## 5 Discharge Characteristics and Energy
### Energy Transfer Process
During the high voltage pulse, \(Q\_O\), \(Q\_N_{2}\), and \(Dis\_O_{2}\) are the main exothermic reactions, which is consistent with the conclusions of [PERSON] et al. [37], when \(E/N\leq 200\) Td. The energy of other reactions is at least one order of magnitude smaller and can be neglected. The increase of \(Q\_N_{2}\) mainly happens at two time scales 85 ns and \(10^{4}\) ns, which correspond to the quench of \(N_{2}(C^{3}\Gamma I)\), \(N_{2}(a^{\dagger}\Sigma)\) and \(N_{2}(A^{3}\Sigma)\), \(N_{2}(B^{3}\Gamma I)\), respectively, as can be seen in Figure 12:0 \(VT\) increases from the timescale 1 ms, which is mainly the result of the quench of \(N_{2}\left(v=1-2\right)\), as shown in Figure 16a. It is mainly responsible for the slow gas heating. \(Q\_O_{2}\) and \(Q\_N\) release slowly after the pulse, which starts at the time scale 1 \(\upmu\)s and 1 ms, respectively. At a long time after the pulse, \(Q\_O\), \(Q\_N_{2}\), and \(Dis\_O_{2}\) are still the dominant exothermic reactions. \(Q\_O_{2}\) and \(Q\_N\) are comparable to that of the dominant reactions, which also contribute to the slow gas heating. However, [PERSON] et al. [37] found that the gas heating of the dissociations of the nitrogen molecules and the processes involving the charged particles are the main precesses when \(E/N>400\) Td. Figure 12:1 _Cont._  
To study the energies of different reactions at different electric field regions in detail, the distributions of the number densities of the typical species that involved in the entomic reactions at time 35 ns during the pulse are shown in Figure 22a,b, respectively. In the low \(E/N\) (<200 Td) region, \(O\), \(N_{2}\left(A^{3}\Sigma\right)\) and \(O\left({}^{3}P\right)\) are the dominant species, which are associated with the \(Q\_O\), \(Q\_N_{2}\) and \(Dis\_O_{2}\) reactions, as shown in Figure 23a. In most parts of the sheath, where \(E/N\) is higher than >400 Td, \(Dis\_N_{2}\) and \(Pic\) are the dominant exothermic reactions, as shown in Figure 23a. However, the dominant species are \(O\), \(N\), and \(O\left({}^{3}P\right)\) there. The disparity is the result of the different reaction heats of the corresponding reactions. At extremely high \(E/N\) (>12,300 Td) in the sheath, all the power densities are very small, and the power density of \(Ges\) reactions become the largest one. However, [PERSON] et al. [37] revealed that the \(Dis\_N_{2}\) and the processes involving charged particles are still dominant. The difference may be caused by the limitations of the two-term approximation of the Boltzmann equation and the drift-diffusion approximation at a very high \(E/N\) region [33]. It can be concluded that the energies of the dominant reactions are determined by the reactions power densities at low \(E/N\) region, as the length of the high \(E/N\) sheath is small and the power densities are quite low there. Finally, according to the energies of the dominant reactions, the total gas heating \(P_{GH}\), \(Q_{GH}\) in the whole domain and the efficiency \(\eta_{GH}\) in \(R99\) are calculated and shown in Figure 12:2 The gas heating releases mainly in two time scales 85 ns and 7000 ns, which are corresponding to the fast and slow gas heating. The power \(P_{GH}\) in the fast and slow gas heating processes are higher than \(10^{5}\) W and lower than \(10^{3}\) W, respectively. The comparison of the contributions of the reaction heat and the ions are shown in Figure 12:3 According to the magnitudes of \(P_{R}\) and \(P_{ion}\), the fast gas heating is at timescale 85 ns, which is dominated by \(P_{ion}\). The slow gas heating is at timescale 7000 ns, which is dominated by \(P_{R}\). It can be seen that the fraction of the contribution of ions is larger than the one of the reactions in the fast gas heating. However, the contributions of the ions are lower than that of the reactions for the slow gas heating at a long time scale. The slow gas heating is the result of the exothermic reactions, which are mainly the quench of the vibrational excited nitrogen molecules.