<sub>2</sub> + O<sub>3</sub><sup>-</sup></td>
      <td>1.1 × 10<sup>-42</sup> T<sub>0</sub><sup>-1</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R156</td>
      <td>O<sup>-</sup> + He + O<sub>2</sub> → He + O<sub>3</sub><sup>-</sup></td>
      <td>1 × 10<sup>-42</sup> T<sub>0</sub><sup>-1</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R157</td>
      <td>O + He<sup>+</sup> → He + O<sup>+</sup></td>
      <td>5 × 10<sup>-17</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R158</td>
      <td>O<sub>2</sub> + He<sup>+</sup> → He + O + O<sup>+</sup></td>
      <td>1.07 × 10<sup>-15</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R159</td>
      <td>O<sub>3</sub> + He<sup>+</sup> → He + O<sub>2</sub> + O<sup>+</sup></td>
      <td>1.07 × 10<sup>-15</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R160</td>
      <td>OH + He<sup>+</sup> → He + H + O<sup>+</sup></td>
      <td>1.1 × 10<sup>-15</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R161</td>
      <td>O + He<sub>2</sub><sup>+</sup> → 2He + O<sup>+</sup></td>
      <td>1 × 10<sup>-15</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R162</td>
      <td>O<sub>2</sub> + He<sub>2</sub><sup>+</sup> → 2He + O + O<sup>+</sup></td>
      <td>1.05 × 10<sup>-15</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R163</td>
      <td>O<sub>3</sub> + He<sub>2</sub><sup>+</sup> → 2He + O<sub>2</sub> + O<sup>+</sup></td>
      <td>1 × 10<sup>-15</sup> T<sub>0</sub><sup>0.5</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R164</td>
      <td>O<sub>2</sub> + O<sup>+</sup> → O + O<sub>2</sub><sup>+</sup></td>
      <td>2 × 10<sup>-17</sup> T<sub>0</sub><sup>-0.4</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R165</td>
      <td>O<sub>3</sub> + O<sup>+</sup> → O<sub>2</sub> + O<sub>2</sub><sup>+</sup></td>
      <td>1 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R166</td>
      <td>OH + O<sup>+</sup> → H + O<sub>2</sub><sup>+</sup></td>
      <td>3.6 × 10<sup>-16</sup></td>
      <td>[65]</td>
    </tr>
    <tr>
      <td>R167</td>
      <td>He<sup>*</sup> + O<sub>2</sub><sup>+</sup> → O + He + O<sup>+</sup></td>
      <td>1 × 10<sup>-26</sup></td>
      <td>[65]</td>
    </tr>
  </tbody>
</table>

(Continued.)
(Continued.)

<table><thead><tr><th>Reaction number</th><th>Reaction formula</th><th>Reaction coefficient</th><th>Energy cost (eV)</th><th>References</th></tr></thead><tbody><tr><td>R168</td><td>He<sub>2</sub><sup>*</sup> + O<sub>2</sub><sup>+</sup> → O + 2He + O<sup>+</sup></td><td>1 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R169</td><td>He<sub>2</sub><sup>*</sup> + He → 3He</td><td>4.9 × 10<sup>-22</sup></td><td></td><td>[65]</td></tr><tr><td>R170</td><td>He<sup>*</sup> + O → He + e + O<sup>+</sup></td><td>2.6 × 10<sup>-16</sup></td><td></td><td>[65]</td></tr><tr><td>R171</td><td>O + He + O<sup>+</sup> → He + O<sub>2</sub><sup>+</sup></td><td>1 × 10<sup>-41</sup> T<sub>0</sub><sup>0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R172</td><td>O + O<sub>2</sub> + O<sup>+</sup> → O<sub>2</sub> + O<sub>2</sub><sup>+</sup></td><td>1 × 10<sup>-41</sup> T<sub>0</sub><sup>0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R173</td><td>He + He<sup>*</sup> + O → 2He + e + O<sup>+</sup></td><td>1 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R174</td><td>He + He<sup>*</sup> + O<sub>3</sub> → 2He + O + e + O<sub>2</sub><sup>+</sup></td><td>1.6 × 10<sup>-43</sup></td><td></td><td>[65]</td></tr><tr><td>R175</td><td>He + O + H → He + OH</td><td>3.2 × 10<sup>-45</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R176</td><td>O<sup>-</sup> + O<sup>+</sup> → 2O</td><td>2.7 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[65]</td></tr><tr><td>R177</td><td>O<sub>2</sub><sup>-</sup> + O<sup>+</sup> → O + O<sub>2</sub></td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R178</td><td>O<sub>3</sub><sup>-</sup> + O<sup>+</sup> → O + O<sub>3</sub></td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[65]</td></tr><tr><td>R179</td><td>O<sup>-</sup> + He + O<sup>+</sup> → He + 2O</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R180</td><td>O<sup>-</sup> + O<sub>2</sub> + O<sup>+</sup> → O<sub>2</sub> + 2O</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R181</td><td>O<sup>-</sup> + O<sub>2</sub> + O<sup>+</sup> → 2O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R182</td><td>O<sub>2</sub><sup>-</sup> + He + O<sup>+</sup> → He + O + O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R183</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub> + O<sup>+</sup> → 2O<sub>2</sub> + O</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R184</td><td>O<sub>2</sub><sup>-</sup> + O<sub>2</sub> + O<sup>+</sup> → O<sub>2</sub> + O<sub>3</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R185</td><td>O<sub>3</sub><sup>-</sup> + He + O<sup>+</sup> → He + O + O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R186</td><td>O<sub>3</sub><sup>-</sup> + O<sub>2</sub> + O<sup>+</sup> → O<sub>3</sub> + O + O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R187</td><td>O<sub>3</sub><sup>-</sup> + He + O<sub>2</sub><sup>+</sup> → O<sub>3</sub> + He + O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R188</td><td>O<sub>3</sub><sup>-</sup> + O<sub>2</sub> + O<sub>2</sub><sup>+</sup> → O<sub>3</sub> + 2O<sub>2</sub></td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[65]</td></tr><tr><td>R189</td><td>OH<sup>-</sup> + He → He + OH + e</td><td>2 × 10<sup>-15</sup> exp(-24030/T<sub>g</sub>)</td><td></td><td>[66]</td></tr><tr><td>R190</td><td>OH<sup>-</sup> + H → H<sub>2</sub>O + e</td><td>1.8 × 10<sup>-15</sup></td><td></td><td>[66]</td></tr><tr><td>R191</td><td>O<sup>-</sup> + H<sub>2</sub>O → OH + OH<sup>-</sup></td><td>1.4 × 10<sup>-15</sup></td><td></td><td>[66]</td></tr><tr><td>R192</td><td>OH<sup>-</sup> + He<sub>2</sub><sup>+</sup> → OH + 2He</td><td>1 × 10<sup>-13</sup></td><td></td><td>[66]</td></tr><tr><td>R193</td><td>OH<sup>-</sup> + O<sub>2</sub><sup>+</sup> → OH + O<sub>2</sub></td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[66]</td></tr><tr><td>R194</td><td>M + OH<sup>-</sup> + He<sub>2</sub><sup>+</sup> → 2He + OH + M</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[66]</td></tr><tr><td>R195</td><td>H + O<sup>+</sup> → O + H<sup>+</sup></td><td>6.8 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R196</td><td>H<sup>+</sup> + O<sup>-</sup> → O + H</td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[66]</td></tr><tr><td>R197</td><td>O<sup>-</sup> + H<sub>2</sub> → H<sub>2</sub>O + e</td><td>6 × 10<sup>-16</sup> T<sub>0</sub><sup>-0.24</sup></td><td></td><td>[66]</td></tr><tr><td>R198</td><td>He<sup>+</sup> + H → H<sup>+</sup> + He</td><td>1.9 × 10<sup>-21</sup></td><td></td><td>[66]</td></tr><tr><td>R199</td><td>He<sup>+</sup> + H<sub>2</sub> → H<sup>+</sup> + H + He</td><td>3.7 × 10<sup>-20</sup> exp(-35/T<sub>g</sub>)</td><td></td><td>[66]</td></tr><tr><td>R200</td><td>He<sup>+</sup> + H<sub>2</sub> → H<sub>2</sub><sup>+</sup> + He</td><td>7.2 × 10<sup>-21</sup></td><td></td><td>[66]</td></tr><tr><td>R201</td><td>He<sup>+</sup> + H<sub>2</sub>O → H<sup>+</sup> + OH + He</td><td>2.04 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R202</td><td>He<sub>2</sub><sup>+</sup> + H → H<sup>+</sup> + 2He</td><td>3.5 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R203</td><td>He<sub>2</sub><sup>+</sup> + H<sub>2</sub> → H<sub>2</sub><sup>+</sup> + 2He</td><td>3.5 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R204</td><td>He<sub>2</sub><sup>+</sup> + H<sub>2</sub>O → O<sup>+</sup> + H<sub>2</sub> + 2He</td><td>2.1 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R205</td><td>He<sub>2</sub><sup>+</sup> + H<sub>2</sub>O → H<sup>+</sup> + OH + 2He</td><td>2.1 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R206</td><td>He<sub>2</sub><sup>+</sup> + H<sub>2</sub>O → H<sub>2</sub><sup>+</sup> + O + 2He</td><td>2.1 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R207</td><td>H<sup>+</sup> + H + M → H<sub>2</sub><sup>+</sup> + M</td><td>2.1 × 10<sup>-44</sup></td><td></td><td>[66]</td></tr><tr><td>R208</td><td>H<sup>+</sup> + O → O<sup>+</sup> + H</td><td>7 × 10<sup>-16</sup> exp(-232/T<sub>g</sub>)</td><td></td><td>[66]</td></tr><tr><td>R209</td><td>H<sup>+</sup> + O<sub>2</sub> → O<sub>2</sub><sup>+</sup> + H</td><td>2 × 10<sup>-15</sup></td><td></td><td>[66]</td></tr><tr><td>R210</td><td>H + H<sub>2</sub><sup>+</sup> → H<sup>+</sup> + H<sub>2</sub></td><td>6.39 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R211</td><td>O<sub>2</sub> + H<sub>2</sub><sup>+</sup> → O<sub>2</sub><sup>+</sup> + H<sub>2</sub></td><td>8 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R212</td><td>H<sub>2</sub> + O<sup>-</sup> → OH<sup>-</sup> + H</td><td>3.6 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R213</td><td>H<sup>+</sup> + OH<sup>-</sup> + M → H<sub>2</sub>O + M</td><td>2 × 10<sup>-37</sup> T<sub>0</sub><sup>-2.5</sup></td><td></td><td>[66]</td></tr><tr><td>R214</td><td>H<sub>2</sub><sup>+</sup> + O<sup>-</sup> → H<sub>2</sub>O</td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[66]</td></tr><tr><td>R215</td><td>H<sub>2</sub><sup>+</sup> + O<sub>2</sub><sup>-</sup> → H<sub>2</sub> + O<sub>2</sub></td><td>2 × 10<sup>-13</sup> T<sub>0</sub><sup>-0.5</sup></td><td></td><td>[66]</td></tr><tr><td>R216</td><td>H<sub>2</sub><sup>+</sup> + OH<sup>-</sup> → H<sub>2</sub>O + H</td><td>1 × 10<sup>-13</sup></td><td></td><td>[66]</td></tr><tr><td>R217</td><td>He<sup>*</sup> + H → H<sup>+</sup> + He + e</td><td>1.1 × 10<sup>-15</sup></td><td></td><td>[66]</td></tr><tr><td>R218</td><td>He<sup>*</sup> + H<sub>2</sub> → H<sub>2</sub><sup>+</sup> + He + e</td><td>2.9 × 10<sup>-17</sup></td><td></td><td>[66]</td></tr><tr><td>R219</td><td>He<sub>2</sub><sup>*</sup> + H → 2He + H<sup>+</sup> + e</td><td>2.2 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R220</td><td>He<sub>2</sub><sup>*</sup> + H<sub>2</sub> → 2He + H<sub>2</sub><sup>+</sup> + e</td><td>2.2 × 10<sup>-16</sup></td><td></td><td>[66]</td></tr><tr><td>R221</td><td>He<sup>*</sup> + H<sub>2</sub> → He + 2H</td><td>1.4 × 10<sup>-17</sup></td><td></td><td>[66]</td></tr><tr><td>R222</td><td>He + 2H → He + H<sub>2</sub></td><td>5.8 × 10<sup>-45</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[66]</td></tr><tr><td>R223</td><td>He + H + OH → He + H<sub>2</sub>O</td><td>1.56 × 10<sup>-43</sup> T<sub>0</sub><sup>-2.6</sup></td><td></td><td>[66]</td></tr><tr><td>R224</td><td>2H → H<sub>2</sub></td><td>6.04 × 10<sup>-39</sup> T<sub>0</sub><sup>-1</sup></td><td></td><td>[66]</td></tr></tbody></table>

(Continued.)
(Continued.)

<table><tr><td>R225</td><td>H + O → OH</td><td>4.36 × 10<sup>-38</sup> T<sub>0</sub><sup>-1</sup></td><td>[66]</td></tr><tr><td>R226</td><td>H + OH → O + H<sub>2</sub></td><td>8 × 10<sup>-27</sup> T<sub>g</sub><sup>2.8</sup> exp(-1950/T<sub>g</sub>)</td><td>[66]</td></tr><tr><td>R227</td><td>H + OH → H<sub>2</sub>O</td><td>8 × 10<sup>-27</sup> T<sub>g</sub><sup>2.8</sup> exp(-1950/T<sub>g</sub>)</td><td>[66]</td></tr><tr><td>R228</td><td>3H → H + H<sub>2</sub></td><td>6 × 10<sup>-43</sup> T<sub>0</sub><sup>-1</sup></td><td>[66]</td></tr><tr><td>R229</td><td>2H + H<sub>2</sub> → 2H<sub>2</sub></td><td>8.1 × 10<sup>-45</sup> T<sub>0</sub><sup>-0.6</sup></td><td>[66]</td></tr><tr><td>R230</td><td>2H + H<sub>2</sub>O → H<sub>2</sub>O + H<sub>2</sub></td><td>1.32 × 10<sup>-43</sup> T<sub>0</sub><sup>-1.25</sup></td><td>[66]</td></tr><tr><td>R231</td><td>H + O + H<sub>2</sub> → OH + H<sub>2</sub></td><td>9.19 × 10<sup>-45</sup> T<sub>0</sub><sup>-1</sup></td><td>[66]</td></tr><tr><td>R232</td><td>H + OH + H<sub>2</sub> → H<sub>2</sub>O + H<sub>2</sub></td><td>4.92 × 10<sup>-43</sup> T<sub>0</sub><sup>-2</sup></td><td>[66]</td></tr><tr><td>R233</td><td>O + H<sub>2</sub> → OH + H</td><td>3 × 10<sup>-20</sup> T<sub>g</sub> exp(-4480/T<sub>g</sub>)</td><td>[66]</td></tr><tr><td>R234</td><td>2O + H<sub>2</sub> → H<sub>2</sub> + O<sub>2</sub></td><td>2.65 × 10<sup>-45</sup> T<sub>0</sub><sup>-1</sup></td><td>[66]</td></tr><tr><td>R235</td><td>H<sub>2</sub> + OH → H + H<sub>2</sub>O</td><td>5.3 × 10<sup>-22</sup> T<sub>g</sub><sup>1.47</sup> exp(-1761/T<sub>g</sub>)</td><td>[66]</td></tr><tr><td>R236</td><td>H<sub>2</sub> + H<sub>2</sub>O → OH + H + H<sub>2</sub></td><td>5.8 × 10<sup>-15</sup> exp(52 900/T<sub>g</sub>)</td><td>[66]</td></tr></table>

All rate coefficients have volume units of m³ s⁻¹ for two body reactions and m⁶ s⁻¹ for three body. ε<sub>avg</sub>, defined as 3/2T<sub>e</sub>, is the average electron energy in eV, x<sub>gas</sub> is the initial mole fraction, T<sub>e</sub> is the electron temperature in eV, T<sub>eg</sub> is the electron temperature normalized to the gas temperature (T<sub>eg</sub> = T<sub>e</sub>/T<sub>g</sub>), and T<sub>0</sub> = T[K]/300 K is the normalized gas temperature. Rate coefficients for O₂ and H₂ electron impact reactions were calculated assuming a Maxwellian EEDF. Electronically excited states of O₂ and O were assumed to instantaneously deexcite. He⁺ represents the groups He(2³S) and He(2¹S). He₂⁺ represents He₂(a³Σ<sup>+</sup><sub>u</sub>).

## ORCID iDs

Alexandra Brisset https://orcid.org/0000-0003-3217-1106

Matthew Bieniek https://orcid.org/0000-0001-5847-2228

Laurent Invernizzi https://orcid.org/0000-0003-4525-8921

Mohammad Hasan https://orcid.org/0000-0001-6993-933X

James Walsh https://orcid.org/0000-0002-6318-0892

Kari Niemi https://orcid.org/0000-0001-6134-1974

Erik Wagenaars https://orcid.org/0000-0002-5493-3434

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