Numerical 3D Modeling: Microwave Plasma Torch at Intermediate Pressure

SL

Comments

Author Response

1

Please specify in more detail the numerical procedure you used in your simulations. Please provide more detail on the governing equations solution methods (FEM?) and also if you performed any integrity checks, such as convergence.

In this paper, the fluid approximation method has used to couple the Boltzmann equation to the Maxwell equation for calculating the density of charged particles, the electron temperature, and the electromagnetic field. The Boltzmann equation embodies the change of ion velocity distribution equationwith time, where is the velocity, is the position, and  time. The calculation process as follows: the energy distribution function of electron brought into the Boltzmann equation to solve the electron transport coefficient through the BOLSIG+ solver. The electron transport coefficient and the experimentally determined plasma chemical cross-section data are formed into the continuous equation, momentum conservation equation, and energy conservation equation. After that, these three equations are coupled with the electromagnetic field to solve the electromagnetic field and plasma characteristic parameters. Because the Boltzmann equation is highly nonlinear, so it is difficult to use directly in the analytical solution. Therefore, we used the finite element method and a numerical technique to solve the equations. Before solving the finite element method, the space and time of the solution target must discretized. In this paper, a tetrahedral mesh is used to divide the solution domain of the three-dimensional graphics, and a boundary layer has used to encrypt and divide the boundary. The total number of the mesh elements is 183448. The model executed on a computer with an i9-9900U CPU and 64 GB RAM, which takes approximately 101 minutes duration. The specific modifications is mentioned on line 110-125.

2

Please improve the terminology and the English language, I have highlighted some incorrect statements and sentences in the attached file.

The paper English language has now been updated by an experienced researcher to greatly reduce the typos, grammatical errors and issues with sentence structured.

Thanks for detail comments on attached file.

3

Please pay attention to Eqs. (5), (6): what is "i" in these equations?

The symbol represents. The specific modification is mentioned on line 176-177.

4

Please consider using subsections in the results analysis section: in each sub-section, summarize the most important results using 1-2 sentences.

Thanks for valued comment and we have revised them in the article. The specific modification is mentioned on line 256,367-372 and 400-402.

SL

Comments

Author Response

1

The paper is dedicated to numerical modelling and the description of the model is very poor (in some parts there are some mistakes).

Many thanks for valued suggestions, and we made corresponding amendments based on your comments

2

The minimum required for a publication is to provide the right equations, show the coupling terms between the different models and describe clearly the numerical method. The minimum when one show the results of the simulation is to provide the numerical parameters of the simulation.

In this paper, the fluid approximation method has used to couple the Boltzmann equation to the Maxwell equation for calculating the density of charged particles, the electron temperature, and the electromagnetic field. The Boltzmann equation embodies the change of ion velocity distribution equation with time, where  is the velocity, is the position, and  time. The calculation process as follows: the energy distribution function of electron brought into the Boltzmann equation to solve the electron transport coefficient through the BOLSIG+ solver. The electron transport coefficient and the experimentally determined plasma chemical cross-section data are formed into the continuous equation, momentum conservation equation, and energy conservation equation. After that, these three equations are coupled with the electromagnetic field to solve the electromagnetic field and plasma characteristic parameters. Because the Boltzmann equation is highly nonlinear, so it is difficult to use directly in the analytical solution. Therefore, we used the finite element method and a numerical technique to solve the equations. Before solving the finite element method, the space and time of the solution target must discretized. In this paper, a tetrahedral mesh is used to divide the solution domain of the three-dimensional graphics, and a boundary layer has used to encrypt and divide the boundary. The total number of the mesh elements is 183448. The specific modification is mentioned on line 110-124.

3

Fluid approximation is used to high pressure approximation and not for efficiency.

The articles [Similarity principle of microwave argon plasma at low pressure (https://iopscience.iop.org/article/10.1088/1674-1056/27/8/085206/meta)] and [3-D Numerical Characterization of a Microwave Argon PECVD Plasma Reactor at Low Pressure (DOI: 10.1109/TPS.2016.2619696)] are all simulation of plasma using fluid approximation method under low pressure, so we think that fluid approximation method can also be used to simulate plasma analysis under intermediate pressure.

4

3.2 there is a mistake between E and H. E and H are the complex amplitude of the electromagnetic fields. They appear also in equation (9) and (10)? It cannot be complex. the equation (12) is wrong. There is a factor 5/3...

Transfer attributes can be in vector form. Equation (9) and Equation (10) can refer to the articles [Two- and three-dimensional simulation analysis of microwave excited plasma for deposition applications: operation with argon at atmospheric pressure (https://iopscience.iop.org/article/10.1088/1361-6463/aad537/meta)], [Modeling of Argon Plasma Excited by Microwave at Atmospheric Pressure in Ridged Waveguide (DOI: 10.1109/TPS.2016.2568266)], [Numerical study on microwave-sustained argon discharge under atmospheric pressure (https://doi.org/10.1063/1.4872000)], [3-D Numerical Characterization of a Microwave Argon PECVD Plasma Reactor at Low Pressure(DOI: 10.1109/TPS.2016.2619696)] and so on. and represents the electric field strength and magnetic field strength vector, not the amplitude. Equation 12 also appears in the above article.

5

What are the boundary conditions?

Boundary conditions have been added in 

Section 2.3. The specific modification is mentioned on line 144-146.

6

The relation between the solution of the equation (9) to (12) and the time evolution of electrons is not described.

In plasma convection diffusion and plasma reaction process, the electric field vector, electron diffusion coefficient, electron mobility, etc. have an influence on electron density and electron density energy. Equations (9) and (10) describe the changes in electron density with time and the spatial distribution, while Equations (11) and (12) describe the changes in electron density energy with time and the spatial distribution. The specific modification is on line 202-206.

7

3.3 Lorentz force is not described, BC are not given. What is the coupling term between electrons and flow?

Lorentz force experienced by the plasma in the presence of electromagnetic field , denote the complex conjugates of . Lorentz force is affected by electric field and magnetic field, while electric field and magnetic field are affected by electron distribution. We have added the description of Lorentz force and coupling term between electrons and flow to the section 3.3. The specific modification is mentioned on line 224-226.

8

3.5 What is the role of ambipolar diffusion ?

The particles of plasma diffusion divided into two categories: one is the ambipolar diffusion of charged particles (electrons, ions). The other type is the diffusion of neutral particles or atoms. Among them ambipolar diffusion is a unique way 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, so it reaches the vessel wall first and makes it negatively charged. However, the mass of ions is much larger than that of ions, which is relatively slow. Therefore, there are 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 ion to move towards the vessel wall, inhibiting the free diffusion of electrons and ions .The specific modification is mentioned on line 237-247.

9

No description of the numerical method is given.

In this paper, the fluid approximation method has used to couple the Boltzmann equation to the Maxwell equation for calculating the density of charged particles, the electron temperature, and the electromagnetic field. The Boltzmann equation embodies the change of ion velocity distribution equation with time, where  is the velocity, is the position, and  time. The calculation process as follows: the energy distribution function of electron brought into the Boltzmann equation to solve the electron transport coefficient through the BOLSIG+ solver. The electron transport coefficient and the experimentally determined plasma chemical cross-section data are formed into the continuous equation, momentum conservation equation, and energy conservation equation. After that, these three equations are coupled with the electromagnetic field to solve the electromagnetic field and plasma characteristic parameters. Because the Boltzmann equation is highly nonlinear, so it is difficult to use directly in the analytical solution. Therefore, we used the finite element method and a numerical technique to solve the equations. Before solving the finite element method, the space and time of the solution target must discretized. In this paper, a tetrahedral mesh is used to divide the solution domain of the three-dimensional graphics, and a boundary layer has used to encrypt and divide the boundary. The total number of the mesh elements is 183448. The specific modification is mentioned on line 110-124.

10

No information about the cell number, the CPU, step time.

The model executed on a computer with an i9-9900U CPU and 64 GB RAM, which takes approximately 101 minutes duration. The specific modification is mentioned on line 124-125.

SL

Comments

Author Response

1

Could you please check your text for misspellings and the English language style. Clarity could also be improved in some places.

Thank you much for your comment. We really appreciate your valuable time and the effort for this review. The manuscript has certainly benefited from these insightful revision suggestions. The English has been revised thoroughly and all grammar mistakes have been corrected by native English proofreader.

SL

Comments

Author Response

1

2. The corrections provided by the authors are not detailed enough. So, they did not responded to the main critics about the description of the numerical method. Is there any paper (or preprint) where it is possible to find the details? Or the authors used some commercial or freeware code? If not, they have to show a good presentation of numeric part.

Thank you very much for your comment. Actually, the mathematical model is implemented and solved in a commercial software package named COMSOL Multiphysics. The plasma module of COMSOL is specially used to simulate the source or system of low-temperature plasma to deeply understand the physical process of discharge. The specific modification is mentioned on line 108- 109.

2

4. When they solve the Helmholtz equation (7), the field calculated is a complex field. It is not well explained how they introduce the complex field in (7), (9). In the references cited, it is not also well established.

Thank you very much for your comment. We really appreciate your valuable time and the effort for this review. The Eq. (7) is the electromagnetic wave frequency domain equation. The electric field is transformed from time domain to frequency domain by Fourier transform equation, so the electric field value is expressed by complex number in frequency domain. In additional, this equation itself contains the imaginary part representing the time phase. Solving the equation directly can get the electric field result including the imaginary part.

The Eq. (9) is the equation of the electron transport in the plasma. At this time, the electric field is not the result in the frequency domain. The electric field result is converted into a quasi-steady electric field by the time average method to calculate the electron transport problem. It is a real number obtained by multiplying the electric field of any component and its conjugate, but it is still a vector.

More specific theoretical analysis is found in the user manual of RF module in COMSOL.

3

Some assumptions about the magnitude of the wave frequency with typical frequency of the plasma which are not given.

Thank you very much for point out this issue. Actually, microwave directly incident into plasma, accord to the Eq. (5), it found that the real part of becomes negative for the plasma of collisionless when. So, the electron density has a critical number density of approximately 7.6 × 10¹⁶ m^-3, which corresponds to  and . The specific modification is mentioned on line 196-199.

4

8. the ambipolar diffusion coefficient appear only in eq (16). Where this coefficient is used?

Thanks for point out this issue. The ambipolar diffusion coefficient is used in section 4.2 to explain the reason for the radial inhomogeneity of the plasma as the pressure increases. The specific modification is on line 400-404.