## 3 Results and Discussion
[20; 33]. Figure 4: Spatial distributions of cycle-averaged **(a)** Ar\({}_{2}^{+}\) ion density, **(b)** Ar\({}^{+}\) ion density and (c) metastable Ar\({}^{*}\) atom density at SEE coefficients of 0.001, 0.005, and 0.01. The above analysis of particle densities clearly shows that the positive ions are mainly Ar\({}_{2}^{+}\) ions in the plasma, and the negative ions are mainly O\({}^{-}\) ions. Figure 6 shows the spatial distributions of the main particle density and electric field when the SEE coefficient is set to 0.01. Due to the large electron mobility, the electron density is higher than the O\({}^{-}\) ion density in the sheath. Overall, the density of positively charged particles in the sheath is higher than that of negatively charged particles. This is because of the electron loss at the wall. The distributions of particle density are symmetrical in the double sheath near the electrode walls on both sides. The total charge density at the cathode and anode is positive, while directly determining the distribution of the electric field. It is also a characteristic of continuous-power-driven discharge. The time required for the maximum density to stabilize can be used to estimate the discharge time from non-self-maintained to self-maintained. Figure 7a shows the maximum electron density over time as the SEE coefficient increases from 0.001 to 0.01. The maximum electron density rises rapidly at the beginning of discharge because of ionization and then gradually decreases until it becomes stable due to dissociative electron attachment. In addition, the maximum electron density increases as the SEE coefficient increases. Figure 7b-d show the maximum O\({}^{-}\) ion density, maximum O atom density, and maximum metastable O\({}_{2}^{*}\) molecule density over time. They gradually increase with time until they are stable. The time required for the maximum density to reach steady state is the shortest for the metastable O\({}_{2}^{*}\) density molecule; however, the maximum O\({}^{-}\) ion density needs the longest time to stabilize. We can  
Figure 5: Spatial distributions of cycle-averaged (**a**) metastable O\({}_{2}^{*}\) molecule density, (**b**) O\({}_{2}^{+}\) ion density, (**c**) O\({}^{-}\) ion density, and (**d**) O atom density at SEE coefficients of 0.001, 0.005, and 0.01.  
also clearly see that the time required for the maximum density to reach steady state decreases as the SEE coefficient increases, as shown in Figure 7c,d. Figure 8 shows the spatial distributions of cycle-averaged electron ohmic heating and collisionless pressure heating mechanisms as the SEE coefficient increases from 0.001 to 0.01. Figure 6: Spatial profiles of the density of the main ions and the electric field when the SEE is set to 0.01. Figure 7: Variation of time the maximum of (**a**) electron density, (**b**) \(\mathrm{O^{-}}\) ion density, (**c**) \(\mathrm{O}\) atom density, and (**d**) metastable molecular \(\mathrm{O_{2}^{*}}\) density at different SEE coefficients. The spatial distribution of electron ohmic heating is shown in Figure 8a. From the electron energy equation, electron heating can be written as \(P_{c}=e\mu_{e}E^{2}+eD_{e}E\cdot\
abla n_{e}\), electron ohmic heating is \(P_{H}=e\mu_{e}E^{2}\), and collisionless pressure heating is \(P_{p}=eD_{e}E\cdot\
abla n_{e}\)[35; 36; 37]. Electron ohmic heating appears in the form of double peaks in the sheath regions, which is due to a strong electric field accelerating electrons in the sheath. The spatial distribution of collisionless pressure heating is shown in Figure 8b. We can see that the distribution of collisionless pressure heating appears in the form of double peaks in the sheath regions. From the formula \(P_{p}=eD_{e}E\cdot\
abla n_{e}\), collisionless pressure heating depends on the electron density gradient in electric fields. The electric field and electron density gradient in the plasma center area are smaller, but the plasma density gradient is larger in the sheath regions, hence the larger collisionless pressure heating in the sheath regions.