# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 3 Results  
### General Consideration  
To facilitate the analysis of simulation results, the whole process is distinguished as the before-breakdown stage, the breakdown stage, and the after-breakdown stage, which is illustrated in Figure 3.  
Since the breakdown process occurs within a very short time span and it takes considerably longer to reach the stabilization stage, the length of the time axis in the graph is not set in proportion to the actual time. In addition, different applied voltages and air pressures affect the breakdown time, and the time nodes in the graph are specific to the simulation parameters outlined in this section.  
During the before-breakdown stage, the electric field uniformly permeates the polar plate. In the breakdown stage, the reaction is very violent, which leads to the formation of the cathode sheath. The after-breakdown stage can be divided into the anode sheath formation phase and the stable phase, distinguished by the presence or absence of a stable anode sheath. During the anode sheath formation phase of the after-breakdown stage, the density and distribution of charged particles undergo gradual changes. In the stable phase of the after-breakdown stage, the anode sheath becomes clearly visible, and various parameters such as particle density, energy, current density, and heating power stabilize.  
Figure 3: Flowchart of the breakdown process: divided into before-breakdown stage, breakdown stage, and after-breakdown stage.  
Table 1 presents the evolution of the density and energy parameters for electrons, negative ions, and positive ions. Here, \(\overline{n}\) and \(\overline{E}\) denote the spatial average density and energy, respectively.  
The density of electrons initially experiences a slight decrease in the before-breakdown stage, followed by a substantial increase in the subsequent stage. During the breakdown stage, the ionization reaction intensifies, further augmenting the electron density. In the after-breakdown stage, the fully formed cathode sheath induces an electric field shielding effect, leading to a gradual decrease in electron energy. The slow decrease in electron density during this stage is attributed to the dominance of adsorption reactions at lower electron energies.  
The density of negative ions (I\({}^{-}\)) steadily increases throughout the breakdown process. When no breakdown occurs, the uniform penetration of the electric field between the polar plates drives the negative ions away from the cathode, where they are energized by the force of the electric field. In the after-breakdown stage, the electric field close to the anode is weakened, causing I\({}^{-}\) to primarily distribute in the bulk region. This distribution results from the shielding of the electric field in the bulk region, leading to lower electron energies and predominantly adsorption reactions. Being heavy ions with low mobility, I\({}^{-}\) primarily resides in the bulk region and does not get accelerated by the electric field, leading to a rapid decrease in negative ion energy to less than 1 eV.  
The density of positive ions experiences a significant increase in the before-breakdown stage, followed by a continued rise by one to two orders of magnitude in the breakdown stage, and eventual slowing down in the after-breakdown stage. The phenomenon of electric field shielding is absent in the before-breakdown stage, allowing the electric field to penetrate through the entire polar plate and greatly enhance positive ion energy. In the after-breakdown stage, the cathode sheath forms, and positive ions, characterized by their large mass and low mobility, gradually become confined to the cathode sheath by strong electric fields.