# Numerical Analysis of the Breakdown Process of CF\({}_{3}\)I at Low Pressure
## 4 Discussions  
### Particle Kinetics  
The previous sections have completely discussed the dynamics of particles. This section analyzes the whole breakdown process from the perspective of particle balance. To better explain the mechanism of the whole breakdown process, this section selects several representative moments from three stages: 1 \(\upmu\)s time, corresponding to the beforehand stage; 6.4 \(\upmu\)s, corresponding to the starting time of the breakdown stage; 10 \(\upmu\)s, corresponding to breakdown stage; 15 \(\upmu\)s, corresponding to the end of the breakdown stage; 25 \(\upmu\)s, corresponding to the anode sheath formation phase in the after-breakdown stage; and 150 \(\upmu\)s, corresponding to the stable phase in the after-breakdown stage. The instantaneous distributions of the electron, negative ion, and positive ion densities, energies, current densities, and space potentials are presented in Figures 11, 12, 13, and 14, respectively. In the before-breakdown stage, the overall electron density is low, ranging between 10\({}^{8}\) m\({}^{-3}\) and 10\({}^{10}\) m\({}^{-3}\) at each location, allowing the external electric field to permeate the entire discharge gap. As depicted in Figure 14a, the electric field between the electrodes is uniformly distributed, as evidenced by the potential difference between them. The density and energy of the electron are used to compute the Debye length, estimated at approximately 5.4 m, significantly exceeding the inter-electrode spacing. This confirms the confinement of the entire discharge region within the electric field. Since the electric field in the before-breakdown stage remains unshielded, particles between the electrodes experience acceleration, resulting in a substantial increase in their energies. Under the influence of the electric field, positive ions migrate from the anode to the cathode, resulting in higher energy positive ions near the cathode location. The exact opposite is true for electrons and negative ions. The overall energy of positive ions surpasses that of negative ions and electrons because of their higher density. Ions, having greater mass and lower  
Figure 11: Density snapshots at (**a**) 1 \(\upmu\)s, (**b**) 6.4 \(\upmu\)s, (**c**) 10 \(\upmu\)s, (**d**) 15 \(\upmu\)s, (**e**) 25 \(\upmu\)s, and (**f**) 150 \(\upmu\)s.  
mobility compared to electrons, exhibit a more uniform density distribution. Because of their high velocity, the electron density increases closer to the anode, while decreasing closer to the cathode. However, in Figure 14a, a \"paradoxical\" increase in the electron density is observed at the cathode, attributed to positive ions on the cathode plate causing a secondary electron emission effect, thus slightly elevating the electron density near the cathode. As depicted in Figure 13a, both electrons and negative ions exhibit a higher current density near the anode, whereas positive ions exhibit a larger current density at the cathode. In general, particle energy, current density, and other parameters in the before-breakdown stage are significantly low. The breakdown stage begins at 6.4 us, and the transient distributions at this point are specifically highlighted in this paper, as shown in the (b) plots of Figures 11-14. During this phase, the collision of high-energy electrons with the background gas primarily instigates ionization reactions. The newly generated electrons from these reactions are then accelerated by the electric field, further initiating additional ionization reactions, leading to a rapid surge in the electron density, known as electron avalanche. In this process, not only does the electron density increase dramatically, but the density of positive ions also experiences a significant upsurge. A comparison between Figure 11a,b reveals that the density of positive ions and electrons during the breakdown process increases by two orders of magnitude compared to the before-breakdown stage.