applied sciences

Article Numerical 3D Modeling: Microwave Torch at Intermediate Pressure

Qinghao Shen 1, Run Huang 1, Zili Xu 2 and Wei Hua 1,*

1 School of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China; [email protected] (Q.S.); [email protected] (R.H.) 2 Second Research Institute of CAAC, Chengdu 610041, China; [email protected] * Correspondence: [email protected]

 Received: 29 June 2020; Accepted: 31 July 2020; Published: 4 August 2020 

Abstract: This study represents a self-consistent three-dimensional (3D) fluid plasma model coupled with Maxwell equations at an intermediate pressure between 1000 and 5000 Pa. The model was established using the finite element method to analyze the effects of time–space characteristics, which is the variation of with time and the 3D spatial distribution of plasma parameters in the plasma torch at various times. The numerical modeling was demonstrated in three different stages, where the growth of density is associated with time. From the distribution characteristics of molecular , it can be concluded that they are distributed mainly at the port of the quartz tube of the torch, which is larger than the center of the tube. The density ratio of molecular to electron is decreased because of the reduction of pressure and distance, which has been calculated from the port to the center of the quartz tube. The analysis of microwave plasma parameters indicated that intermediate pressure is useful for modeling and plasma source designing, especially for carbon dioxide conversion.

Keywords: electron density; microwave plasma; molecular ion; modeling; space-time characteristics

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 (CO2) under intermediate pressure has become an attractive research topic [9–12]. Methods involving the enrichment of plasma by a massive number of active particles can reduce the threshold energy of the CO2 decomposition reaction that converts it into carbon monoxide (CO), which has become a promising approach for decreasing CO2, as well as providing a new energy source [13–15]. Argon (Ar) has a low threshold to produce energetic particles (electron/metastable); thus, argon–plasma promotes the excitation and dissociation of CO2. In the process of CO2 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 . Second, exciting argon or energetic electrons or species transfers the plasma’s energy to CO2 in a collision for making CO2 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 CO2 conversion.

Appl. Sci. 2020, 10, 5393; doi:10.3390/app10155393 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 5393 2 of 16

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 [18–20]. Models of low pressure [21–23] and atmospheric-pressure [24–26] microwave plasmas were extensively studied; however, there remains demand to analyze plasma parameters in the intermediate-pressure environment [27]. Bouherine 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 Jimenez-Diaz 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, Baeva 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]. To overcome these problems, this study constructs a plasma model with Maxwell equations by considering Ar atoms in the ground and metastable state, and as atomic and molecular ions, by considering coupling with the flow, heat transfer, and microwave multi-physical fields. Simulations based on this model are used to analyze the transient circulation of plasma parameters. In this study, excitation characteristics of the microwave plasma torch in the range 1000–5000 Pa at intermediate pressure are supplemented. The results obtained will be helpful in the construction of plasma sources and specifically for applications to CO2 decomposition [15,35]. The remainder part of the paper is structured as follows: Section2 describes the plasma model; Section3 explains the governing equations; Section4 presents the results and analysis; finally, Section5 provides the conclusions.

2. Model Description

2.1. Microwave Plasma System Figure1 shows a schematic of the microwave excitation device; 2.45 GHz electromagnetic waves enter the WR-430 waveguide from the right-hand side through a circulator, after which there are three stub tuners, and there is a short-circuit board on the left side. Figure2 represents the cutaway view of the microwave plasma torch, and Figure3 shows a 2D section along the central axis in the x–z plane, which is the cross-sectional dimension of the rectangular excitation waveguide with AB = 54.6 mm, length as AH = 218 mm, and width of the WR-430 rectangular waveguide in the x–y plane as 109.2 mm. To prevent microwave leakage, the quartz tube is surrounded by a cylindrical metal cage, which is modeled as a perfect electrical conductor. Ar was fed axially through the quartz tube at the flow rate of 1 L/min. The pressure in the quartz tube was 2000 Pa, initial gas temperatures was 293.15 K, the initial 16 3 electron density was 10 m− , the initial average electron energy ε was 4 eV, and the initial potential was 0 V. Appl.Appl. Sci. Sci. 2020 2020, 10, 10, x, xFOR FOR PEER PEER REVIEW REVIEW 3 3of of 18 18

Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 18 Appl. Sci. 2020, 10, 5393 3 of 16

Figure 1. Graphical representation of the microwave excitation device. FigureFigure 1. Graphical 1. Graphical representation representation ofof thethe microwave microwave excitation excitation device. device.

Figure 1. Graphical representation of the microwave excitation device.

FigureFigureFigure 2. 2. 2.Cutaway Cutaway Cutaway view view view of ofof the thethe microwave microwave plasma plasma plasma torch. torch. torch.

Figure 2. Cutaway view of the microwave plasma torch.

FigureFigureFigure 3. 3.Two-dimensional 3. Two-dimensional Two-dimensional (2D)(2D) (2D) section section of ofof the the model model (y ( y= (y =0), =0), with0), with with dimensions. dimensions. dimensions.

InIn this this study, study, the the fluid fluid approximation approximation method method wa was sused used to to couple couple the the Boltzmann Boltzmann equation equation to to the the In this study, theFigure fluid 3. Two-dimensional approximation (2D) method section of was the usedmodel to(y = couple 0), with thedimensions. Boltzmann equation to Maxwell equation for calculating the density of charged particles, electron temperature, and the the MaxwellMaxwell equationequation forfor calculating the the density density of of ch chargedarged particles, particles, electron electron temperature, temperature, and andthe the electromagnetic field. The Boltzmann equation embodies the change of ion velocity distribution electromagneticIn this study, field. the Thefluid Boltzm approximationann equation method embodies was used the to changecouple theof Boltzmannion velocity equation distribution to the electromagneticequation f(r,v,t field.) with Thetime,Boltzmann where v is the equation velocity, embodies r is the position, the change and t ofis time. ion velocity The calculation distribution equationMaxwell f (equationr,v,t) with for time, calculating where v theis the density velocity, of ch r argedis the position,particles, andelectron t is time.temperature, The calculation and the equationprocessf ( wasr,v,t )as with follows: time, the whereenergy vdistributionis the velocity, functionr is of theelectrons position, was brought and t is into time. the Boltzmann The calculation processelectromagnetic was as follows: field. theThe energy Boltzm distributionann equation function embodies of electrons the change was broughtof ion velocityinto the Boltzmanndistribution processequation was asto follows:solve the the electron energy transport distribution coeffi functioncient through of electrons the BOLSIG+ was brought solver. into The the electron Boltzmann equationequation tof( r,solvev,t) with the time,electron where transport v is the coeffivelocity,cient r throughis the position, the BOLSIG+ and t is solver.time. The The calculation electron equationtransport to solve coefficient the electron and the transport experimentally coefficient deter throughmined plasma the BOLSIG chemical+ solver. cross-section The electron data were transport transportprocess was coefficient as follows: and the the energy experimentally distribution deter functionmined of plasma electrons chemical was brought cross-section into the dataBoltzmann were formed into the continuous equation, momentum conservation equation, and the energy coefficientformedequation and into theto solve experimentallythe continuousthe electron determinedequation, transport moment plasmacoefficientum chemical throughconservation cross-section the BOLSIG+ equation, data solver. wereand Thethe formed energyelectron into the conservation equation. Then, these three equations were coupled with the electromagnetic field to continuousconservationtransport equation, coefficient equation. momentum and Then, the thes experimentally conservatione three equations equation, deter minedwere and coupled plasma the energy wichemicalth the conservation electromagnetic cross-section equation. data field were to Then, solve the electromagnetic field and plasma characteristic parameters. As the Boltzmann equation is thesesolve threeformed the equations electromagneticinto the were continuous coupled field and withequation, plasma the electromagnetic charactemomentristicum parameters.conservation field to solve As equation, the the Boltzmann electromagnetic and equationthe energy field is and plasmaconservation characteristic equation. parameters. Then, thes Ase the three Boltzmann equations equation were coupled is highly with nonlinear,the electromagnetic it is diffi cultfield toto use directlysolve in the the analytical electromagnetic solution. field Thus, and plasma we used characte the finiteristicelement parameters. method As the and Boltzmann a numerical equation technique is to solve the equations. Before solving the finite element method, the space and time of the solution target must be discretized. In this study, a tetrahedral mesh was used to divide the solution domain of the 3D graphics, and a boundary layer was used to encrypt and divide the boundary. The total number of the mesh elements was 183,448. The model was executed on a computer with an i9-9900U CPU and 64 GB RAM; the execution duration was approximately 101 min. Appl. Sci. 2020, 10, 5393 4 of 16

2.2. Plasma Chemistry When an electromagnetic wave propagates in the plasma, there will be some reactions between the particles. The main reaction types include: (1) Elastic collision and inelastic collision: such reactions will lead to energy exchange in particles; the difference between them is that the elastic collision only leads to the transfer of kinetic energy between the colliding particles, but does not change internal energy. (2) Excitation and ionization: such reactions result in growth in the number of free electrons or a change in the energy level of an atom. The probability of their counter occurrence is related to the collision cross-section. (3) Charge transfer: this type of reaction results in the equivalent transfer of charge between particles. The kind of reaction mainly occurs in the collision process of ions and neutral particles. (4) Charge recombination: there are two forms—diffusion and recombination. Diffusion is the process by which the charged particle reaches the wall and electrode to disappear. Recombination is a process by which positive ions capture a free electron and combine with electrons or negative ions to form new neutral atoms. Table1 shows the main reaction and collision processes [30,35,36].

Table 1. Main chemical reactions and collision processes during argon discharge.

NO Process Reaction Rate Coefficient (m3/s) ∆E

1 Elastic scattering Ar + e Ar + e kes → 2 Ground state excitation Ar + e Ar + e kex 11.56 → ∗ 3 Ground state ionization Ar + e Ar+ + 2e k 15.8 → i 4 Step-wise ionization Ar + e Ar+ + 2e k 4.24 ∗ → si 5 Superelastic collision Ar + e Ar + e ksc 11.56 ∗ → − 6 Metastable pooling Ar + Ar Ar+ + Ar + e 1.625 10 16T0.5 ∗ ∗ → × − 7 Two-body quenching Ar + Ar 2Ar 3 10 21 ∗ → × − 8 Three-body recombination Ar+ + 2e e + Ar 8.75 10 39T 4.5m6/s 15.76 → × − − − + 12 0.026 0.67 1 exp( 418/T) 9 Dissociative recombination Ar + e Ar∗ + Ar 1.03 10− − − 2 → × Te 1 0.31 exp( 418/T) + + 12 h −  T − 0.026 i 10 Electron impact Ar + e e + Ar + Ar 1.11 10− exp 2.94 + 3 2 → × − 11600 − Te 11 Atomic ions conversion Ar+ + 2Ar Ar + Ar+ 7.5 10 41T 1m6/s → 2 × − − Molecular ions dissociation h i 12 Ar+ + Ar 2Ar + Ar+ 6.06 10 12 exp 12580 atom impact 2 → × − − T 13 Diffusion m wall(Ar, Ar+, e, Ar , Ar+) → ∗ 2

2.3. Boundary Condition Table2 shows the boundary conditions.

Table 2. Boundary conditions to the model equations.

Physical Field Plasma Boundary

KJ n Γe = 0 n Γ = 0 nJ = 0 n ε εrpE = 0 − · − · ∆ k · 0 DE n Γe = 0 n Γ∆ = 0 nJk = 0 n ε0εrpE = 0 − · ve,thne − · 5ve,thn∆ · DK, EJ n Γe = n Γ = Surface Reactions V = 0 · 2 · ∆ 6 Physical Field Boundary Electromagnetic Wave

GH Pin BA, BC, FG, AL, IH, GH n E = 0 × Physical Field Boundary Laminar Flow KJ uin DE P0 DK, EJ u = 0 Physical Field Boundary Heat Transfer in Fluids KJ T = T0 DE n q = q , q = h(Text T) − · 0 0 − DK, EJ n q = 0 − · Appl. Sci. 2020, 10, 5393 5 of 16

3. Governing Equations Generally, three approaches are used to model plasmas—the kinetic method, fluid approximation, and hybrid approaches. Among the three, fluid approximation was used in this study for the simulation of our model because of its efficiency in solving partial differential equations, modeling significant arbitrarily complex plasma chemistry, and modeling electron dynamics to electromagnetic areas. The fluid approximation method requires complex modeling to take account of gas discharge processes, boundary conditions, thermodynamics, gas reactions, collision processes, electromagnetic phenomena, plasma dynamics, and power conservation of electrons, as well as heavy particles. The absorption of electromagnetic wave energy is the major cause of plasma excitation. Thus, it is necessary to incorporate the dynamical changes of the electromagnetic waves involved in the effects of microwave on the reaction process. The model is not time-independent and quasi-stationary accomplishment is the expectation using the wave equations. Therefore, the electromagnetic wave formula in the plasma needs to be established to perform cover analysis of the influence of various related plasma parameters on electromagnetic wave propagation. Then, under the assumption of ambipolar diffusion, a fluid equation for the plasma was established to analyze the changes in electron density with time, while the Boltzmann equation was used to analyze the heating effect of strong electromagnetic pulses on the electrons. The accelerated electrons transfer power to heavy particles via collisions. The heavy particles are expected to be in thermal balance at a specific temperature T, and the electrons are categorized by the Maxwellian power spreading with a specific temperature Te. The heat conduction formula was used to compute the rate of change of particle energy, which is affected by the electromagnetic field. Finally, an iterative approach was utilized to analyze the behavior of various parameters of the plasma [34,35].

3.1. Wave Equation The incident electromagnetic wave on the plasma satisfies Maxwell equations:

H = iωε εrE (1) ∇ × 0 E = iωµ H (2) ∇ × − 0 where E and H represent the electric and magnetic field strength vectors, respectively. In addition, p i is ( 1), ω signifies the angular wave frequency, and ε and µ denote the permittivity and − 0 0 permeability of the vacuum, respectively. The symbols εr express the relative electric permittivity [30]. The substitution of Equation (1) into Equation (2) provides Equation (3) as follows:

2 E = ω µ ε εrE (3) ∇ × ∇ × 0 0

The wavenumber in a vacuum is given by k0 = ω/c, c = ε0/µ0 thus, Equation (3) can be rewritten as Equation (4): 2 E = k εrE (4) ∇ × ∇ × The relative permittivity of the plasma in Equation (4) is given by Equation (5):

2 ωp εr = 1 (5) − ω(ω iυ) −

q 2 where υ is used to express the electron elastic collision frequency; ω = nee denotes the angular p ε0me frequency of the plasma; and the terms ne, me, and e stand for the electron density, electronic mass, and fundamental charge, respectively. The electronic conductivity is given by Equation (6).

n e2 1 σ = e (6) me υ + iω Appl. Sci. 2020, 10, 5393 6 of 16

Now Equation (4) is rewritten as Equation (7): ! 2 σ E = k εr 1 i E (7) ∇ × ∇ × − ε0ω

When the microwave directly incidents into plasma, according to Equation (5), we find that the 2 2 real part of εr becomes negative for the plasma, which is collisionless when ωp > ω . Thus, the electron 16 3 density ne has a critical number density of approximately 7.6 10 m− , which corresponds to 2 2 × ωp = ω and εr = 0. When a medium is present between the plasma and the incident wave, the plasma frequency is expressed by Equation (8) [37]. 2 2 ωp = (1 + εd)ω (8) In the model, the effective permittivity of the quartz tube is 4.0, and the incident wave operating frequency is 2.45 GHz. Therefore, the cutoff electron density value of the collisionless plasma is calculated to be 4 1017 m 3. × − 3.2. Equations of the Plasma Model In plasma convection–diffusion and in the plasma reaction process, the electric field vector, electron diffusion coefficient, and electron mobility affect the electron density and electron density energy. Equations (9) and (10) describe the changes in the electron density with time and spatial distribution, while Equations (11) and (12) describe the changes in the electron density energy with time and spatial distribution. The electron density change rate can be described by the drift–diffusion formula, as shown in Equations (9)–(12):

∂ne + (u )ne + Γe = Re (9) ∂t ·∇ ∇ ·

Γe = (µe E)ne De ne (10) − · − · ∇ and ∂ (nε) + Γε + E Γε = Rε (u )nε (11) ∂t ∇ · · − · ∇

Γε = (µε E)nε Dε nε (12) − · − · ∇ where symbols Γe and Γε express electron flux and electron energy flux, respectively; terms ne, µe, nε, µε, and u denote the electron density, electron mobility, electron energy density, electron energy mobility, and velocity vector of the fluid, respectively. Symbol De signifies the electron diffusion coefficient, Dε denotes the electron energy diffusivity, and Re and Rε express the electron rate expression and energy loss or gain, respectively, because of inelastic collisions [32].

3.3. Fluid Equation The gas flow in the quartz tube can be defined by the mass continuity and Navier–Stokes with respect to Equations (13) and (14): ∂ρ + (ρu) = 0 (13) ∂t ∇ · ∂u 2 ρ + ρ(u )u = p + [µ( u + ( u)T) µ( u)I] + F (14) ∂t · ∇ −∇ ∇ · ∇ ∇ − 3 ∇ · where p, ρ, µ, and I denote the pressure, mass density, dynamic viscosity, and unit tensor, µ0 respectively [28]. The Lorentz force is F = Re(σE H∗), where H∗ expresses the complex conjugates 2 × of H. Appl. Sci. 2020, 10, 5393 7 of 16

3.4. Heat Transfer Equation A common mixture-sharing temperature T was taken by the heavy species, including the ions and neutral atoms which were taken as a mixture sharing with a common temperature T. The rate of change of heavy-particle energy is described by Equation (15):

∂T ρCp + ρCpu T = (σ T) + Q Qw (15) ∂t · ∇ ∇ · k∇ el − where Cp, σk, Qel, and Qw represent the specific heat capacity, thermal conductivity, the gain of energy because of elastic collisions between heavy particles and electrons, and heat release because of non-electronic collisions, respectively [20,38].

3.5. Ambipolar Diffusion The particles of plasma diffusion were divided into two categories: ambipolar diffusion of charged particles (electrons, ions) and the diffusion of neutral particles or atoms. Among them, ambipolar diffusion is a unique characteristic of plasma; this movement occurs near the solid surface bordering the plasma, which controls the disappearance process of charged particles. In the initial free diffusion process, the electron diffuses much faster than the atom; thus, it reaches the vessel wall first and makes it negatively charged. Therefore, there are an equal amount of positive space charges in the plasma, causing charge separation. The positive and negative charges appear in pairs and produce a radial electric field pointing to the wall of the container. The radial electric field can inhibit the flow of electrons to the vessel wall and promote the ions to move toward the vessel wall, inhibiting the free diffusion of electrons and ions. The ambipolar diffusion coefficient is expressed by Equation (16):

µiDe + µeDi Da = (16) µi + µe where µi, µe, Di, and De denote the ion mobilities, electron mobilities, ion diffusion coefficients, and electron diffusion coefficients, respectively. For a weakly ionized discharge, because µi<<µe, use of the Einstein relation expressed by Equation (17):

Te Da Di(1 + ) (17) ≈ Ti

4. Results and Analysis

4.1. Analysis of Plasma Parameters at Different Times under the Same Pressure Figure4 demonstrates the spatial distribution of the electron density. If the electron density increases from 1016 to 4 1017 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 Figure3, 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 Figure4c. 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 TE10 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 Figure5, 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 Figure5, 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 still Appl. Sci. 2020, 10, 5393 8 of 16

reach the other end of the waveguide. In the meantime, on that side, there will also be a standing wave, 5 from which energy is fed into the plasma. At the time of 10− 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 Figure6. At intermediate pressures, owing to the low collision frequency, the high particle Appl.diff Sci.usion 2020,rate, 10, x FOR the PEER high REVIEW meanfree path, and electrons gathered at the edge of the quartz tube10 of will18 diAppl.ffuse Sci. gradually2020, 10, x FOR to thePEER middle REVIEW of the tube. Moreover, the spatial distribution of electron density10 willof 18 4 Appl.remain Sci. 2020 steady, 10, x after FOR PEER the microwave REVIEW plasma torch has been fully excited at 10− s. 10 of 18

Figure 4. Slice plots of the distribution of the electron density (m−3) inside the quartz tube in the x–z −3 (y Figure= 0) plane 4. Slice under plots a pressure of the distribution of 2000 Pa: (ofa) the10− 12electron s; (b) 10 density−7 s; (c) 10(m−6 s;) inside(d) 10− 5the s; ( quartze) 10−4 s; tube (f) 1 in s. the x–z 3 Figure 4. Slice plots of the distribution of the electron−12 density−7 (m −)6 inside the−5 quartz− tube4 in the x–z Figure(y = 0) 4.plane Slice under plots ofa pressure the distribution of 2000 Pa:of the (a) electron10 s; (b density) 10 s; ((mc) −10−3) inside s; (d) the10 quartzs; (e) 10 tubes; (inf) the1 s. x–z 12 7 6 5 4 (y = 0) plane under a pressure of 2000 Pa: (a) 10− s; (b) 10− s; (c) 10− s; (d) 10− s; (e) 10− s; (f) 1 s. (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) planeFigure at 10 5.5.− 6Slice s under plots a ofpressure the distribution of 2000 Pa. of the microwavemicrowave electric fieldfield modulemodule (V(V/m)/m) inin thethe xx––zz ((yy == 0) 6 plane at 10 −6 s under a pressure of 2000 Pa. Figureplane 5.at Slice10− s plots under of a the pressure distribution of 2000 of Pa. 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 Figure 6. Slice plots of the distribution of the electron density− (m−3) inside the quartz tube at pressure at 1 s in (a) the z–y plane (at x = 27.3 mm, i.e., CF in Figure3) and−3 ( b) the x–z plane (at y = 0), atmosphericFigure 6. Slicepressure plots at of1 s thein (adistribution) the z–y plane of the(at xelectron = 27.3 mm, density i.e., CF(m in) Figureinside 3)the and quartz (b) the tube x–z at the flow rate is 1 L/min. planeFigureatmospheric (at 6.y =Slice 0), pressurethe plots flow of rateat the1 iss indistribution1 L/min.(a) the z–y ofplane the (atelectron x = 27.3 density mm, i.e., (m CF−3) insidein Figure the 3) quartz and (b tube) the xat– z atmosphericplane (at y = pressure 0), the flow at 1 rate s in is (a 1) L/min.the z–y plane (at x = 27.3 mm, i.e., CF in Figure 3) and (b) the x–z Becauseplane (at electrons y = 0), the areflow 1000–10,000 rate is 1 L/min. times lighter than the heavy particles, they can obtain more energyBecause from the electrons incident are electromagnetic 1000–10,000 times field. lighter Electrons than accelerated the heavy particles,by the electromagnetic they can obtain field more transferenergyBecause their from energy electrons the incident to theare heavy 1000–10,000electromagnetic particles times through field. lighter Electronscollisions. than the accelerated Thus, heavy energy particles, by can the theybe electromagnetic transferred can obtain to more thefield plasma.energytransfer from their the energy incident to the electromagnetic heavy particles field. through Electrons collisions. accelerated Thus, energy by the can electromagnetic be transferred tofield the transferplasma.Figure their 7 shows energy that to the the heavy growth particles trend of through the elec collisions.tron density Thus, in theenergy quartz can tube be transferred can be divided to the intoplasma. threeFigure stages 7 shows during that the the excitati growthon trend process. of the In electhe tronfirst densitystage (10 in− 12the s–5 quartz × 10 −tube7 s), owingcan be todivided the existenceintoFigure three of a7stages potentialshows during that barrier the the growth insideexcitati thetrendon plasma,process. of the in elecInterference thetron first density fromstage inexternal (10 the−12 quartz s–5 factors × tube10 −can7 s),can beowing be hindered divided to the orintoexistence suppressed, three stagesof a thereby potential during allowing barrierthe excitati an inside internalon the process. plasma,balance. In inThe theterference appliedfirst stage fromelectromagnetic (10 external−12 s–5 ×factors 10 field−7 s), cannotcan owing be changehindered to the existenceor suppressed, of a potential thereby barrier allowing inside an internal the plasma, balance. interference The applied from electromagnetic external factors field can cannot be hindered change or suppressed, thereby allowing an internal balance. The applied electromagnetic field cannot change Appl. Sci. 2020, 10, 5393 9 of 16

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. Figure7 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 10 7 s), owing to the − × − Appl.existence Sci. 2020 of, a10 potential, x FOR PEER barrier REVIEW inside the plasma, interference from external factors can be hindered11 of or18 suppressed, thereby allowing an internal balance. The applied electromagnetic field cannot change the theparticle particle balance balance in the in plasma. the plasma. As su ffiAscient sufficient power cannotpower becannot supplied be supplied over a short over time a short for collisional time for collisionalreactions to reactions occur easily, to occur such reactionseasily, such within reactions the plasma within remain the plasma at a lower remain level, at and a lower electron level, density and 16 3 16 −3 electronremains atdensity about remains 10 m− at. As about less 10 energy m is. As absorbed, less energy even is when absorbed, a large even amount when of a microwave large amount passes of microwavethrough the passes plasma, through the electron the plasma, density the remains electron unchanged. density remains In the secondunchanged. stage In (5 the10 second7 s–10 stage4 s), × − − (5adequate × 10−7 s–10 energy−4 s), is adequate accumulated energy to disrupt is accumulated the internal to balancedisrupt ofthe the internal plasma, balance because of of the which plasma, there becauseare relatively of which strong there collisions are relatively in the plasma. strong Thus,collisions the electronin the plasma. density increasesThus, the rapidlyelectron in density a short increasestime; it exceeds rapidly the in a cuto shortff electrontime; it ex densityceeds the 4 cutoff1017 m electron3 for the density collisionless 4 × 1017 m regime,−3 for the and collisionless causes an × − regime,effect of and electron causes avalanche an effect [of42 electron]. Owing avalanche to the eff [42].ect of Owing collisions, to the a effect microwave of collisions, is not reflecteda microwave and iscan not penetrate reflected the and region can penetrate where the the electron region density where is the much electron higher density compared is much with higher the critical compared value; withthat area,the critical thus, becomes value; that the bestarea, microwave thus, become absorber,s the best which microwave can reduce absorber, undesirable which radiation can reduce [43], 4 −4 undesirableand the electron radiation density [43], continues and the toelectron increase. densit In they continues third stage to (10increase.− s–1 s),In withthe third increasing stage (10 electron s–1 s),density, with increasing the plasma electron sheath density, becomes the thicker plasma and sheath thicker, becomes its ability thicker to resistand thicker, microwave its ability is enhanced, to resist microwaveand the absorption is enhanced, energy and is the reduced. absorption Finally, energy the lossis reduced. of charged Finally, particles the loss by diofff chargedusion to particles the wall bybecomes diffusion basically to the the wall same becomes as the gainbasically of charged the same particles as the from gain theof charged plasma sheath;particles thus from the the generation plasma sheath;and disappearance thus the generation of electrons and disappearance reach a dynamic of balance,electrons and reach the a electrondynamic density balance, becomes and the stableelectron at density2.76 10 becomes18 m 3. stable at 2.76 × 1018 m−3. × −

3 12 FigureFigure 7.7. VariationVariation inin electronelectron densitydensity (m(m−−3) from 10−12 ss to to 1 1 s sunder under a a pressure pressure of of 2000 2000 Pa. Pa.

12 Figure 88 showsshows thatthat thethe conductivityconductivity isis lowlow atat 10 10−−12 ss because because the the internal internal electrons electrons are very sparsely distributed. During During the the pr processocess of excitation, excitation, after the the electr electronon density density increases to the cutoff cutoff value, the relative permittivity of the plasma beco becomesmes negative because of strong internal collisions, collisions, and with the increasing electron density, the tendencytendency 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 Ss/m,/m, a co coaxialaxial waveguide is formed with the outside metal wall, thereby preventing leakage of the microwave.microwave. Consequently, surface waves are generated and propagate the microwave energy to both ends of thethe quartz tube; this propagated energy excites the plasma that has not been previously excited at eacheach end.end. In turn, the upper and lower ends start exhibiting metal-like properties that allow the surface waves toto continuecontinue toto propagatepropagate [[24].24]. Appl. Sci. 20202020,, 1010,, x 5393 FOR PEER REVIEW 1210 of 18 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 18

Figure 8. Slice plots of the distribution of conductivity (S/m) inside the quartz tube in the x–z (y = 0) Figure 8. Slice plots of the distribution of conductivity (S/m) inside the quartz tube in the x–z (y = 0) planeFigure under 8. a Slice pressure plots of of 2000 the distributionPa: (a) 10−12 s;of ( conductib) 10−7 s; vity(c) 10 (S/m)−6 s; ( dinside) 10−5 s;the (e quartz) 10−4 s; tube(f) 1 s.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. 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 9 reveals that the modulus of the electric field in the waveguide is greatest at 10–12 s. Figure9 reveals that the modulus of the electric field in the waveguide is greatest at 10 –12 s. Owing toFigure the influence 9 reveals of that the thesheath modulus at 10–7 of s, thethe electrmodulusic field of thein theelectric waveguide field at isthe greatest center atof 10the–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 plasmaOwing torch to startsthe influence to decrease. of the Over sheath time, at at 10 10–7 –6s, s,the because modulus the ofsheath the electric resists mostfield atof the incomingcenter of the torch starts to decrease. Over time, at 10–6 s, because the sheath resists most of the incoming microwave, microwave,plasma torch surface starts waves to decrease. start propagating Over time, alongat 10–6 the s, because plasma thetorch sheath surface resi stsin bothmost positiveof the incoming and surface waves start propagating along the plasma torch surface in both positive and negative x negativemicrowave, x directions. surface At waves 10–4 s, start the surfacepropagating waves along stop thepropagating plasma torch and thesurface conductivity in both positivebecomes and directions. At 10–4 s, the surface waves stop propagating and the conductivity becomes steady. steady.negative x directions. At 10–4 s, the surface waves stop propagating and the conductivity becomes steady.

Figure 9. Slice plots of the distribution of electric field field (V/m) (V/m) inside the quartz tube in the x–z (y = 0)0) 12 7 6 5 4 planeFigure under 9. aSlice pressure plots ofof 2000the distribution Pa: (a) (a) 10 –12− s;ofs; (b) electric (b )10 10–7−s; field (c)s; (10c )(V/m)–6 10 s;− (d) s;inside (10d)–5 10 s; the− (e) s; quartz10 (e–4) s; 10 (f)−tube 1s; s. (inf ) 1the s. x–z (y = 0) plane under a pressure of 2000 Pa: (a) 10–12 s; (b) 10–7s; (c) 10–6 s; (d) 10–5 s; (e) 10–4 s; (f) 1 s. + + Figure 10 shows the spatialspatial distributiondistribution ofof ArAr22+ under intermediate pressure; ArAr22+ isis concentrated concentrated outside the waveguide, contrary to the electron density, which is concentrated in the region CFIL outside theFigure waveguide, 10 shows contrary the spatial to thedistribution electron density, of Ar2+ under which intermediate is concentrated pressure; in the regionAr2+ is concentratedCFIL (see Figure(seeoutside Figure 3) inside 3the) inside waveguide, the theplasma plasma contrary torch. torch. Owingto Owingthe electron to tothe the intensedensity, intense reactions, which reactions, is concentrated the the gas gas temperature in the region inside CFIL thethe (see waveguideFigure 3) is insidehigher the than plasma the outside torch. temperature.Owing to the On On intense the one reactions, hand, the the high gas gas temperature temperature inside will the reducewaveguide thethe rate rate is of ofhigher the the atom–ion thanatom–ion the recombination outside recombination temperature. (Table (Table1), therebyOn 1),the therebyone inhibiting hand, inhibiting thethe formationhigh thegas temperatureformation of molecular of will molecularions.reduce On the ions.the other rateOn hand, theof otherthe rateatom–ion hand, of dissociation the recombination rate of ofdissociation molecular (Table ionsof molecular1), (Table thereby1) will ions inhibiting increase (Table with1)the will increasingformation increase of withtemperature.molecular increasing ions. Thus, temperature. On an the increase other Thus, inhand, temperaturean increasethe rate inof will temperaturedissociation lead to a decreasewillof molecular lead into thea ionsdecrease number (Table in of 1)the molecularwill number increase ofions molecularwith and increasing an increaseions and temperature. in an the increase number Thus, in ofthe an atomic numberincrease ions, ofin soatomictemperature the uneven ions, willso heating the lead uneven to of a thedecrease heating gas would inof the the a numberff gasect wouldmolecularof molecular affect ion molecular dynamics ions and ion [25 an ].dynamics Inincrease addition, [25].in the as In shown numberaddition, in of Figure as atomic shown 11, ions, the in Figure electrons so the 11, uneven transfer the electrons heating their power transfer of the to gas theirthewould Ar power species affect to throughthe molecular Ar species elastic ion through and dynamics inelastic elastic [25]. collisions, and In addition, inelastic which collisions,as ultimately shown inwhich increasesFigure ultimately 11, the the gas electrons increases temperature transfer the gasin the theirtemperature high power electron to in the densitiesthe Ar high species region.electron through However, densities elastic theregion. and gas in temperature elasticHowever, collisions, the and gas electron which temperature densityultimately and show increases electron similar the densitytrends,gas buttemperatureshow the similar electron in trends, densitythe high but drops electron the byelectron two densities levels dens ofregion.ity magnitude drops However, by fromtwo the levels insidegas of temperature magnitude to the outside andfrom part electron the of insidethedensity waveguide. to the show outside similar part oftrends, the waveguide. but the electron density drops by two levels of magnitude from the inside to the outside part of the waveguide. Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 18 Appl. Sci. 2020, 10, 5393 11 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 18

Figure 10. Slice plots of the distribution of the Ar2++ density (m–3) inside the quartz tube under a Figure 10. Slice plots of the distribution of the Ar2 density (m ) inside the quartz tube under a Figure 10. Slice plots of the distribution of the Ar2+ density (m–3) inside the quartz tube under a pressure of 2000 2000 Pa Pa at at 1 1s sin in (a) ( athe) the z–yz –planey plane (x = ( x27.3= 27.3 mm, mm, i.e., CF i.e., in CF Figure in Figure 3) and3) ( andb) the ( bx)–z the (y =x –0)z 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.y = 0) plane. plane.

+ Figure 11. Distributions of electron density,density, gasgas temperaturetemperature (K),(K), andand ArAr22+ atat MN (see Figure 33)) atat 11 ss Figureunder 11. a pressureDistributions of 2000 of electron Pa. density, gas temperature (K), and Ar2+ at MN (see Figure 3) at 1 s under a pressure of 2000 Pa. The content mentioned above shows the changes in electron density, conductivity, and electric fieldfieldThe modulus content with mentioned time. In above this section, shows overall the changes results in represent electron density,the changes conductivity, in electron and density electric with fieldtime modulus and space with in time. the case In this ofof intermediateintermediate section, overall pressure.pressure. results represent the changes in electron density with time and space in the case of intermediate pressure. 4.2. Analysis of the E ect of Di erent Pressures on Plasma Parameters 4.2. Analysis of the Effectff of Differentff Pressures on Plasma Parameters 4.2. Analysis of the Effect of Different Pressures on Plasma Parameters As shown inin FigureFigure 12 12,, thethe ratio ratio of of molecular molecular ion ion density density to to electron electron density density on on MN MN (Figure (Figure3) in3) thein theAs axial shownaxial direction direction in Figure of theof 12,the plasma the plasma ratio torch torchof exhibits molecular exhibits diff erention different density trends trends to at electron di ffaterent different density pressures. pressures. on OwingMN (FigureOwing to a large 3)to a innumberlarge the axial number of direction molecular of molecular of ions the andplasma ions the and smalltorch the electronexhibits small electron densitydifferent density at trends the quartz at at the different tubequartz port, pressures.tube the port, ratio theOwing near ratio the to near port a largeisthe far numberport greater is far of than greatermolecular that than near ions that the and centernear the the small of center the electron tube. of the The density tube. ratio The ofat the theratio molecularquartz of the tube molecular ion port, density the ion ratio todensity electron near to thedensityelectron port is increases densityfar greater increases gradually than that gradually with near respect the with center to respect the ofpressure the to tube. the increases, pressureThe ratio increases,withof the the molecular ratio with near the ion theratio density port near being tothe electroncloseport being to density 1 when close increases theto 1 pressure when gradually the reaches pressure with 5000 reaches respect Pa. 5000 to the Pa. pressure increases, with the ratio near the port being close to 1 when the pressure reaches 5000 Pa. Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 18 Appl. Sci. 2020, 10, 5393 12 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 18

Figure 12. Axial profiles of the ratio of molecular ion density to electron density at 1 s under different Figurepressures.Figure 12. 12. Axial Axial profiles profiles of the of ratio the ratioof molecular of molecular ion density ion density to electron to electrondensity at density 1 s under at 1different s under pressures.different pressures. Figures 13 and 14 show the temporal and spatial changes in electron density at different pressures.FiguresFigures In 1313 Figure andand 14 1413, show showwith the increasingthe temporal temporal andpressure and spatial spatial, the changes overall changes in electron electron in electron density density atin di thefferent plasmaat different pressures. torch × 18 × 18 –3 pressures.increasesIn Figure from13In, Figure with 2.75 increasing 13, 10 with to 4 pressure,increasing 10 m the. pressureThe overall radial, electronthe profile overall densityof the electron electron in the density plasma density in torch isthe shown increasesplasma in Figuretorch from 18 18 –3 142.75 at CH10 (seeto 4Figure10× 3),m18 and. The it× can radial18 be–3 seen profile that of wh theen electron the pressure density is is 1000 shown Pa, inthe Figure electron 14 atdensity CH (see at increases× from 2.75× 10 to 4 10 m . The radial profile of the electron density is shown in Figure 14theFigure at plasma CH3), (see and location Figure it can has3), be and seena Gaussian-like it thatcan whenbe seen distributi the that pressure whon,en thedecreasing is 1000pressure Pa, toward the is 1000 electron both Pa, thesides density electron from at a the density maximum plasma at thevaluelocation plasma at hasthe location acenter. Gaussian-like has With a Gaussian-like increasing distribution, pressure,distributi decreasing on,the decreasing towardelectron both distribution toward sides fromboth changes—the sides a maximum from a valuemaximummaximum at the valuemovescenter. at Withalongthe center. increasing the central With pressure, axisincreasing away the electronfrompressure, the distribution center,the electron the changes—thepeak distribution becomes maximum changes—thesharper, movesand themaximum along plasma the movesbecomescentral along axis inhomogeneous; away the central from the axis the center, awayreason the from peakfor this becomesthe phenomenon center, sharper, the peakis and that thebecomes the plasma increase sharper, becomes in pressure and inhomogeneous; the results plasma in a becomesdecreasethe reason inhomogeneous; in for the this mean phenomenon free the path reason is thatand for thean this increaseincrease phenomenon in in pressure the isoperating that results the in increasefrequency a decrease in pressureof in thecollisions mean results free among in path a decreaseparticles,and an increase in as the shown mean in the in operatingfreeFigure path 15. frequencyand Thus, an manyincrease of collisions particles in the amonghave operating already particles, frequency collided as shown beforeof incollisions Figure moving 15among .to Thus, the particles,low-concentrationmany particles as shown have region,in already Figure which collided15. Thus, directly before many leads moving particles to anto uneven have the low-concentration already distribution collided of electronsbefore region, moving which in the directly toquartz the low-concentrationtube,leads which to an uneven can also region, distribution be explained which ofdirectly electrons from leadsthe in perspe theto an quartzctive uneven tube,of thedistribution which electron can temperature.of also electrons be explained inAccording the from quartz the to tube,Equationperspective which (17), ofcan thethe also electronambipolar be explained temperature. diffusion from coefficient Accordingthe perspe is toctive co-related Equation of the (17),to electron the the ion ambipolar temperature.diffusion di coefficientffusion According coe andfficient theto Equationelectronis co-related (17),and toionthe the ambipolartemperatures. ion diffusion diffusion The coe ffimicrowave coefficientcient and theisplas co-related electronma torch andto is the in ion iona temperatures.non-th diffusionermal coefficient equilibrium The microwave and state the electronunderplasma intermediate torchand ion is intemperatures. a pressure, non-thermal with The equilibrium T microwavee >> Ti>> T stateg, whichplas underma implies torch intermediate isthat in thea non-th ambipolar pressure,ermal withdiffusion equilibrium Te >> coefficientTi >>stateTg , is determined mainly by the electron temperature. With increasing pressure, the electron temperature underwhich intermediate implies that thepressure, ambipolar with di Tffe >>usion Ti>> coe Tgffi, whichcient is implies determined that the mainly ambipolar by the diffusion electron temperature. coefficient isWithin determined the increasing quartz mainly tube pressure, will by thedecrease the electron electron and, temperature. temperaturethus, so will With inthe the increasing ambipolar quartz tubepressure, diffusion will decrease the coefficient; electron and, temperature that thus, is, so with will inincreasingthe the ambipolar quartz pressure, tube diff willusion the decrease speed coeffi cient;of and, plasma thatthus, is,diffusio so with willn increasing thefrom ambipolar the boundary pressure, diffusion theto the speed coefficient; middle of plasma will that slow diis,ff down, withusion increasingwhichfrom the will boundary pressure, increase tothethe the speedinhomogeneity. middle of plasma will slow diffusio down,n from which the will boundary increase to the the inhomogeneity. middle will slow down, which will increase the inhomogeneity.

–12 Figure 13. EEffectffect of Ar pressure onon thethe electronelectron densitydensity fromfrom 1010–12 ss to to 1 1 s. s. Figure 13. Effect of Ar pressure on the electron density from 10–12 s to 1 s. Appl. Sci. 2020, 10, 5393 13 of 16 Appl.Appl. Sci.Sci. 20202020,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 1515 ofof 1818

FigureFigureFigure 14.14. 14. RadialRadialRadial profileprofile profile atat at CHCH CH (see(see (see FigureFigure Figure 3)33)) of of the the electron electron density density from from 1000 10001000 toto 30003000 PaPa atat 1 1 s. s.

Figure 15. Variation of the plasma degrees of freedom and collision frequency from 1000 to 3000 Pa. FigureFigure 15.15. VariationVariation ofof thethe plasmaplasma degreesdegrees ofof freedomfreedom andand collisioncollision frequencyfrequency fromfrom 10001000 toto 30003000 Pa.Pa. This section explains the effect of different pressures on plasma parameters. With the increase of ThisThis sectionsection explainsexplains thethe effecteffect ofof differentdifferent prpressuresessures onon plasmaplasma parameters.parameters. WithWith thethe increaseincrease pressure, the collision frequency and the electron density increase, but the uniformity of the electron ofof pressure,pressure, thethe collisioncollision frequencyfrequency andand thethe electrelectronon densitydensity increase,increase, butbut thethe uniformityuniformity ofof thethe density will also become worse. electronelectron densitydensity willwill alsoalso becomebecome worse.worse. 5. Conclusions 5.5. ConclusionsConclusions The temporal and spatial variations in the electron density during the excitation of a TheThe temporaltemporal andand spatialspatial variationsvariations inin thethe electronelectron densitydensity duringduring thethe excitationexcitation ofof aa microwave-microwave- microwave-induced argon plasma were studied by simulations based on a self-consistent 3D fluid inducedinduced argonargon plasmaplasma werewere studiedstudied byby simulationssimulations basedbased onon aa self-consistentself-consistent 3D3D fluidfluid plasmaplasma modelmodel plasma model with Maxwell equations at intermediate pressures. The growth over time of the withwith MaxwellMaxwell equationsequations atat intermediateintermediate pressures.pressures. TheThe growthgrowth overover timetime ofof thethe plasmaplasma electronelectron plasma electron density can be divided into three stages. In the first stage, there is an equilibrium densitydensity cancan bebe divideddivided intointo threethree stages.stages. InIn thethe firstfirst stage,stage, therethere isis anan equilibriumequilibrium potentialpotential barrierbarrier inin potential barrier in the plasma. Consequently, the electron density remains unchanged and the thethe plasma.plasma. Consequently,Consequently, thethe electronelectron densitydensity remaremainsins unchangedunchanged andand thethe interferenceinterference byby externalexternal interference by external factors over short time scales is suppressed. In the second stage, an avalanche factorsfactors overover shortshort timetime scalesscales isis suppressed.suppressed. InIn thethe secondsecond stage,stage, anan avalancheavalanche effecteffect occurs,occurs, andand thethe effect occurs, and the electron density increases rapidly to exceed its cutoff value. In the third electronelectron densitydensity increasesincreases rapidlyrapidly toto exceedexceed itsits cutoffcutoff value.value. InIn thethe thirdthird stage,stage, thethe increasingincreasing electronelectron stage, the increasing electron density boosts up the ability that make plasma microwaves resistant, densitydensity boostsboosts upup thethe abilityability thatthat makemake plasmaplasma microwavesmicrowaves resistant,resistant, andand finallyfinally achievesachieves aa dynamicdynamic and finally achieves a dynamic balance that assists in the growth of the electron density. The simulation balancebalance thatthat assistsassists inin thethe growthgrowth ofof thethe electronelectron density.density. TheThe simulationsimulation reresultssults demonstratedemonstrate thatthat thethe results demonstrate that the permittivity becomes negative when the electron density of the plasma permittivitypermittivity becomesbecomes negativenegative whenwhen thethe electronelectron dedensitynsity ofof thethe plasmaplasma exceedsexceeds thethe cutoffcutoff valuevalue inin exceeds the cutoff value in the second stage, and the plasma then exhibits metal-like characteristics. thethe secondsecond stage,stage, andand thethe plasmaplasma thenthen exhibitsexhibits metal-likemetal-like characteristics.characteristics. TheThe resultingresulting higherhigher The resulting higher conductivity allows the formation of a coaxial waveguide with the external metal conductivityconductivity allowsallows thethe formationformation ofof aa coaxialcoaxial wawaveguideveguide withwith thethe externalexternal metalmetal wall,wall, andand surfacesurface wall, and surface waves then propagate and excite previously unexcited regions at the two ends of the waveswaves thenthen propagatepropagate andand exciteexcite previouslypreviously unexciteunexcitedd regionsregions atat thethe twotwo endsends ofof thethe plasma.plasma. InIn thisthis plasma. In this circumstance, the electron density increases consistently. The spatial distribution of circumstance,circumstance, thethe electronelectron densitydensity increasesincreases consisteconsistently.ntly. TheThe spatialspatial distributiondistribution ofof electronelectron densitydensity electron density in the case of intermediate pressure is different from that in the case of atmospheric inin thethe casecase ofof intermediateintermediate pressurepressure isis differentdifferent fromfrom thatthat inin thethe casecase ofof atmosphericatmospheric pressure.pressure. TheThe highesthighest electronelectron densitydensity isis concentratedconcentrated onon thethe sideside ofof thethe quartzquartz tubetube nearnear thethe wavewave feedfeed port.port. OwingOwing Appl. Sci. 2020, 10, 5393 14 of 16 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 CO2. 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 Ar2 and increase the consumption rate, + thereby reducing the number of Ar2 ions. Electrons will then become concentrated mainly inside the + waveguide, and Ar2 will become concentrated mainly outside the waveguide in the quartz tube.

Author Contributions: 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. Funding: This work was supported by National Key Research and Development Program of China (Grant No. 2017YFB0308601) and Civil Aviation Joint Fund of the National Natural Science Foundation of China (Grant No. U1733109). Acknowledgments: The authors are pleased to acknowledge M. C. M. van de Sanden for helpful discussions. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Hui, G.; Dongxue, H.; Li, X.; Ying, T.; Zhaobo, C.; Yimin, Z. Removal of low-concentration benzene in indoor air with plasma-MnO2 catalysis system. J. Electrost. 2015, 76, 216–221. 2. Zhang, L.; Sha, X.; Zhang, L.; He, H.; Ma, Z.; Wang, L.; Wang, Y.; She, L. Synergistic catalytic removal NOX and the mechanism of plasma and hydrocarbon gas. AIP Adv. 2016, 6, 075015. [CrossRef] 3. Ficek, M.; Sankaran, K.J.; Ryl, J.; Bogdanowicz, R.; Lin, I.; Haenen, K.; Darowicki, K. Ellipsometric investigation of nitrogen doped diamond thin films grown in microwave CH4/H2/N2 plasma enhanced chemical vapor deposition. Appl. Phys. Lett. 2016, 108, 241906. [CrossRef] 4. Baranov, O.; Bazaka, K.; Kersten, H.; Keidar, M.; Cvelbar, U.; Xu, S.; Levchenko, I. Plasma under control: Advanced solutions and perspectives for plasma flux management in material treatment and nanosynthesis. Appl. Phys. Rev. 2017, 4, 041302. [CrossRef] 5. Norberg, S.A.; Johnsen, E.; Kushner, M.J. Helium atmospheric pressure plasma jets touching dielectric and metal surfaces. J. Appl. Phys. 2015, 118, 013301. [CrossRef] 6. Bai, B.; Li, X.; Xu, J.; Liu, Y. Reflections of electromagnetic waves obliquely incident on a multilayer stealth structure with plasma and radar absorbing material. IEEE Trans. Plasma Sci. 2015, 43, 2588–2597. 7. Xu, J.; Bai, B.; Dong, C.; Dong, Y.; Zhu, Y.; Zhao, G. Evaluations of plasma stealth effectiveness based on the probability of radar detection. IEEE Trans. Plasma Sci. 2018, 45, 938–944. [CrossRef] 8. Rincon, R.; Marinas, A.; Munoz, J.; Melero, C.; Calzada, M. Experimental research on ethanol-chemistry decomposition routes in a microwave plasma torch for hydrogen production. Chem. Eng. J. 2016, 284, 1117–1126. [CrossRef]

9. Barankova, H.; Bardos, L. Atmospheric pressure plasma conversion of CO2 to solid deposits. Results Phys. 2015, 5, 257–258. [CrossRef]

10. Qin, Y.; Niu, G.; Wang, X.; Luo, D.; Duan, Y. Status of CO2 conversion using microwave plasma. J. CO2 Util. 2018, 28, 283–291. [CrossRef] 11. Javier, F.; Moreno, S.H.; Stankiewicz, A.I.; Stefanidis, G.D. On the improvement of chemical conversion in a

surface-wave microwave plasma reactor for CO2 reduction with hydrogen (The Reverse Water-Gas Shift reaction). Int. J. Hydrogen Energy 2017, 42, 12943–12955.

12. Bogaerts, A.; Berthelot, A.; Heijkers, S.; Kolev, S.; Snoeckx, R.; Sun, S.; Trenchev, G.; Van, L.K.; Wang, W. CO2 conversion by plasma technology: Insights from modeling the plasma chemistry and plasma reactor design. Plasma Sources Sci. Technol. 2017, 26, 063001. [CrossRef] Appl. Sci. 2020, 10, 5393 15 of 16

13. Mohsenian, S.; Nagassou, D.; Elahi, R.; Yu, P.; Nallar, M.; Wong, H.; Trelles, J.P. Carbon dioxide conversion by

solar-enhanced microwave plasma: Effect of specific power and argon/nitrogen carrier gases. J. CO2 Util. 2019, 35, 725–732. [CrossRef] 14. Rutberg, P.G.; Kuznetsov, V.A.; Popov, V.E.; Popov, S.D.; Surov, A.V.; Subbotin, D.I.; Bratsev, A.N. Conversion

of methane by CO2+ H2O+ CH4 plasma. Appl. Energy 2015, 148, 159–168. [CrossRef] 15. Moreno, S.H.; Stankiewicz, A.I.; Stefanidis, G.D. A two-step modelling approach for plasma

reactors–Experimental validation for CO2 dissociation in surface wave microwave plasma. React. Chem. Eng. 2019, 4, 1253–1269. [CrossRef]

16. Stewig, C.; Schüttler, S.; Urbanietz, T.; Böke, M.; von Keudell, A. Excitation and dissociation of CO2 heavily diluted in noble gas atmospheric pressure plasma. J. Phys. D Appl. Phys. 2020, 13, 125205. [CrossRef] 17. Fu, Y.; Krek, J.; Parsey, G.M.; Verboncoeur, J.P. Characterizing the dominant ions in low-temperature argon plasmas in the range of 1–800 Torr. Phys. Plasmas 2018, 25, 033505. [CrossRef] 18. Arcese, E.; Rogier, F.; Boeuf, J. Plasma fluid modeling of microwave streamers: Approximations and accuracy. Phys. Plasmas 2017, 24, 113517. [CrossRef] 19. Miotk, R.; Jasinski, M.; Mizeraczyk, J. Electromagnetic optimisation of a 2.45 GHz microwave plasma source operated at atmospheric pressure and designed for hydrogen production. Plasma Sources Sci. Technol. 2018, 27, 035011. [CrossRef] 20. Gudmundsson, J.T.; Kawamura, E.; Lieberman, M.A. A benchmark study of a capacitively coupled oxygen discharge of the oopd1 particle-in-cell Monte Carlo code. Plasma Sources Sci. Technol. 2013, 22, 035011. [CrossRef] 21. Lebedev, Y.A. Microwave discharges at low pressures and peculiarities of the processes in strongly non-uniform plasma. Plasma Sources Sci. Technol. 2015, 24, 053001. [CrossRef] 22. Bernatskiy, A.; Kochetov, I.; Lagunov, V.; Ochkin, V. Electric fields and concentrations of charged and neutral hydrogen isotopic particles in the plasma of low pressure DC discharge. Phys. Plasmas 2019, 26, 083511. [CrossRef] 23. Zhonghang, W.; Rongqing, L.; Masaaki, N.; Xijiang, C. The Characteristics of Columniform Surface Wave Plasma Excited Around a Quartz Rod by 2.45 GHz Microwaves. Plasma Sci. Technol. 2016, 18, 987. 24. Xiao, W.; Huang, K.; Zhang, W.; Lin, Y. Modeling of argon plasma excited by microwave at atmospheric pressure in ridged waveguide. IEEE Trans. Plasma Sci. 2016, 44, 1075–1082. [CrossRef] 25. Kabouzi, Y.; Graves, D.; Castanos-Martinez, E.; Moisan, M. Modeling of atmospheric-pressure plasma columns sustained by surface waves. Phys. Rev. E 2007, 75, 016402. [CrossRef][PubMed] 26. Kabouzi, Y.; Calzada, M.; Moisan, M.; Tran, K.; Trassy, C. Radial contraction of microwave-sustained plasma columns at atmospheric pressure. J. Appl. Phys. 2002, 91, 1008–1019. [CrossRef] 27. Georgieva, V.; Berthelot, A.; Silva, T.; Kolev, S.; Graef, W.; Britun, N.; Chen, G.; Mullen, J.; Godfroid, T.; Mihailova, D. Understanding Microwave Surface-Wave Sustained Plasmas at Intermediate Pressure by 2D Modeling and Experiments. Plasma Process. Polym. 2017, 14, 1600185. [CrossRef] 28. Bouherine, K.; Tibouche, A.; Ikhlef, N.; Leroy, O. 3-D numerical characterization of a microwave argon PECVD plasma reactor at low pressure. IEEE Trans. Plasma Sci. 2016, 44, 3409–3416. [CrossRef] 29. Jimenez-Diaz, M.; Carbonem, E.A.D.; Dijk, J.; Mullen, J.J. A two-dimensional Plasimo multiphysics model for the plasma-electromagnetic interaction in surface wave discharge: The surfatron source. J. Phys. D Appl. Phys. 2012, 17, 335204. [CrossRef] 30. Baeva, M.; Hempel, F.; Baierl, H.; Trautvetter, T.; Foest, R.; Loffhagen, D. Two-and three-dimensional simulation analysis of microwave excited plasma for deposition applications: Operation with argon at atmospheric pressure. J. Phys. D Appl. Phys. 2018, 51, 385202. [CrossRef] 31. Bogdanov, T.; Tsonev, I.; Marinova, P.; Benova, E.; Rusanov, K.; Rusanova, M.; Atanassov, I.; Kozáková, Z.; Krˇcma,F. Microwave Plasma Torch Generated in Argon for Small Berries Surface Treatment. Appl. Sci. 2018, 8, 1870. [CrossRef] 32. Lee, B.-J.; Jo, S.-I.; Jeong, G.-H. Synthesis of ZnO Nanomaterials Using Low-Cost Compressed Air as Microwave Plasma Gas at Atmospheric Pressure. Nanomaterials 2019, 9, 942. [CrossRef][PubMed] 33. Zhao, G.; Hua, W.; Guo, S.; Liu, Z. Three-dimensional simulation of microwave-induced helium plasma under atmospheric pressure. Phys. Plasmas 2016, 23, 073503. [CrossRef] 34. Yang, Y.; Hua, W.; Guo, S. Numerical study on microwave-sustained argon discharge under atmospheric pressure. Phys. Plasmas 2014, 21, 040702. [CrossRef] Appl. Sci. 2020, 10, 5393 16 of 16

35. Chen, G.; Georgieva, V.; Godfroid, T.; Snyders, R.; Delplancke-Ogletree, M. Plasma assisted catalytic

decomposition of CO2. Appl. Catal. B Environ. 2016, 190, 115–124. [CrossRef] 36. Jonkers, J.; Sande, M.; Sola, A.; Gamero, A.; Rodero, A.; Mullen, J. The role of molecular rare gas ions in plasmas operated at atmospheric pressure. Plasma Sources Sci. Technol. 2003, 12, 464. [CrossRef] 37. Kaw, P.; Valeo, E.; Dawson, J.M. Interpretation of an experiment on the anomalous absorption of an electromagnetic wave in a plasma. Phys. Rev. Lett. 1970, 25, 430. [CrossRef] 38. Baeva, M.; Bosel, A.; Ehlbeck, J.; Loffhagen, D. Modeling of microwave-induced plasma in argon at atmospheric pressure. Phys. Rev. E 2012, 85, 056404. [CrossRef] 39. Naito, T.; Yamaura, S.; Fukuma, Y.; Sakai, O. Radiation characteristics of input power from surface wave sustained plasma antenna. Phys. Plasmas 2016, 23, 93504. [CrossRef] 40. Zhang, W.; Wu, L.; Huang, K.; Tao, J. Propagating modes of the travelling wave in a microwave plasma torch with metallic enclosure. Phys. Plasmas 2019, 26, 042101. [CrossRef] 41. Moisan, M.; Nowakowska, H. Contribution of surface-wave (SW) sustained plasma columns to the modeling of RF and microwave discharges with new insight into some of their features. A survey of other types of SW discharges. Plasma Sources Sci. Technol. 2018, 27, 073001. [CrossRef] 42. Zhigang, L.; Zhongcai, Y.; Jiachun, W.; Jiaming, S. Simulation of propagation of the HPM in the low-pressure argon plasma. Plasma Sci. Technol. 2017, 20, 025401. 43. Meindl, A.; Loehle, S.; Kistner, I.; Schulz, A.; Fasoulas, S. Two-Photon Induced Polarization Spectroscopy for Atomic Oxygen in Atmospheric Plasma and Xenon. In Proceedings of the AIAA Scitech 2019 Forum, San Diego, CA, USA, 7–11 January 2019.

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