# Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure
## 1 Introduction  
Microwave plasmas are extensively applied in various fields because of the advantages such as high electron density, high efficiency, wide working pressure range, and no need for electrodes. In particular, it is used to deal with gas pollution [1; 2], plasma-enhanced chemical vapor deposition [3], surface material treatment [4; 5], plasma stealth [6; 7], and hydrogen production [8]. Owing to the adverse effect of greenhouse gas on the modern world, the use of plasma to decompose carbon dioxide (CO\({}_{2}\)) under intermediate pressure has become an attractive research topic [9; 10; 11; 12]. Methods involving the enrichment of plasma by a massive number of active particles can reduce the threshold energy of the CO\({}_{2}\) decomposition reaction that converts it into carbon monoxide (CO), which has become a promising approach for decreasing CO\({}_{2}\), as well as providing a new energy source [13; 14; 15]. Argon (Ar) has a low threshold to produce energetic particles (electron/metastable); thus, argon-plasma promotes the excitation and dissociation of CO\({}_{2}\). In the process of CO\({}_{2}\) dissociation by Ar plasma excitation, first plasma energy is mainly reduced by ionization and excitation of the 99% argon atoms in the plasma leading to exciting argon species (ion, excimer, metastable) and energetic electrons. Second, exciting argon or energetic electrons or species transfers the plasma's energy to CO\({}_{2}\) in a collision for making CO\({}_{2}\) in an electronically excited state [16]. Thus, analysis of the electron behavior over time and the spatial distribution of electrons in the excitation process is helpful for the plasma sources design. Furthermore, the information obtained from the three-dimensional (3D) argon model can be useful to have a spatial description of the microwave plasma. Hence, Ar can be used for making efficient plasma technologies for CO\({}_{2}\) conversion. Regarding the limitations of experimental techniques and plasma diagnostics [17], plasma modeling has become a fruitful key method for plasma research. Plasma modeling must consider electromagnetic effects, plasma dynamics, thermodynamics, chemical reaction, and equilibrium. Thus, among other things, the inevitable simplified nature of the models leads to discrepancies between modeling results and experimental results; hence, optimization and improvement of plasma models are of utmost significance [18; 19; 20]. Models of low pressure [21; 22; 23] and atmospheric-pressure [24; 25; 26] microwave plasmas were extensively studied; however, there remains demand to analyze plasma parameters in the intermediate-pressure environment [27]. [PERSON] et al. established a 3D model of a plasma-enhanced chemical vapor deposition reactor at low pressure, based on which they analyzed the electron, heavy-particle densities, electric field distribution, and electron heat discharge behavior [28]. A two-dimensional (2D) surface-wave plasma model at an intermediate pressure between 660 and 8800 Pa was simulated by [PERSON] et al., who demonstrated the reliability of the model and wave plasma interconnection with the axial distribution of the power and electron density, at both sides of the launcher [29]. By exploring the electric field distribution and the plasma parameters of an atmospheric-pressure microwave plasma torch under both 2D and 3D conditions, [PERSON] et al. demonstrated that the 2D model had certain limitations concerning its description of the spatial distribution of plasma parameters [30]. In a previous study, a 3D waveguide plasma model with excitation by microwave at atmospheric pressure was constructed [31; 32]; it illustrated some properties of plasma factors such as electron density, temperature, and gas temperature during excitation processing. However, it did not consider the significant molecular ion recombination reaction at atmospheric pressure, which led to differences between the results of modeling and those of experiments [33; 34].