## 3 Simulation Setup  
A low-pressure plane to plane DBD is adopted from the experiments conducted by [PERSON] et al. (2017) to investigate the effects of kinetic reactions on the discharge characteristics and energy. The referred experiment contains abundant experimental data. The actuator consists of two rectangular copper plate electrodes with each one covered by a 1.75 mm thickness quartz layer as a dielectric barrier, where \(\varepsilon=4.8\). The electrode is 14 mm wide and 65 mm long. The length of the discharge gap between the two dielectric barriers is 1 cm. In the experiment, the discharge was sustained in the dry air. The pressure and temperature of the dry air are 60 Torr and 300 K, respectively. The discharge is powered by a Chemical Physics Technologies (CPT) generator, which generates a bipolar negative-positive wave shape with peaks of \(-22.9\) kV and \(+18.5\) kV, respectively. The pulse duration is 85 ns with 45 ns and 40 ns full widths in the negative and positive pulses, respectively. The pulse repetition rate is 10 kHz. The experimental estimated and the fitted voltage waveforms are shown in Figure 2. \(Exp\) denotes the experimental waveform. The Gaussian functions fitting to \(Exp\) is denoted as \(Gaussian\). The decrease and oscillations of the voltage after 75 ns in \(Exp\) is neglected in \(Gaussian\). Time durations of 10\(\sim\)33 ns, 33\(\sim\)45 ns and 45\(\sim\)55 ns correspond to the fall and rise phases in the negative pulse and ascending phase in the positive pulse. Time duration from 55 ns to 85 ns corresponds to the decaying phase of the positive pulse in \(Gaussian\). The decaying phase after 55 ns in \(Exp\) voltage lasts more than 125 ns. According to the transition conditions [41; 42], the mode of the present discharge is considered as a quasi-uniform mode, which is validated by the ICCD camera images in the experiment [27]. Because of the quasi-uniform characteristics, a two-dimensional computation model is adopted. The computational domain is shown in Figure 3, where both dielectric barriers have a thickness of 1.75 mm, and the length of the discharge gap between the dielectric barriers is 10 mm. The surfaces of the left and the right dielectric barriers locate in lines of \(x=0\) mm and \(x=10\) mm. The upper and lower boundaries are imposed by the continuity of periodic boundaries conditions, where the physical variables on one boundary are the same as the ones on the destination boundary. \begin{table}
\begin{tabular}{c c c} \hline
**Name** & **Power** & **Energy** \\ \hline \multirow{4}{*}{GH} & \(P_{GH}=P_{ion}+P_{R}\) & \(Q_{GH}=Q_{ion}+Q_{R}\) \\  & \(P_{ion}=\vec{J}_{ion}\cdot\vec{E}\) & \(Q_{ion}=\int_{0}^{T_{p}}P_{ion}dt\) \\  & \(P_{R}=\sum\ \left(\Delta E\cdot r\right)\) & \(Q_{R}=\int_{0}^{T_{p}}P_{R}dt\) \\ \hline \end{tabular}
\end{table} 
Table 1: The gas heating model. Figure 1: The energy transfer path. The structured mesh is adopted in the simulation. The mesh in the y-axis is uniform, with a size of 100 \(\upmu\)m. The maximum mesh sizes in the x-axis in the discharge gap and the dielectric barriers are 5 \(\upmu\)m and 10 \(\upmu\)m, respectively. The minimum mesh is located at \(x=0\) mm and \(x=10\) mm, and the size is 2 \(\upmu\)m. The mesh across the entire domain is generated from the minimum mesh to the maximum mesh by a linear growth function, and the growth rate is 1.3. The total number of mesh elements is 175,464. Because the discharge is quasi-uniform, quasi-one-dimensional simulation models are used to investigate the effects of chemical reactions to reduce the computational costs, which is the same as the models used by [PERSON] et al. [7] in a similar simulation. The one dimensional simulation is established in the x-axis, and the grid distributions are the same as the one in the two-dimensional model. In \(R99\) and \(R85\), the initial number densities of the electrons and the negative ions are \(5\times 10^{11}\) m\({}^{-3}\), and the sum of the number densities of positive ions is \(1\times 10^{12}\) m\({}^{-3}\).