# Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure
## 5 Conclusions  
The temporal and spatial variations in the electron density during the excitation of a microwave-induced argon plasma were studied by simulations based on a self-consistent 3D fluid plasma model with Maxwell equations at intermediate pressures. The growth over time of the plasma electron density can be divided into three stages. In the first stage, there is an equilibrium potential barrier in the plasma. Consequently, the electron density remains unchanged and the interference by external factors over short time scales is suppressed. In the second stage, an avalanche effect occurs, and the electron density increases rapidly to exceed its cutoff value. In the third stage, the increasing electron density boosts up the ability that make plasma microwaves resistant, and finally achieves a dynamic balance that assists in the growth of the electron density. The simulation results demonstrate that the permittivity becomes negative when the electron density of the plasma exceeds the cutoff value in the second stage, and the plasma then exhibits metal-like characteristics. The resulting higher conductivity allows the formation of a coaxial waveguide with the external metal wall, and surface waves then propagate and excite previously unexcited regions at the two ends of the plasma. In this circumstance, the electron density increases consistently. The spatial distribution of electron density in the case of intermediate pressure is different from that in the case of atmospheric  
Figure 14: Radial profile at CH (see Figure 3) of the electron density from 1000 to 3000 Pa at 1 s.  
Figure 15: Variation of the plasma degrees of freedom and collision frequency from 1000 to 3000 Pa.  
pressure. The highest electron density is concentrated on the side of the quartz tube near the wave feed port. Owing to diffusion, electrons will move toward the middle of the quartz tube, and the diffusion will become stronger with decreasing pressure. Thus, a decrease in pressure can improve the uniformity of the plasma, but a decrease of pressure will also cause the electron density to decrease. A reduction in electron density is not helpful to the decomposition of CO\({}_{2}\). In addition, owing to the strong interaction between the microwaves and the plasma, the temperature of the gas will increase, and a high gas temperature will reduce the production rate of Ar\({}_{2}\)\({}^{+}\) and increase the consumption rate, thereby reducing the number of Ar\({}_{2}\)\({}^{+}\) ions. Electrons will then become concentrated mainly inside the waveguide, and Ar\({}_{2}\)\({}^{+}\) will become concentrated mainly outside the waveguide in the quartz tube.  
Conceptualization, Q.S.; methodology, Q.S.; software, Q.S.; validation, Q.S., and R.H.; formal analysis, R.H.; investigation, R.H.; data curation, Q.S.; writing--original draft preparation, Q.S.; writing--review and editing, Z.X. and W.H.; visualization, Q.S.; supervision, W.H.; project administration, W.H.; funding acquisition, W.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Key Research and Development Program of China (Grant No. 2017 YFB0308601) and Civil Aviation Joint Fund of the National Natural Science Foundation of China (Grant No. U1733109). The authors are pleased to acknowledge [PERSON] for helpful discussions.  
The authors declare no conflict of interest.