# Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure
## 4 Results and Analysis  
### Analysis of Plasma Parameters at Different Times under the Same Pressure  
Figure 4 demonstrates the spatial distribution of the electron density. If the electron density increases from \(10^{16}\) to \(4\times 10^{17}\) m\({}^{-3}\), it generates a surface wave [39], and the electrons start spreading from the region CFIL, which is the mainly excited region of plasma shown in Figure 3, to the upper and lower ends of the quartz tube. As the microwave is fed into the waveguide along the \(-z\) direction, there is a radial heterogeneity of electric field modulus in the plasma torch, which causes electrons to move toward the right side of the quartz tube, while the plasma torch discharges and contracts, as shown in Figure 4c. Meanwhile, there will be a few excitations on the left side of the tube; there are two reasons for this phenomenon. First, if the plasma forms a coaxial waveguide with the outer metal wall, then a TE\({}_{10}\) wave propagates along the \(-z\) direction, which changed into a transverse electromagnetic (TEM) wave that propagated with the upper and lower sides of the quartz tube [40; 41]. As shown in Figure 5, there is a nonzero electric field in the quartz tube outside the waveguide; thus, some surface wave energy can be fed into the left side of the tube. Second, according to the results for the electric field shown in Figure 5, even if the plasma fills the whole quartz tube, it is still only part of the microwave transmission path. Owing to diffraction, a small portion of the microwave can stillreach the other end of the waveguide. In the meantime, on that side, there will also be a standing wave, from which energy is fed into the plasma. At the time of \(10^{-5}\) s, on the one hand, the electron density in the top and bottom parts of the quartz tube can increase owing to the effect of the surface wave. On the other hand, it is different from the atmospheric-pressure plasma that is dominated by collisions, as shown in Figure 6. At intermediate pressures, owing to the low collision frequency, the high particle diffusion rate, the high mean free path, and electrons gathered at the edge of the quartz tube will diffuse gradually to the middle of the tube. Moreover, the spatial distribution of electron density will remain steady after the microwave plasma torch has been fully excited at \(10^{-4}\) s.  
Figure 4: Slice plots of the distribution of the electron density (m\({}^{-3}\)) inside the quartz tube in the \(x\)–\(z\) (\(y=0\)) plane under a pressure of 2000 Pa: (a) \(10^{-12}\) s; (b) \(10^{-7}\) s; (c) \(10^{-6}\) s; (d) \(10^{-5}\) s; (e) \(10^{-4}\) s; (f) \(1\) s.  
Figure 5: Slice plots of the distribution of the microwave electric field module (V/m) in the \(x\)–\(z\) (\(y=0\)) plane at \(10^{-6}\) s under a pressure of 2000 Pa.  
Figure 6: Slice plots of the distribution of the electron density (m\({}^{-3}\)) inside the quartz tube at atmospheric pressure at \(1\) s in (a) the \(z\)–\(y\) plane (at \(x=27.3\) mm, i.e., CF in Figure 3) and (b) the \(x\)–\(z\) plane (at \(y=0\)), the flow rate is \(1\) L/min. Because electrons are 1000-10,000 times lighter than the heavy particles, they can obtain more energy from the incident electromagnetic field. Electrons accelerated by the electromagnetic field transfer their energy to the heavy particles through collisions. Thus, energy can be transferred to the plasma. Figure 7 shows that the growth trend of the electron density in the quartz tube can be divided into three stages during the excitation process. In the first stage (\(10^{-12}\) s-\(5\times 10^{-7}\) s), owing to the existence of a potential barrier inside the plasma, interference from external factors can be hindered or suppressed, thereby allowing an internal balance. The applied electromagnetic field cannot change the particle balance in the plasma.