## 4 Discussion
### Advective Ambipolar Self-Coagulation
#### 4.2.2 Semi-Circle Structure for Ambipolar Type
The discharge conditions are the same as in Figure 4. The sampled position corresponds to the summed anions density peak and its coordinates are given in the figure. Figure 17: Simulated two-dimensional profiles of total anion density at two simulating times, (**a**) \(10^{-5}\) s and (**b**) \(10^{-4}\) s, and of their net chemical source at the two times, (**c**) \(10^{-5}\) s (before self-coagulation) and (**d**) \(10^{-4}\) s (after self-coagulation). The discharge conditions are the same as in Figure 4.  
Figure 18: (**a**) Simulated and partial axial profiles of total anion density (near the coil) in Ar/SF6 plasma at two simulating times, \(10^{-5}\) s (before self-coagulation) and \(10^{-4}\) s (after self-coagulation). In panel (**b**), the decreasing curves of total anion density border beneath the coil is enlarged to compare the curve characteristics, steep (corresponding to the physical coagulation) and gentle (corresponding to the chemical coagulation). The discharge conditions are the same as in Figure 4.  
In Equation (45), the flux balance is rewritten to utilize the drift and diffusion approximation of the momentum equation. Herein, \(\mu_{i}\) and \(\mu_{e}\) are the mobilities of ions and electrons, respectively. \(D_{i}\) and \(D_{e}\) are the diffusion coefficients of ions and electrons, respectively. \(\overset{\rightarrow}{E}\) represents the electrostatic field that is caused by the ambipolar diffusion potentail. \[\mu_{i}n\overset{\rightarrow}{E}-D_{i}\
abla n=-\mu_{e}n\overset{ \rightarrow}{E}-D_{e}\
abla n. \tag{45}\]  
In Equation (46), the electric field is expressed as a funciton of the transport coefficients and density gradient. The field expression is then inserted into the flux of ions in Equation (47) and the flux is thereby reformed. \[\overset{\rightarrow}{\Gamma}_{e}=\overset{\rightarrow}{\Gamma}_{i}= \overset{\rightarrow}{\Gamma}, \tag{43}\]0  
\[\overset{\rightarrow}{\Gamma}_{e}=\overset{\rightarrow}{\Gamma}_{i}= \overset{\rightarrow}{\Gamma}, \tag{43}\]1  
In Equation (48), an ambipolar diffusion coefficient, \(D_{a}\), is introduced based on the reformed flux. In Equation (49) the approximation between the mobilities of electrons and ions is utilized and the ambipolar coefficient is simplified. Then in Equation (50), the normally used expression of ambipolar diffusion coefficient is obtained at utilizing [PERSON]'s relation. \[\overset{\rightarrow}{\Gamma}_{e}=\overset{\rightarrow}{\Gamma}_{i}= \overset{\rightarrow}{\Gamma}, \tag{43}\]2  
\[\overset{\rightarrow}{\Gamma}_{e}=\overset{\rightarrow}{\Gamma}_{i}= \overset{\rightarrow}{\Gamma}, \tag{43}\]3  
\[\overset{\rightarrow}{\Gamma}_{e}=\overset{\rightarrow}{\Gamma}_{i}= \overset{\rightarrow}{\Gamma}, \tag{43}\]4  
It is seen that the ambipolar diffusion potential is created self-consistently in the electropositive plasma because of the huge difference between the masses of electrons and ions. Without this potential barrel, all electrons escape to the chamber wall, and the gaseous discharge is extinguished. That's why the ambipolar diffusion potential established is usually high, around ten volts, as seen in the Ar/O\({}_{2}\) plasma of Figure 1d and in the early stage of simulated Ar/SF\({}_{6}\) plasma of Figure 19a (see next). The ambipolar self-coagulation discovered in electronegative plasma has the same meaning as the ambipolar diffusion, i.e., to sustain the plasma's neutrality. In particular, the ambipolar diffusion potential is used to sustain the neutrality of electrons and ions plasma, and the ambipolar self-coagulation is used to sustain the neutrality of anions and cations plasma. Since there is no obvious difference between the masses of anions and cations, the ambipolar self-coagulation potential (if exised) is not needed for sustaining the neutrality, as the simulation has predicted. It is then expected from the simulation that the cations instantaneously follow the self-coagulation of anions through the electrically appealing role between them. (c).