# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 3 Results
### Positive Ion Kinetics  
Positive ions encompass I\({}^{+}\), CF\({}_{3}^{+}\), CF\({}_{3}\)I\({}^{+}\), and CF\({}_{2}\)I\({}^{+}\). The spatial and temporal distributions of positive ions are shown in Figures 5-8. Figure 5: Spatiotemporal distribution of (**a**) \(\mathrm{I}^{+}\) density, (**b**) \(\mathrm{I}^{+}\) current density, (**c**) average \(\mathrm{I}^{+}\) energy, (**d**) \(\mathrm{I}^{+}\) heating rate. Figure 6: Spatiotemporal distribution of (**a**) \(\mathrm{CF}_{3}^{+}\) density, (**b**) \(\mathrm{CF}_{3}^{+}\) current density, (**c**) average \(\mathrm{CF}_{3}^{+}\) energy, (**d**) \(\mathrm{CF}_{3}^{+}\) heating rate. Figure 8: Spatiotemporal distribution of (**a**) CF\({}_{2}\)I\({}^{+}\) density, (**b**) CF\({}_{2}\)I\({}^{+}\) current density, (**c**) average CF\({}_{2}\)I\({}^{+}\) energy, (**d**) CF\({}_{2}\)I\({}^{+}\) heating rate. Figure 7: Spatiotemporal distribution of (**a**) CF\({}_{3}\)I\({}^{+}\) density, (**b**) CF\({}_{3}\)I\({}^{+}\) current density, (**c**) average CF\({}_{3}\)I\({}^{+}\) energy, (**d**) CF\({}_{3}\)I\({}^{+}\) heating rate. During the before-breakdown stage, positive ions exhibit distinct characteristics compared to electrons and negative ions. In the presence of an electric field, positive ions migrate from the anode to the cathode. Unlike electrons, the density of positive ions does not initially decrease but continues to rise steadily, as depicted in Figures 5a-8a. This phenomenon arises because all positive ions involved in the reaction are heavy ions, resulting in significantly lower ion mobility compared to electrons. Consequently, positive ions near the cathode are not lost as rapidly as electrons. In contrast to negative ions, positive ions are more evenly distributed. This occurs as positive ions gradually approach the cathode under the influence of the electric field, leading to an increase in positive ion density near the cathode. As previously mentioned, electrons accelerate from the cathode to the anode under the influence of the electric field. Closer proximity to the anode results in higher electron energy, increasing the likelihood of ionization reactions. Ionization reactions generate a substantial number of positive ions. Therefore, despite a portion of positive ions gradually moving toward the cathode from the anode due to the electric field, the vigorous ionization reactions near the anode replenish the depleted positive ion density, preventing the density near the anode from dropping to zero. During the before-breakdown stage, the density of I\({}^{+}\) near the anode increases to \(10^{11}\) m\({}^{-3}\), while near the cathode, it rises to \(10^{14}\) m\({}^{-3}\), resulting in an overall average density elevation to \(10^{13}\) m\({}^{-3}\). Similar density distributions are observed for CF\({}_{3}^{+}\), CF\({}_{3}\)I\({}^{+}\), and CF\({}_{2}\)I\({}^{+}\), with higher densities near the anode. Although the density of positive ions during the before-breakdown stage has increased compared to the initial density of \(5\times 10^{9}\) m\({}^{-3}\), it remains relatively low compared to the breakdown stage. Consequently, the current density and heating rate of positive ions during this stage are substantially lower than during the breakdown stage. For instance, considering I\({}^{+}\), its current density before breakdown consistently remains below 1 Am\({}^{-2}\), with a heating rate also below 1 kWm\({}^{-3}\). Similar current densities and heating rates are observed for CF\({}_{3}^{+}\), CF\({}_{3}\)I\({}^{+}\), and CF\({}_{2}\)I\({}^{+}\). During the breakdown stage, the intense ionization reaction triggers a rapid surge in positive ion density. In the bulk region, the density of I\({}^{+}\) sharply rises to \(2.5\times 10^{15}\) m\({}^{-3}\), while within the cathode sheath, it reaches \(10^{14}\) m\({}^{-3}\), resulting in an overall average density of \(10^{15}\) m\({}^{-3}\). Similar trends are observed for \(CF_{3}^{+}\), \(CF_{3}\)I\({}^{+}\), and CF\({}_{2}\)I\({}^{+}\).