# Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure
## 4 Results and Analysis
### Analysis of the Effect of Different Pressures on Plasma Parameters  
As shown in Figure 12, the ratio of molecular ion density to electron density on MN (Figure 3) in the axial direction of the plasma torch exhibits different trends at different pressures. Owing to a large number of molecular ions and the small electron density at the quartz tube port, the ratio near the port is far greater than that near the center of the tube. The ratio of the molecular ion density to electron density increases gradually with respect to the pressure increases, with the ratio near the port being close to 1 when the pressure reaches 5000 Pa.  
Figure 11: Distributions of electron density, gas temperature (K), and Ar\({}_{2}\)\({}^{+}\) at MN (see Figure 3) at 1 s under a pressure of 2000 Pa.  
Figure 10: Slice plots of the distribution of the Ar\({}_{2}\)\({}^{+}\) density (m\({}^{-3}\)) inside the quartz tube under a pressure of 2000 Pa at 1 s in (**a**) the \(z\)–\(y\) plane (\(x\) = 27.3 mm, i.e., CF in Figure 3) and (**b**) the \(x\)–\(z\) (\(y\) = 0) plane.  
Figures 13 and 14 show the temporal and spatial changes in electron density at different pressures. In Figure 13, with increasing pressure, the overall electron density in the plasma torch increases from \(2.75\times 10^{18}\) to \(4\times 10^{18}\) m\({}^{-3}\). The radial profile of the electron density is shown in Figure 14 at CH (see Figure 3), and it can be seen that when the pressure is 1000 Pa, the electron density at the plasma location has a Gaussian-like distribution, decreasing toward both sides from a maximum value at the center. With increasing pressure, the electron distribution changes--the maximum moves along the central axis away from the center, the peak becomes sharper, and the plasma becomes inhomogeneous; the reason for this phenomenon is that the increase in pressure results in a decrease in the mean free path and an increase in the operating frequency of collisions among particles, as shown in Figure 15. Thus, many particles have already collided before moving to the low-concentration region, which directly leads to an uneven distribution of electrons in the quartz tube, which can also be explained from the perspective of the electron temperature. According to Equation (17), the ambipolar diffusion coefficient is co-related to the ion diffusion coefficient and the electron and ion temperatures. The microwave plasma torch is in a non-thermal equilibrium state under intermediate pressure, with T\({}_{\rm e}>>\) T\({}_{\rm i}\)\(>\)> T\({}_{\rm g}\), which implies that the ambipolar diffusion coefficient is determined mainly by the electron temperature. With increasing pressure, the electron temperature in the quartz tube will decrease and, thus, so will the ambipolar diffusion coefficient; that is, with increasing pressure, the speed of plasma diffusion from the boundary to the middle will slow down, which will increase the inhomogeneity.  
Figure 12: Axial profiles of the ratio of molecular ion density to electron density at 1 s under different pressures.  
Figure 13: Effect of Ar pressure on the electron density from 10\({}^{-12}\) s to 1 s.  
This section explains the effect of different pressures on plasma parameters. With the increase of pressure, the collision frequency and the electron density increase, but the uniformity of the electron density will also become worse.