# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 3 Results
### Negative Ion Kinetics  
The negative ion considered in this paper is I\({}^{-}\). The spatial and temporal distributions of negative ions are shown in Figure 9.  
In the before-breakdown stage, negative ions migrate from the cathode toward the anode under the influence of the electric field, increasing the density of I\({}^{-}\) near the anode. However, as the I\({}^{-}\) near the cathode is not replenished, its density gradually diminishes. Notably, the spatial distribution of negative ions appears less uniform compared to positive ions. By approximately 6.4 us, the I\({}^{-}\) density near the cathode approaches zero, while near the anode, it elevates to 10\({}^{12}\) m\({}^{-3}\), yielding an average density of \(3\times 10^{11}\) m\({}^{-3}\) at this juncture. It's evident that the density of I\({}^{-}\) in the before-breakdown stage only increases by one order of magnitude, which is substantially smaller compared to the increments observed for electrons and positive ions. The energy of I\({}^{-}\) escalates as it approaches the anode due to the accelerating effect of the electric field, reaching approximately 15 eV near the anode, while remaining below 1 eV near the cathode. Moreover, the heating rate and current density of I\({}^{-}\) are notably lower compared to positive ions and electrons. This disparity can be attributed to the heavy mass, low mobility, and lower spatial density of I\({}^{-}\) relative to electrons and positive ions.  
During the breakdown stage, the density of I\({}^{-}\) in the bulk region experiences a rapid escalation from 10\({}^{12}\) m\({}^{-3}\) to nearly 10\({}^{16}\) m\({}^{-3}\). In contrast, the density of I\({}^{-}\) in the cathode sheath remains extremely low, approaching zero. This disparity arises from the propensity of electrons with lower energies to induce adsorption reactions, while those in the cathode sheath, characterized by significantly higher energies, predominantly undergo ionization reactions. Consequently, there is minimal addition of new I\({}^{-}\) in the cathode sheath, leading to continuous consumption and limited replenishment, resulting in a much lower density  
Figure 9: Spatiotemporal distribution of (**a**) I\({}^{-}\) density, (**b**) I\({}^{-}\) current density, (**c**) average I\({}^{-}\) energy, (**d**) I\({}^{-}\) heating rate.  
compared to the bulk region. However, the average density of I\({}^{-}\) increases substantially to \(4\times 10^{15}\) m\({}^{-3}\), marking a four-order-of-magnitude increase relative to the before-breakdown stage. The extremely low density of I\({}^{-}\) in the cathode sheath translates into minimal heating rate and current density values. Although there is a substantial amount of I\({}^{-}\) in the bulk region, the shielding effect of the electric field by the sheath layer prevents its acceleration, thus maintaining its energy below 1 eV. Consequently, the heating rate of I\({}^{-}\) in the bulk region remains below 1 kWm\({}^{-3}\), with a current density of \(-0.02\) Am\({}^{-2}\), reflecting the limited influence of I\({}^{-}\) in this region.  
In the after-breakdown stage, the higher energy of electrons in the anode sheath compared to those in the bulk reduces the probability of adsorption reactions, leading to the depletion of I\({}^{-}\) in the anode sheath. This results in an I\({}^{-}\) density of \(10^{14}\) m\({}^{-3}\) in the anode sheath, which is much lower than \(10^{16}\) m\({}^{-3}\) in the bulk region.  
In the stable phase after the formation of the anode sheath, each parameter remains basically constant. However, because of the existence of an electric field in the anode sheath, the current density and heating rate of I\({}^{-}\) are significantly higher than those of the bulk region. For example, the heating rate of the anode sheath is 2.6 kWm\({}^{-3}\), while that of the bulk region is only 0.05 kWm\({}^{-3}\). In contrast, the electric field in the cathode sheath is strong, but the heating rate and current density are close to zero due to the low density of I\({}^{-}\).