## Materials and Methods
### Two-Dimensional Fluid Model
#### 2.2.1 Model Equations
The mobility of ions was calculated according to the [PERSON] equation:  
\[\mu_{i}=0.514m_{i}^{1/2}\frac{T_{g}}{P_{tot}}\alpha_{i}^{-1/2} \tag{7}\]  
where \(\alpha_{i}\) is the polarization of background gas per unit of cubic angstroms; its value for various gases is presented in the existing literature on gaseous discharges [27]. In this work, the mobilities for CO2\({}^{+}\) and C\({}^{+}\) species were 0.0012 and 0.0009 m\({}^{2}\)/Vs, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Num.** & **Process Name** & **Reactions** & **Reaction Rate Constants** & **Ref.** \\ \hline \multicolumn{4}{c}{_Electron Collisions_} \\ \hline
1 & Vibrational Excitation & \(e+CO_{2}\to e+CO_{2}(V1)\) & \(k_{1}\) & [19] \\ \hline
2 & Vibrational Excitation & \(e+CO_{2}\to e+CO_{2}(Va)\) & \(k_{2}\) & [19] \\ \hline
3 & Vibrational Excitation & \(e+CO_{2}\to e+CO_{2}(Vb)\) & \(k_{3}\) & [19] \\ \hline
4 & Vibrational Excitation & \(e+CO_{2}\to e+CO_{2}(Vc)\) & \(k_{4}\) & [19] \\ \hline
5 & Vibrational Excitation & \(e+CO_{2}\to e+CO_{2}(Vd)\) & \(k_{5}\) & [19] \\ \hline
6 & Electronic Excitation & \(e+CO_{2}\leftrightarrow e+CO_{2}^{*}\) & \(k_{6}\) & [21] \\ \hline
7 & Dissociative De-excitation Collision & \(e+CO_{2}(Vx)\to e+CO+O\) & \(k_{7}\) & [19] \\ \hline
8 & Electron Ionization & \(e+CO_{2}\to 2e+O_{2}+C^{+}\) & \(k_{8}\) & [19] \\ \hline
9 & Electron Dissociation & \(e+CO_{2}\to e+O+CO\) & \(k_{9}\) & [19] \\ \hline
10 & Electronic Excitation & \(e+CO_{2}\leftrightarrow e+CO_{2}^{*}\) & \(k_{10}\) & [21] \\ \hline
11 & Elastic Collision & \(e+CO_{2}\leftrightarrow e+CO_{2}\) & \(k_{11}\) & [21] \\ \hline
12 & Electron Ionization & \(e+CO_{2}\leftrightarrow 2e+CO_{2}^{+}\) & \(k_{12}\) & [22] \\ \hline
13 & Electron Ionization & \(e+CO_{2}\to 2e+CO+O^{+}\) & \(k_{13}\) & [22] \\ \hline
14 & Dissociative Electron-Ion Recombination & \(e+CO_{2}^{+}\to CO+O\) & \(k_{14}\) & [22] \\ \hline
15 & Dissociative Attachment & \(e+CO_{2}\leftrightarrow CO+O^{-}\) & \(k_{15}\) & [23] \\ \hline
16 & Electron Dissociation & \(e+O_{2}\to e+2O\) & \(k_{16}\) & [23] \\ \hline \multicolumn{4}{c}{_Atomic Collisions_} \\ \hline
17 & Neutral Dissociation & \(O+CO_{2}\to CO+O_{2}\) & \(k_{17}\) & [20] \\ \hline
18 & Charge Exchange & \(CO_{2}+CO_{2}^{+}\leftrightarrow\Box CO_{2}^{+}+CO_{2}\) & \(k_{18}\) & [20] \\ \hline
19 & Scattering & \(O+O_{2}\to O+O_{2}\) & \(k_{19}\) & [20] \\ \hline
20 & 3-body Recombination & \(O+O+CO_{2}\to O_{2}+CO_{2}\) & \(k_{20}\) & [23] \\ \hline
21 & 3-body Neutral-Neutral Collision & \(O+C+CO_{2}\to CO+CO_{2}\) & \(k_{21}\) & [24] \\ \hline
22 & 3-body Neutral-Neutral Collision & \(O+CO+CO_{2}\to CO_{2}+CO_{2}\) & \(k_{22}\) & [24] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected reactions for different formed species in the AC-PPP reactor. The diffusion coefficient of the electrons and ions were instead calculated from the Einstein relation:  
\[D_{e(i)}=\frac{k_{B}T_{e(i)}}{q_{e(i)}}\mu_{e(i)} \tag{8}\]  
with \(T_{e(i)}\) and \(q_{e(i)}\) being the temperature and charge of electrons and ions [28]. For neutral species, the diffusion coefficients were calculated using the distribution coefficients of Lennard-Jones [29].