## 3 Results and Discussion
### Effect of Electrode Diameter on NO Oxidation  
Figure 10 shows the effect of electrode diameter on NO oxidation under different SED conditions. The experimental results show that increasing the electrode diameter can obtain higher oxidation degree of NO\({}_{X}\) and reduce the energy consumption of DBD reactor. Increasing inner electrode diameter can reduce the gas gap of DBD reactor, which promotes the E/N of gas gap with the same supply voltage [16; 19]. As E/N increases, the mean electron energy increases as well; thus, increasing the inner electrode diameter makes it easier for DBD reactor to generate O radicals and promote NO oxidation. Figure 9: (**a**) The effect of E/N on mean electron energy; and (**b**) the effect of E/N on G-value of particularly reaction process (The G-value of reaction R1 is drawn separately on the left vertical axis). Figure 11 shows the relationship between SED and discharge voltage for different electrode diameters. The results show that the discharge voltage decreases with the increase of inner electrode diameter under the same SED. The breakdown voltage (\(U_{b}\)) of coaxial cylindrical DBD reactor can be calculated by the following formula [37]:  
\[U_{b}=\frac{BPd}{ln\left(\frac{APd}{1+\frac{1}{\gamma}}\right)} \tag{9}\]  
where \(U_{b}\) is the gas breakdown voltage; \(P\) is the gas pressure; \(d\) is the distance between the electrodes; \(\gamma\) is the secondary electron emission coefficient; and \(A\) and \(B\) are gas-related constants. It can be seen from Equation (9) that increasing the diameter of the inner electrode can reduce the distance between the electrodes (\(d\)), thus the breakdown voltage (\(U_{b}\)) is reduced, as shown in Figure 11a. Increasing inner electrode diameter reduces the gas gap of DBD reactor and makes gas discharge easier. Therefore, the DBD reactor with smaller gas gap has better discharge performance  
Figure 11: (**a**) The influence of electrode diameter on breakdown voltage; and (**b**) the relationship between SED and discharge voltage for different electrode diameters. Figure 10: Effect of electrode diameter on oxidation degree of NOx (electrode length is 100 mm; inner electrode diameter is 10, 12 and 14 mm; and gas gap is 2.5, 1.5 and 0.5 mm, respectively). and higher oxidation efficiency under the same SED [38]. In addition, according to the theory of Townsend discharge, the discharge current increases exponentially with the increase of gas gap [39]:  
\[I=I_{0}e^{ax} \tag{10}\]  
where \(I\) is the discharge current; \(I_{0}\) is the initial electron flow from the cathode; \(x\) is the gas gap; and \(a\) is the first Townsend ionization coefficient. It can be seen from Equation (10) that the larger the gas gap \((x)\) has stronger electron avalanche effect and higher current growth rate [39]. Therefore, the DBD reactor with smaller the electrode diameter has a smaller discharge voltage change during the increase of SED, as shown in Figure 11b. This indicates that the DBD reactor with smaller electrode diameter needs to consume more SED to increase the discharge voltage and E/N. In addition, the stronger electron avalanche effect causes a greater heat loss of DBD reactor, which also increases the energy consumption. As a result, the energy efficiency of DBD reactor decreases with the decrease of electrode diameter. However, it cannot accurately explain the experimental results only from the perspective of E/N and electron avalanche. The increase of E/N increases the electron energy, resulting in more O radicals, but also more N radicals. N radicals generate more NO via reactions R11, R14 and R15, which causes the increase of total NO\({}_{\text{X}}\) concentration under oxygen-enriched condition.