# Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure
## 4 Results and Analysis
### Analysis of Plasma Parameters at Different Times under the Same Pressure
As sufficient power cannot be supplied over a short time for collisional reactions to occur easily, such reactions within the plasma remain at a lower level, and electron density remains at about \(10^{16}\) m\({}^{-3}\). As less energy is absorbed, even when a large amount of microwave passes through the plasma, the electron density remains unchanged. In the second stage (\(5\times 10^{-7}\) s-\(10^{-4}\) s), adequate energy is accumulated to disrupt the internal balance of the plasma, because of which there are relatively strong collisions in the plasma. Thus, the electron density increases rapidly in a short time; it exceeds the cutoff electron density \(4\times 10^{17}\) m\({}^{-3}\) for the collisionless regime, and causes an effect of electron avalanche [42]. Owing to the effect of collisions, a microwave is not reflected and can penetrate the region where the electron density is much higher compared with the critical value; that area, thus, becomes the best microwave absorber, which can reduce undesirable radiation [43], and the electron density continues to increase. In the third stage (\(10^{-4}\) s-\(1\) s), with increasing electron density, the plasma sheath becomes thicker and thicker, its ability to resist microwave is enhanced, and the absorption energy is reduced. Finally, the loss of charged particles by diffusion to the wall becomes basically the same as the gain of charged particles from the plasma sheath; thus the generation and disappearance of electrons reach a dynamic balance, and the electron density becomes stable at \(2.76\times 10^{18}\) m\({}^{-3}\). Figure 8 shows that the conductivity is low at \(10^{-12}\) s because the internal electrons are very sparsely distributed. During the process of excitation, after the electron density increases to the cutoff value, the relative permittivity of the plasma becomes negative because of strong internal collisions, and with the increasing electron density, the tendency of the plasma to exhibit metal-like properties becomes stronger. When the plasma starts behaving like a good conductor, and the maximum value of conductivity increases suddenly to \(12\) S/m, a coaxial waveguide is formed with the outside metal wall, thereby preventing leakage of the microwave. Consequently, surface waves are generated and propagate the microwave energy to both ends of the quartz tube; this propagated energy excites the plasma that has not been previously excited at each end. In turn, the upper and lower ends start exhibiting metal-like properties that allow the surface waves to continue to propagate [24]. Figure 7: Variation in electron density (m\({}^{-3}\)) from \(10^{-12}\) s to \(1\) s under a pressure of 2000 Pa. Figure 9 reveals that the modulus of the electric field in the waveguide is greatest at 10\({}^{-12}\) s. Owing to the influence of the sheath at 10\({}^{-7}\) s, the modulus of the electric field at the center of the plasma torch starts to decrease. Over time, at 10\({}^{-6}\) s, because the sheath resists most of the incoming microwave, surface waves start propagating along the plasma torch surface in both positive and negative \(x\) directions. At 10\({}^{-4}\) s, the surface waves stop propagating and the conductivity becomes steady. Figure 10 shows the spatial distribution of Ar\({}_{2}\)\({}^{+}\) under intermediate pressure; Ar\({}_{2}\)\({}^{+}\) is concentrated outside the waveguide, contrary to the electron density, which is concentrated in the region CFIL (see Figure 3) inside the plasma torch. Owing to the intense reactions, the gas temperature inside the waveguide is higher than the outside temperature. On the one hand, the high gas temperature will reduce the rate of the atom-ion recombination (Table 1), thereby inhibiting the formation of molecular ions. On the other hand, the rate of dissociation of molecular ions (Table 1) will increase with increasing temperature.