## 3 Results and Discussion
It is clear that a positive current pulse with a smaller peak value of 0.98 mA/cm\({}^{2}\) can be observed during the voltage rise phase, while a larger positive current pulse is generated during the voltage fall phase; the corresponding breakdown voltage and current density are \(-\)865 V and \(-\)7.1 mA/cm\({}^{2}\), respectively. Figure 3.0 Spatial distributions of positive charge density, negative charge density, electron density, and electric field at the beginning of the positive discharge in RP2 discharge with a gap width of 5.1 mm. charged particles are the same. The maximum densities of CO\({}_{3}^{-}\) and CO\({}_{2}^{+}\) ions staying in the anode sheath and cathode sheath are \(1.25\times 10^{9}\) and \(1.43\times 10^{9}\) cm\({}^{-3}\), respectively. In fact, under the same discharge conditions, if the density and spatial distribution of the charged particles staying in the sheath at the beginning of the negative discharge for two consecutive voltage periods are the same, the discharge will be a stable RP1 discharge. As shown in Figure 10f, the reverse discharge in the RP1 state also operates in glow mode. Figure 12 shows the residual ions density in the sheath region at the beginning of negative discharge for two consecutive voltage periods as a function of gap width in the evolution from RP2 discharge to RP1 discharge. In Figure 12, the black solid line and black dashed line represent the densities of CO\({}_{2}^{+}\) and CO\({}_{3}^{-}\) ions staying in the sheath region at the beginning of negative discharge in the first voltage period (that is, the moment b in Figure 8), respectively, and the red solid line and the red dashed line represent the densities of CO\({}_{2}^{+}\) and CO\({}_{3}^{-}\) ions remaining in the sheath region at the beginning of negative discharge in the second voltage period (i.e., the e moment in Figure 8), respectively. As the gap width increases, the densities of residual CO\({}_{2}^{+}\) and CO\({}_{3}^{-}\) ions in the first voltage period of RP2 discharge increase, while the densities of CO\({}_{2}^{+}\) and CO\({}_{3}^{-}\) ions in the second voltage period decrease. When the gap width increases to 5.16 mm, the density and spatial distribution of residual ions in the sheath region are completely equal, thus the discharge evolves from RP2 discharge into RP1 discharge. In general, in the RP2 discharge, there are differences in the density and spatial distributions of residual ions in the sheath region at the beginning of the negative discharge for the consecutive voltage periods. As the gap width increases, the density and spatial distribution of the residual ions are gradually equal, resulting in the discharge evolving from RP2 state into RP1 state. It is necessary to investigate the effect of the nonlinear behaviors generated by the increasing gap width on the decomposition of CO\({}_{2}\). In this paper, the discharge power density \(P_{\text{d}}\), Specific Energy Input (SEI), and CO\({}_{2}\) conversion (\(\chi_{\text{CO}_{2}}\)) are determined by  
Figure 3.1  
Figure 3.2 The residual ions density in the sheath region at the beginning of the negative discharge for two consecutive voltage periods as a function of gap width in the evolution from RP2 discharge to RP1 discharge. Figure 3.3  
Figure 3.4  
where \(T\) is the duration of a voltage cycle consisting of the power-on and power-off phases, \(t_{\text{r}}\) is the residence time of plasma, \(N_{\text{CO}_{2}t_{0}}\) and \(N_{\text{CO}_{2}t_{\text{r}}}\) are the initial CO\({}_{2}\) density and the CO\({}_{2}\) density at the moment \(t_{\text{r}}\), respectively. According to Figures 2 and 3, an increase in gap width leads to the appearance of temporal nonlinear behaviors in CO\({}_{2}\) discharges and decreases the discharge current density, which reduces the discharge power density \(P_{\text{d}}\). Furthermore, Equation (16) analytically describes that the SEI is mainly determined by power density \(P_{\text{d}}\) at a given residence time. Therefore, the growth of gap width can decrease the SEI.