## 6 Effects of Chemical Reactions
Although the negative ion, the associative ionization, the electronic excited state nitrogen atoms and oxygen molecules are removed from \(R85\) to \(R50\), the energies of \(Q\_O\) and \(Q\_N_{2}\) in \(R85\) and \(R50\) are nearly the same. Therefore, the reduction from \(R85\) to \(R50\) has no effects on the dominant exothermic reactions. The corresponding total number densities of \(O(^{1}D)\) and \(N_{2}(A^{3}\Sigma)\) are shown in Figure 28a,b, respectively. The total number densities of \(N_{2}(A^{3}\Sigma)\) are almost the same. Therefore, all the reductions from \(R99\) to \(R42\) have no effects on the reactions related to the excited nitrogen molecules. The total number densities of \(O(^{1}D)\) in \(R99\) is higher than the ones in all the other models, but they are nearly the same in \(R85\), \(R50\), and \(R42\). Because \(O(^{1}D)\) is one of the productions of the dissociation of \(O_{2}\), all the reductions except the dissociations have no effects on the reactions related to the excited oxygen atoms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{2}{c}{\(Ee\) (mJ)} & \multicolumn{2}{c}{\(Ei\) (mJ)} & \multicolumn{2}{c}{\(Ve\) (mJ)} & \multicolumn{2}{c}{\(\Delta En_{e}\) (mJ)} & \multicolumn{2}{c}{\(Q_{ion}\) (mJ)} \\ \cline{2-10}  & **35 ns** & **85 ns** & **35 ns** & **85 ns** & **35 ns** & **85 ns** & **35 ns** & **85 ns** & **35 ns** & **85 ns** \\ \hline R99 & \(-0.41\) & \(-0.85\) & \(-0.05\) & \(-0.09\) & \(-0.04\) & \(-0.18\) & \(0.01\) & \(0.006\) & \(0.25\) & \(0.55\) \\Figure 27: Comparison of the energies of \(Q\_N_{2}\) (**a**) and \(Q\_O\) (**b**) in the \(N_{2}/\mathrm{O}_{2}\) mixtures reaction models. To study the effects of different kinetic models on the gas heating, the comparison of the total gas heating energies and the corresponding efficiencies in all the kinetic models are shown in Figure 29a,b, where the gas-heating energy in all the kinetic models are \(Q_{GH}\_R99\), \(Q_{GH}\_R85\), \(Q_{GH}\_R50\), \(Q_{GH}\_R42\), and \(Q_{GH}\_R4\), and the corresponding efficiencies are \(\eta_{GH}\_R99\), \(\eta_{GH}\_R85\), \(\eta_{GH}\_R50\), \(\eta_{GH}\_R42\), and \(\eta_{GH}\_R4\). Figure 28: Comparison of the total number densities of \(\mathcal{O}(^{1}D)\) (**a**) and \(N_{2}(A^{3}\Sigma)\) (**b**) in the \(N_{2}/O_{2}\) mixtures reaction models. The sequence of the gas-heating energy is \(Q_{GH}\_R99>Q_{GH}\_R85>Q_{GH}\_R42>Q_{GH}\_R50\). The \(\eta_{GH}\) also follows the same relation. \(Q_{GH}\) and \(\eta_{GH}\) in \(R4\) are much more different than that in the other models. The gas heating \(Q_{GH}\), \(\eta_{GH}\), \(Q_{R}\), and \(Q_{ion}\) at the end of pulse (85 ns) and the long time after the pulse (up to \(10^{3}\) ns and \(10^{5}\) ns) are shown in Table 3.  
At 85 ns, from \(R99\) to \(R42\), \(Q_{GH}\) ranges from 0.63 mJ to 0.74 mJ, and \(\eta_{GH}\) ranges from 41% to 47%. \(Q_{GH}\) predicted by \(R4\) is lower (0.42 mJ) and the corresponding \(\eta_{GH}\) is 52%. It has been concluded that the fast gas heating efficiency is in the range of 30%\(\sim\)50% [37,38,45,46]. Therefore, the predictions of gas heating are reasonable. \(Q_{GH}\) and \(\eta_{GH}\) from \(R99\) to \(R42\) at \(10^{3}\) ns and \(10^{5}\) ns are all larger than the ones at 85 ns mainly due to the increase of \(Q_{R}\). However, due to the different \(Q_{R}\) predicted in the models, \(Q_{GH}\) and \(\eta_{GH}\) are very different. The difference of \(\eta_{GH}\) is up to 20% at \(10^{5}\) ns. It can be concluded that the reduction of the kinetic models have very weak effects on the prediction of fast gas heating. However, because the reductions have effects on the prediction of \(Q_{R}\) at a long time scale, the  
Figure 29: Comparison of the total gas-heating energies \(Q_{GH}\) (**a**) and the corresponding efficiencies \(\eta_{GH}\) (**b**) in all the reaction models. reduction has considerable effects on the prediction of the slow gas heating.