## 6 Effects of Chemical Reactions  
In this section, the comparison of the discharge energy and the gas heating predicted by the kinetic models are conducted, the energies and the densities of the preserved dominant processes are also compared to study the effects of the reductions of the kinetic models. To investigate the effects of chemical reactions on the discharge characteristics and energy, the energy transfer of the electrons and the ions are analyzed. The comparison of \(P_{A\_ui}\) and \(Q_{A\_ui}\) predicted by using all the kinetic models is shown in Figure 26a,b, respectively. Figure 24: The total gas heating \(P_{GH}\), \(Q_{GH}\) in the whole domain and the efficiency \(\eta_{GH}\) in \(R99\), the discharge energy \(Q_{A\_ui}\) is also shown in the figure. The corresponding fast and slow energy release times are also labeled. Figure 25: Comparison of the powers and energies of reaction heat \(P_{R}\), \(Q_{R}\) and the ions \(P_{ion}\), \(Q_{ion}\) in the gas heating. The corresponding fast and slow energy release times are also labeled. The \(N_{2}/O_{2}\) mixtures reaction models \(R99\), \(R85\), \(R50\), and \(R42\) predict almost the same \(P_{A\_ui}\), which are qualitatively similar to that of \(R4\). However, the positive peaks in \(R4\) are lower than that in the other models, which result in a lower \(Q_{A\_ui}\) in \(R4\) than that in the experiment and the other models. Therefore, the reductions from \(R99\) to \(R42\) have very weak effects on the prediction of the discharge energy. During the pulse, \(R4\) under-predicts the discharge energy, but \(R99\), \(R85\), \(R50\), and \(R42\) over-predict the discharge energy, which agrees better with the experiment. Because \(P_{A\_ui}\) is calculated by the current on the electrode, the currents in the \(N_{2}/O_{2}\) mixtures reaction models are also nearly the same, which are also different from that in \(R4\). Figure 26: Comparison of the \(P_{A\_ui}\) (**a**) and \(Q_{A\_ui}\) (**b**) predicted by all the kinetic models and the ones in the experiment [27]. According to the energy transfer path, the energies of the electron impact exothermic reactions, the electron-energy change and the energy gained by ions in all the kinetic models are compared, which are shown in Table 2. As the energies are qualitatively similar, the values at time 35 ns in the pulse and 85 ns after the pulse are compared quantitatively. The energies of \(Ei\) increase from \(R99\) to \(R42\) and the maximum increments at 35 ns and 85 ns are about 29% and 18%. However, because \(Ee\) and \(Ve\) are not considered in \(R4\), the energies are mainly consumed by \(Ei\). The energy of \(Ei\) is much higher than that in the \(N_{2}/O_{2}\) mixtures reaction models. The energies of \(Ee\) from \(R99\) to \(R42\) also increase, the maximum increments at 35 ns and 85 ns are 12% and 4%. Similarly, the increments of \(Ve\) are 15% and 13%. Compared with the difference of the energies in the \(N_{2}/O_{2}\) mixtures reaction models and \(R4\), the energies of the electron impact exothermic reactions in \(R99\), \(R85\), \(R50\), and \(R42\) can be considered nearly the same. Similar conclusions can be made as to the energies of \(\Delta En_{e}\) and \(Q_{ion}\). The main exothermic reactions are \(Q\_O\), \(Q\_N_{2}\), \(Dis\_N_{2}\), and \(Dis\_O_{2}\). Because \(Q\_O\) and \(Q\_N_{2}\) are all included in the \(N_{2}/O_{2}\) mixtures reaction models, to investigate the effects of the neglected reactions on the preserved reactions, the comparison of the energies of \(Q\_O\), \(Q\_N_{2}\) in the \(N_{2}/O_{2}\) mixtures reaction models is shown in Figure 27a,b, respectively. In all the models, the energies of \(Q\_N_{2}\) are nearly the same. Because \(Dis\_N_{2}\) and \(Dis\_O_{2}\) are reduced in \(R85\), \(R50\), and \(R42\), \(O(^{1}S)\) and \(O(^{3}P)\) are also reduced there, the energy of \(Q\_O\) in \(R99\) is higher than that in the other models. However, the energy of \(Q\_N_{2}\) is not affected a lot by the dissociation reactions.