CN112949045A - Method for measuring and calculating steady-state microwave plasma - Google Patents
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Abstract
The invention discloses a method for measuring and calculating a steady-state microwave plasma, which comprises the steps of performing macroscopic equivalent characterization on parameters such as electron density and dielectric coefficient of the plasma under the condition of the steady-state microwave plasma, establishing a multi-physical-field coupling calculation model of the steady-state microwave plasma, and searching the distribution of the electron density in a steady state through an iterative solution process so as to obtain the steady-state plasma. The method aims to avoid the middle complex calculation process of generating plasma, directly solve the problem through the distribution of electron density under each steady state, and is simple in calculation method and easier to simulate and calculate.
Description
Technical Field
The invention relates to the field of microwaves, in particular to a method for measuring and calculating steady-state microwave plasma.
Background
Plasma is an ionized gaseous substance consisting of positive and negative ions generated by ionization of atoms and radicals after partial electron deprivation, the movement of which is mainly governed by electromagnetic force, and exhibits remarkable collective behavior. The plasma can be captured, moved and accelerated by using the magnetic field which is skillfully designed.
At present, the numerical simulation of microwave plasma is realized by modeling the excitation process of the microwave plasma, but the excitation process of the plasma is a strong collision and strong coupling discharge process and is a nonlinear space-time kinetic system which relates to multiple physical fields, multiple space-time scales and multiple interfaces, the non-equilibrium transport runs through the whole process of plasma generation, maintenance and extinction, the instability of the plasma is shown, the excitation process comprises a plurality of chemical reaction models among electrons, ions and neutral particles, and the boltzmann equation of each substance is difficult to solve; in the time domain, a plurality of partial differential equations are calculated, strong nonlinear coupling relations exist among the equations, the three-dimensional numerical simulation of the microwave plasma by the finite element method needs extremely large grid number and degree of freedom, and serious convergence problems are involved, so that the plasma in a steady state is difficult to obtain by the calculation method.
Disclosure of Invention
The invention aims to: in order to solve the problem that a steady-state plasma is difficult to obtain by a calculation method due to the complex excitation process of the plasma in the simulation process, the method provides a method for measuring and calculating the steady-state microwave plasma.
The technical scheme adopted by the invention is as follows:
1) performing initial modeling by software, establishing a simulation cavity according to the set microwave input frequency, input power, pressure of gas in the simulation cavity and boundary conditions of the simulation cavity, and setting the relative dielectric constant and conductivity of the gas in the simulation cavity and the initial value n of electron densitye0；
2) Calculating to obtain the distribution state of the electric field E in the simulated cavity;
3) according to the distribution of the electric field E obtained in the step 2) and the set initial value n of the electron densitye0And calculating to obtain the distribution n of the first electron density in the simulation cavitye1；
4) According to the distribution n of the first electron density obtained in step 3)e1And calculating to obtain the dielectric constant epsilon of the plasmapAnd the obtained plasma dielectric constantεpIterating to the step 2), continuously calculating the distribution state of the electric field E in the simulated cavity, and repeating the step 3) to obtain the distribution n of the secondary electron densitye2；
5) Subjecting the distribution n of the secondary electron density obtained in step 4) toe2Distribution n of first order electron densitye1Comparing, and if the two are the same, ending; if not, re-entering the step 4) according to ne2Calculating the dielectric constant ε of the plasmapUp to the distribution n of the electron density finally obtainedeiDistribution n of electron density from the previous timeei-1The same as above, wherein i is 1 … … n; distribution n of the finally obtained electron densityeiI.e. the calculated microwave plasma in steady state.
According to the technical scheme, the electron density distribution state in the initial steady state is simulated by assuming the initial conditions, and the electron density distribution state in the final steady state is obtained in a finite iteration mode, so that the position and the size of the plasma in the simulated cavity in the steady state are obtained in a simulation calculation mode, and a foundation is provided for subsequent research.
Preferably, the calculation of the electric field distribution obtained in step 2) is obtained by maxwell's equation, which is as follows:
preferably, the distribution n of the first electron density in step 3)e1Is determined by the formula:
wherein D iseIs the bipolar diffusion coefficient of the electron, RiIs the ionization coefficient, R, of the gas molecules due to collisions with electronsvrIs the electron recombination coefficient, RaIs the electron to neutral particle attachment coefficient.
Preferably, the dielectric constant of the plasma in step 4)εpIs determined by the formula:
wherein
ε0Is dielectric constant under vacuum, meFor electron mass, e is the charge, ω is the microwave angular frequency, and v is the collision frequency.
Preferably, the gas environment in step 1) is a hydrogen environment, the relative dielectric constant of which is 1 and the electrical conductivity of which is 0.
Preferably, the microwave input frequency f in step 1) is 2.45GHz, the input power P is 2kW, and the pressure P of the gas is 18 kPa; the boundary condition is that the walls of the simulation chamber are ideal conductors.
Preferably, the initial value of the electron density in step 1) is ne0＝1014m-3The electron density on the wall of the simulation cavity is 0; bipolar diffusion coefficient D of electrons in step 3)eIs equal to the diffusion coefficient D of hydrogen ionsiA value of 2.07X 104m2S, electron recombination coefficient RvrIs 10-13m3S, ionization coefficient R of gas molecules due to collisions with electronsiIs 1.
Preferably, the dielectric constant ε in the vacuum described in step 4)0Is 8.85X 10-12F/m, electron mass meIs 9.1X 10-31kg, charge e of 1.6X 10-19c, microwave angular frequency ω 2 pi f 2 pi · 2.45 × 109Hz, collision frequency
Wherein the constant a is 1010k·Pa-1·s-1Temperature T of gasg＝300K。
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that: obtaining initial electric field distribution by using a Maxwell equation under the assumption of initial conditions, obtaining initial electron density distribution under a stable state according to the initial electric field distribution, solving electron density distribution under a second stable state according to the initial electron density distribution, comparing the electron density distribution of two times, and obtaining final electron density distribution under the stable state after multiple iterations and comparisons if the electron density distribution is inconsistent, thereby obtaining the microwave plasma under the stable state; the measuring and calculating method avoids the middle complex calculation process of generating plasma, directly solves the problem through the distribution of electron density under each steady state, is simple in calculation method and is easier to simulate and calculate.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a simulated cavity obtained by simulation;
FIG. 3 is a graph of a first time electron density distribution obtained from a simulation;
FIG. 4 is a graph of simulated distribution of electron density for intermediate states;
fig. 5 is a simulated distribution diagram of the electron density at the steady state.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It should be noted that the generation of plasma is a process of gas breakdown discharge, and only when the electric field strength reaches the breakdown field strength threshold E required for gas dischargemIn time, only can gas discharge to generate plasma, therefore, the electric field strength needs to be judged in the discharge cavity:
at E<EmThe region (2) where plasma is not considered to be present, and the equivalent dielectric constant: ε is 1.
At E>EmThe region (2) in which plasma is considered to exist, and the equivalent medium thereofElectric constant epsilonplasI.e. epsilonp。
A method for measuring and calculating a steady-state microwave plasma is shown in FIG. 1, and is a flow chart of the method, and specifically comprises the following steps: .
1) Performing initial modeling through comsol software, wherein the initial modeling is as shown in figure 2, the method calculates the steady-state plasma in the area 1, establishes a simulation cavity according to the set microwave input frequency and input power of the simulation cavity, the pressure of the gas in the simulation cavity and boundary conditions, sets the relative dielectric constant and conductivity of the gas in the simulation cavity and the initial value n of the electron densitye0. The simulated gaseous environment can be any gaseous environment, such as air, hydrogen and the like, the simulated hydrogen environment is taken as an example, the initial value is set to be 1 in dielectric constant, the conductivity is 0, and the breakdown field strength threshold value required by gas discharge in the hydrogen environment is 3-7 multiplied by 104V/m; setting the microwave input frequency f as 2.45GHz, the input power P as 2kW, and the gas pressure P as 18 kPa; the boundary condition is that the simulated cavity wall is an ideal conductor except the quartz window (the position where the microwave enters).
2) By Maxwell's equations
Obtaining the distribution state of the electric field E in the simulation cavity; since the first calculation is started and no plasma exists in the simulation cavity, the initial electric field distribution is calculated according to the Maxwell equation, and the initial electric field distribution is calculated according to the dielectric constant of the hydrogen.
3) Substituting the electric field distribution obtained in step 2) into the equation:
in (1), an initial value n according to the electron density is sete0Obtaining the distribution n of the first electron density in the simulation cavitye1；
Wherein D iseIs the bipolar diffusion coefficient of the electrons and,Riis the ionization coefficient, R, of the gas molecules due to collisions with electronsvrIs the electron recombination coefficient, RaIs the coefficient of attachment of electrons to neutral particles and can be ignored; diffusion coefficient D of the hydrogen ionseIs 2.07 x 104m2S, electron recombination coefficient RvrIs 10-13m3S, ionization coefficient R of gas molecules due to collisions with electronsiIs 1.
4) Subjecting the distribution n of the first electron density obtained in step 3) toe1Calculation formula of substituted plasma frequency
By the formula
Calculating to obtain the dielectric constant epsilon of the plasmap；
Wherein epsilon0Is dielectric constant under vacuum, meElectron mass, e charge, ω microwave angular frequency, v collision frequency; the obtained plasma dielectric constant epsilonpIterating the solution back to the Maxwell equation in the step 2), continuously calculating the distribution state of the electric field in the simulated cavity, and repeating the step 3) to obtain the distribution n of the secondary electron densitye2；
The dielectric constant ε under vacuum0Is 8.85X 10-12F/m, electron mass meIs 9.1X 10-31kg, charge e of 1.6X 10-19c, microwave angular frequency ω 2 pi f 2 pi · 2.45 × 109Hz, collision frequency
Wherein the constant a is 1010k·Pa-1·s-1Temperature T of gasg＝300K。
5) Subjecting the distribution n of the secondary electron density obtained in step 4) toe2Distribution n of first order electron densitye1Comparing, and if the two are the same, ending; if not, re-entering the step 4) according to ne2Calculating plasmaDaughter dielectric constant εpUp to the distribution n of the electron density finally obtainedeiDistribution n of electron density from the previous timeei-1The same as above, wherein i is 1 … … n; distribution n of the finally obtained electron densityeiI.e. the calculated microwave plasma in steady state.
As shown in fig. 3-5, the simulated first-time electron density distribution map, the intermediate-state electron density distribution map and the finally obtained electron density distribution map in the steady state are calculated by simulation software, and it can be seen from the figures that the brighter region in the figures, i.e. the simulated plasma region, becomes an ellipsoidal plasma in fig. 5, which shows that a more ideal plasma can be obtained by calculation.
Therefore, by the method, a simulation area of the plasma in a steady state, namely an area with brighter color in a graph, can be finally obtained according to finite iterative computation, namely the distribution state of the plasma in the steady state in the simulation state is obtained, so that a direction is provided for subsequent research, and the method has high application value.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (8)
1. A method for measuring and calculating steady-state microwave plasma is characterized by comprising the following steps: the method comprises the following steps:
1) performing initial modeling by software, establishing a simulation cavity according to the set microwave input frequency, input power, pressure of gas in the simulation cavity and boundary conditions of the simulation cavity, and setting the relative dielectric constant and conductivity of the gas in the simulation cavity and the initial value n of electron densitye0；
2) Calculating to obtain the distribution state of the electric field E in the simulated cavity;
3) according to the distribution of the electric field E obtained in the step 2) and the set initial value n of the electron densitye0Meter for measuringCalculating to obtain the distribution n of the first electron density in the simulation cavitye1；
4) According to the distribution n of the first electron density obtained in step 3)e1And calculating to obtain the dielectric constant epsilon of the plasmapAnd the obtained plasma dielectric constant εpIterating to the step 2), continuously calculating the distribution state of the electric field E in the simulated cavity, and repeating the step 3) to obtain the distribution n of the secondary electron densitye2；
5) Subjecting the distribution n of the secondary electron density obtained in step 4) toe2Distribution n of first order electron densitye1Comparing, and if the two are the same, ending; if not, re-entering the step 4) according to ne2Calculating the dielectric constant ε of the plasmapUp to the distribution n of the electron density finally obtainedeiDistribution n of electron density from the previous timeei-1The same as above, wherein i is 1 … … n; distribution n of the finally obtained electron densityeiI.e. the calculated microwave plasma in steady state.
2. The method of claim 1, wherein the step of measuring the steady state microwave plasma comprises: the calculation of the electric field distribution obtained in step 2) is obtained by Maxwell's equation, and the formula is as follows:
3. the method of claim 1, wherein the step of measuring the steady state microwave plasma comprises: distribution n of first-time electron density in step 3)e1Is determined by the formula:
calculating to obtain;
wherein D iseIs the bipolar diffusion coefficient of the electron, RiIs the ionization coefficient, R, of the gas molecules due to collisions with electronsvrIs an electronic composite systemNumber, RaIs the electron to neutral particle attachment coefficient.
4. The method of claim 1, wherein the step of measuring the steady state microwave plasma comprises: step 4) dielectric constant ε of plasmapIs determined by the formula:
calculating to obtain;
wherein
ε0Is dielectric constant under vacuum, meFor electron mass, e is the charge, ω is the microwave angular frequency, and v is the collision frequency.
5. A method for estimation of a steady state microwave plasma according to any one of claims 1 to 4, wherein: the gas environment in the step 1) is a hydrogen environment, the relative dielectric constant of the gas environment is 1, and the conductivity of the gas environment is 0.
6. The method of claim 5, wherein the step of measuring the steady state microwave plasma comprises: the microwave input frequency f in the step 1) is 2.45GHz, the input power P is 2kW, and the pressure P of the gas is 18 kPa; the boundary condition is that the walls of the simulation chamber are ideal conductors.
7. The method of claim 6, wherein the step of measuring the steady state microwave plasma comprises: the initial value of the electron density in the step 1) is ne0＝1014m-3The electron density on the wall of the simulation cavity is 0;
bipolar diffusion coefficient D of electrons in step 3)eIs equal to the diffusion coefficient D of hydrogen ionsiA value of 2.07X 104m2S, electron recombination coefficient RvrIs 10-13m3S, ionization coefficient R of gas molecules due to collisions with electronsiIs 1.
8. The method of claim 7, wherein the step of measuring the steady state microwave plasma comprises: dielectric constant ε under vacuum in step 4)0Is 8.85X 10-12F/m, electron mass meIs 9.1X 10-31kg, charge e of 1.6X 10-19c, microwave angular frequency ω 2 pi f 2 pi · 2.45 × 109Hz, collision frequency
Wherein the constant a is 1010k·Pa-1·s-1Temperature T of gasg＝300K。
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Effective date of registration: 20240620 Address after: No. 1, 21st Floor, Unit 1, Building 10, No. 88 Niushahou Street, Jinjiang District, Chengdu City, Sichuan Province, 610000 Patentee after: Zhu Huacheng Country or region after: China Patentee after: Yang Yang Address before: 610041, No. 24, south section of first ring road, Chengdu, Sichuan, Wuhou District Patentee before: SICHUAN University Country or region before: China |