Zero-dimensional and pseudo-one-dimensional models of atmospheric-pressure plasma jets in binary and ternary mixtures of oxygen and nitrogen with helium background

Atmospheric-pressure plasma jets have attracted growing interest over the last decades owing to their efficiency in converting ordinary gas content into diverse reactive species for a wide range of purposes [1], such as biomedical applications [2, 3], catalytic greenhouse gas conversion [4, 5], and vacuum-free etching [6] and deposition [7–9]. The small electrode gap of micro-scaled atmospheric-pressure plasma jets (μAPPJs) ensures uniformity at low voltage and sustains the characteristics of a glow discharge. The non-equilibrium character permits an efficient electron heating while keeping the neutral species near ambient temperature suitable for the treatment of heat-sensitive materials. An accurate control of the reactive species concentrations is of fundamental importance to achieve an optimized treatment performance.

The atomic structure of the noble gas conduces to ignite and sustain an atmospheric-pressure discharge at a relatively low absorbed power. Helium is usually preferred over argon due to the lower breakdown voltage [10] and higher discharge stability [11]. A wide variety of reactive species is usually generated by the addition of reactive admixtures (e.g. O₂, N₂ typically in the order of 0%–2%) to the feed noble gas. A challenge still to be addressed is the full picture of the convoluted plasma chemistry defining the reactive species concentrations. The chemical complexity is attributed to the multitude of interactions between neutral and ion, as well as atomic and molecular species. It is further increased through the introduction of several gases. Therefore, a deep understanding of the rich chemical kinetics is of the essence for characterization and optimization of the device. In view of this, zero-dimensional modelling approaches [12–26] were used to report a detailed chemical description and avoid the resulting drastic computational load (simultaneously keeping the simulated plasma properties within certain accuracy). A fast solution to the equilibrium chemical state was obtained with the zero-dimensional model developed by Lazzaroni et al [12], and a reasonable agreement for both the neutral and charged species was observed in comparison with the fluid simulation results of He/N₂ and He/O₂ plasma. Up to 46 species and 577 reactions were incorporated by Liu et al [13] and Schröter et al [14] to describe He/H₂O chemical models. A more detailed composition space of humid air (up to 59 species and 1048 reactions) was considered by Murakami et al [16–18] and Sun et al [19] in He/air models. Much more complicated chemical sets (84 species and 1880 reactions) were included by Van Gaens et al [20–22] in Ar/air models. Since accurate concentrations are required for optimal plasma treatment, the influence of operation conditions (e.g. the gas mixture ratio, gas flow rate and absorbed power) and underlying reaction mechanisms on the concentrations of diverse biologically relevant reactive species was intensively analysed with the aforementioned models.

Zero-dimensional modelling approaches are implemented either in volume-averaged formalism [12, 13, 15–17, 19] or in plug-flow formalism [14, 18, 20–22]. The former gives volume-averaged plasma properties of the whole jet chamber, whereas the latter provides one-dimensional spatially resolved simulation results in the gas flow direction [27]. The plug-flow model is preferred for a spatial resolution often in a single-operation condition whereas the zero-dimensional model is used for volume-averaged data in a series of operation conditions or in a time resolution during a pulse-modulated power input. The models are used in combination with experiments to investigate the concentrations and chemical kinetics of ozone [20], atomic oxygen and nitric oxide [22], atomic oxygen and hydroxyl radicals [14], helium metastable and reactive oxygen species [16], as well as argon metastable, ozone and nitrogen oxide species [25]. However, an effort on the benchmark against a broad range of experimental data (in view of diverse species, operation parameters, measurement techniques) is still missing for an atmospheric-pressure discharge. Such a validation is of crucial significance to further ensure the predictive capability of the model calculations.

Nitric oxide (NO) is one of the key species for biomedical applications [28] (e.g. it plays an essential role in wound healing). It has been intensively studied, both experimentally [29–34] and computationally [19–21, 25, 26]. The measurements of production rate [29, 30] and absolute density [31] are carried out in a Herriott cell. Spatially resolved densities in the effluent have been reported [32, 33]. Similar experiments with a variation of the gas mixture ratio, helium flow rate and absorbed power were recently conducted on the COST reference microplasma jet (COST-Jet) [34]. In this device, the non-reproducibility due to gas contamination and power measurement is minimized by the refinement of the mechanical and electrical design [35]. This is extremely suitable for the benchmark of model calculations. The dominant reaction mechanisms have beed discussed in simulation studies [19, 21, 22, 25, 26], and the influence of operation parameters on the species concentrations has been presented [20]. The NO concentration was characterized by the simulation results and measurement data of a high-pressure discharge [36] and an atmospheric-pressure plasma [22]. Nevertheless, there is still a lack of validation for a variation of operation parameters.

The detailed resolution of the vibrational distribution function (VDF) has gained much attention in low-pressure plasma [37–44] (e.g. N₂(v < 46) [37], O₂(v < 42) [38, 40]). Its influence on the electron energy distribution function (EEDF) [37, 39, 43–45] and the plasma properties [38, 40] has been presented. An important role of the nitrogen VDF in the production of NO and nitrogen atoms was reported [42, 46], and the VDF was intensively investigated [44]. However, the influence of a detailed VDF on an atmospheric-pressure discharge is not yet fully understood. The vibrationally excited states in the zero-dimensional model have either been neglected [19, 25, 26] or included with a few vibrational levels [16–18, 20, 21, 23]. On the other hand, their high excited states are suggested to play a role in the ozone formation [47], and this in turn affects the chemical kinetics of other species. Further study on the detailed VDF and the corresponding vibrational kinetics will contribute to a better accuracy of the simulation results.

Wall reactions [13–19, 24] and gas impurities [13, 14, 16–22, 26] are usually taken into account in zero-dimensional models due to their underlying effects on the plasma properties. The role of wall reactions has been presented for the feed gas mixtures of Ar/H₂O [24] and He/H₂O [15], for example. The influence of gas impurities has been shown, e.g. on a He [13, 14, 19] and He/O₂ [16–18] discharge. In parallel with these studies, the highlight of this work is to make a systematic analysis gradually for several gas mixtures: He, He/O₂, He/N₂ and He/N₂/O₂.

The main goals of this paper are as follows:

• For a confirmed prediction capability, the developed zero-dimensional and plug-flow models are well benchmarked against spatially resolved simulation results and numerous measurement data for distinct species densities under different operation conditions from various studies, as shown in section 5.1.
• The NO concentration in the COST-Jet is intensively characterized by the simulations and experiments with a variation of the gas mixture ratio, helium flow rate and absorbed power (see section 5.2).
• The role of the detailed resolution of O₂(v < 41) and N₂(v < 58) VDFs in an atmospheric-pressure discharge is presented in section 5.4.

The atmospheric-pressure plasma jets simulated in this work are described in section 2. The computational method for a prediction of the plasma properties in these jets is reported by the developed models in section 3 and the considered chemical kinetics in section 4. The spatial evolution of the NO concentration in the gas flow direction and the main gain/loss channels are exhibited in section 5.2. The VDFs and their spatial evolution as a function of the operation conditions are demonstrated in section 5.3. The sensitivity of the plasma properties to the wall reaction probabilities and the synthetic air (N₂:O₂ = 8:2) impurity levels is addressed in section 5.4. The main results are summarized in the conclusion given in section 6.

Atmospheric-pressure plasma jets of planar electrode configuration in five different sizes [48–54] are simulated for the purpose of benchmarking. The jets are constructed with the cross-field configuration, i.e. the applied electric field is oriented perpendicular to the feed gas flow direction [22, 55]. The specific operation conditions are presented in section 5.1. A plasma jet [50] is investigated as a preliminary test of the model predictive capability to a pulse-modulated discharge. The old versions of the radiofrequency-driven COST-Jet (i.e. μAPPJ) [49, 51, 52, 54] might be insufficiently sealed. The resulting unknown high impurity levels in the experiments [49] may impact the results and need to be considered in the simulations. Furthermore, a power transfer efficiency of around 5% is usually assumed in the modelling of these old versions for converting the provided generator input power to the absorbed power in the plasma. The irreproducible experimental results of aμAPPJ are mainly ascribed to the gas impurity and the power uncertainty. Hence, they are minimized by the COST-Jet [48, 53] with a large amount of effort [35] (e.g. the sealing improvement and the absorbed power measurements with integrated probes).

The COST-Jet is investigated with a focus in this paper owing to the above-mentioned advantages. The jet chamber structure is illustrated in figure 1 together with a depiction of the used modelling formalisms. More details of this setup are reported in the work of Golda et al [35]. In section 5.2, the operation conditions are rightfully addressed based on the measurements of Preissing et al [34]. In sections 5.3 and 5.4, the jet is simulated with the typical operation conditions provided in [35]: a plasma volume of 1 × 1 × 30 mm³ sustained by an absorbed power of 0.6 W at a pressure of 101 325 Pa and a gas temperature of 345 K, is fed with 1400 sccm He, 1400 sccm He + 0.5% O₂, 1400 sccm He + 0.5% N₂ or 1400 sccm He + 0.5% N₂ + 0.5% O₂, unless stated otherwise.

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The species particle balance equations and an electron energy balance equation are incorporated in the model to calculate the plasma properties: the species concentrations and the effective electron temperature T_e. The effective electron temperature is derived from the mean electron energy of a non-Maxwellian EEDF as described in [56, 57]. The electron density is calculated by imposing a constraint on its wall flux based on the quasi-neutrality implementation [58]. A constant gas temperature T_g estimated from the measurements under the considered operation conditions is used in the simulations. Both the zero-dimensional formalism [12, 13] and the plug-flow formalism [14, 20, 27] are implemented. The balance equations are averaged over the whole chamber volume in the zero-dimensional formalism (see figure 1(a)), and the steady or transient volume-averaged plasma properties are calculated [59, 60]. In the plug-flow formalism, the equations are averaged over an infinitesimal plug volume (see figure 1(b)). The volume is equal to the area of the chamber cross section multiplying an infinitely small length in the gas flow direction. Since the plug co-moves with the net mass flow [27], the time evolution of the plasma properties in this volume is mapped to the spatial position in the whole discharge channel by multiplying the velocity V_plug (see equation (5)).

The non-Maxwellian EEDFs are calculated by using a Boltzmann solver, the open-source simulation tool Lisbon kinetics Boltzmann (LoKI-B) published by Tejero-del-Caz et al [61], based on the steady-state solution of the Boltzmann equation under the two-term approximation. A self-consistent calculation of the EEDFs is considered as follows. LoKI-B is called with the input parameters (e.g. the collision cross-sections available from the literature and the plasma composition computed from the balance equations). Then the calculated EEDFs from LoKI-B are used to update look-up tables consisting of the effective electron temperatures and the corresponding electron-impact collision rate coefficients (LoKI-B is adapted in this work to properly fit in the iteration scheme). The balance equations implemented in MATLAB in this study are re-solved again with the updated look-up tables, and the re-computed plasma composition is fed into the next call to LoKI-B. The iterations between the calculations of the EEDFs and the plasma composition are conducted until the simulated plasma properties are invariant under a given operation condition. Note that super-elastic collisions are incorporated in the calculation for a better resolution of the electron kinetics, since they have a significant influence on the EEDFs [62–64]. The time variation of the plasma composition in the transient simulations (e.g. the pulse-modulated zero-dimensional and the plug-flow models) necessitates multiple subsequent LoKI-B calculations to involve the corresponding evolution of the electron kinetics. However, the electron kinetics are mainly controlled by the virtually invariant dominant background helium gas density. This is furthermore confirmed by the insensitivity of the simulation results to the number of calls to LoKI-B (multiple times during the pulse/plug flow or once in advance). In order to reduce the computationally demanding transient simulation duration, LoKI-B is deployed in advance by a single call to calculate the EEDF for a corresponding steady-state plasma composition.

A time-dependent solution of the Boltzmann equation would better represent the transient phenomena [44]. However, at atmospheric pressure, the time necessary to establish a steady-state EEDF is in the order of nanoseconds, approximated by the reduced momentum-transfer collision frequency (i.e. the collision frequency divided by the gas density, as described in [65] (page 10)). The range of the time value is also numerically verified (e.g. a few nanoseconds in the kinetic models [62]). Therefore, the stationary solution of the Boltzmann equation is considered in the transient simulations (microsecond-pulsed modulation) of this work, in parallel with the available implementations of time-dependent (nanosecond-range) models [66–68].

The considered species in this study are reported in table 1. The generic form of the volume-averaged particle balance equation is

$$\begin{equation}\frac{\mathrm{d}{n}_{i}}{\mathrm{d}t}={\left.\sum\limits _{j}{\mathcal{W}}_{ij}{R}_{i}^{j}\right\vert }_{\mathrm{V}}+{\left.\sum\limits _{j}{\mathcal{W}}_{ij}{R}_{i}^{j}\right\vert }_{\mathrm{W}},\end{equation} \tag{ 1 }$$

where n_i is the volume-averaged density of the species denoted by i, ${\mathcal{W}}_{ij}$ is the net stoichiometric coefficient for a gain/loss mechanism denoted by j, and ${R}_{i}^{j}$ is the reaction rate. The subscript '_V' denotes the chemical reactions inside the plasma volume and '_W' the flux (e.g. convective and diffusive) source term including the heterogeneous reactions on the solid walls.

Table 1. The considered species in the models of He, He/O₂, He/N₂ and He/N₂/O₂ are selected from the table below. Each vibrational level is also treated as a separate species to provide state-by-state resolution.

He, He(23S), ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$, He+, ${\mathrm{H}\mathrm{e}}_{2}^{+}$,

$\mathrm{O}({}^{3}\mathrm{P})$, O2, O3, $\mathrm{O}({}^{1}\mathrm{D})$, O2(a1Δg), O+, ${\mathrm{O}}_{2}^{+}$, ${\mathrm{O}}_{4}^{+}$, O−, ${\mathrm{O}}_{2}^{-}$, ${\mathrm{O}}_{3}^{-}$, ${\mathrm{O}}_{4}^{-}$,

$\mathrm{N}({}^{4}\mathrm{S})$, N2, $\mathrm{N}({}^{2}\mathrm{D})$, N2(A3Σ), N2(B3Π), N+, ${\mathrm{N}}_{2}^{+}$, ${\mathrm{N}}_{3}^{+}$, ${\mathrm{N}}_{4}^{+}$,

NO, NO2, NO3, N2O, N2O3, N2O4, N2O5, NO+,${\mathrm{N}\mathrm{O}}_{2}^{+}$, N2O+, NO−,${\mathrm{N}\mathrm{O}}_{2}^{-}$, ${\mathrm{N}\mathrm{O}}_{3}^{-}$, N2O−,

N2(0 < v < 58), O2(0 < v < 41), e

The rate of a plasma volume chemical reaction j is

$$\begin{equation}{\left.{R}_{i}^{j}\right\vert }_{\mathrm{V}}={k}^{j}\prod\limits _{l}{n}_{l}^{{\nu }_{lj}},\end{equation} \tag{ 2 }$$

where k^j is the rate coefficient, l is the reactant and ν_lj is the forward stoichiometric coefficient. The rate coefficients are tabulated in tables A1–A9. The electronic rate coefficients are mostly computed from the enlisted set of cross-sections available in the literature together with the self-consistently calculated EEDF.

The flow-in rate in the zero-dimensional formalism is given by the relation [69]

$$\begin{equation}{\left.{R}_{{\mathrm{H}\mathrm{e},\mathrm{O}}_{2}{,\mathrm{N}}_{2}}^{\text{F}-\text{in}}\right\vert }_{\mathrm{W}}=c\frac{{Q}_{{\mathrm{H}\mathrm{e},\mathrm{O}}_{2}{,\mathrm{N}}_{2}}{P}_{\mathrm{a}\mathrm{t}\mathrm{m}}}{V{k}_{\mathrm{B}}{T}_{\mathrm{i}\mathrm{n}}},\end{equation} \tag{ 3 }$$

where ${Q}_{{\mathrm{H}\mathrm{e},\mathrm{O}}_{2}{,\mathrm{N}}_{2}}$ (sccm) is the partial mass flow rate of each species fed into the plasma domain, P_atm the atmospheric pressure, V the plasma volume, T_in the feed gas temperature and c the unit conversion factor. The flow-out rate of a species i is [69]

$$\begin{equation}{\left.{R}_{i}^{\text{F}-\text{out}}\right\vert }_{\mathrm{W}}=cQ\frac{{P}_{\mathrm{a}\mathrm{t}\mathrm{m}}{T}_{\text{g}}}{VP{T}_{\mathrm{i}\mathrm{n}}}{n}_{i},\end{equation} \tag{ 4 }$$

where Q denotes the total mass flow rate and P the plasma pressure. The flow-in and flow-out rates are excluded in the plug-flow formalism due to the motion of the plug with the net mass flow [27]. The velocity of the plug in the gas flow direction is calculated by

$$\begin{equation}{V}_{\text{plug}}=cQ\frac{{P}_{\mathrm{a}\mathrm{t}\mathrm{m}}{T}_{\text{g}}}{{A}_{\text{c}}P{T}_{\mathrm{i}\mathrm{n}}},\end{equation} \tag{ 5 }$$

where A_c denotes the constant area of the chamber cross section perpendicular to the mass flow field (e.g. 1 × 1 mm² for the COST-Jet in figure 1).

The ion and neutral wall flux at the surfaces perpendicular to the mass flow field is ignored in the zero-dimensional formalism due to the negligibly small area (mostly forming below 2% of the total plasma surface area). This term is also neglected in the plug-flow formalism since the convective mass flow mechanism prevails the flux vector [27]. The considered ion wall reactions are tabulated in table A10. The wall loss of an ion i at the surfaces parallel to the mass flow field is modelled as [57, 60, 70]

$$\begin{equation}{R}_{i}^{+}{\left.\right\vert }_{\mathrm{W}}=\left({u}_{i\mathrm{B}}\frac{{h}_{iX}^{+}2{A}_{X}^{f}}{{V}^{f}}+{u}_{i\mathrm{B}}\frac{{h}_{iY}^{+}2{A}_{Y}^{f}}{{V}^{f}}\right){n}_{i},\end{equation} \tag{ 6 }$$

where u_iB denotes the Bohm velocity, ${h}_{iX}^{+}$ and ${h}_{iY}^{+}$ are the ion edge-to-center ratios, the superscript ^f specifies either the zero-dimensional or the plug-flow implementation, V^f is the corresponding volume, and ${A}_{X}^{f}$ and ${A}_{Y}^{f}$ are their surface areas. Namely, the values of ${V}^{f},{A}_{X}^{f}$ and ${A}_{Y}^{f}$ are either the plasma volume and surface in the zero-dimensional formalism, or the plug volume and surface in the plug-flow formalism.

The edge-to-center ratio definition is adapted in the ion wall flux, following conventional global model studies [71, 72]. It should be noted that the edge-to-volume-averaged ratio [73] physically represents a more realistic description at intermediate or atmospheric pressure (the so-called collisional regime [57]); however, the resulting variations in the calculations are numerically negligible [60]. The ion velocity at the plasma-sheath edge is expected to deviate from the Bohm velocity at high pressure values due to the larger collisionality of the sheath region compared to the low-pressure plasma [74]. Nevertheless, the deviation is negligible at atmospheric pressure since the ratio of the ion-neutral collision to the direct ionization frequencies of the helium atomic ion is less than the critical value of 10 (larger values represent the transition into the collisional sheath regime) based on the analyses by Franklin and Snell [74] and Valentini et al [75, 76]. Additionally, assuming an effective ionization frequency to include the space-charge dominating excimer ions as well as the prevailing mechanisms of Penning and stepwise ionization schemes lead to a much smaller ratio compared to the critical value. In other words, the validity range of the Bohm criterion is not breached at atmospheric pressure. Furthermore, our model calculations are not sensitive to the ion wall loss; hence, any deviation from the Bohm velocity is not influential on the simulation results.

The ion edge-to-center ratios in the collisional regime are defined as [57, 60]

$$\begin{equation}\begin{aligned}{h}_{iX}^{+}& =\frac{1}{1+\alpha }({u}_{i\text{BE}}/{u}_{i\mathrm{B}}){\left(1+{\left(\frac{X{u}_{i\text{BE}}}{\pi {D}_{i+}}\right)}^{2}\right)}^{-1/2},\\ {h}_{iY}^{+}& =\frac{1}{1+\alpha }({u}_{i\text{BE}}/{u}_{i\mathrm{B}}){\left(1+{\left(\frac{Y{u}_{i\text{BE}}}{\pi {D}_{i+}}\right)}^{2}\right)}^{-1/2},\end{aligned}\end{equation} \tag{ 7 }$$

where α represents the degree of electronegativity, u_iBE the electronegative Bohm velocity [77, 78], u_iB the electropositive Bohm velocity, X and Y the plasma dimensions, and D_i+ the multiple-ion ambipolar diffusion coefficient [59].

The considered neutral wall reactions are tabulated in table A11. The reaction rate due to the diffusion of a reactive neutral i to the wall and its subsequent heterogeneous reaction in the zero-dimensional and plug-flow formalisms is given as [79, 80]

$$\begin{equation}{\left.{R}_{i}^{N}\right\vert }_{\mathrm{W}}={n}_{i}{\left(\frac{{{\Lambda}}_{0}^{2}}{{D}_{i}}+\frac{2{V}^{f}(2-{\gamma }_{i})}{2({A}_{X}^{f}+{A}_{Y}^{f}){v}_{i}{\gamma }_{i}}\right)}^{-1},\end{equation} \tag{ 8 }$$

where Λ₀ is the effective diffusion length, D_i the diffusion coefficient, V^f the volume, $2({A}_{X}^{f}+{A}_{Y}^{f})$ the net surface area, v_i the mean neutral velocity and γ_i the wall reaction probability. The superscript ^f denotes the corresponding parameters in the considered formalism: either those of the plasma in the zero-dimensional or those of the plug in the plug-flow formalism.

The volume-averaged electron energy balance equation is given in the form [57, 60, 77]

$$\begin{equation}\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{3}{2}{n}_{\mathrm{e}}{T}_{\text{e}}\right)={Q}_{\mathrm{a}\mathrm{b}\mathrm{s}}-({Q}_{\mathrm{C}\mathrm{h}\mathrm{e}}+{Q}_{\mathrm{E}\mathrm{l}\mathrm{a}}+{Q}_{\text{W}}),\end{equation} \tag{ 9 }$$

where n_e represents the electron density, T_e the effective electron temperature, Q_abs the electrical power absorbed by the plasma as well as the energy loss due to chemical reactions Q_Che, elastic collisions Q_Ela and wall flux Q_W.

The power absorbed by the plasma, assuming a homogeneous distribution, is defined by the relation

$$\begin{equation}{Q}_{\mathrm{a}\mathrm{b}\mathrm{s}}=\beta \mathcal{P}/V,\end{equation} \tag{ 10 }$$

where $\mathcal{P}$ is the input power, V is the plasma volume and β is the power transfer efficiency. The electron energy loss in the chemical reactions is given in the following form

$$\begin{equation}{Q}_{\mathrm{C}\mathrm{h}\mathrm{e}}={\left.\sum\limits _{j}{\mathcal{E}}_{j}{R}_{\mathrm{e}}^{j}\right\vert }_{\mathrm{V}},\end{equation} \tag{ 11 }$$

where ${R}_{\mathrm{e}}^{j}$ denotes the rate of an electronic reaction j, ${\mathcal{E}}_{j}={\sum }_{i}{\mathcal{W}}_{ij}{{\epsilon}}_{i}$ is the net energy released or absorbed in the reaction and _i is the internal energy of the species i [58]. The principle of detailed balancing is used in calculating the backward rate coefficients of the electron-impact excitation reactions [57]. The energy loss due to elastic collisions Q_Ela is calculated by the individual elastic rate coefficients [58, 59]. The considered elastic collisions are tabulated in table A12 with a reference to the used cross-section. The energy loss due to the wall flux is given in the form [60]

$$\begin{equation}{Q}_{\mathrm{W}}={\left.\sum\limits _{i\in \mathrm{I}\mathrm{o}\mathrm{n}\mathrm{s}}\left({\mathcal{E}}_{\mathrm{P}}+{\mathcal{E}}_{\mathrm{s}}+{\mathcal{E}}_{\mathrm{e}}\right){R}_{i}^{+}\right\vert }_{\mathrm{W}},\end{equation} \tag{ 12 }$$

where ${\mathcal{E}}_{\mathrm{P}}$ and ${\mathcal{E}}_{\mathrm{s}}$ are the plasma potential and the sheath potential, respectively, for an ion in free-fall through the sheath [77], and ${\mathcal{E}}_{\mathrm{e}}=2{T}_{\text{e}}$ is the mean kinetic energy lost per electron crossing the sheath to the wall [57]. The electron energy balance equation is identically implemented in the zero-dimensional and the plug-flow formalism. The only distinction is the aforementioned calculation of the ion wall loss rate due to the differing volume and surface area.

The gas mixtures He, He/O₂, He/N₂ and He/N₂/O₂ are considered in this study. The considered species are given in table 1. The corresponding reactions and elastic collision sets are listed in appendix A, tables A1–A12. The reactions are separated into several tables for the sake of clarity, and tabulated according to the mixture composition and reaction type. The bulk of the He and He/O₂ chemical sets is adopted from a study by Waskoenig et al [51], with the exception of the vibrational kinetics. This maximizes the consistency in the model-to-model benchmark of our zero-dimensional simulation results to that of the one-dimensional model provided by Waskoenig et al [51] (see figure 4). Comparatively, the chemical sets here are supplemented with the reaction mechanisms of ${\mathrm{O}}_{4}^{+}$ and ${\mathrm{O}}_{4}^{-}$ for a better agreement of the calculated $\mathrm{O}({}^{3}\mathrm{P})$ density with the measurement (in particular, due to reactions 49, 73 and 74 in table A2). Additionally, more detailed helium excimer reaction mechanisms are included in this work. The chemical sets of He/N₂ and He/N₂/O₂ are established based on a wide variety of studies available in the literature (explicitly given in appendix A). Both available databases [81, 82] and individual studies (e.g. [83–88]) are referred to in the data collection. A recent set of electron-impact cross-sections are adopted for N₂O and NO₂ [89].

The vibrationally excited molecules O₂(v < 41) and N₂(v < 58) are incorporated in the species set. The detailed vibrational kinetics in tables A5–A9 are divided into electron–vibrational (e–V), vibrational–translational (V–T) and vibrational–vibrational (V–V) energy transfer mechanisms, mainly based on databases [90, 91] and studies [37, 40, 42, 87, 92, 93]. Moreover, the Penning ionization and charge exchange reactions between helium and vibrationally excited molecules are integrated into the kinetics. The resonant vibrational excitation cross-sections [92, 93] are favoured in the e–V transfer due to their efficiency. Only the cross-sections of the first six vibrational levels are used in the solution to the Boltzmann equation, while those of the higher levels are directly evaluated to the corresponding rate coefficients according to the established EEDF. The reverse rate coefficients of all the e–V excitation are calculated via the principle of detailed balancing [57]. The V–T transitions are substantially dominated by the strong He background gas; however, the transitions due to the second dominant species $\mathrm{O}({}^{3}\mathrm{P})$, $\mathrm{N}({}^{4}\mathrm{S})$, O₂ and N₂ are considered as well. The rate coefficients of the N₂(v > 0)-O₂ and O₂(v > 0)-N₂ V–T reactions are calculated with the equation (27) in [37] based on those of N₂(v > 0)-N₂ and O₂(v > 0)-O₂, respectively. A negligible contribution of the calculated rate coefficients to the O₂ and N₂ VDFs is observed under the considered operation conditions in this work. Only the N₂(v > 0)-N channel is taken into account among the nitrogen atom-induced V–T mechanisms, whereas the inefficient O₂(v > 0)-N channel is neglected [37]. Furthermore, the dissociation mechanism of $\mathrm{O}({}^{3}\mathrm{P})$ + O₂(v > 0) [94] and the NO formation reaction of $\mathrm{O}({}^{3}\mathrm{P})$ + N₂(v ⩾ 13) [37] are involved in the calculations owing to their underlying role in the production of $\mathrm{O}({}^{3}\mathrm{P})$ and NO. The ozone production channel of O₂ + O₂(v > 0) [47] is ignored due to the insensitivity of the simulation results to its presence. The V–V mechanisms are thoroughly considered; however, N₂(v ⩾ 0) + O₂(w > 1) → N₂(v + 1) + O₂(w − 1) is excluded on account of its inefficient contribution to the quenching of O₂(w > 0) [95]. Both O₂(v' = 41) and N₂(v' = 58), referred to as pseudo levels, are assumed to instantaneously dissociate due to the proximity of the vibrational energy to the dissociation energy [96]. In total, the He/N₂ set includes 72 distinct species and 5831 reactions, the He/O₂ set 58 species and 3216 reactions, and the He/N₂/O₂ set 138 species and 11 799 reactions.

The considered ion and neutral reactions at the wall are tabulated in tables A10 and A11, respectively. The quenching of the excited states and the recombination of nitrogen atoms on the chamber surface are taken into account. The oxygen atom wall recombination is ignored since volume processes are expected to dominate over surface reactions under the considered operation conditions [51]. Nevertheless, the influence of the recombination probability value on the simulation results is discussed (see figure 4(b)). An ion impinging on the surface is assumed to capture an electron via the Auger effect or resonant electron transfer and then return back to the plasma region.

By modifications of the underlying production channels based on the above-mentioned reference chemical kinetics, four sets of additional analyses are conducted on the NO density in He/N₂/O₂ mixtures (see section 5.2):

• (a)  
  A rate coefficient value of 1 × 10⁻¹⁹ m³ s⁻¹ is used for the reaction $\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}(v\geqslant 13)\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})$ in this study, suggested by Guerra et al [37, 41, 42] and Pintassilgo et al [97]. A distinct value of 1 × 10⁻¹⁷ m³ s⁻¹ is used by Gordiets et al [98] and the influence of this value on the NO density is quantified.
• (b)  
  NO wall formation by the adsorbed $\mathrm{O}({}^{3}\mathrm{P})$ and $\mathrm{N}({}^{4}\mathrm{S})$ on the surface is ignored due to the negligible probability measured at a lower pressure regime [99]. However, the probability is not confirmed for atmospheric-pressure plasma jets. The presence of a NO wall formation $\mathrm{N}({}^{4}\mathrm{S})+\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}\to \mathrm{N}\mathrm{O}$ (i.e. an effective form of the surface reactions given by a set of adsorbed layer reaction mechanisms [100]) is further considered with a maximum probability of 1 based on set (a), and its role in the NO density is shown. This wall reaction is constructed under the presumption that $\mathrm{O}({}^{3}\mathrm{P})$ is sufficiently adsorbed on the surface due to its much larger concentration compared to that of $\mathrm{N}({}^{4}\mathrm{S})$ under the considered operation conditions.
• (c)  
  A well-accepted value of 7 × 10⁻¹⁸ m³ s⁻¹ [37, 86, 87] is used for the reactive quenching ${\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})$ in this work. The value is confirmed for the vibrational ground state N₂(A³Σ, v = 0). Note that a much larger value is observed for the higher vibrational quantum numbers N₂(A³Σ, v > 0) [101–106]. Furthermore, the virtually identical NO density is obtained between the measurements and the simulations considering the reactive quenching of multiple N₂ electronically excited states by $\mathrm{O}({}^{3}\mathrm{P})$ [36]. In order to estimate the role of the vibrationally excited molecules N₂(A³Σ, v > 0) and of multiple higher N₂ electronically excited states, a larger hypothetical rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ is considered for the aforementioned quenching reaction, and the resulting NO density is revealed.
• (d)  
  The reactive quenching of N₂(B³Π) by $\mathrm{O}({}^{3}\mathrm{P})$ is neglected in many chemical kinetics studies [19, 37, 86–88], with the exception of a handful of publications [36, 107, 108] that assign a rate coefficient value of 3 × 10⁻¹⁶ m³ s⁻¹. On the other hand, larger quenching rates of N₂(B³Π, v > 0) are observed at its higher vibrational levels [109]. Thus, the same hypothetical rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ for the reactive quenching ${\mathrm{N}}_{2}({\text{B}}^{3}{\Pi})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})$ is additionally included to estimate the role of N₂(B³Π, v ⩾ 0) and of multiple higher N₂ electronically excited states based on set (c). Their influence on the NO concentration is presented.

It should be noted that the state-by-state resolution of the vibrational distribution function N₂(A³Σ, B³Π; v > 0) is not preferred in the current study due to the lack of necessary data and the excessive computational load. Moreover, the kinetics of the above-mentioned multiple N₂ electronically excited states are intensively discussed in a nanosecond-pulsed air discharge at a pressure of 13 332 Pa [36]. Compared to the measured peak NO density, a factor of ∼5 is underestimated by the simulations considering the reactive quenching of N₂(A³Σ, B³Π, C³Π) by $\mathrm{O}({}^{3}\mathrm{P})$. The underestimation is minimized by an introduction of the triplet states ${\mathrm{N}}_{2}({\mathrm{W}}^{3}{{\Delta}}_{\mathrm{u}},{\mathrm{B}}^{\prime 3}{{\Sigma}}_{\text{u}}^{-},{\mathrm{E}}^{3}{{\Sigma}}_{\text{g}}^{+})$ and the singlet states ${\mathrm{N}}_{2}({\mathrm{a}}^{\prime 1}{{\Sigma}}_{\text{u}}^{-},{\mathrm{a}}^{1}{{\Pi}}_{\text{g}},{\mathrm{w}}^{1}{{\Delta}}_{\text{u}},{\mathrm{a}}^{{\prime\prime}1}{{\Sigma}}_{\text{g}}^{+})$ in this quenching with a gas kinetic rate coefficient value of 3 × 10⁻¹⁶ m³ s⁻¹ (except that of N₂(A³Σ) with ∼10⁻¹⁸ m³ s⁻¹). The role of these multiple higher electronically excited states is estimated in our study by the hypothetically large rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ in sets (c) and (d). The value is reported as a result of an available best agreement between the measured and simulated NO density (see figure 7). Note that an 'effective' value of 1.5 × 10⁻¹⁵ m³ s⁻¹ for set (d) can be suggested by the aforementioned factor of ∼5 (observed in [36]). However, the NO density is still underestimated by our simulations using this value relative to the measurements at low power (e.g. by a factor of around 2 at 0.6 W, as shown in figure B1). Although 7 × 10⁻¹⁵ m³ s⁻¹ is evidently not regarded as a realistic rate coefficient value for the reactive quenching channels of N₂(A³Σ, B³Π) in set (d), a strong signal is shown that their vibrationally excited levels and the multiple higher N₂ electronically excited states play an underlying role in the NO formation at low power. A development of the chemical kinetics involving these levels and states is desirable in the future.

The sensitivity of the simulation results with respect to the considered wall reaction mechanisms is investigated. A small oxygen atom wall recombination probability value was observed by Booth et al [110] at relatively low pressure values; however, the measurements in the considered pressure regime are still absent. Furthermore, a much larger value was assigned in the study of an atmospheric-pressure plasma jet by Schröter et al [14], in contradiction with the negligible value suggested by Waskoenig et al [51]. Likewise, based on the estimated values at low-pressure plasma sources [111–113], it is assumed that the ozone wall formation is negligible under the considered operation conditions. The influence of the oxygen and nitrogen atom wall recombination as well as the first-order ozone wall formation probabilities are analysed (see table 2).

Table 2. The variation of the simulated plasma properties for a wall reaction probability value of 1 relative to that of 0 is presented with a percentage of increase ('') or decrease (''). Those smaller than 1% are set to 0% for the sake of clarity. For the wall reactions labelled by the symbol under '→', the corresponding reactions are only included in this table for a sensitivity analysis, unless stated otherwise (see section 4 and table A11). In the zero-dimensional simulations, the COST-Jet is sustained by an absorbed power of 0.6 W at a pressure of 101 325 Pa and a gas temperature of 345 K for a feed gas mixture of 1400 sccm He + 0.5% O₂, 1400 sccm He + 0.5% N₂, or 1400 sccm He + 0.5% N₂ + 0.5% O₂.

The developed models in section 3 and 4 are firstly benchmarked against the spatially resolved simulations and a wide variety of measurements available from the literature [48–54]. The NO concentration is then characterized with a focus on the comparison between the model calculations and the recently published measurement data [34]. Lastly, the VDFs, the wall reaction probabilities and the synthetic air impurity levels are computationally investigated based on the validity of the models. In this section, a pressure of 101 325 Pa and a gas temperature of 345 K are used in the simulations, unless stated otherwise.

5.1. Benchmark against measurement data and simulation results

5.1.1. Helium plasma

The volume-averaged electron density in a He COST-Jet was reported by Golda et al [48]. The plasma is operated at a net mass flow rate of 1000 sccm and a pressure of 99 000 Pa. The gas temperature is fixed at about 345 K. Similar density values and trends are observed between the reported electron density and the zero-dimensional simulation results shown in figure 2(a). Compared with the simulations for an assumption of a Maxwellian EEDF (not shown here), the self-consistent EEDF calculation reduces the electron density (by around 28%) and increases the electron temperature (from about 2.0 eV to 2.5 eV) due to the depletion in the EEDF tail. It should be emphasized that the electron density is associated with much less susceptibility to the impurities relative to the other species (e.g. helium metastable). Furthermore, the plasma source under investigation is tightly controlled during the measurements to achieve a maximum purity.

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The helium metastable density measurements taken close to the powered electrode (i.e. highest density value) in a He μAPPJ with plasma dimensions 1 × 1.8 × 40 mm³ are provided by Niermann et al [49]. The feed helium gas flow rate value ranges from 500 sccm to 4500 sccm at a pressure of 1 × 10⁵ Pa. The gas temperature is estimated as 333 K. An input power of 23 W is fed into the discharge and a power transfer efficiency of 5% is assumed in the simulations. Both pure helium and helium with a linearly decreasing synthetic air impurity between 100–10 ppm with respect to the increasing helium flow rate are simulated due to both the back diffusion from the effluent [114] and the air leakage into the feed gas [49]. The metastable density measurement data and the zero-dimensional simulation results are shown in figure 2(b). The Penning ionization is a significant loss mechanism, and an almost two orders of magnitude smaller metastable density is predicted by the simulations in the presence of the impurity compared with that of pure helium. Note that the impurity level as a function of the gas flow rate here is not well explained by the considered form, i.e. the inverse exponentially increasing trend of the measured metastable density is not captured by the simulation results considering a linearly decreasing impurity. A likely reason is that the total impurity in the measurements exponentially decreases as the flow rate value increases, i.e. the impurity level is almost constant at high flow rate value, leading to a constant measured metastable density over 4000 sccm. This suggests that the impurity levels are strongly correlated with the feed gas flow rate.

The helium metastable density in a He atmospheric-pressure plasma jet for both continuous and pulse-modulated power input was measured by Nayak et al [50]. The plasma is confined in a volume of 2 × 9.5 × 19.1 mm³ with a mass flow rate of 5000 sccm He at a gas temperature of around 335 K. An absorbed power of 15 W is measured in the continuous discharge. The pulse modulation is applied in a period of 100 μs at a power-on duration of 20 μs and a peak power of around 15 W. The peak (inter-electrode) and the spatially averaged He(2³S) density measurements for the continuous power input as well as the corresponding zero-dimensional simulation results for a variation of the absorbed power are shown in figure 3(a). A linearly increasing He(2³S) density profile is observed in the simulations with respect to the power. The simulation results represent the volume-averaged density and show a better proximity to the spatially averaged measurement value than that of the peak. The time-resolved peak He(2³S) and ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$ density measurements as well as the zero-dimensional simulation results during a modulation cycle in the pulsed operation are shown in figure 3(b). Relative to the measurements, the simulations suggest a slightly smaller He(2³S) density. Note that only the peak density measurements between the electrodes are provided by Nayak et al [50]. The spatially averaged measurements would show a better agreement with the simulations. The overestimated ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$ density in the calculations relative to the peak measurements can be partially attributed to the role of the humid air impurities reported by Nayak et al [50]. An inclusion of 10 ppm synthetic air impurity in this work reduces the simulated ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$ density by a factor of about 0.15 (He(2³S) density about 0.25). Hence, this inclusion improves the agreement between the simulations and the spatially averaged measurements.

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5.1.2. Helium/oxygen plasma

A spatially resolved one-dimensional model was developed and its simulation results together with a set of oxygen atom density measurements in a He/O₂ μAPPJ were reported by Waskoenig et al [51]. The plasma dimensions are given as 1 × 1 × 40 mm³ at a fixed gas temperature value of 345 K and a pressure of 1 × 10⁵ Pa. A total mass flow rate of 1000 sccm helium and oxygen is fed into the plasma domain at the ratio of 1000:5. A power transfer efficiency of 5% is calculated. The simulation results and the measurements are shown in figure 4(a): the time- and space-averaged electron density and temperature calculated by Waskoenig's one-dimensional simulation as well as our zero-dimensional model, and 4(b): the oxygen atom density measurements in the discharge centre as well as the one- and zero-dimensional model calculations. The zero-dimensional simulation results for an assumed and maximum oxygen atom wall recombination probability (see reaction 9 in table A11) are also provided in figure 4(b). It should be emphasized that the deviations between the simulation results of both models are ascribed to the supplement of ${\mathrm{O}}_{4}^{+}$ and ${\mathrm{O}}_{4}^{-}$ into the zero-dimensional calculations for an improved chemical description. A much better agreement of electron temperature and oxygen atom density is achieved without this supplement. Furthermore, the oxygen atom concentration is overestimated by both modelling approaches relative to the measurements. This overestimation is minimized with an assumed wall recombination probability of 0.003. The electron density and temperature calculations are negligibly altered with a variation of the wall recombination probability between a maximum and a vanishing value, below 2%. Furthermore, the simulation results are not highly sensitive to the exclusion of the vibrationally excited levels. The absence of these levels (not shown here) raises the oxygen atom density by 5.74% and the electron density by 5.23%, whereas it reduces the electron temperature by 0.39%.

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The spatial variation of the oxygen atom, ozone and electron densities in the gas flow direction was measured inside the chamber of a He/O₂ μAPPJ by Bibinov et al [52]. The plasma is formed within a volume of 1 × 1.3 × 40 mm³ at a gas temperature of 370 K. The helium and oxygen mass flow rates are fixed at 1500 sccm and 22.5 sccm, respectively. An input power of 30 W is fed into the plasma and a power transfer efficiency of 5% is assumed. The measurement data together with the simulation results for both the plug-flow and zero-dimensional models are displayed in figure 5. The plug-flow model calculations are in agreement with the measurements. Continuously growing oxygen atom and ozone densities are observed in the gas flow direction (also confirmed by Liu et al [115]). A likely reason for this growth is that the dominant gain/loss reactions of oxygen atoms and ozone are mostly neutral–neutral collisions belonging to slower dynamics. In contrast, a maximal value of the electron density is achieved at the beginning of the jet chamber due to the faster dynamics. Similar values are shown between the measured and simulated electron density. However, the measured slightly decreasing electron density in the gas flow direction is not captured by the plug-flow model calculations. A potential cause is that the electron acceleration far away from the gas inlet [52] cannot be captured by the constant power density assumed in the plug (see equation (10)). Note that the calculated EEDFs are invariant in the gas flow direction (see section 3). It should be emphasized that a close proximity is obtained between the simulation results of both models, i.e. the spatial averages of the plug-flow results are virtually identical to the zero-dimensional results.

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5.1.3. Helium/nitrogen plasma

The space- and time-averaged helium metastable density measurements in a He/N₂ COST-Jet were reported by Korolov et al [53, 116]. The plasma jet is operated at a pressure of about 1 × 10⁵ Pa with an estimated gas temperature of 345 K. The helium mass flow rate is fixed at 1000 sccm with an additional nitrogen mass flow rate of 0.5 sccm or 1 sccm. The absorbed power values for the measurements are calculated from the particle-in-cell model described in [53]. The measurement data and the zero-dimensional simulation results are shown in figure 6(a). An inverse proportionality between the metastable density and nitrogen content is observed in both the measurement data and the simulation results. However, a slightly smaller density value is predicted by the simulations relative to the measurements. The difference is attributed to the termolecular Penning ionization (reaction 51 in table A3) and the metastable quenching via vibrationally excited nitrogen molecules (reaction 11 in table A7). The termolecular Penning ionization is the most dominant metastable loss mechanism, forming about 40% of the net loss rate. The rate coefficient was determined by Pouvesle et al [117] and later reported with a much smaller value [118]. The difference between the simulations and measurements is lowered by the latter value; however, it is not explicitly preferred in the simulations due to lack of evaluation on the accuracy. The metastable quenching rate coefficient via vibrationally excited molecular nitrogen contributes about 15% of the net metastable loss rate. In parallel with Sommerer et al [119], we assume that the rate coefficient is identical to that of the quenching via the ground state molecular nitrogen estimated by Pouvesle et al [118]. Note that this estimation does not completely exclude the quenching via vibrational levels since it relies on the optical absorption of the 2³S–3³P helium transition. A thorough analysis of the aforementioned rate coefficients is of the essence for a better resolution on the subject.

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The nitrogen atom density in a He/N₂ μAPPJ effluent (e.g. 4 mm away from the jet nozzle) was measured by Schneider et al [54]. A plasma volume of 1 × 1 × 30 mm³ is fed with a fixed helium mass flow rate of 1400 sccm and a variable nitrogen mass flow rate. An absorbed power of 0.8 W is assumed in the simulations based on the estimated relation between the applied electrode voltage and absorbed power [54]. Additionally, a gas temperature of 345 K is estimated following the similarity of the operation conditions to those of Korolov et al [53]. The measurement data and the zero-dimensional simulation results are given in figure 6(b) for a variation of the nitrogen percentage in the helium background gas. The measured density profile of below 0.5% N₂ is captured by the model; however, the experimentally predicted decay at larger percentage values is not observed in the simulations. A likely reason for this discrepancy is the presence of a solid wall in the plasma chamber that is absent in the effluent region. The disappearance of the wall induces deviations in the presumed transport (e.g. diffusion and flow) properties, which are more definitive on the effluent concentration due to the vanishing electron-impact reactions. Additionally, the quenching of $\mathrm{N}({}^{2}\mathrm{D})$ at the wall plays a relatively more important role in the $\mathrm{N}({}^{4}\mathrm{S})$ production with an increasing nitrogen content in the background gas. The difference in transport properties and the lack of wall quenching in the effluent might lead to the decay of the measured nitrogen atom density for the plasma at a large nitrogen percentage.

5.2. Characterization of NO

The absolute NO concentration produced by a He/N₂/O₂ COST-Jet was recently measured by Preissing et al [34]. A plasma volume of 1 × 1 × 30 mm³ is fed with a synthetic air mixture in a helium background at a pressure of 98 000 Pa for an estimated gas temperature of 345 K. The measurement data at the beginning of the effluent (at 0.5 mm away from the jet nozzle) and the zero-dimensional simulation results are shown in figure 7: (a) for a variation of the synthetic air mixture ratio at a helium mass flow rate of 1000 sccm and at an absorbed power of 0.8 W, (b) for a variation of the helium gas flow diluted with 0.5% synthetic air mixture at an absorbed power of 0.6 W, and (c) for a variation of the absorbed power at 1000 sccm helium mixed with 0.5% synthetic air. The simulations are presented for four more distinct sets of NO formation mechanisms in addition to the reference chemical kinetics (see section 4):

• (a)  
  A rate coefficient value of 1 × 10⁻¹⁷ m³ s⁻¹ [98] is used for the reaction

  $$\begin{equation}{\mathrm{N}}_{2}(v\geqslant 13)+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})\end{equation} \tag{ 13 }$$

  instead of 1 × 10⁻¹⁹ m³ s⁻¹ [37, 41, 42, 97].
• (b)  
  A rate coefficient value of 1 × 10⁻¹⁷ m³ s⁻¹ is used for reaction (13) with an additional NO wall formation $\mathrm{N}({}^{4}\mathrm{S})+\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}\to \mathrm{N}\mathrm{O}$ [99, 100] defined by a maximum probability of 1.
• (c)  
  A hypothetical rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ is assigned for the reactive quenching

  $$\begin{equation}{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})\end{equation} \tag{ 14 }$$

  instead of 7 × 10⁻¹⁸ m³ s⁻¹ [37, 86, 87], in order to imitate the role of N₂(A³Σ, v > 0) [101–106] and of multiple higher N₂ electronically excited states [36].
• (d)  
  A hypothetical rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ is assigned for reaction (14) as well as an additional reactive quenching

  $$\begin{equation}{\mathrm{N}}_{2}({\mathrm{B}}^{3}{\Pi})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})\end{equation} \tag{ 15 }$$

  with an identical value of 7 × 10⁻¹⁵ m³ s⁻¹ to estimate the influence of N₂(B³Π, v ⩾ 0) [107–109] and of multiple higher N₂ electronically excited states [36].

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Considerably similar NO density trends are obtained by the measurements and simulations in figure 7 with a variation of (a) the synthetic air mixture ratio, (b) the helium gas flow and (c) the absorbed power. Accordingly, a maximal net NO production is achieved by 0.5% synthetic air mixture, a low helium gas flow rate and a high absorbed power, while the NO concentration saturates at around 2 W with a variation of the power. However, the concentration values are underestimated by the simulations with the reference chemical kinetics (solid lines) relative to the experimental data (similarly observed in [36], see section 4). The amount of underestimation is mainly correlated with the absorbed power (i.e. the amount is enhanced with decreasing power). The introduction of a rate coefficient value of 1 × 10⁻¹⁷ m³ s⁻¹ for reaction (13) in set (a) (dashed lines) reduces the difference between the measurements and the simulations, whereas an additional consideration of the NO wall formation in set (b) (dashed-dotted lines) further improves the agreement between them. A much better agreement is achieved by the use of a rate coefficient value of 7 × 10⁻¹⁵ m³ s⁻¹ for reaction (14) in set (c) (dotted lines), while virtually identical NO density calculations to the measurements are obtained by an additional consideration of reaction (15) in set (d) (star lines). The inclusion of state-by-state vibrational levels N₂(A³Σ, B³Π; v > 0) and of multiple N₂ electronically excited states would better address the resolution; however, this is out of the scope of the current study due to lack of data. A thorough analysis and quantification of all these rate coefficients are prerequisites for a more accurate NO resolution in the simulations.

The plug-flow simulation results corresponding to the COST-Jet measurements by Preissing et al [34] are shown in figure 8 for a helium mass flow rate of 1000 sccm with 0.5% synthetic air mixture at absorbed power values of (a) 0.1 W, (b) 1.0 W and (c) 2.2 W. The density profiles for the above-mentioned distinct sets of NO formation mechanisms are individually shown. For each set of formation mechanisms, a close similarity is observed between the NO density at the jet nozzle and the corresponding volume-averaged value (not shown here) calculated by the zero-dimensional simulations. This confirms that the difference between the measurement data and the zero-dimensional simulation results in figure 7 is not generated by the lack of spatial resolution. The role of the power in the NO density is additionally verified by the plug-flow simulation results. An approximately linear density growth in the gas flow direction is obtained at an absorbed power of 0.1 W in figure 8(a). The steepest growths are produced by set (c) (dotted lines) and set (d) (star lines), while much flatter growth rates are observed among the remaining chemical sets at this low power operation. The influence of both set (a) and (b) increases with the increasing power, leading to a parabolic NO growth in figures 8(b) and (c). On the other hand, the reference chemical kinetics (solid lines), set (c) (dotted lines) and set (d) (star lines) induce relatively lower density values at larger power. They impose a saturation at an absorbed power of 2.2 W in figure 8(c).

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The contributions of the dominant NO gain and loss channels associated with the aforementioned COST-Jet measurements [34] are provided in figure 9 for a variation of (a) the synthetic air mixture ratio, (b) the helium gas flow and (c) the absorbed power. The reaction rates are calculated by the zero-dimensional model using the reference chemical kinetics. The NO production rate is mostly manipulated by the reactions

$$\begin{equation}\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}\mathrm{O}}_{2}\to \mathrm{N}\mathrm{O}+{\mathrm{O}}_{2},\end{equation} \tag{ 16 }$$

$$\begin{equation}\mathrm{N}({}^{2}\mathrm{D})+{\mathrm{O}}_{2}\to \mathrm{N}\mathrm{O}+\mathrm{O}({}^{1}\mathrm{D}),\end{equation} \tag{ 17 }$$

both in agreement with earlier studies [18, 19, 22, 120]. The former reaction generally plays a relatively more crucial role, while the latter gains significance at high helium gas flow and low absorbed power. In comparison with these, the contribution of reaction (13) is likewise substantial at a low synthetic air percentage and low helium gas flow. Furthermore, it solely dominates the production rate at high absorbed power. Although the source channel via reaction (14) contributes less than 10%, it forms a significant portion of the production within set (c) (see figure 7). Additionally, this channel indirectly enhances the influence of reaction (17) due to its essence on the first stage $\mathrm{N}({}^{2}\mathrm{D})$ generation [121]. The NO loss channels are mainly governed by its flow-out rate and the reactions

$$\begin{equation}\mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}\mathrm{O}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{M},\end{equation} \tag{ 18 }$$

$$\begin{equation}\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}\mathrm{O}\to {\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P}),\end{equation} \tag{ 19 }$$

both confirmed via observations [18, 19, 21, 22, 120]. The loss percentages, except that of reaction (18), are virtually invariant with the variation of the synthetic air mixture and the helium gas flow. The strong influence of reaction (18) is minimized by the other two dominant loss channels at both low and high absorbed power.

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The $\mathrm{O}({}^{3}\mathrm{P})$ density measurements in the COST-Jet fed with 1000 sccm He + 0.5% synthetic air mixture are shown in figure 10(a): data at the jet nozzle with a variation of the absorbed power, and 10(b): one-dimensional data in the gas flow direction at an absorbed power of 0.4 W. The experimental details to obtain these measurements are summarized in an investigation of a helium oxygen mixture by Steuer et al [122]. The zero-dimensional and the plug-flow $\mathrm{O}({}^{3}\mathrm{P})$ simulation results of the aforementioned distinct sets of NO formation mechanisms are presented, accordingly. A pressure of 98 000 Pa and a gas temperature of 345 K are used in the simulations following the same operation conditions as those of Preissing et al [34]. Similar values and trends are observed between the measured and simulated $\mathrm{O}({}^{3}\mathrm{P})$ densities for all the chemical sets; however, the closest agreement is obtained via set (d).

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It should be emphasized that in section 5.2, both the NO and $\mathrm{O}({}^{3}\mathrm{P})$ density measurements at low power are not captured by the simulations adopting the reference chemical kinetics (i.e. the well-accepted rate coefficient values within the literature). Four additional sets of chemical kinetics are considered to investigate their influence on the NO and $\mathrm{O}({}^{3}\mathrm{P})$ densities. The density measurements are better described by the simulations adopting an 'effective' rate coefficient value 1.5 × 10⁻¹⁵ m³ s⁻¹ (see section 4) for the reactive quenching ${\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma},{\mathrm{B}}^{3}{\Pi})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})$ as presented in figures B1 and B2. However, the measurements in the low-power region are still not yet well predicted by the simulations. Comparatively, virtually identical density calculations to the measurements are reported by those using a hypothetical larger rate coefficient value 7 × 10⁻¹⁵ m³ s⁻¹ for the aforementioned reactive quenching in set (d) as observed in figures 7 and 10. This hints that the reactive quenching of the species N₂(A³Σ, B³Π; v > 0) and multiple higher N₂ electronically excited states estimated in set (d) plays an underlying role in the NO and $\mathrm{O}({}^{3}\mathrm{P})$ density values at low power.

The accuracy of the simulation results is discussed with regard to the above-shown benchmark and characterization results. A computational insight into the detailed vibrational kinetics and the sensitivity analyses is presented for the COST-Jet in the following sections.

5.3. Population of the vibrationally excited molecules

The zero-dimensional simulation results of the vibrational distribution functions in a He/N₂/O₂ COST-Jet are shown in figure 11 with a variation of (a) and (b) the gas mixture ratio (0.1%–1.0% N₂ + 0.1%–1.0% O₂), (c) and (d) the helium flow rate (200–2500 sccm), and (e) and(f) the absorbed power (0.2–2.0 W). A close similarity is obtained between the distribution functions of the gas mixtures He/N₂/O₂, He/O₂ and He/N₂; therefore, only those of He/N₂/O₂ are addressed here. Three distinct regions are located in the oxygen distribution function: (1) fast depletion at low, (2) plateau area at intermediate and (3) Boltzmann tail at high vibrational levels, similar to low-pressure oxygen plasma [40, 123]. The synergistic role of all vibrational chemical kinetics (i.e. e–V, V–V and V–T reactions) is important for the profile at low quantum numbers, whereas the V–T mechanism is more influential on the intermediate and high vibrational levels. A Maxwellian-like distribution function at low and intermediate vibrational quanta is obtained for nitrogen molecules, similar to those at low pressure [37, 124, 125]. The tail of the distribution function is slightly elevated, except at a high power of 2.0 W. The vibrational population is initially driven by e–V energy transfer; however, the quasi-steady distribution function is mainly shaped by the V–V collisions. The negligible role of the electron-impact vibrational excitation at low quantum numbers is attributed to much higher densities of vibrationally excited nitrogen than that of electrons. On the other hand, a more important influence of the e–V mechanisms on the high quantum number region is observed at lower absorbed power due to the significantly reduced vibrational population. Additionally, the increasing influence of the e–V mechanisms with decreasing power is the main mechanism responsible for the elevated tail at the low-power operation (see figure 11(f)).

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The N₂ VDF shows a substantial dependency on the operation parameters relative to the weak response of the oxygen vibrational population. A likely reason is that the higher efficiency of nitrogen up-pumping promotes a larger variation with respect to the operation parameters. Furthermore, nitrogen levels store more internal energy with a reinforcement at higher quantum numbers. Hence, these levels are far more influential on the EEDF as well as on the resultant chemical kinetics [37]. For the high mixture ratio in figures 11(a) and (b), the collisions significantly re-distribute the vibrational energy stored in nitrogen and hence reduce the N₂ VDF. The re-distributed energy is partially transferred to a slightly enhanced oxygen vibrational population. The role of the gas flow rate in both the oxygen and nitrogen vibrational populations in figures 11(c) and (d) is less important than those of the mixture ratio and the absorbed power due to the lesser influence of the flow on the electron density and temperature. The N₂ VDF is reduced as the gas flow rate increases. A potential cause is that the N₂ VDF continuously grows in the gas flow direction until reaching the jet nozzle (see figure 12), i.e. less time exists for the accumulation of the N₂ VDF at a higher gas flow rate. On the contrary, the oxygen vibrational population saturates at the beginning of the jet chamber resulting in its insensitivity to the varied gas flow rate. This implies that the time scale of the oxygen vibrational kinetics (e.g. the e–V, V–V and V–T reactions) is much faster than that of the gas flow, whereas for nitrogen that is not the case. Both VDFs are enhanced with higher absorbed power, as shown in figures 11(e) and (f), as a result of the sufficient energy input to the e–V and V–V transfer for climbing the vibrational ladder.

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The spatial evolution of the N₂ VDF in the gas flow direction of the He/N₂/O₂ COST-Jet calculated by the plug-flow model is given in figure 12 for absorbed powers of (a) 0.2 W, (b) 0.6 W, (c) 1.0 W and (d) 2.0 W. The oxygen vibrational population is already saturated at a quarter of the plasma chamber length (1/4 L) and therefore it is not depicted in the figure. A significant growth of the N₂ VDF is observed in the direction of the flow. It is amplified with an increase of the absorbed power, specifically at the tail region. The vibrational temperature T_v=1 increases from 2097 K to 3358 K along the electrodes at an absorbed power of 0.2 W, whereas it raises from 6696 K to 16 347 K at 2.0 W.

5.4. Sensitivity analyses

The variation of the simulated COST-Jet plasma properties for varying numbers of vibrationally excited levels considered in the zero-dimensional model is given in figure 13 relative to those including the whole set, N₂(v < 58) & O₂(v < 41). Those of the He/O₂ plasma jet are not shown here since they are below 10%. A virtually negligible deviation of the simulation results is observed between the cases of N₂(v < 7) & O₂(v < 7) and N₂(v < 58) & O₂(v < 41). However, the deviation substantially increases with the decreasing number of vibrationally excited levels in the model. For a feed gas mixture of He/N₂, the densities of N₂, N₂(A³Σ) and N₂(B³Π) are altered significantly as shown in figure 13(a). The electron and helium metastable densities as well as the electron temperature are varied up to about 35% when the vibrational levels are completely ignored. The variation is remarkably larger for a feed gas mixture of He/N₂/O₂, up to about 234% as presented in figure 13(b). The plasma properties are strongly altered by the inclusion of N₂(v < 4) & O₂(v < 4), particularly on the densities of N₂(A³Σ) and N₂(B³Π). It should be emphasized that the quantitative analysis here is only valid for the considered operation conditions and the variation is reinforced with increasing absorbed power (not shown here).

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The modification of the simulated plasma properties in the COST-Jet to the changes of the wall reaction probabilities from 0 to 1 is summarized in table 2 psstac278dt2 for the gas mixtures He/O₂, He/N₂ and He/N₂/O₂. The simulations are conducted with the zero-dimensional model. The COST-Jet He plasma is not altered by these changes and it is excluded from the table. The electron density and temperature are negligibly affected by the neutral wall reaction mechanisms within the considered gas mixtures. Additionally, it is observed that all the plasma properties are insensitive to the wall quenching of He(2³S), ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$, N₂(A³Σ), N₂(B³Π), $\mathrm{O}({}^{1}\mathrm{D})$ and O₂(v < 41). The quenching of $\mathrm{N}({}^{2}\mathrm{D})$ is of importance merely for its concentration in a He/N₂ jet (not shown here). In the He/O₂ and He/N₂/O₂ mixtures, an increase of the O₂(a¹Δ_g) quenching probability reduces the density of O₂(a¹Δ_g) and raises that of O₃. The oxygen atom wall recombination and ozone wall formation probabilities have a significant influence on the $\mathrm{O}({}^{3}\mathrm{P})$ density. Moreover, the recombination probability plays an important role in the concentrations of O₃ and O₂(a¹Δ_g). In the He/N₂ and He/N₂/O₂ mixtures, a rise of the nitrogen atom wall recombination probability reduces the densities of $\mathrm{N}({}^{4}\mathrm{S})$ and $\mathrm{N}({}^{2}\mathrm{D})$. The wall quenching of N₂(v < 58) has an impact on the vibrationally excited nitrogen molecule densities, particularly on those with high quantum numbers. This quenching additionally alters the concentrations of nitrogen atoms and nitrogen oxides for a feed gas mixture of He/N₂/O₂.

The variation of the simulated plasma properties at varying orders of synthetic air impurity relative to those with a pure feed gas in the COST-Jet is shown in figure 14 for gases (a) He, (b) He/O₂ and (c) He/N₂. The zero-dimensional simulation results confirm the substantial influence of the impurity level on the plasma properties. The electron density increases with the increasing amount of synthetic air in He plasma, whereas the electron temperature as well as the densities of He(2³S) and ${\mathrm{H}\mathrm{e}}_{2}^{\ast }$ decrease. The metastable densities experience the largest variation due to the efficient Penning ionization by nitrogen and oxygen species [19]. The role of the synthetic air impurity in He/O₂ plasma is limited and produces less than 10% variation at a value of 100 ppm. The He/N₂ mixture is comparatively more sensitive to this impurity level, and up to 60% reduction of the concentrations is observed.

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Atmospheric-pressure plasma jets of planar electrode configuration fed with He, He/O₂, He/N₂ and He/N₂/O₂ mixtures are investigated by a zero-dimensional (volume-averaged) and a pseudo-one-dimensional plug-flow (spatially resolved) modelling approach. The models are developed with a focus on the vibrational kinetics and are self-consistently coupled with a Boltzmann solver (LoKI-B) under the two-term approximation to properly address the electron kinetics. A good agreement is obtained between the model calculations in this study and the spatially resolved simulation results as well as diverse measurements available from the literature, including the electron density, the electron temperature, and the concentrations of helium metastable, helium excimer, ozone, oxygen atoms and nitrogen atoms in distinct operation conditions.

NO is thoroughly characterized with the variation of the gas mixture ratio, helium flow rate and absorbed power. The measurements at low power are better described by introducing the reactive quenching of N₂(A³Σ, B³Π; v > 0) and of multiple higher N₂ electronically excited states with an 'effective' and a hypothetical larger rate coefficient value in the simulations, that forms underlying NO production mechanisms as well as significant $\mathrm{O}({}^{3}\mathrm{P})$ loss channels. A continuous growth of the NO spatial density profile is obtained in the gas flow direction, and the saturation is merely observed at a relatively high absorbed power of about 2.2 W. Within the range of the considered operation conditions, the NO loss is governed by its flow-out rate, the $\mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}\mathrm{O}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{M}$ and $\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}\mathrm{O}\to {\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$ reactions, while the formation is dominated by the $\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}\mathrm{O}}_{2}\to \mathrm{N}\mathrm{O}+{\mathrm{O}}_{2}$ and $\mathrm{N}({}^{2}\mathrm{D})+{\mathrm{O}}_{2}\to \mathrm{N}\mathrm{O}+\mathrm{O}({}^{1}\mathrm{D})$ channels. The contribution of the vibrationally excited nitrogen molecules N₂(v ⩾ 13) to the net NO formation is enhanced with increasing power.

The vibrationally excited levels of O₂(v < 41) and N₂(v < 58) are analysed. A larger response of the N₂ VDF to the variation of the gas mixture ratio, helium flow rate and absorbed power is observed relative to that of the O₂ VDF. A continuous spatial growth of the N₂ vibrational population is obtained in the gas flow direction (i.e. the population is not yet saturated at the jet nozzle). On the contrary, a fast spatial equilibrium of the O₂ vibrational population is acquired at the beginning of the plasma chamber. The simulation results are affected by the total number of vibrationally excited nitrogen molecules considered in the chemical model. However, the influence of N₂(v < 58) on the overall plasma behaviour is captured by a limited set of vibrational levels depending on the applied power value.

The sensitivity of the simulation results to the variation of the wall reaction probabilities and the synthetic air impurity levels is shown. The concentrations of nitrogen atoms and nitrogen oxides are influenced by the wall quenching of vibrationally excited nitrogen molecules. A dramatic sensitivity of the atomic oxygen and ozone densities to the oxygen atom wall recombination is observed. The plasma properties of pure He gas are significantly altered in the presence of the impurity due to the efficient Penning ionization mechanism. An impurity level up to 100 ppm has no influence on the simulation results of He/O₂ mixture, but has a strong impact on those of He/N₂ plasma.

A further analysis of the rate coefficients of the termolecular Penning ionization $\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to \mathrm{e}+{\mathrm{N}}_{2}^{+}+2\mathrm{H}\mathrm{e}$, the metastable quenching via vibrationally excited nitrogen molecules $\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{N}}_{2}(v > 0)\to \mathrm{e}+\mathrm{H}\mathrm{e}+{\mathrm{N}}_{2}^{+}$ and the NO formation channels ${\mathrm{N}}_{2}({\mathrm{X},\mathrm{A}}^{3}{\Sigma},{\mathrm{B}}^{3}{\Pi},\dots ;\enspace v)+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{2}\mathrm{D})$ is of importance for a more accurate model prediction.

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 327886311 (SFB 1316: simulations by A9 & A8 and measurements by B2 & A4). The authors are indebted to Antonio Tejero del Caz and Luis L Alves for discussions on the self-consistent LoKI-B adaptation, to Peter Bruggeman and Nader Sadeghi for discussions on the pulse-modulated plasma jet, and to Judith Golda for discussions on the experimental details of the He COST-Jet. Vasco Guerra was partially funded by the Portuguese FCT-Fundacao para a Ciencia e a Tecnologia, under projects UIDB/50010/2020 and UIDP/50010/2020.

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

See tables A1–A12.

Table A1. The volume reactions included in the He model. The rate coefficient units are given in s⁻¹, m³ s⁻¹ and m⁶ s⁻¹ for one-, two- and three-body reactions, respectively. T_e is in eV and T_g in K, if not stated otherwise. The rate coefficient f() is taken from a look-up table calculated via the referred cross-section self-consistently coupled to the EEDF [61]. The reverse reaction rate coefficient of the electron-impact excitation labelled with the symbol '^*' near the number is calculated via the principle of detailed balancing [57].

#	Reaction	Rate coefficient	Reference
1	e + He → 2e + He+	f()	[90]
2*	e + He → e + He(23S)	f()	[90]
3	e + He(23S) → 2e + He+	f()	[126]
4	$\mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to \mathrm{e}+2\mathrm{H}\mathrm{e}$	3.8 × 10−15	[14]
5	$\mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to 2\mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}$	f()	[127]
6	e + He+ → He(23S)	5.95 × 10−17 Te (K)−0.5	[27]
7	2e + He+ → e + He(23S)	1.63 × 10−21 Te (K)−4.5	[27]
8	e + He+ + He → He(23S) + He	$7.4\times 1{0}^{-47}\enspace {({T}_{\text{e}}/{T}_{\text{g}})}^{-2}$	[128]
9	$\mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}\to \mathrm{H}\mathrm{e}+\mathrm{H}\mathrm{e}$	1.0 × 10−15	[128]
10	$\mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}\to \mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+\mathrm{H}\mathrm{e}$	$8.9\times 1{0}^{-15}\enspace {({T}_{\text{g}}/{T}_{\text{e}}\enspace (\mathrm{K}))}^{-1.5}$	[129]
11	${\mathrm{H}\mathrm{e}}^{+}+2\mathrm{H}\mathrm{e}\to {\mathrm{H}\mathrm{e}}_{2}^{+}+\mathrm{H}\mathrm{e}$	1.1 × 10−43	[129]
12	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+2\mathrm{H}\mathrm{e}\to {\mathrm{H}\mathrm{e}}_{2}^{\ast }+\mathrm{H}\mathrm{e}$	2 × 10−46	[129]
13	He(23S) + 2He → 3He	2 × 10−46	[128]
14	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})\to \mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}$	1.5 × 10−15	[129]
15	He(23S) + He(23S) → e + He+ + He	$8.7\times 1{0}^{-16}\enspace {({T}_{\text{g}}/300)}^{0.5}$	[128]
16	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to \mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}+\mathrm{H}\mathrm{e}$	2.0 × 10−15	[128]
17	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to \mathrm{e}+{\mathrm{H}\mathrm{e}}^{+}+2\mathrm{H}\mathrm{e}$	5.0 × 10−16	[128]
18	${\mathrm{H}\mathrm{e}}_{2}^{\ast }\to 2\mathrm{H}\mathrm{e}$	1 × 104	[130]
19	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+\mathrm{H}\mathrm{e}\to 3\mathrm{H}\mathrm{e}$	1.5 × 10−21	[128]
20	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to \mathrm{e}+{\mathrm{H}\mathrm{e}}_{2}^{+}+2\mathrm{H}\mathrm{e}$	1.5 × 10−15	[129]
21	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+{\mathrm{H}\mathrm{e}}_{2}^{\ast }\to \mathrm{e}+{\mathrm{H}\mathrm{e}}^{+}+3\mathrm{H}\mathrm{e}$	3.0 × 10−16	[128]

Table A2. The oxygen volume reactions in the He/O₂ model. M is the background gas helium. The rate coefficient units are given in m³ s⁻¹ and m⁶ s⁻¹ for two- and three-body reactions, respectively. T_e is in eV and T_g in K, if not stated otherwise. The rate coefficient f() is taken from a look-up table calculated via the referred cross-section self-consistently coupled to the EEDF [61]. The reverse reaction rate coefficients of the electron-impact excitation labelled with the symbol '^*' near the number are calculated via the principle of detailed balancing [57].

#	Reaction	Rate coefficient	Reference
1	$\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to {\mathrm{O}}^{-}+{\mathrm{O}}_{2}$	1 × 10−43	[87]
2	$\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−43	[87]
3*	$\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{e}+\mathrm{O}({}^{1}\mathrm{D})$	f()	[90]
4	$\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})\to 2\mathrm{e}+{\mathrm{O}}^{+}$	f()	[90]
5	$\mathrm{e}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{-}$	f()	[131]
6	$\mathrm{e}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}$	1.4 × 10−41 (Tg/Te (K))exp(−600/Tg) × exp{700(Te (K) − Tg)/(Te (K)Tg)}	[132]
7	$\mathrm{e}+{\mathrm{O}}_{2}+\mathrm{H}\mathrm{e}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{-}$	8.8 × 10−42 Te (K)−0.5	[27]
8	$\mathrm{e}+{\mathrm{O}}_{2}\to {\mathrm{O}}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	f()	[90]
9	$\mathrm{e}+{\mathrm{O}}_{2}\to \mathrm{e}+2\mathrm{O}({}^{3}\mathrm{P})$	f()	[90]
10	$\mathrm{e}+{\mathrm{O}}_{2}\to \mathrm{e}+\mathrm{O}({}^{1}\mathrm{D})+\mathrm{O}({}^{3}\mathrm{P})$	f()	[90]
11	$\mathrm{e}+{\mathrm{O}}_{2}\to 2\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	f()	[126]
12*	e + O2 → e + O2(a1Δg)	f()	[90]
13	$\mathrm{e}+{\mathrm{O}}_{2}\to 2\mathrm{e}+{\mathrm{O}}_{2}^{+}$	f()	[90]
14	$\mathrm{e}+{\mathrm{O}}_{3}+\mathrm{M}\to {\mathrm{O}}_{3}^{-}+\mathrm{M}$	1 × 10−43	[87]
15	e + O3 → O− + O2	f()	[133]
16	$\mathrm{e}+{\mathrm{O}}_{3}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}^{-}$	f()	[133]
17	$\mathrm{e}+{\mathrm{O}}_{3}\to \mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	8.8 × 10−16	[134]
18	$\mathrm{e}+\mathrm{O}({}^{1}\mathrm{D})\to 2\mathrm{e}+{\mathrm{O}}^{+}$	f()	[135]
19	$\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}^{-}$	f()	[126]
20	$\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{e}+2\mathrm{O}({}^{3}\mathrm{P})$	f()	[126]
21	$\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{O}({}^{1}\mathrm{D})$	f()	[126]
22	$\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to 2\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}^{+}$	f()	[126]
23	$\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to 2\mathrm{e}+{\mathrm{O}}_{2}^{+}$	f()	[126]
24	$\mathrm{e}+\mathrm{e}+{\mathrm{O}}^{+}\to \mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})$	$1\times 1{0}^{-31}\enspace {({T}_{\text{g}}/{T}_{\text{e}}\enspace (\mathrm{K}))}^{4.5}$	[86]
25	$\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{M}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{M}$	3.12 × 10−35/Te (K)1.5	[86]
26	$\mathrm{e}+{\mathrm{O}}^{+}\to \mathrm{O}({}^{1}\mathrm{D})$	4.66 × 10−17 Te (K)−0.5	[27]
27	$2\mathrm{e}+{\mathrm{O}}^{+}\to \mathrm{e}+\mathrm{O}({}^{1}\mathrm{D})$	1.628 × 10−21 Te (K)−4.5	[27]
28	$\mathrm{e}+{\mathrm{O}}_{2}^{+}+\mathrm{M}\to {\mathrm{O}}_{2}+\mathrm{M}$	3.12 × 10−35/Te (K)1.5	[86]
29	$\mathrm{e}+\mathrm{e}+{\mathrm{O}}_{2}^{+}\to \mathrm{e}+{\mathrm{O}}_{2}$	$1\times 1{0}^{-31}\enspace {({T}_{\text{g}}/{T}_{\text{e}}\enspace (\mathrm{K}))}^{4.5}$	[86]
30	$\mathrm{e}+{\mathrm{O}}_{2}^{+}\to 2\mathrm{O}({}^{3}\mathrm{P})$	f()	[136]
31	$\mathrm{e}+{\mathrm{O}}_{2}^{+}\to \mathrm{O}({}^{1}\mathrm{D})+\mathrm{O}({}^{3}\mathrm{P})$	4.688 × 10−12 Te (K)−0.7	[27]
32	$\mathrm{e}+{\mathrm{O}}_{4}^{+}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	2.42 × 10−11/Te (K)0.5	[87]
33	$\mathrm{e}+{\mathrm{O}}^{-}\to 2\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})$	2.2 × 10−20 Te (K)0.5 exp(−26356/Te (K))	[27]
34	$\mathrm{H}\mathrm{e}+{\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}^{-}\to 2\mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[27]
35	$\mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}^{+}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{+}$	$1\times 1{0}^{-41}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
36	$\mathrm{H}\mathrm{e}+{\mathrm{O}}^{-}+{\mathrm{O}}^{+}\to \mathrm{H}\mathrm{e}+2\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[27]
37	$\mathrm{H}\mathrm{e}+{\mathrm{O}}^{-}+{\mathrm{O}}_{2}^{+}\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[27]
38	${\mathrm{H}\mathrm{e}}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}^{+}$	$5\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
39	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{2}\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}^{+}$	$1.07\times 1{0}^{-15}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
40	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{2}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{+}$	$3.3\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
41	He+ + O3 → He + O+ + O2	$1.07\times 1{0}^{-15}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
42	${\mathrm{H}\mathrm{e}}^{+}+\mathrm{O}({}^{1}\mathrm{D})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}^{+}$	$5\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
43	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}^{+}$	$1.07\times 1{0}^{-15}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
44	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{+}$	$3.3\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
45	${\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{+}$	$1\times 1{0}^{-42}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
46	${\mathrm{O}}^{+}+{\mathrm{O}}_{2}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}^{+}$	$2\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{0.4}$	[27]
47	${\mathrm{O}}^{+}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{+}$	1 × 10−16	[27]
48	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}+\mathrm{M}\to {\mathrm{O}}_{4}^{+}+\mathrm{M}$	$5.5\times 1{0}^{-43}\enspace {(300/{T}_{\text{g}})}^{2.7}$	[137]
49	${\mathrm{O}}_{4}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{3}$	3 × 10−16	[86]
50	${\mathrm{O}}_{4}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	$3.3\times 1{0}^{-12}\enspace {(300/{T}_{\text{g}})}^{4}\enspace \mathrm{exp}(-5030/{T}_{\text{g}})$	[86]

Table A2. Continued.

51	${\mathrm{O}}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{e}+{\mathrm{O}}_{2}$	$2\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
52	${\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	$2.7\times 1{0}^{-16}\enspace {({T}_{\text{g}}/300)}^{0.5}\enspace \mathrm{exp}(-5590/{T}_{\text{g}})$	[87]
53	O− + O2 → e + O3	$5\times 1{0}^{-18}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
54	${\mathrm{O}}^{-}+{\mathrm{O}}_{2}+\mathrm{M}\to {\mathrm{O}}_{3}^{-}+\mathrm{M}$	1.1 × 10−42 (300/Tg)	[87]
55	${\mathrm{O}}^{-}+{\mathrm{O}}_{2}+{\mathrm{O}}^{+}\to 2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[27]
56	${\mathrm{O}}^{-}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{+}\to \mathrm{O}({}^{3}\mathrm{P})+2{\mathrm{O}}_{2}$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[27]
57	${\mathrm{O}}^{-}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{+}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{3}$	$2\times 1{0}^{-37}\enspace {(300/{T}_{\text{g}})}^{2.5}$	[57]
58	O− + O3 → e + 2O2	$3.01\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
59	${\mathrm{O}}^{-}+{\mathrm{O}}_{3}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}^{-}$	$1.99\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
60	${\mathrm{O}}^{-}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{-}$	$1.02\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
61	O− + O2(a1Δg) → e + O3	$3\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[27]
62	${\mathrm{O}}^{-}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}^{-}$	1 × 10−16	[51]
63	${\mathrm{O}}_{2}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}_{2}+{\mathrm{O}}^{-}$	$1.5\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
64	${\mathrm{O}}_{2}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{e}+{\mathrm{O}}_{3}$	$1.5\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
65	${\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}+\mathrm{M}\to {\mathrm{O}}_{4}^{-}+\mathrm{M}$	3.5 × 10−43 (300/Tg)	[87]
66	${\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{3}^{-}$	$6\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
67	${\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{3}+{\mathrm{O}}_{2}+\mathrm{e}$	6 × 10−16	[138]
68	${\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{e}+2{\mathrm{O}}_{2}$	$2\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[27]
69	${\mathrm{O}}_{3}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}^{-}$	$2.5\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
70	${\mathrm{O}}_{3}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	3 × 10−16	[87]
71	${\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{3}+{\mathrm{O}}_{2}+\mathrm{e}$	2.3 × 10−17	[138]
72	${\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	3 × 10−16	[138]
73	${\mathrm{O}}_{4}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}^{-}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	3 × 10−16	[87]
74	${\mathrm{O}}_{4}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}$	4 × 10−16	[87]
75	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}^{-}\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})$	2 × 10−13 (300/Tg)	[27]
76	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{2}^{-}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}$	2 × 10−13 (300/Tg)	[27]
77	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{O}}_{3}^{-}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{3}$	2 × 10−13 (300/Tg)	[27]
78	${\mathrm{O}}^{+}+{\mathrm{O}}^{-}\to 2\mathrm{O}({}^{3}\mathrm{P})$	2 × 10−13 (300/Tg)	[27]
79	${\mathrm{O}}^{+}+{\mathrm{O}}_{2}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	2 × 10−13 (300/Tg)	[27]
80	${\mathrm{O}}^{+}+{\mathrm{O}}_{3}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}$	2 × 10−13 (300/Tg)	[27]
81	${\mathrm{O}}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
82	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}^{-}\to 3\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[27]
83	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	2 × 10−13 (300/Tg)	[27]
84	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to 2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	1 × 10−13	[27]
85	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to 2{\mathrm{O}}_{2}$	2 × 10−13 (300/Tg)	[27]
86	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to 2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}$	2 × 10−13	[27]
87	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{3}$	2 × 10−13 (300/Tg)	[27]
88	${\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
89	${\mathrm{O}}_{4}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
90	${\mathrm{O}}_{4}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
91	${\mathrm{O}}_{4}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
92	${\mathrm{O}}_{4}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
93	$\mathrm{H}\mathrm{e}+2\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}$	1 × 10−45	[27]
94	$\mathrm{H}\mathrm{e}+2\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})$	$9.88\times 1{0}^{-47}\enspace {(300/{T}_{\text{g}})}^{0.63}$	[27]
95	$\mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{3}$	$3.4\times 1{0}^{-46}\enspace {(300/{T}_{\text{g}})}^{1.2}$	[27]
96	$\mathrm{H}\mathrm{e}+\mathrm{O}({}^{1}\mathrm{D})\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−19	[27]
97	He + O2(a1Δg) → He + O2	$8\times 1{0}^{-27}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
98	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{e}$	$2.54\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
99	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{O}}_{2}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{+}+\mathrm{e}$	$2.54\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
100	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{O}}_{3}\to \mathrm{H}\mathrm{e}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}^{+}+\mathrm{e}$	$2.54\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
101	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+\mathrm{O}({}^{1}\mathrm{D})\to \mathrm{H}\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{e}$	$2.54\times 1{0}^{-16}\enspace {(300/{T}_{\text{g}})}^{-0.5}$	[27]
102	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+{\mathrm{O}}_{2}\to \mathrm{e}+2\mathrm{H}\mathrm{e}+{\mathrm{O}}_{2}^{+}$	3.6 × 10−16	[50, 139]
103	$3\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	$9.21\times 1{0}^{-46}\enspace {(300/{T}_{\text{g}})}^{0.63}$	[27]
104	$3\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})$	$6.93\times 1{0}^{-47}\enspace {(300/{T}_{\text{g}})}^{0.63}$	[27]
105	$\mathrm{O}({}^{3}\mathrm{P})+2{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{3}$	$6\times 1{0}^{-46}\enspace {(300/{T}_{\text{g}})}^{2.8}$	[27]
106	$2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}$	$3.4\times 10-46\enspace {(300/{T}_{\text{g}})}^{1.2}$	[27]
107	$2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to 2{\mathrm{O}}_{2}$	$2.56\times 10{0}^{-46}\enspace {(300/{T}_{\text{g}})}^{0.63}$	[27]

Table A2. Continued.

108	$2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})$	$1.93\times 1{0}^{-47}\enspace {(300/{T}_{\text{g}})}^{0.63}$	[27]
109	$\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}+{\mathrm{O}}_{3}\to 2{\mathrm{O}}_{3}$	2.27 × 10−47 exp(1057/Tg)	[140]
110	$\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}\to 2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	1.56 × 10−15 exp(−11490/Tg)	[27]
111	$\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}\to 2{\mathrm{O}}_{2}$	1.5 × 10−17 exp(−2250/Tg)	[140]
112	${\mathrm{O}}_{2}+{\mathrm{O}}_{3}\to \mathrm{O}({}^{3}\mathrm{P})+2{\mathrm{O}}_{2}$	1.56 × 10−15 exp(−11490/Tg)	[27]
113	$2{\mathrm{O}}_{3}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}+{\mathrm{O}}_{3}$	1.56 × 10−15 exp(−11490/Tg)	[27]
114	${\mathrm{O}}_{3}+\mathrm{M}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}+\mathrm{M}$	3.92 × 10−16 exp(−11400/Tg)	[140]
115	$\mathrm{O}({}^{1}\mathrm{D})+\mathrm{O}({}^{3}\mathrm{P})\to 2\mathrm{O}({}^{3}\mathrm{P})$	8 × 10−18	[27]
116	$\mathrm{O}({}^{1}\mathrm{D})+{\mathrm{O}}_{2}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	4.8 × 10−18 exp(−67/Tg)	[27]
117	$\mathrm{O}({}^{1}\mathrm{D})+{\mathrm{O}}_{2}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})$	1.6 × 10−18 exp(−67/Tg)	[27]
118	$\mathrm{O}({}^{1}\mathrm{D})+{\mathrm{O}}_{3}\to 2\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	1.2 × 10−16	[27]
119	$\mathrm{O}({}^{1}\mathrm{D})+{\mathrm{O}}_{3}\to 2{\mathrm{O}}_{2}$	1.2 × 10−16	[27]
120	$\mathrm{O}({}^{1}\mathrm{D})+{\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	1 × 10−17	[82]
121	${\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})+\mathrm{O}({}^{3}\mathrm{P})\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{2}$	2 × 10−22	[27]
122	${\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})+{\mathrm{O}}_{2}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{O}}_{3}$	$2.95\times 1{0}^{-27}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[27]
123	O2(a1Δg) + O2 → 2O2	3 × 10−24 exp(−200/Tg)	[27]
124	${\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})+{\mathrm{O}}_{3}\to \mathrm{O}({}^{3}\mathrm{P})+2{\mathrm{O}}_{2}$	5.2 × 10−17 exp(−2840/Tg)	[27]
125	${\mathrm{O}}_{2}({\mathrm{a}}^{1}{{\Delta}}_{\text{g}})+{\mathrm{O}}_{3}\to \mathrm{O}({}^{1}\mathrm{D})+2{\mathrm{O}}_{2}$	1.01 × 10−17	[51]
126	2O2(a1Δg) → 2O2	9 × 10−23 exp(−560/Tg)	[27]

Table A3. The nitrogen volume reactions in the He/N₂ model. M is the background gas helium. The rate coefficient units are given in s⁻¹, m³ s⁻¹ and m⁶ s⁻¹ for one-, two- and three-body reactions, respectively. T_e is in eV and T_g in K, if not stated otherwise. The rate coefficient f() is taken from a look-up table calculated via the referred cross-section self-consistently coupled to the EEDF [61]. The reverse reaction rate coefficients of the electron-impact excitation labelled with the symbol '^*' near the number are calculated via the principle of detailed balancing [57].

#	Reaction	Rate coefficient	Reference
1*	$\mathrm{e}+\mathrm{N}({}^{4}\mathrm{S})\to \mathrm{e}+\mathrm{N}({}^{2}\mathrm{D})$	f()	[90]
2	$\mathrm{e}+\mathrm{N}({}^{4}\mathrm{S})\to 2\mathrm{e}+{\mathrm{N}}^{+}$	f()	[90]
3	$\mathrm{e}+\mathrm{N}({}^{2}\mathrm{D})\to 2\mathrm{e}+{\mathrm{N}}^{+}$	$1.67\times 1{0}^{-14}\enspace {T}_{\text{e}}^{0.50}\enspace \mathrm{exp}(-13.07/{T}_{\text{e}})$	[83]
4	$\mathrm{e}+{\mathrm{N}}_{2}\to \mathrm{e}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	f()	[91]
5	$\mathrm{e}+{\mathrm{N}}_{2}\to \mathrm{e}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{2}\mathrm{D})$	f()	[91]
6*	e + N2 → e + N2(A3Σ)	f()	[90]
7*	e + N2 → e + N2(B3Π)	f()	[90]
8	$\mathrm{e}+{\mathrm{N}}_{2}\to 2\mathrm{e}+{\mathrm{N}}_{2}^{+}$	f()	[90]
9	$\mathrm{e}+{\mathrm{N}}_{2}\to 2\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{N}({}^{2}\mathrm{D})$	$5.88\times 1{0}^{-16}\enspace {T}_{\text{e}}^{1.17}\enspace \mathrm{exp}(-22.36/{T}_{\text{e}})$	[83]
10	e + N2 → 3e + N+ + N+	$9.95\times 1{0}^{-16}\enspace {T}_{\text{e}}^{0.56}\enspace \mathrm{exp}(-43.62/{T}_{\text{e}})$	[83]
11	$\mathrm{e}+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})\to 2\mathrm{e}+{\mathrm{N}}_{2}^{+}$	$1.08\times 1{0}^{-14}\enspace {T}_{\text{e}}^{0.71}\enspace \mathrm{exp}(-12.04/{T}_{\text{e}})$	[83]
12	$\mathrm{e}+{\mathrm{N}}_{2}({\mathrm{B}}^{3}{\Pi})\to 2\mathrm{e}+{\mathrm{N}}_{2}^{+}$	$1.08\times 1{0}^{-14}\enspace {T}_{\text{e}}^{0.71}\enspace \mathrm{exp}(-12.04/{T}_{\text{e}})$	[83]
13	$2\mathrm{e}+{\mathrm{N}}^{+}\to \mathrm{e}+\mathrm{N}({}^{4}\mathrm{S})$	$5.4\times 1{0}^{-36}\enspace {T}_{\text{e}}^{-4.5}$	[85]
14	$\mathrm{e}+{\mathrm{N}}^{+}+{\mathrm{N}}_{2}\to \mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	$6\times 1{0}^{-39}\enspace {(300/{T}_{\text{e}}\enspace (\mathrm{K}))}^{1.5}$	[85]
15	$\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to \mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	$6\times 1{0}^{-39}\enspace {(300/{T}_{\text{e}}\enspace (\mathrm{K}))}^{1.5}$	[85]
16	$\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{H}\mathrm{e}\to \mathrm{N}({}^{4}\mathrm{S})+\mathrm{H}\mathrm{e}$	$1\times 1{0}^{-39}\enspace {({T}_{\text{e}}\enspace (\mathrm{K})/300)}^{-1.5}\enspace {({T}_{\text{g}}/300)}^{-1}$	[141]
17	$\mathrm{e}+{\mathrm{N}}_{2}^{+}\to 2\mathrm{N}({}^{4}\mathrm{S})$	$4.8\times 1{0}^{-13}\enspace {({T}_{\text{e}}/{T}_{\text{g}})}^{-0.5}$	[128]
18	$\mathrm{e}+{\mathrm{N}}_{2}^{+}\to \mathrm{N}({}^{2}\mathrm{D})+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}{T}_{\text{e}}^{-0.5}$	[84]
19	$\mathrm{e}+{\mathrm{N}}_{2}^{+}\to {\mathrm{N}}_{2}$	4 × 10−18	[142]
20	$2\mathrm{e}+{\mathrm{N}}_{2}^{+}\to \mathrm{e}+{\mathrm{N}}_{2}$	3.17 × 10−42	[128]
21	$\mathrm{e}+{\mathrm{N}}_{3}^{+}\to \mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{e}}\enspace (\mathrm{K}))}^{0.5}$	[85]
22	$\mathrm{e}+{\mathrm{N}}_{4}^{+}\to 2{\mathrm{N}}_{2}$	3 × 10−13	[128]
23	$2\mathrm{e}+{\mathrm{N}}_{4}^{+}\to \mathrm{e}+2{\mathrm{N}}_{2}$	3.17 × 10−42	[128]
24	${\mathrm{H}\mathrm{e}}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}^{+}+\mathrm{H}\mathrm{e}$	1.6 × 10−15	[84]
25	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}^{+}+\mathrm{H}\mathrm{e}$	6.5 × 10−16	[128, 141]
26	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{N}}_{2}\to {\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{H}\mathrm{e}$	6.5 × 10−16	[141]
27	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to {\mathrm{N}}_{2}^{+}+2\mathrm{H}\mathrm{e}$	1.1 × 10−41	[117, 128, 141]
28	${\mathrm{H}\mathrm{e}}^{+}+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to {\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+2\mathrm{H}\mathrm{e}$	1.1 × 10−41	[117, 141]
29	${\mathrm{H}\mathrm{e}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}}^{+}$	1.2 × 10−15	[84]
30	${\mathrm{H}\mathrm{e}}_{2}^{+}+{\mathrm{N}}_{2}\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}}_{2}^{+}$	1.1 × 10−15	[128, 141, 143]
31	${\mathrm{H}\mathrm{e}}_{2}^{+}+{\mathrm{N}}_{2}\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	7 × 10−16	[85]
32	${\mathrm{H}\mathrm{e}}_{2}^{+}+\mathrm{H}\mathrm{e}+{\mathrm{N}}_{2}\to 3\mathrm{H}\mathrm{e}+{\mathrm{N}}_{2}^{+}$	1.6 × 10−41	[128, 141, 144]
33	${\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	$3.3\times 1{0}^{-43}\enspace {(300/{T}_{\text{g}})}^{0.75}$	[85]
34	${\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{H}\mathrm{e}\to {\mathrm{N}}_{2}^{+}+\mathrm{H}\mathrm{e}$	6.8 × 10−44	[141]
35	${\mathrm{N}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}$	1 × 10−41	[85]
36	${\mathrm{N}}^{+}+{\mathrm{N}}_{2}\to \mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}^{+}$	4.45 × 10−16	[85]
37	${\mathrm{N}}^{+}+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to {\mathrm{N}}_{3}^{+}+\mathrm{H}\mathrm{e}$	$8.2\times 1{0}^{-42}\enspace {({T}_{\text{g}}/300)}^{-1.69}$	[145]
38	${\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}_{2}+{\mathrm{N}}^{+}$	5 × 10−18	[84]
39	${\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}\to {\mathrm{N}}_{3}^{+}+{\mathrm{N}}_{2}$	9 × 10−42 exp(400/Tg)	[85]
40	${\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{M}\to {\mathrm{N}}_{3}^{+}+\mathrm{M}$	1 × 10−41 (300/Tg)	[146]
41	${\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{2}\mathrm{D})\to {\mathrm{N}}_{2}+{\mathrm{N}}^{+}$	1 × 10−16	[84]
42	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to {\mathrm{N}}_{4}^{+}+\mathrm{H}\mathrm{e}$	$8.9\times 1{0}^{-42}\enspace {({T}_{\text{g}}/300)}^{-1.54}$	[128, 141, 147]
43	${\mathrm{N}}_{2}^{+}+2{\mathrm{N}}_{2}\to {\mathrm{N}}_{4}^{+}+{\mathrm{N}}_{2}$	5 × 10−41	[148]
44	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})\to {\mathrm{N}}_{3}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	3 × 10−16	[86]
45	${\mathrm{N}}_{3}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}$	6.6 × 10−17	[85]
46	${\mathrm{N}}_{3}^{+}+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	6.6 × 10−17	[85]
47	${\mathrm{N}}_{4}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to 2{\mathrm{N}}_{2}+{\mathrm{N}}^{+}$	1 × 10−17	[84]
48	${\mathrm{N}}_{4}^{+}+{\mathrm{N}}_{2}\to 2{\mathrm{N}}_{2}+{\mathrm{N}}_{2}^{+}$	2.1 × 10−16 exp(121/Tg)	[84]
49	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})\to \mathrm{e}+{\mathrm{N}}^{+}+\mathrm{H}\mathrm{e}$	1.5 × 10−16	[84]
50	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{N}}_{2}\to \mathrm{e}+{\mathrm{N}}_{2}^{+}+\mathrm{H}\mathrm{e}$	5 × 10−17	[128]
51	$\mathrm{H}\mathrm{e}({2}^{3}\mathrm{S})+{\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}\to \mathrm{e}+{\mathrm{N}}_{2}^{+}+2\mathrm{H}\mathrm{e}$	3.3 × 10−42	[148]
52	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+\mathrm{N}({}^{4}\mathrm{S})\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{e}$	1.5 × 10−16	[84]
53	${\mathrm{H}\mathrm{e}}_{2}^{\ast }+{\mathrm{N}}_{2}\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}}_{2}^{+}+\mathrm{e}$	5 × 10−17	[128]
54	$\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})\to \mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})$	1 × 10−44	[149]

Table A3. Continued.

55	$\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	8.27 × 10−46 exp(500/Tg)	[86]
56	$\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})$	8.27 × 10−46 exp(500/Tg)	[86]
57	$\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}+{\mathrm{N}}_{2}({\mathrm{B}}^{3}{\Pi})$	8.27 × 10−46 exp(500/Tg)	[150]
58	$\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{H}\mathrm{e}\to {\mathrm{N}}_{2}+\mathrm{H}\mathrm{e}$	$2.5\times 1{0}^{-44}\enspace {({T}_{\text{g}}/300)}^{0.33}$	[141]
59	$\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})\to {\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	4 × 10−17	[85]
60	${\mathrm{N}}_{2}\to {\mathrm{N}}_{2}^{+}+\mathrm{e}$	1 × 10−15	[84]
61	${\mathrm{N}}_{2}+\mathrm{M}\to \mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{M}$	4.29 × 10−16 exp(−86460/Tg)	[84]
62	${\mathrm{N}}_{2}+\mathrm{N}({}^{2}\mathrm{D})\to \mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	2.4 × 10−20	[84]
63	N2 + N2(A3Σ) → N2 + N2	1.9 × 10−18	[84]
64	N2 + N2(B3Π) → N2 + N2	1.9 × 10−18	[84]
65	N2 + N2(B3Π) → N2(A3Σ) + N2	2.85 × 10−17	[85]
66	2N2(A3Σ) → N2(A3Σ) + N2	1.36 × 10−15	[119]
67	2N2(A3Σ) → N2(B3Π) + N2	7.7 × 10−17	[85]
68	N2(A3Σ) + N2(B3Π) → N2(A3Σ) + N2	1.36 × 10−15	[119]
69	N2(A3Σ) + N2(B3Π) → N2(B3Π) + N2	1.36 × 10−15	[119]
70	N2(B3Π) → N2(A3Σ)	2 × 105	[85]
71	2N2(B3Π) → N2(A3Σ) + N2	1.36 × 10−15	[119]
72	2N2(B3Π) → N2(B3Π) + N2	1.36 × 10−15	[119]

Table A4. The oxygen and nitrogen volume reactions in the He/N₂/O₂ model. M is the background gas helium. The rate coefficient units are given in m³ s⁻¹ and m⁶ s⁻¹ for two- and three-body reactions, respectively. T_e is in eV and T_g in K, if not stated otherwise. The rate coefficient f() is taken from a look-up table calculated via the referred cross-section self-consistently coupled to the EEDF [61].

#	Reaction	Rate coefficient	Reference
1	$\mathrm{e}+{\mathrm{O}}_{2}+{\mathrm{N}}_{2}\to {\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}$	$1.1\times 1{0}^{-43}\enspace {({T}_{\text{g}}/{T}_{\text{e}}\enspace (\mathrm{K}))}^{2}\enspace \mathrm{exp}(-70/{T}_{\text{g}})\times \mathrm{exp}\left\{1500({T}_{\text{e}}\enspace (\mathrm{K})-{T}_{\text{g}})/({T}_{\text{e}}\enspace (\mathrm{K}){T}_{\text{g}})\right\}$	[132]
2	e + NO → NO−	f()	[151]
3	e + NO + M → NO− + M	8 × 10−43	[87]
4	$\mathrm{e}+\mathrm{N}\mathrm{O}\to {\mathrm{O}}^{-}+\mathrm{N}({}^{4}\mathrm{S})$	f()	[152]
5	e + NO → e + e + NO+	f()	[151]
6	$\mathrm{e}+\mathrm{N}\mathrm{O}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	f()	[152]
7	$\mathrm{e}+\mathrm{N}\mathrm{O}\to \mathrm{e}+\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	f()	[152]
8	$\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{M}$	1.5 × 10−42	[146]
9	e + NO2 → O− + NO	f()	[89]
10	$\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	f()	[89]
11	e + NO2 → e + e + N+ + O2	f()	[89]
12	e + NO2 → e + e + O+ + NO	f()	[89]
13	$\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}^{+}$	f()	[89]
14	$\mathrm{e}+{\mathrm{N}\mathrm{O}}_{3}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{M}$	1 × 10−42	[146]
15	e + N2O → N2O−	f()	[151]
16	e + N2O → O− + N2	f()	[89]
17	$\mathrm{e}+{\mathrm{N}}_{2}\mathrm{O}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	f()	[89]
18	$\mathrm{e}+{\mathrm{N}}_{2}\mathrm{O}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	f()	[89]
19	e + N2O → e + e + N+ + NO	f()	[89]
20	e + N2O → e + e + O+ + N2	f()	[89]
21	e + N2O → e + e + N2O+	f()	[151]
22	$\mathrm{e}+{\mathrm{N}}_{2}{\mathrm{O}}_{5}\to \mathrm{e}+\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}$	f()	[153–155]
23	$\mathrm{e}+{\mathrm{N}\mathrm{O}}^{+}\to \mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	f()	[156]
24	$\mathrm{e}+{\mathrm{N}\mathrm{O}}^{+}\to \mathrm{N}({}^{2}\mathrm{D})+\mathrm{O}({}^{3}\mathrm{P})$	f()	[156]
25	e + NO+ + M → NO + M	3.12 × 10−35/Te (K)1.5	[86]
26	e + e + NO+ → NO + e	$1\times 1{0}^{-31}\enspace {({T}_{\text{g}}/{T}_{\text{e}}\enspace (\mathrm{K}))}^{4.5}$	[86]
27	$\mathrm{e}+{\mathrm{N}\mathrm{O}}_{2}^{+}\to \mathrm{N}\mathrm{O}+\mathrm{O}({}^{3}\mathrm{P})$	3.46 × 10−12/Te (K)0.5	[87]
28	$\mathrm{e}+{\mathrm{N}}_{2}{\mathrm{O}}^{+}\to {\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	3.46 × 10−12/Te (K)0.5	[87]
29	He + NO− → He + NO + e	$2.4\times 1{0}^{-19}\enspace {({T}_{\text{g}}/300)}^{0.5}$	[157]
30	He+ + NO → He + NO+	1.6 × 10−15	[157]
31	${\mathrm{H}\mathrm{e}}^{+}+\mathrm{N}\mathrm{O}\to \mathrm{H}\mathrm{e}+{\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	4.2 × 10−16	[157]
32	${\mathrm{H}\mathrm{e}}^{+}+\mathrm{N}\mathrm{O}\to \mathrm{H}\mathrm{e}+{\mathrm{N}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	1.5 × 10−15	[158]
33	${\mathrm{H}\mathrm{e}}_{2}^{+}+\mathrm{N}\mathrm{O}\to 2\mathrm{H}\mathrm{e}+{\mathrm{N}\mathrm{O}}^{+}$	1.3 × 10−15	[158]
34	${\mathrm{N}}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−18	[159]
35	${\mathrm{N}}^{+}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{M}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{M}$	1 × 10−41	[159]
36	${\mathrm{N}}^{+}+{\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	2.7 × 10−16	[160]
37	N+ + O2 → O+ + NO	2.8 × 10−17	[160]
38	${\mathrm{N}}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	3 × 10−16	[159]
39	N+ + O3 → NO+ + O2	5 × 10−16	[86]
40	${\mathrm{N}}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	4.72 × 10−16	[161]
41	${\mathrm{N}}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	8.33 × 10−17	[161]
42	N+ + NO → O+ + N2	1 × 10−18	[86]
43	${\mathrm{N}}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	3 × 10−16	[159]
44	N+ + NO2 → NO+ + NO	5 × 10−16	[159]
45	N+ + N2O → NO+ + N2	5.5 × 10−16	[161]
46	${\mathrm{N}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	1.4 × 10−16	[146]
47	${\mathrm{N}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{2}\mathrm{D})$	1.8 × 10−16 (300/Tg)	[146]
48	${\mathrm{N}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}^{+}+{\mathrm{N}}_{2}$	$1\times 1{0}^{-17}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
49	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}$	5 × 10−17	[161]
50	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}$	1 × 10−16	[87]
51	${\mathrm{N}}_{2}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}$	3.9 × 10−16	[160]
52	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}\mathrm{O}$	5 × 10−17	[162]
53	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}$	3 × 10−16	[163]
54	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}}_{2}$	6 × 10−16	[161]
55	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	4 × 10−16	[86]

Table A4. Continued.

56	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	2.3 × 10−17	[87]
57	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}$	2 × 10−17	[87]
58	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}$	4.4 × 10−17	[87]
59	${\mathrm{N}}_{3}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	7 × 10−17	[87]
60	${\mathrm{N}}_{3}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}}_{2}$	7 × 10−17	[87]
61	${\mathrm{N}}_{3}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}\mathrm{O}+{\mathrm{N}}_{2}$	7 × 10−17	[162]
62	${\mathrm{N}}_{3}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	7 × 10−17	[162]
63	${\mathrm{N}}_{3}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	5 × 10−17	[162]
64	${\mathrm{N}}_{4}^{+}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	2.5 × 10−16	[87]
65	${\mathrm{N}}_{4}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	2.4 × 10−16	[160]
66	${\mathrm{N}}_{4}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	3.9 × 10−16	[160]
67	${\mathrm{N}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	2.5 × 10−16	[162]
68	${\mathrm{N}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}\mathrm{O}+{\mathrm{N}}_{2}$	5 × 10−17	[162]
69	${\mathrm{N}}_{4}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	3 × 10−16	[146]
70	${\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{M}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{M}$	1 × 10−41	[87]
71	${\mathrm{O}}^{+}+\mathrm{N}({}^{2}\mathrm{D})\to {\mathrm{N}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	1.3 × 10−16	[87]
72	${\mathrm{O}}^{+}+{\mathrm{N}}_{2}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{M}$	$6\times 1{0}^{-41}\enspace {(300/{T}_{\text{g}})}^{2}$	[87]
73	${\mathrm{O}}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−18	[146]
74	${\mathrm{O}}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})$	3 × 10−18	[86]
75	O+ + NO2 → NO+ + O2	5 × 10−16	[146]
76	${\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	1.6 × 10−15	[146]
77	${\mathrm{O}}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}}_{2}{\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	6.3 × 10−16	[161]
78	O+ + N2O → NO+ + NO	2.3 × 10−16	[87]
79	${\mathrm{O}}^{+}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}$	2 × 10−17	[87]
80	${\mathrm{O}}_{2}^{+}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{O}({}^{3}\mathrm{P})$	1.5 × 10−16	[161]
81	${\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}\mathrm{O}$	1 × 10−23	[86]
82	${\mathrm{O}}_{2}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{2}$	4.6 × 10−16	[161]
83	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}$	6.6 × 10−16	[161]
84	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{3}$	1 × 10−17	[86]
85	${\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}_{5}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}+{\mathrm{O}}_{2}$	8.8 × 10−16	[86]
86	${\mathrm{O}}_{4}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	6.8 × 10−16	[160]
87	${\mathrm{O}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	3 × 10−16	[163]
88	${\mathrm{O}}^{-}+\mathrm{N}({}^{4}\mathrm{S})\to \mathrm{N}\mathrm{O}+\mathrm{e}$	2.6 × 10−16	[87]
89	O− + N2 → N2O + e	1 × 10−18	[138]
90	${\mathrm{O}}^{-}+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})\to {\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{e}$	2.2 × 10−15	[87]
91	${\mathrm{O}}^{-}+{\mathrm{N}}_{2}({\mathrm{B}}^{3}{\Pi})\to {\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{e}$	1.9 × 10−15	[87]
92	O− + NO → NO2 + e	2.6 × 10−16	[87]
93	${\mathrm{O}}^{-}+\mathrm{N}\mathrm{O}+\mathrm{M}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{M}$	1 × 10−41	[87]
94	${\mathrm{O}}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	1.2 × 10−15	[87]
95	${\mathrm{O}}^{-}+{\mathrm{N}\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	3 × 10−16	[146]
96	O− + N2O → NO− + NO	2 × 10−16	[87]
97	${\mathrm{O}}^{-}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}}_{2}{\mathrm{O}}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	2 × 10−18	[87]
98	${\mathrm{O}}_{2}^{-}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{e}$	5 × 10−16	[87]
99	${\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}\to {\mathrm{N}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	$1.9\times 1{0}^{-18}\enspace {({T}_{\text{g}}/300)}^{0.5}\enspace \mathrm{exp}(-4990/{T}_{\text{g}})$	[87]
100	${\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}({\mathrm{A}}^{3}{\Sigma})\to {\mathrm{N}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	2.1 × 10−15	[87]
101	${\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}({\mathrm{B}}^{3}{\Pi})\to {\mathrm{N}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	2.5 × 10−15	[87]
102	${\mathrm{O}}_{2}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}$	7 × 10−16	[87]
103	${\mathrm{O}}_{2}^{-}+{\mathrm{N}\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}$	5 × 10−16	[87]
104	${\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{O}}_{3}^{-}+{\mathrm{N}}_{2}$	1 × 10−17	[138]
105	${\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}$	1 × 10−17	[87]
106	${\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−17	[87]
107	${\mathrm{O}}_{3}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}$	2 × 10−17	[87]
108	${\mathrm{O}}_{3}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{3}$	7 × 10−17	[87]
109	${\mathrm{O}}_{3}^{-}+{\mathrm{N}\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{3}$	5 × 10−16	[87]
110	${\mathrm{O}}_{4}^{-}+{\mathrm{N}}_{2}\to {\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{2}+{\mathrm{N}}_{2}$	1 × 10−16 exp(−1044/Tg)	[87]
111	${\mathrm{O}}_{4}^{-}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}$	2.5 × 10−16	[87]
112	${\mathrm{N}\mathrm{O}}^{+}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{M}\to {\mathrm{N}}_{2}{\mathrm{O}}^{+}+\mathrm{M}$	1 × 10−41 (300/Tg)	[146]
113	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}$	1 × 10−21	[86]
114	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}_{5}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}\mathrm{O}}_{2}$	5.9 × 10−16	[86]

Table A4. Continued.

115	${\mathrm{N}\mathrm{O}}_{2}^{+}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}$	2.75 × 10−16	[161]
116	N2O+ + O2 → NO+ + NO2	4.59 × 10−17	[161]
117	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}\mathrm{O}$	2.24 × 10−16	[161]
118	N2O+ + NO → NO+ + N2O	2.3 × 10−16	[161]
119	N2O+ + NO2 → NO+ + N2 + O2	4.29 × 10−16	[161]
120	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}\mathrm{O}$	2.21 × 10−16	[161]
121	N2O+ + N2O → NO+ + NO + N2	1.2 × 10−17	[161]
122	${\mathrm{N}\mathrm{O}}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{O}}^{-}+\mathrm{N}\mathrm{O}$	3 × 10−16	[146]
123	${\mathrm{N}\mathrm{O}}^{-}+{\mathrm{O}}_{2}\to {\mathrm{O}}_{2}^{-}+\mathrm{N}\mathrm{O}$	5 × 10−16	[87]
124	${\mathrm{N}\mathrm{O}}^{-}+{\mathrm{O}}_{3}\to {\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}$	3 × 10−16	[146]
125	NO− + NO → NO + NO + e	5 × 10−18	[164]
126	${\mathrm{N}\mathrm{O}}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{N}\mathrm{O}$	3 × 10−16	[146]
127	${\mathrm{N}\mathrm{O}}^{-}+{\mathrm{N}\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}$	3 × 10−16	[146]
128	NO− + N2O → NO + N2O + e	5.1 × 10−18	[164]
129	${\mathrm{N}\mathrm{O}}^{-}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}$	2.8 × 10−20	[87]
130	${\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	1 × 10−18	[138]
131	${\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{e}$	1 × 10−18	[86]
132	${\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{O}}_{2}$	1.8 × 10−17	[87]
133	${\mathrm{N}\mathrm{O}}_{2}^{-}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}^{-}+{\mathrm{N}\mathrm{O}}_{2}$	2.75 × 10−16	[161]
134	${\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}\mathrm{O}}_{2}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}$	4 × 10−18	[87]
135	${\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}\mathrm{O}}_{3}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{N}\mathrm{O}}_{2}$	5 × 10−16	[87]
136	${\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{N}}_{2}$	5 × 10−19	[162]
137	${\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}}_{2}{\mathrm{O}}_{5}\to {\mathrm{N}\mathrm{O}}_{3}^{-}+{\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}\mathrm{O}$	7 × 10−16	[87]
138	${\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{N}({}^{4}\mathrm{S})\to {\mathrm{N}}_{2}+{\mathrm{O}}_{3}+\mathrm{e}$	1 × 10−18	[138]
139	${\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{O}({}^{3}\mathrm{P})\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{e}$	1 × 10−18	[138]
140	${\mathrm{N}\mathrm{O}}_{3}^{-}+\mathrm{N}\mathrm{O}\to {\mathrm{N}\mathrm{O}}_{2}^{-}+{\mathrm{N}\mathrm{O}}_{2}$	3 × 10−21	[87]
141	${\mathrm{N}}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
142	${\mathrm{N}}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
143	${\mathrm{N}}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
144	${\mathrm{N}}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
145	${\mathrm{N}}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
146	${\mathrm{N}}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
147	${\mathrm{N}}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
148	${\mathrm{N}}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
149	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
150	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
151	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
152	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
153	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
154	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
155	${\mathrm{N}}_{2}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
156	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
157	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
158	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
159	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
160	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
161	${\mathrm{N}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
162	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{N}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
163	${\mathrm{N}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
164	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
165	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
166	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
167	${\mathrm{N}}_{3}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{N}}_{2}$	1 × 10−13	[86]
168	${\mathrm{N}}_{3}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
169	${\mathrm{N}}_{3}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
170	${\mathrm{N}}_{3}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
171	${\mathrm{N}}_{3}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{N}}_{2}+\mathrm{N}({}^{4}\mathrm{S})$	1 × 10−13	[86]
172	${\mathrm{N}}_{4}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
173	${\mathrm{N}}_{4}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[146]
174	${\mathrm{N}}_{4}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]

Table A4. Continued.

175	${\mathrm{N}}_{4}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
176	${\mathrm{N}}_{4}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
177	${\mathrm{N}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
178	${\mathrm{N}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
179	${\mathrm{N}}_{4}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{N}}_{2}+{\mathrm{N}}_{2}$	1 × 10−13	[86]
180	${\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
181	${\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
182	${\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
183	${\mathrm{O}}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{O}({}^{3}\mathrm{P})$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
184	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
185	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
186	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
187	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
188	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
189	${\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
190	${\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
191	${\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{O}({}^{3}\mathrm{P})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
192	${\mathrm{O}}_{4}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
193	${\mathrm{O}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
194	${\mathrm{O}}_{4}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
195	${\mathrm{O}}_{4}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{O}}_{2}+{\mathrm{O}}_{2}$	1 × 10−13	[87]
196	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
197	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
198	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[87]
199	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+\mathrm{N}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[87]
200	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
201	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+\mathrm{N}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
202	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+\mathrm{N}\mathrm{O}$	1 × 10−13	[146]
203	NO+ + NO− → NO + NO	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
204	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
205	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{N}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
206	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
207	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
208	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
209	NO+ + N2O− → N2O + NO	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
210	${\mathrm{N}\mathrm{O}}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
211	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
212	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
213	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
214	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
215	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
216	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
217	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{N}\mathrm{O}}_{2}$	1 × 10−13	[146]
218	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
219	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
220	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
221	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
222	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
223	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}\mathrm{O}}_{3}^{-}\to {\mathrm{N}\mathrm{O}}_{3}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
224	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+{\mathrm{N}\mathrm{O}}_{2}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
225	${\mathrm{N}\mathrm{O}}_{2}^{+}+{\mathrm{N}}_{2}{\mathrm{O}}^{-}\to {\mathrm{N}}_{2}\mathrm{O}+\mathrm{N}({}^{4}\mathrm{S})+{\mathrm{O}}_{2}$	1 × 10−13	[86]
226	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
227	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}^{-}\to \mathrm{O}({}^{3}\mathrm{P})+{\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
228	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}}_{2}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[86]
229	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{2}^{-}\to {\mathrm{O}}_{2}+{\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
230	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}}_{2}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
231	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{3}^{-}\to {\mathrm{O}}_{3}+{\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
232	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{O}}_{4}^{-}\to {\mathrm{O}}_{2}+{\mathrm{O}}_{2}+{\mathrm{N}}_{2}\mathrm{O}$	1 × 10−13	[86]
233	N2O+ + NO− → NO + N2O	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]
234	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}^{-}\to \mathrm{N}\mathrm{O}+{\mathrm{N}}_{2}+\mathrm{O}({}^{3}\mathrm{P})$	1 × 10−13	[86]
235	${\mathrm{N}}_{2}{\mathrm{O}}^{+}+{\mathrm{N}\mathrm{O}}_{2}^{-}\to {\mathrm{N}\mathrm{O}}_{2}+{\mathrm{N}}_{2}\mathrm{O}$	$2\times 1{0}^{-13}\enspace {(300/{T}_{\text{g}})}^{0.5}$	[146]