## 5 Discharge Characteristics and Energy
### Energy Transfer Process
According to the analysis of the number densities, the comparison of \(Q_{Ee}\), \(Q_{Ei}\), and \(Q_{Ve}\) is shown in Figure 17, and \(\Delta Ent  
The magnitudes of \(Q_{Ee}\), \(Q_{Ei}\), and \(Q_{Ve}\) all increase in the two discharges during the pulse, which is the same as that in the change of the number densities, and they keep nearly constant after the discharges. Since the number densities of nitrogen excited species are higher than that of the ions, the magnitude of \(Q_{Ee}\) is higher than that of \(Q_{Ei}\), and they reach the magnitudes up to 0.85 mJ and 0.09 mJ. As the number densities of \(N_{2}\) (\(v=1\)-8) are lower than the nitrogen excited species, the maximum magnitude of \(Q_{Ve}\) is about 0.1 mJ. \(\Delta En_{e}\) mainly increases to 0.015 mJ during the pulse in the discharges and decays rapidly after the discharge. \(Q_{ions}\) increases to 0.55 mJ in the two discharges and keeps almost constant after the discharges. Therefore, \(Q_{A\_ui}\) is mainly transferred to \(Ee\) and the energy of the ions. However, the energy transfer to \(Ei\), \(Ve\), and \(\Delta En_{e}\) is neglectable. Second, according to the energy transfer path, the electron impact endothermic reactions transfer a part of energy from the electrons to the chemical energy stored in the heavy species, which includes \(N_{2}\) (\(v=1\)-8), the electronic excited state species (\(Ee\) species), the ground excited state species (\(Ges\) species) and the ions. Since the chemical energy in the heavy species correlates to the corresponding number densities, the total number densities of \(N_{2}\) (\(v=1\)-8), the \(Ee\) species and the  
Figure 17: Comparison of the energies of the electron impact endothermic reactions \(Q_{Ee}\), \(Q_{Ei}\), and \(Q_{Ve}\) in \(R99\). Figure 18: Comparison of the electron-energy change \(\Delta En_{e}\) and the energy of the ions \(Q_{ions}\) in \(R99\). ions are shown in Figures 14-16, respectively. The total number densities of the \(G\)\(e\)\(s\) species are shown in Figure 19. It can be seen from the figure that \(O_{3}\) and \(O\) are the dominate species. \(O\) is primarily formed by the electron impact dissociation (8) and the quenching of electronically excited nitrogen (33), (39), (44) in Table 11, and \(O_{3}\) is primarily formed by the \(G\)\(e\) reactions (31) and (32). The decay of \(O_{3}\) and \(O\) mainly starts at the time scale of 1 ms. The comparison of the chemical energy stored in \(N_{2}\left(v=1\text{--}8\right)\), the \(E\)\(e\) species, the \(G\)\(e\)\(s\) species, and the ions is shown in Figure 20.  
The chemical energy stored in the heavy species mainly increases during the pulse and the energies stored in \(E\)\(e\) and \(G\)\(s\) are larger than the ones in the other species. The energy stored in \(E\)\(e\) and \(G\)\(s\) decreases due to the quench reactions and \(G\)\(s\) reactions, respectively, which are also closely related to the change of the corresponding species number densities. The energy stored in \(E\)\(e\) decreases  
Figure 19: The total number densities of the ground excited state species \(N\), \(O\), \(O_{3}\), and \(NO\) in \(R99\). Figure 20: Chemical energy stored in the vibrational excited nitrogen molecules \(N_{2}\left(v=1\text{--}8\right)\), the electronically excited state species (\(E\)\(e\) species), ground excited state species (\(G\)\(s\) species), and the ions in \(R99\). in about 3000 ns after the pulse, while the energy stored in _Ges_ still increases slowly after the pulse and decays from \(10^{5}\) ns. Therefore, the time scale of the energy release of the quench of electronically excited reactions is much lower than the ones of the other reactions. Third, to investigate the energies of the exothermic reactions, the comparisons of the energies of \(Q\_N_{2}\), \(Q\_N\), \(Q\_O\), \(Q\_O\), VT relaxations, _Dis_N\({}_{2}\), _Dis_O\({}_{2}\)_Re_ei_, _Re_ii_, _Pic_, _Ges_, and _Ai_ are shown in Figure 21a-c, respectively.