A method for analyzing microwave low-pressure discharge

Abstract

A method for analyzing microwave low-pressure discharge, in view of the characteristics of microwave low-pressure discharge being sensitive to the field and having obvious electron avalanche effect, adopts the time-domain finite-difference method to accurately calculate the microwave field distribution, and then combines the particle continuity equation fluid to simulate the process of low-pressure discharge in a microwave field environment. The accuracy of discharge analysis can be guaranteed by controlling the accuracy of electromagnetic field calculation, and the problem of low calculation efficiency of microwave low-pressure discharge when the number of charged particles is large is solved through the fluid algorithm.

Description

Technical Field

[0001] The invention relates to an analysis method for microwave low-pressure discharge, and belongs to the technical field of space high-power microwave technology research. Background Art

[0002] In order to achieve the functions of long-distance transportation, stable landing measurement and control, and long-distance data transmission in deep space, the microwave components used in the spacecraft payload require wider bandwidth, higher component integration and greater power capacity, which will inevitably lead to higher electric field density and smaller gap size in the microwave components. Accurate and efficient microwave low-pressure discharge analysis methods will provide a powerful analysis tool for the design of high-power microwave components in spacecraft payload systems. The low-pressure discharge effect is an important factor affecting the stability of spacecraft microwave components. The damage to microwave components is usually serious. Once it occurs, the reflected power will be absorbed by the microwave components, causing permanent damage to the components. Summary of the invention

[0003] The technical problem solved by the present invention is: in view of the problem that there is a lack of a method for simulating and analyzing the low-pressure discharge effect in the current prior art, a method for analyzing microwave low-pressure discharge is proposed.

[0004] The present invention solves the above technical problems by the following technical solutions:

[0005] A method for analyzing microwave low-pressure discharge, the steps are as follows:

[0006] (1) Read the target model structure, set the initial value of the electromagnetic field, gas temperature T, gas pressure P, boundary conditions, and initial ion number density Initial electron number density The secondary electron emission coefficient of the structural material is γ, the initial electron energy, the time step Δt, the simulation time, the particles include electrons, ions and excited state particles, the subscripts are e, ion, exe respectively, and the model structure is meshed after the settings are completed;

[0007] (2) Perform electromagnetic field propulsion according to the finite-difference time-domain method to obtain the electric field E and magnetic field H at any position and time after grid division;

[0008] (3) Solve the particle continuity equation to obtain the electron flux at any position at time t+Δt and number density Ion flux and number density Excited state particle flux and number density

[0009] (4) The electron flux obtained according to step (3) and number density Solve to get the average energy of the electron Then we get the average temperature of electrons T e ;

[0010] (5) Determine whether there are secondary electrons at the boundary based on the model structure material. If so, determine the initial electron number density. The ion number density obtained in step (3) and ion boundary velocity Electron boundary velocity Substituting the electron continuity equation on the boundary into the boundary secondary electron flux Then the boundary secondary electron flux Substituting into the particle continuity equation in step 1, we can obtain the electron flux at any position at time t+Δt: and number density Otherwise, directly output the electron flux obtained in step (3) and number density

[0011] In the step (1), the model is divided into equally spaced staggered grids according to the electromagnetic field input frequency, and main grid nodes, corresponding potential nodes, and particle density nodes are set. The grid division size is determined according to the Courant stability condition.

[0012] In step (3), the chemical reaction rate constant k of each particle in the gas required to solve the continuity equation of the particle is r The particle mobility μ is obtained by solving the steady-state Boltzmann equation, and the particle diffusion coefficient D is obtained by the Einstein relation.

[0013] In the step (3), the particle continuity equation is integrated in time and space and discretized into a grid to obtain a discrete expression of the particle continuity equation:

[0014]

[0015] Where S is the source term of the continuity equation of each particle, expressed as:

[0016]

[0017] In the formula, r represents the rth reaction process, k r represents the reaction rate constant corresponding to the reaction, N r represents the number of particle types participating in the rth reaction process, n r,m represents the number density of the mth particle participating in the rth reaction process, where the number density of neutral molecules in the gas is nε =P / k B T.s r is a symbolic function, defined as:

[0018]

[0019] In the formula, Γ e , Γ w , Γ s , Γ n are the total particle fluxes at nodes e, w, s, and n at any time. The particle flux density Γ at time t t for:

[0020]

[0021] In the formula, sgn(q) represents the charge sign of the charged particle. For neutral particles, sgn(q)=0, for positive ions, sgn(q)=1, for negative ions and electrons, sgn(q)=-1, μ represents the mobility of the particle, E t is the electric field corresponding to time t, n t is the particle number density corresponding to time t;

[0022] By taking the value of the source term S in the discrete expression of the particle continuity equation at time t, the continuity equation of each particle can be decoupled, and then the electron flux at any position at time t+Δt can be obtained. and number density Ion flux and number density Excited state particle flux and number density

[0023] In the step (4), according to the electron flux obtained in step 3 and number density The average energy of the electrons is obtained from the following formula:

[0024]

[0025] Calculate the average electron temperature T e :

[0026]

[0027] In the formula, k B is the Boltzmann constant.

[0028] In step (5), if the boundary is material, it is considered that secondary electrons exist. Then, according to the initial electron number density Step 3 Ion number density and ion boundary velocity Electron boundary velocity Substituting the electron continuity equation on the boundary into the boundary secondary electron flux

[0029]

[0030] In the formula, is the ion boundary velocity, Ion thermal velocity T ion is the average temperature of the ions, which is the same as the gas temperature T, m ion is the mass of the ion. The electron boundary velocity Electron thermal velocity v e；th for m e is the mass of the electron. Then the boundary secondary electron flux Substituting into the particle continuity equation in step 1, we can obtain the electron flux at any position at time t+Δt: and number density

[0031] The method also includes step (6), calculating the current formed by the charged particles based on the particle flux, and feeding the current back to the electromagnetic field to determine whether the predetermined simulation time is exceeded. If not, steps (2)-(5) are repeated. If the predetermined simulation time is exceeded, the microwave low-pressure discharge analysis process is terminated and the results are output.

[0032] The advantages of the present invention compared with the prior art are:

[0033] (1) The present invention provides a microwave low-pressure discharge analysis method, which is based on electromagnetic-fluid direct coupling modeling, realizes time-domain finite difference joint fluid numerical modeling, and takes into account the influence of charged particles in the plasma region formed by discharge on the electromagnetic field, which can accurately solve the electromagnetic field distribution and has high computational efficiency. It provides reference data for the reliability design of satellites and saves the design cost of space microwave components;

[0034] (2) In view of the fact that microwave low-pressure discharge is sensitive to the field and has a significant electron avalanche effect, the finite-difference time-domain method is used to accurately calculate the microwave field distribution, and the particle continuity equation fluid is combined to simulate the process of low-pressure discharge in a microwave field environment. The accuracy of the discharge analysis is guaranteed by controlling the accuracy of the electromagnetic field calculation. The fluid algorithm solves the problem of low calculation efficiency when the number of charged particles is large, and the secondary electron multiplication effect on the metal surface of the space microwave component is taken into account, which can analyze the entire process of microwave structure from low vacuum discharge to gas discharge. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1A microwave low-pressure discharge analysis flow chart provided for the invention;

[0036] Figure 2 Schematic diagram of the mesh control volume provided for the invention

[0037] Figure 3 A structural diagram of the coaxial model provided for the invention;

[0038] Figure 4 A schematic diagram of the change of average electron density and electron temperature over time when the electric field strength provided by the invention is 1.5e5V / m;

[0039] Figure 5 A schematic diagram showing the variation of average electron density and electron temperature over time when the electric field strength is 5e6V / m provided for the invention; DETAILED DESCRIPTION

[0040] A microwave low-pressure discharge analysis method is based on electromagnetic-fluid direct coupling modeling, realizes time-domain finite difference joint fluid numerical modeling, and considers the influence of charged particles in the plasma region formed by discharge on the electromagnetic field, which can accurately solve the electromagnetic field distribution and has high computational efficiency. It provides reference data for the reliability design of satellites and saves the design cost of space microwave components. The specific method steps are as follows:

[0041] (1) Read the target model structure, set the initial value of the electromagnetic field, gas temperature T, gas pressure P, boundary conditions, and initial ion number density Initial electron number density The secondary electron emission coefficient of the structural material is γ, the initial electron energy, the time step Δt, the simulation time, the particles include electrons, ions and excited state particles, the subscripts are e, ion, exe respectively, and the model structure is meshed after the settings are completed;

[0042] (2) Perform electromagnetic field propulsion according to the finite-difference time-domain method to obtain the electric field E and magnetic field H at any position and time after grid division;

[0043] (3) Solve the continuity equation of the particle and obtain the electron flux at any position at time t+Δt and number density Ion flux and number density Excited state particle flux and number density

[0044] (4) The electron flux obtained according to step (3) and number density Solve to get the average energy of the electron Then we get the average temperature of electrons Te ;

[0045] (5) Determine whether there are secondary electrons at the boundary based on the model structure material. If so, determine the initial electron number density. The ion number density obtained in step (3) and ion boundary velocity Electron boundary velocity Substituting the electron continuity equation on the boundary into the boundary secondary electron flux Then the boundary secondary electron flux Substituting into the particle continuity equation in step 1, we can obtain the electron flux at any position at time t+Δt: and number density Otherwise, directly output the electron flux obtained in step (3) and number density

[0046] (6) The current formed by the charged particles is calculated based on the particle flux, and the current is fed back to the electromagnetic field to determine whether it exceeds the predetermined simulation time. If not, steps (2)-(5) are repeated. If it exceeds the predetermined simulation time, the microwave low-pressure discharge analysis process is terminated and the results are output.

[0047] The following is further described in conjunction with specific embodiments:

[0048] Specific steps are as follows Figure 1 As shown:

[0049] (1) Read the target model structure, set the initial value of the electromagnetic field, gas temperature T, gas pressure P, boundary conditions, and initial ion number density Initial electron number density The secondary electron emission coefficient of the structural material is γ, the initial electron energy, the time step Δt, the simulation time, and the chemical reaction rate constant k of each particle in the gas r The particle mobility μ is obtained by solving the steady-state Boltzmann equation, and the particle diffusion coefficient D is obtained by the Einstein relation. Particles include electrons, ions, and excited state particles, with subscripts e, ion, and exe, respectively. The model structure is meshed after the setting is completed;

[0050] The model is divided into equally spaced staggered grids according to the input electromagnetic field frequency, such as Figure 2 As shown, the intersection of the solid lines in the figure It is called the main grid node, corresponding to the node of scalars such as potential φ and particle density n. The corresponding control volume is composed of the control interface lines adjacent to the main grid node, such as Figure 2The dashed line is called the control interface line, and the intersection point "×" between the control interface line and the main grid line is applicable to the nodes of vectors such as the electric field intensity E and the particle flux density Γ. Figure 2 The shaded area in (b) represents the volume controlled by node e.

[0051] (2) Perform electromagnetic field propulsion according to the finite-difference time-domain method to obtain the electric field E and magnetic field H at any position and time after grid division;

[0052] (3) Solve the continuity equation of the particle (non-electron) to obtain the electron flux at any position at time t+Δt and number density Ion flux and number density Excited state particle flux and number density

[0053] After integrating the particle continuity equation in time and space and discretizing the grid, we get:

[0054]

[0055] S is the source term of the continuity equation of each particle, and its expression is:

[0056]

[0057] In the formula, r represents the rth reaction process, k r represents the reaction rate constant corresponding to the reaction, N r represents the number of particle types participating in the rth reaction process, n r,m represents the number density of the mth particle participating in the rth reaction process, where the number density of neutral molecules in the gas is n ε =P / k B T.s r is a symbolic function, defined as:

[0058]

[0059] Γ e , Γ w , Γ s , Γ n are the total particle fluxes at nodes e, w, s, and n at any time.

[0060] Particle flux density Γ at time t t for

[0061]

[0062] In the formula, sgn(q) represents the charge sign of the charged particle. For neutral particles, sgn(q)=0, for positive ions, sgn(q)=1, for negative ions and electrons, sgn(q)=-1, μ represents the mobility of the particle, E t is the electric field corresponding to time t, n t is the particle number density corresponding to time t.

[0063] By taking the value of the source term S in equation (1) at time t, the continuity equation of each particle can be decoupled, and then the electron flux at any position at time t+Δt can be obtained. and number density Ion flux and number density Excited state particle flux and number density

[0064] (4) According to the electron flux obtained in step 3 and number density Solving equation (5) yields the average energy of the electron: Then we get the average temperature of electrons T e .

[0065]

[0066]

[0067] In the formula, k B is the Boltzmann constant,

[0068] (5) Determine whether secondary electrons exist at the boundary based on the model structure material.

[0069] If the boundary is material, it is considered that there are secondary electrons, then according to the initial electron number density Step 3 Ion number density and ion boundary velocity Electron boundary velocity Substituting the electron continuity equation (7) on the boundary, we get the boundary secondary electron flux

[0070]

[0071] Ion boundary velocity for Ion thermal velocity T ion is the average temperature of the ions, which is the same as the gas temperature T, m ion is the mass of the ion. The electron boundary velocity Electron thermal velocity v e；th for m e is the mass of the electron.

[0072] Then the boundary secondary electron flux Substituting into the particle continuity equation in step 1, we can obtain the electron flux at any position at time t+Δt: and number density

[0073] If the boundary is a port, it is assumed that there are no secondary electrons. The particle continuity equation in step 1 is directly solved to obtain the electron flux at any position at time t+Δt. and number density

[0074] (6) The current formed by the charged particles is calculated based on the particle flux, and the current is fed back to the electromagnetic field to determine whether it exceeds the predetermined simulation time. If not, steps (2)-(5) are repeated. If it exceeds the predetermined simulation time, the microwave low-pressure discharge analysis process is terminated and the results are output.

[0075] Among them, the establishment of Figure 3 The coaxial model structure shown simulates the low-pressure discharge process in the coaxial structure. The outer conductor radius of the coaxial structure is 3.55mm, the inner conductor radius is 1.54mm, the coaxial structure length is 10mm, the operating frequency is 3.2GHz, and the simulation time is 100ns. The background gas is a mixture of Ne (95%) and Xe (5%), and the gas pressure is 30Torr.

[0076] like Figure 4 As shown, the electric field strength obtained by simulation is 1.5×10 5 V / m Figure 3 The discharge result diagram of the coaxial structure shown in the figure, Figure 4 (a) is the change of average electron density with time under this condition, Figure 4 (b) shows the change of average electron temperature with time under this condition. The average electron density increases first and then decreases, which means that no discharge occurs.

[0077] like Figure 5 As shown, the simulated electric field strength is 5×10 6 V / m Figure 3 The discharge result diagram of the coaxial structure shown in the figure, Figure 5 (a) is the change of average electron density with time under this condition, Figure 5 (b) shows the change of average electron temperature with time under this condition. The average electron density increases exponentially with time, indicating that discharge occurs.

[0078] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0079] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for analyzing microwave low-pressure discharge, characterized in that Here are the steps: (1) Read the target model structure, set the initial value of the electromagnetic field, gas temperature T, gas pressure P, boundary conditions, and initial ion number density Initial electron number density The secondary electron emission coefficient of the structural material is γ, the initial electron energy, the time step Δt, the simulation time, the particles include electrons, ions and excited state particles, the subscripts are e, ion, exe respectively, and the model structure is meshed after the settings are completed; (2) Perform electromagnetic field propulsion according to the finite-difference time-domain method to obtain the electric field E and magnetic field H at any position and time after grid division; (3) Solve the particle continuity equation to obtain the electron flux at any position at time t+Δt and number density Ion flux and number density Excited state particle flux and number density (4) The electron flux obtained according to step (3) and number density Solve to get the average energy of the electron Then we get the average temperature of electrons T e ; (5) Determine whether there are secondary electrons at the boundary based on the model structure material. If so, determine the initial electron number density. The ion number density obtained in step (3) Ion boundary velocity Electron boundary velocity Substituting the electron continuity equation on the boundary into the boundary secondary electron flux Then the boundary secondary electron flux Substituting into the particle continuity equation in step (3), we can obtain the electron flux at any position at time t+Δt: and number density Otherwise, directly output the electron flux obtained in step (3) and number density In the step (1), the model is divided into equally spaced staggered grids according to the electromagnetic field input frequency, and the main grid nodes, corresponding potential nodes, and particle density nodes are set. The grid division size is determined according to the Courant stability condition; In step (3), the chemical reaction rate constant k of each particle in the gas required to solve the continuity equation of the particle is r , the particle mobility μ is obtained by solving the steady-state Boltzmann equation, and the particle diffusion coefficient D is obtained by the Einstein relation; In the step (3), the particle continuity equation is integrated in time and space and discretized into a grid to obtain a discrete expression of the particle continuity equation: Where S is the source term of the continuity equation of each particle, expressed as: In the formula, r It means the r reaction process, k r represents the reaction rate constant corresponding to the reaction, N r Indicated participation r The number of particle types in a reaction process, n r,m Indicated participation r The number density of the mth particle in the reaction process, where the number density of neutral molecules in the gas is n ε =P / k B T;s r is a symbolic function, defined as: In the formula, Γ e , Γ w , Γ s , Γ n are the total particle flux at nodes e, w, s, and n at any time; the particle flux density Γ at time t t for: In the formula, sgn(q) represents the charge sign of the charged particle. For neutral particles, sgn(q)=0, for positive ions, sgn(q)=1, for negative ions and electrons, sgn(q)=-1, μ represents the mobility of the particle, E t is the electric field corresponding to time t, n t is the particle number density corresponding to time t; By taking the value of the source term S in the discrete expression of the particle continuity equation at time t, the continuity equation of each particle can be decoupled, and then the electron flux at any position at time t+Δt can be obtained. and number density Ion flux and number density Excited state particle flux and number density In the step (4), according to the electron flux obtained in step 3 and number density The average energy of the electrons is obtained from the following formula: Calculate the average electron temperature T e : In the formula, k B is the Boltzmann constant; In step (5), if the boundary is material, it is considered that secondary electrons exist. Then, according to the initial electron number density The ion number density obtained in step (3) and ion boundary velocity Electron boundary velocity Substituting the electron continuity equation on the boundary into the boundary secondary electron flux In the formula, is the ion boundary velocity, Ion thermal velocity T ion is the average temperature of the ions, which is the same as the gas temperature T, m ion is the mass of the ion; the electron boundary velocity Electron thermal velocity v e；th for m e is the mass of the electron; the boundary secondary electron flux Substituting into the particle continuity equation in step (3), we can obtain the electron flux at any position at time t+Δt: and number density 2. The method for analyzing microwave low-pressure discharge according to claim 1, characterized in that: The method also includes step (6), calculating the current formed by the charged particles based on the particle flux, and feeding the current back to the electromagnetic field to determine whether the predetermined simulation time is exceeded. If not, steps (2)-(5) are repeated. If the predetermined simulation time is exceeded, the microwave low-pressure discharge analysis process is terminated and the results are output.

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