A lightweight method for determining the spatial potential of microwave-loaded low-pressure discharge

Abstract

The present invention provides a lightweight determination method for the spatial potential of a microwave-loaded low-pressure discharge: defining any spatial rectangular coordinate system as a discharge space coordinate system to obtain the charge distribution of the microwave-loaded low-pressure discharge space; considering the dynamic change of the spatial charge position under the promotion of the electric field and the magnetic field, solving the spatial charge distribution of the microwave-loaded low-pressure discharge space after the instantaneous change; performing three-dimensional linear unit grid reduction on all charges in the microwave-loaded low-pressure discharge space after the instantaneous change to obtain the spatial grid charge distribution; using Gauss's theorem to obtain the spatial potential form of the elementary charge at each grid point, performing corresponding product superposition on the spatial grid charge distribution classified by the unit grid and the potential data of the spatial elementary charge to obtain the spatial potential after all charges are synthesized; and performing potential difference in the three coordinate axis directions of the discharge space coordinate system to obtain the spatial charge field distribution.

Description

Technical Field

[0001] The invention relates to a lightweight determination method for low-pressure discharge space potential, belonging to the field of electronic technology. Background Art

[0002] The low-pressure discharge effect of high-power space microwave payloads is a significant factor limiting the performance of various microstrip antennas used in aerospace. This low-pressure discharge, generated by the electron multiplication effect, can lead to surface modification of materials, increased dielectric loss, and deviations from designed device parameters. These factors can affect the corresponding antenna parameters and performance, ultimately impacting proper operation. With the increasing demand for high-power and miniaturized antennas, this low-pressure discharge effect has become a significant bottleneck limiting the performance and stability of spacecraft microwave components.

[0003] High-power, highly integrated microwave components can improve the performance of space payload systems, but they also pose reliability challenges. In high microwave fields, charged particles interact with component surfaces, generating electron multiplication effects. These microwave resonant multiplication effects, including microdischarges and low-pressure discharges, significantly limit component performance and even reduce payload system life. Low-pressure discharges, due to the generation of electron clouds and the breakdown of the space gas, lead to increased standing wave ratio (SWR), reflected power, and noise levels, all of which can cause microwave system malfunctions. Furthermore, as byproducts, thermal effects and particle bombardment can cause passive intermodulation and surface corrosion. Therefore, to prevent these destructive phenomena, the playback system is typically shut down before escaping the atmosphere. Even so, given the desorption of material surfaces, low-pressure discharges can still occur under high-power conditions as operating power increases.

[0004] Because dielectric loading can effectively reduce the size of microwave components, dielectric-loaded microstrip lines are widely used in microwave circuits for space-borne systems. Dielectric materials exhibit greater surface roughness and reduced compactness, and are associated with more pronounced outgassing. Furthermore, outgassing from glue in the joint region is another major source of outgassing. All of these factors make low-pressure discharge a critical issue for solid-state microstrip circuits operating at high power. Unlike closed resonant cavity structures, the microwave electric field in the discharge region is not always perpendicular to the surface, which is detrimental to electron acceleration and multiple suppression. Furthermore, the open plate structure allows for diffusion of desorbed gas, slowing the accumulation of gas pressure. These factors result in a higher threshold operating power for low-pressure discharge compared to resonant cavity structures. Under high-power stimulation, low-pressure discharge may couple with microdischarge, making the discharge phenomenon a more complex physical process. Secondary electron emission from the material surface under electron impact may play a significant role, a role often overlooked in previous studies. Due to the inhomogeneity of the three-dimensional field and structure, low-pressure discharge in microwave circuits is difficult to study using two-dimensional simulation models. The electron distribution and dynamic diffusion in the horizontal plane should also be analyzed within the region.

[0005] Predicting and analyzing low-pressure discharge processes in the port region of a microstrip circuit typically requires three-dimensional numerical simulation of the electron evolution during the discharge process. To more accurately describe the electron dynamics, the simulation uses the Monte Carlo method to track the motion of each electron under the microwave electromagnetic field and the accumulated electrostatic field. Furthermore, the simulation considers the interaction between the energetic electrons and the gas, as well as secondary electron emission from the surfaces of different materials. Currently, some simulation software for microwave plasmas, such as Spark3D and Vsim, do not consider the effects of spatial electrostatic fields. In contrast, some simulation software, including CST, uses an iterative method to solve the electrostatic field generated by spatial charges by solving the three-dimensional Poisson equation for charge. Commonly used iterative methods include Newton iteration, Jacobi iteration, super-relaxation iteration, and Runge-Kutta method. Solving the potential is often the most time-consuming step in the entire process.

[0006] Traditionally, spatial potential solutions use an iterative approach to update the Poisson equation in differential form until the potential converges to obtain the spatial potential distribution. Due to the large spatial grid, the iterative solution process usually requires a large amount of computation. Summary of the Invention

[0007] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology and provide a lightweight determination method for the spatial potential of low-pressure discharge of microwave loads, so as to solve the problem of difficulty in solving the spatial potential generated by accumulated charges in the low-pressure discharge simulation of space microwave components under high-power conditions.

[0008] The technical solution of the present invention is: a lightweight method for determining the potential of a microwave-loaded low-pressure discharge space, the method comprising the following steps:

[0009] Define any rectangular coordinate system as the discharge space coordinate system, and obtain the charge distribution of the microwave-loaded low-pressure discharge space based on the process of space charge generated by low-pressure discharge.

[0010] Considering the dynamic changes of space charge position under the propulsion of electric and magnetic fields, the space charge distribution in the low-pressure discharge space of microwave load after instantaneous changes is solved;

[0011] All the charges in the low-pressure discharge space of the microwave load after the instantaneous change are normalized into three-dimensional linear unit grids to obtain the spatial grid charge distribution;

[0012] Gauss's theorem is used to independently solve the elementary charge on each unit grid to obtain the spatial potential form of the elementary charge on each grid point. According to the principle of spatial potential superposition, the spatial grid charge distribution assigned to the unit grid and the potential data of the spatial elementary charge are correspondingly multiplied and superimposed to obtain the spatial potential after all charges are synthesized.

[0013] The space charge field distribution is obtained by taking the potential difference in the three coordinate axis directions of the discharge space coordinate system.

[0014] Preferably, the space charge distribution of the microwave-loaded low-pressure discharge space includes the charge distribution of the deposited charge on the surface of the dielectric material bombarded by electrons. In the discharge space coordinate system, the electron incident position (x se ,y se ,z se ) deposited charge ρ se (x se ,y se ,z se )for:

[0015] ρ se (x se ,y se ,z se )=q e (1-δ)

[0016] Among them, q e is the electron charge, and δ is the secondary electron yield.

[0017] Preferably, the secondary electron yield δ is obtained by fitting the following equation using the experimentally tested secondary electron yield curve:

[0018]

[0019] Where θ pis the electron incident angle, E is the incident electron energy, δ max is the maximum secondary electron yield value, E max is the incident electron energy corresponding to the maximum secondary electron yield, R p is the scattering path coefficient, E RL is the yield energy factor corresponding to the incident electron energy of 0, δ0 is the secondary electron yield corresponding to the incident electron energy of 0, and α is the energy relationship index of the scattering path.

[0020] Preferably, the space charge of the microwave-loaded low-pressure discharge space also includes dynamic gas distribution and space ionization charge generated by electron collision with gas molecules, and the calculation method is:

[0021] Calculate the total gas density Q in the low-pressure discharge space of the microwave load total ;

[0022] According to the principle that the gas distribution on the surface of the open microstrip circuit is uniform in the horizontal direction and exponentially decays in the height direction, the airtight density distribution n is calculated. gas (x, y, z), (x, y, z) is the position in the discharge space coordinate system;

[0023] Monatomic oxygen gas is selected as the gas molecule, and the chemical equation of the desorption process in a space vacuum environment is obtained. The mean free path of the electron-gas collision is obtained based on the cross-sectional data of the analytical process, and a random number is generated. Based on the random number and the cross-sectional data, the type of ionization collision between the electron and the gas and the distance between each collision are obtained, thereby determining the specific position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas );

[0024] The position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ) produces ionized charge.

[0025] Preferably, the position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ) produces an ionization charge ρ e-gas (x e-gas ,y e-gas ,z e-gas )for:

[0026] ρ e-gas (x e-gas ,y e-gas ,z e-gas )=q e·(N e-gas )

[0027] Among them, q e is the electron charge, N e-gas is the charge value of ionization. When the type of ionization collision between electrons and gas is ionization, N e-gas =1, otherwise, N e-gas =0.

[0028] Preferably, the total gas density Q in the microwave load low pressure discharge space in step S1 is total for:

[0029] Q total =Q inital +r PSD (P)·t+r ESD (E)·n

[0030] Among them, Q inital is the initial density, r PSD (P) is the outgassing rate related to power, t is the simulation time, r ESD (E) is the outgassing rate related to the electron energy, and n is the number of times the electron enters the interface.

[0031] Preferably, the dynamics of the space charge position under the propulsion of electric and magnetic fields is expressed by the Newton-Lorentz equations:

[0032]

[0033]

[0034] Among them, m, e, r and are the mass, charge, position and velocity of the charge respectively; is the electric field, is the electrostatic electric field, is the microwave electric field, is the microwave magnetic field.

[0035] Preferably, the specific operation of the grid division is:

[0036] Divide the space x, y, z directions into n i ,n j ,n k nodes, orthogonally combined into n i ·n j ·n k spatial grid points;

[0037] Calculate the contribution of each space charge to the surrounding 8 grid points;

[0038] The contributions of all space charges at each grid point are superimposed to obtain the space grid charge distribution N charge (n i , n j , n k ).

[0039] Preferably, the grid points where the space charge is defined are numbered 1 to 8, and the 8 grid points form a cuboid;

[0040] The plane formed by grid points 5, 6, 7, and 8 and the plane formed by grid points 1, 2, 3, and 4 are grid planes perpendicular to the y-axis. The distance between the space charge and the plane formed by grid points 5, 6, 7, and 8 is the minimum distance a between the space charge and the grid plane perpendicular to the x-axis.

[0041] The plane formed by grid points 1, 3, 5, and 7 and the plane formed by grid points 2, 4, 6, and 8 are grid planes perpendicular to the y-axis. The distance between the space charge and the plane formed by grid points 1, 3, 5, and 7 is the minimum distance b between the space charge and the grid plane perpendicular to the y-axis.

[0042] The plane formed by grid points 1, 2, 7, and 8 and the plane formed by grid points 3, 4, 5, and 6 are grid planes perpendicular to the z-axis. The distance between the space charge and the plane formed by grid points 1, 2, 7, and 8 is the minimum distance c between the space charge and the grid plane perpendicular to the z-axis.

[0043] The contributions of space charge at grid points 1 to 8 are P1 to P8, respectively, and are calculated as follows:

[0044] P1=ac(Ly-b) / LxLyLz

[0045] P2=(Lx-a)c(Ly-b) / LxLyLz

[0046] P3=a(Lz-c)(Ly-b) / LxLyLz

[0047] P4=(Lx-a)(Ly-b)(Lz-c) / LxLyLz

[0048] P5=ab(Lz-c) / LxLyLz

[0049] P6=(Lx-a)b(Lz-c) / LxLyLz

[0050] P7=abc / LxLyLz

[0051] P8=(Lx-a)bc / LxLyLz

[0052] Among them, Lx is the length of the grid where the space charge is located in the x-axis direction, Ly is the length of the grid where the space charge is located in the y-axis direction, and L zis the length of the grid where the space charge is located in the z-axis direction.

[0053] Preferably, the specific steps of performing corresponding product superposition of the spatial grid charge distribution classified by the unit grid and the potential data of the spatial element charge are:

[0054] According to Gauss's theorem, the spatial potential of the elementary charge at each grid point is: V i,j,k (x,y,z), a total of n i ·n j ·n k Space potential data, n i ,n j ,n k are the number of grid points in the grid space in the three directions of grid i, j, and k respectively;

[0055] The space potential generated by the elementary charge is converted into a form of [n i ·n j ·n k ,n x ·n y ·n z ], that is, V[n i ·n j ·n k ,n x ·n y ·n z ], where n x 、n y 、n z are the number of sampling points of the spatial potential in the three directions x, y, and z of the discharge space coordinate system;

[0056] Convert the space charge distribution into the form [1,n i ·n j ·n k ], that is, N charge [1,n i ·n j ·n k ];

[0057] Directly solve the superimposed spatial potential:

[0058] V add-in [1,n x ·n y ·n z ]=N charge [1,n i ·n j ·n k ]V[n i ·n j ·n k ,nx ·n y ·n z ]

[0059] Preferably, the electrostatic field generated by the space charge at (x, y, z) is expressed as:

[0060] E S (x,y,z)=(E x (x,y,z),E y (x,y,z),E z (x,y,z))

[0061] in:

[0062]

[0063]

[0064]

[0065] The beneficial effects of the present invention compared with the prior art are:

[0066] (1) The present invention realizes a lightweight method for determining the potential generated by space charges during low-pressure discharge by adopting a space element charge potential superposition method based on Gauss's theorem. Compared with the prior art method of iteratively solving the potential Poisson equation, the present invention effectively avoids the huge amount of calculation in the iterative convergence process and simplifies the process of solving the space potential by selecting a space grid with appropriate accuracy.

[0067] (2) The present invention takes into account the dynamic processes of secondary electron emission, thermal degassing and electron bombardment degassing in the calculation of the spatial potential of the low-pressure discharge process. Compared with the previous method that only considers the spatial ionization charge, the processing situation is closer to the actual situation and can achieve a more accurate potential solution.

[0068] (3) The collision process between electrons and gas molecules in the present invention takes into account the main processes such as elastic scattering, (elastic) momentum transfer, electronic state excitation, dissociation, and ionization, while ignoring other processes with a very small proportion, thereby reducing the amount of calculation.

[0069] (4) The present invention simulates the process of generating secondary electrons from the collision between electrons and material interfaces using a probabilistic model that takes into account elastic backscattered electrons, inelastic backscattered electrons, and intrinsic secondary electrons. Compared with the classical Vaughan model and the Joy-Everhart model, this model can more accurately describe the secondary electron yield.

[0070] (5) The propulsion process of charged particles in the present invention takes into account the effects of electric and magnetic fields and adopts the Boris half-acceleration-rotation-half-acceleration method to solve it. The ability to use a distributed method to simultaneously consider electric field acceleration and magnetic field rotation facilitates program implementation.

[0071] (6) The present invention uses a three-dimensional linear proportional segmentation method to calculate the contribution of the charge at the surrounding eight grid points for the grid division of space charge. This avoids the crude approximation of the charge simply by nearest neighboring, thereby improving the accuracy of the charge distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 Schematic diagram of a lightweight method for determining the spatial potential of a low-pressure discharge according to an embodiment of the present invention;

[0073] Figure 2 A method for calculating electron-induced outgassing and thermal outgassing factors for gas density changes according to an embodiment of the present invention;

[0074] Figure 3 This is a grid point classification method for three-dimensional linear space charge according to an embodiment of the present invention. DETAILED DESCRIPTION

[0075] The present invention will be further described below in conjunction with the embodiments.

[0076] The present invention provides a lightweight method for determining the spatial potential of a microwave-loaded low-pressure discharge, comprising:

[0077] Step 1, obtaining the charge distribution in the low-pressure discharge space of the microwave load;

[0078] Step 2, solving the space charge distribution of the microwave load low-pressure discharge space after instantaneous change;

[0079] Step 3: The unit grid of the space charge distribution is divided into groups to obtain the space grid charge distribution

[0080] Step 4: Based on the calculation of the spatial element charge potential data and the superposition of the spatial potential, the spatial potential after all charges are synthesized is obtained.

[0081] Step 5: Obtain the space charge field distribution.

[0082] The details are as follows:

[0083] Step 1: Obtain the charge distribution in the low-pressure discharge space of the microwave load. The specific implementation process is as follows:

[0084] The spatial charge distribution in the microwave-loaded low-pressure discharge space includes the deposited charge distribution and dynamic gas distribution caused by electron bombardment on the surface of the dielectric material and the spatial ionization charge generated by electron collision with gas molecules.

[0085] 1.1. The specific implementation process of "obtaining the charge distribution in the low-pressure discharge space of the microwave payload" is as follows:

[0086] When electrons hit the surface of a solid, they scatter from the atoms of the material, resulting in secondary electron emission. When a certain number of electrons are emitted from the surface, according to the principle of charge conservation, the deposited charge at the incident point on the surface can be obtained. Specifically, the electrons moving in the microwave-loaded low-pressure discharge space interact with the interface of the wave-loaded material, and due to the imbalance between the incident electrons and the emitted electrons, the charge distribution accumulates on the surface of the medium with poor electrical conductivity. Although for some simple crystal structures, the Penn dielectric function model based on first principles can describe the microscopic full physical process of secondary electron emission, for most complex organic materials, the calculation method of secondary electron yield still needs to rely on experimental data.

[0087] In the method of the present invention, secondary electron emission is calculated by a probability model. For an energy of E and an incident angle of θ p For the incident electron, the yield of secondary electrons emitted from the interface surface is δ:

[0088]

[0089] Where θ p is the electron incident angle, E is the incident electron energy, δ max is the maximum secondary electron yield value, E max is the incident electron energy corresponding to the maximum secondary electron yield, R p is the scattering path coefficient, E RL is the yield energy factor corresponding to the incident electron energy of 0, δ0 is the secondary electron yield corresponding to the incident electron energy of 0, and α is the energy relationship index of the scattering path.

[0090] δ max 、E max , these two parameters can be directly read from the experimental secondary electron yield curve, R p ,E RL ,δ0,α need to be obtained by fitting the data values ​​of the secondary electron yield curve measured by the material experiment, that is, a series of δ are obtained according to the measurement of different energies E, and the above coefficients are determined by combining the above formulas.

[0091] After obtaining the secondary electron yield δ, it means that the incident electron will deposit a negative charge of 1-δ at the incident position. In the unified spatial rectangular coordinate system, the coordinate of the incident position is (x se ,y se ,z se ), then the charge deposited on the surface is:

[0092] ρse (x se ,y se ,z se )=Q e (1-δ) (2)

[0093] 1.2 The specific implementation process of "dynamic gas distribution and acquisition of spatial ionization charge generated by electron collision with gas molecules" is as follows:

[0094] First, calculate the total gas density Q in the microwave load low pressure discharge space total :

[0095] During the space charge acquisition process, electrons interact with gas molecules to generate space charge. Therefore, during the calculation process, the gas density within the spatial region is directly related to the impact ionization process. The proposed method takes into account the dynamic changes in gas density, where changes in gas density are influenced by two factors: thermal outgassing from the material surface under the microwave power of the space; and electron-induced outgassing from the material surface under electron bombardment.

[0096] Figure 2 The calculation method used in the present invention for these two types of outgassing is as follows. For the thermal outgassing generated by microwave power, the outgassing rate (related to power) obtained by combining experimental data is r PSD (P) and simulation time t to obtain the gas release amount. As for the gas release amount induced by electron bombardment, the gas release rate r obtained by experiment is also combined ESD The outgassing amount is obtained by (E) (related to the electron energy) and the number of electron incidents on the interface n. The number of electron incidents n can be obtained by the statistics of electron and interface incidents in the previous step. Finally, the total gas density is the sum of the initial density and the outgassing amount, so the total gas density Q in the microwave load low pressure discharge space is calculated total The formula is as follows:

[0097]

[0098] Among them, Q inital is the initial density, r PSD (P) is the outgassing rate related to power, t is the simulation time, r ESD (E) is the outgassing rate related to the electron energy, and n is the number of times the electron enters the interface.

[0099] Secondly, according to the principle that the gas distribution on the surface of the open microstrip circuit is uniform in the horizontal direction and exponentially decays in the height direction, the airtight density distribution n is calculated. gas (x, y, z), (x, y, z) is the position in the discharge space coordinate system;

[0100] After obtaining the total outgassing volume, we need to further obtain the spatial gas density distribution. Here we treat the gas distribution on the surface of the open microstrip circuit as an exponential decay in the height z direction. gas (x,y,z)=n gas (x,y,z0)·exp(-z / h gas ), where z0 is the height of the microstrip circuit surface. The horizontal direction is considered to be uniform, that is, n gas (x,y,z)=n gas (z).

[0101]

[0102] Here, h gas The gas density distribution n can be obtained from the above formula: gas (x,y,z).

[0103] Then, monatomic oxygen gas is selected as the gas molecule, and the chemical equation of the desorption process in a space vacuum environment is obtained. The mean free path of the electron-gas collision is obtained based on the cross-sectional data of the analytical process, and a random number is generated. Based on the random number and the cross-sectional data, the type of ionization collision between the electron and the gas and the distance between each collision are obtained, thereby determining the specific position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas );

[0104] Considering that existing gases primarily originate from desorption processes in a space vacuum environment, we selected monatomic oxygen as the gas molecule for this simulation, as an important desorption gas. When electrons collide with oxygen molecules, several major processes may occur, including elastic scattering, (elastic) momentum transfer, electronic state excitation, dissociation, and ionization, as specifically expressed in the following equations (5)-(9).

[0105] e+O2→O2+e (5)

[0106]

[0107] e+O2→O2+e * (7)

[0108] e+O2→O (*) +O+e (8)

[0109]

[0110] In the above formula, e is an electron, O2 is an oxygen molecule, and O * 2 is an excited oxygen molecule, e *For excited state electrons.

[0111] O / O (*) Oxygen atoms and excited oxygen atoms, O + is an ionized oxygen atom, O + 2 is an ionized oxygen molecule.

[0112] When electrons collide with molecules, processes such as electronic excitation, ionization, and dissociation occur, generating space charge. In reality, the interaction between electrons and oxygen molecules also includes rotational and vibrational excitation. However, due to the insufficient cross-section, these processes are neglected here.

[0113] In the present invention, the cross-sectional data of the above process is from Itikawa's data (J. Phys. Chem. Ref. Data, 2009). The mean free path of the electron-gas collision can be obtained from the cross-sectional data, and the type of electron-gas collision and the distance between each collision can be obtained by generating random numbers. Therefore, the type and specific location of the ionization collision can be obtained based on the speed (energy) and direction of the electron movement (x e-gas ,y e-gas ,z e-gas ).

[0114] Finally, the position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ) produces ionized charge.

[0115] For electrons moving in space, the position is (x e-gas ,y e-gas ,z e-gas ), when it collides with the gas emission ionization, the ionization charge generated at this location is:

[0116] ρ e-gas (x e-gas ,y e-gas ,z e-gas )=Q e ·(N e-gas ) (10)

[0117] Among them, Q e is the electron charge, N e-gas is the charge value of ionization. When the type of ionization collision between electrons and gas is ionization, N e-gas =1, otherwise, N e-gas =0.

[0118] Step 2, "Calculating the spatial charge distribution of the microwave load low-pressure discharge space after instantaneous changes" is specifically implemented as follows:

[0119] Under the influence of microwave electric, magnetic, and electrostatic fields, electrons undergo resonant multiplication. After acquiring the latest real-time electric and magnetic fields, the electrons are propelled forward, satisfying the following Newton-Lorentz equations. Because the charge deposited on the interface surface hardly changes, we only consider charges freely moving in space, including electrons and ionized gas molecules.

[0120]

[0121]

[0122] Among them, m, e, r and is the mass, charge, position, and velocity of the charge. Including electrostatic electric field and microwave electric field is the electrostatic electric field, contributed by the accumulated charge, is the microwave electric field, which is contributed by the microwave electric field. The electric field and magnetic field of the microwave field can be directly derived and interpolated by microwave simulation software. The electric field of the electrostatic field is obtained by the gradient of the spatial potential. For the first step, before the space potential is determined, the electrostatic field is set to 0. Since the electron propulsion equation (11) is implicit and its solution is relatively complex, we can use the Boris semi-acceleration-rotation-semi-acceleration method to convert it into an explicit equation by introducing two intermediate variables. Solving the equation of motion allows us to obtain the position (x1, y1, z1) of each space charge at the next moment based on its position (x0, y0, z0) at the previous moment.

[0123] The specific implementation process of step 3 "unit grid division of spatial charge distribution" is as follows:

[0124] Considering that space charge cannot be located at a specific grid point, we need to perform grid point reduction on all space charges. Considering the continuity of space charge and avoiding step-like changes in the reduction of space charge, we cannot simply reduce the space charge to the nearest grid point. Therefore, we linearly distribute any space charge to the eight surrounding space grid points. Figure 3 is the reduction diagram of the spatial grid points of charge.

[0125] Specific methods such as Figure 3 As shown, the steps are as follows:

[0126] 3.1. Divide the space into n parts in the x, y, and z directions respectively. i ,n j ,n k nodes, orthogonally combined into n i ·n j ·n kSpatial grid points.

[0127] 3.2. Calculate the contribution of each space charge to the surrounding 8 grid points;

[0128] The grid points where the space charge is located are numbered 1 to 8, and the 8 grid points form a cuboid;

[0129] The plane formed by grid points 5, 6, 7, and 8 and the plane formed by grid points 1, 2, 3, and 4 are grid planes perpendicular to the y-axis. The distance between the space charge and the plane formed by grid points 5, 6, 7, and 8 is the minimum distance a between the space charge and the grid plane perpendicular to the x-axis.

[0130] The plane formed by grid points 1, 3, 5, and 7 and the plane formed by grid points 2, 4, 6, and 8 are grid planes perpendicular to the y-axis. The distance between the space charge and the plane formed by grid points 1, 3, 5, and 7 is the minimum distance b between the space charge and the grid plane perpendicular to the y-axis.

[0131] The plane formed by grid points 1, 2, 7, and 8 and the plane formed by grid points 3, 4, 5, and 6 are grid planes perpendicular to the z-axis. The distance between the space charge and the plane formed by grid points 1, 2, 7, and 8 is the minimum distance c between the space charge and the grid plane perpendicular to the z-axis.

[0132] The contributions of space charge at grid points 1 to 8 are P1 to P8, respectively, and are calculated using the three-dimensional linear proportion segmentation method. The specific formula is as follows:

[0133] P1=ac(Ly-b) / LxLyLz

[0134] P2=(Lx-a)c(Ly-b) / LxLyLz

[0135] P3=a(Lz-c)(Ly-b) / LxLyLz

[0136] P4=(Lx-a)(Ly-b)(Lz-c) / LxLyLz

[0137] P5=ab(Lz-c) / LxLyLz

[0138] P6=(Lx-a)b(Lz-c) / LxLyLz

[0139] P7=abc / LxLyLz

[0140] P8=(Lx-a)bc / LxLyLz (13)

[0141] Among them, Lx is the length of the grid where the space charge is located in the x-axis direction, Ly is the length of the grid where the space charge is located in the y-axis direction, and L z is the length of the grid where the space charge is located in the z-axis direction.

[0142] 3.3 Superimpose the contributions of all space charges at each grid point to obtain the space grid charge distribution N charge (n i , n j , n k ).

[0143] By dividing all the space charges (including space ionization charge ∑ρ e-gas (x e-gas ,y e-gas ,z e-gas ) and surface deposited charge ∑ρ se (x se ,y se ,z se The grid points at the locations of )) are assigned to N charge (n i , n j , n k +1)=P1,N charge (n i +1,n j , n k +1)=P2,N charge (n i , n j +1,n k +1)=P3,N charge (n i +1,n j +1,n k +1)=P4,N charge (n i , n j +1,n k )=P5,N charge (n i +1,n j +1,n k )=P6,N charge (n i , n j , n k )=P7,N charge (n i +1,n j , n k )=P8. It is necessary to perform superposition and summation for each charge classification, and obtain the spatial grid charge distribution N by superimposing the grid classification of the charge. charge (n i , n j , n k ). That is: N charge (n i , n j , n k)=∑N charge (n i , n j , n k ), update the charge distribution.

[0144] The specific implementation process of step 5 "calculation based on spatial element charge potential data and superposition of spatial potential" is as follows:

[0145] According to Gauss's theorem, the spatial potential of the elementary charge at each grid point is: V i,j,k (x,y,z), a total of n i ·n j ·n k Space potential data, n i ,n j ,n k are the number of grid points in the grid space in the three directions of grid i, j, and k respectively;

[0146] In order to facilitate direct summation and superposition, the space potential generated by the elementary charge is converted into a form of V[n i ·n j ·n k ,n x ·n y ·n z ], that is, V[n i ·n j ·n k ,n x ·n y ·n z ], where n x 、n y 、n z are the number of sampling points of the spatial potential in the three directions of x, y, and z in the discharge space coordinate system; the number of sampling points of the spatial potential is nx·ny·nz.

[0147] Convert the space charge distribution into the form [1,n i ·n j ·n k ], that is, N charge [1,n i ·n j ·n k ];

[0148] Directly solve the superimposed spatial potential:

[0149] V add-in [1,n x ·n y ·n z ]=N charge [1,n i ·nj ·n k ]V[n i ·n j ·n k ,n x ·n y ·n z ] (14)

[0150] Expanding the one-dimensional spatial potential into a three-dimensional form V(x,y,z), the electric field can be obtained by calculating the gradient in the x, y, and z directions:

[0151]

[0152]

[0153]

[0154] The electrostatic field generated by the space charge at (x, y, z) is expressed as:

[0155] E S (x,y,z)=(E x (x,y,z),E y (x,y,z),E z (x,y,z)) (18)

[0156] Under the influence of the microwave field in space, potential energy is transferred to the floating seed electrons, accelerating them and promoting an increase in the system's entropy. This entropy evolution is achieved through the accelerated electrons and their interactions with both the gas and the solid. When electrons of a certain energy collide with gas molecules, they may generate new excited electrons. Furthermore, under electron bombardment, secondary electrons are emitted from the material surface, accumulating charge on the surface. The charge accumulated during the electron bombardment also forms an electrostatic field, which influences the trajectory of the charged particles.

[0157] In summary, the present invention proposes a method of elementary charge space potential superposition based on Gauss's theorem to calculate the spatial field in the low-pressure discharge process under the action of high-power microwaves. The overall calculation method is as follows Figure 1As shown in Figure 1. First, we need to determine the spatial charge distribution across the entire simulation region. The sources of space charge include: a) the interaction between electrons moving in space and the material interfaces within the region, resulting in charge accumulation on the surface of poorly conductive media due to the imbalance between incoming and outgoing electrons; and b) in the presence of gas molecules in the spatial region, electrons collide with molecules, causing processes such as electron excitation, ionization, and dissociation, generating charged space charge. Space charge moves under the influence of the spatial field, changing the charge distribution, which is also something we need to consider. Secondly, after obtaining the charge location information, we need to grid the charges and assign all charges to the grid cells. Charges within the grid cells are still considered point charges at fixed points. Next, we solve Gauss's theorem for the elementary charges at each grid point to obtain the potential distribution data for the spatial region. This calculation is independent of the charge distribution; we select the elementary charges at all grid points. The space potential generated by the elementary charges on each grid cell is weighted by the charge amount to obtain the space potential at that grid point. The space potentials generated by all grid points are then superimposed to obtain the overall space potential. Finally, the spatial electric field is obtained according to the gradients of the obtained spatial potential in the x, y, and z directions.

[0158] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions 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 solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A lightweight method for determining the potential of microwave-loaded low-pressure discharge space, characterized in that Here are the steps: Define any rectangular coordinate system as the discharge space coordinate system, and obtain the charge distribution of the microwave-loaded low-pressure discharge space based on the process of space charge generated by low-pressure discharge. Considering the dynamic changes of space charge position under the propulsion of electric and magnetic fields, the space charge distribution in the low-pressure discharge space of microwave load after instantaneous changes is solved; All the charges in the low-pressure discharge space of the microwave load after the instantaneous change are normalized into three-dimensional linear unit grids to obtain the spatial grid charge distribution; Gauss's theorem is used to independently solve the elementary charge on each unit grid to obtain the spatial potential form of the elementary charge on each grid point. According to the principle of spatial potential superposition, the spatial grid charge distribution assigned to the unit grid and the potential data of the spatial elementary charge are correspondingly multiplied and superimposed to obtain the spatial potential after all charges are synthesized. The potential difference in the three coordinate axis directions of the discharge space coordinate system is used to obtain the space charge field distribution; The space charge distribution of the microwave-loaded low-pressure discharge space includes the charge distribution of the deposited charge on the surface of the dielectric material bombarded by electrons. In the discharge space coordinate system, the electron incident position (x se ,y se ,z se ) deposited charge ρ se (x se ,y se ,z se )for: ρ se (x se ,y se ,z se )=q e ·(1-δ) Among them, q e is the electron charge, δ is the secondary electron yield; The space charge of the microwave-loaded low-pressure discharge space also includes the dynamic gas distribution and the space ionization charge generated by electron collision with gas molecules, and the calculation method is: Calculate the total gas density Q in the low-pressure discharge space of the microwave load total ; According to the principle that the gas distribution on the surface of the open microstrip circuit is uniform in the horizontal direction and exponentially decays in the height direction, the airtight density distribution n is calculated. gas (x, y, z), (x, y, z) is the position in the discharge space coordinate system; Monatomic oxygen gas is selected as the gas molecule, and the chemical equation of the desorption process in a space vacuum environment is obtained. The mean free path of the electron-gas collision is obtained based on the cross-sectional data of the analytical process, and a random number is generated. Based on the random number and the cross-sectional data, the type of ionization collision between the electron and the gas and the distance between each collision are obtained, thereby determining the specific position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ); The position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ) ionization charge generated at; The total gas density Q in the microwave load low pressure discharge space total for: Q total =Q inital +r PSD (P)·t+r ESD (E)·n Among them, Q inital is the initial density, r PSD (P) is the outgassing rate related to power, t is the simulation time, r ESD (E) is the outgassing rate related to the electron energy, and n is the number of times the electron enters the interface.

2. A lightweight determination method for microwave-loaded low-pressure discharge space potential according to claim 1, characterized in that The secondary electron yield δ is obtained by fitting the secondary electron yield curve of the experimental test to the following equation: Where θ p is the electron incident angle, E is the incident electron energy, δ max is the maximum secondary electron yield value, E max is the incident electron energy corresponding to the maximum secondary electron yield, R p is the scattering path coefficient, E RL is the yield energy factor corresponding to the incident electron energy of 0, δ0 is the secondary electron yield corresponding to the incident electron energy of 0, and α is the scattering energy relationship index.

3. The lightweight determination method of microwave-loaded low-pressure discharge space potential according to claim 1 is characterized in that The position of the ionized charge in the discharge space coordinate system (x e-gas ,y e-gas ,z e-gas ) produces an ionization charge ρ e-gas (x e-gas ,y e-gas ,z e-gas )for: ρ e-gas ( x e-gas ,y e-gas ,z e-gas )=q e ·(N e-gas ) Among them, q e is the electron charge, N e-gas is the charge value of ionization. When the type of ionization collision between electrons and gas is ionization, N e-gas =1, otherwise, N e-gas =0.

4. The lightweight method for determining the spatial potential of microwave-loaded low-pressure discharge according to claim 1 is characterized in that the dynamic change of the space charge position under the propulsion of electric and magnetic fields is expressed by the Newton-Lorentz equation: in, m, e, r and are the mass, charge, position and velocity of the charge respectively; is the electric field, is the electrostatic electric field, is the microwave electric field, is the microwave magnetic field.

5. The lightweight determination method of microwave-loaded low-pressure discharge space potential according to claim 1 is characterized in that The specific operation of the grid division is: Divide the space x, y, z directions into n i ,n j ,n k nodes, orthogonally combined into n i ·n j ·n k spatial grid points; Calculate the contribution of each space charge to the surrounding 8 grid points; The contributions of all space charges at each grid point are superimposed to obtain the space grid charge distribution N charge (n i , n j , n k ).

6. A lightweight determination method for microwave-loaded low-pressure discharge space potential according to claim 5, characterized in that The specific steps for multiplying and superimposing the charge distribution of the spatial grid divided by the unit grid and the potential data of the spatial element charge are as follows: According to Gauss's theorem, the spatial potential of the elementary charge at each grid point is: V i,j,k (x,y,z), a total of n i ·n j ·n k Space potential data, n i ,n j ,n k are the number of grid points in the grid space in the three directions of grid i, j, and k respectively; The space potential generated by the elementary charge is converted into a form of [n i ·n j ·n k ,n x ·n y ·n z ], that is, V[n i ·n j ·n k ,n x ·n y ·n z ], where n x 、n y 、n z are the number of sampling points of the spatial potential in the three directions of x, y, and z in the discharge space coordinate system; Convert the space charge distribution into the form [1,n i ·n j ·n k ], that is, N charge [1,n i ·n j ·n k ]; Directly solve the superimposed spatial potential: V add-in [1,n x ·n y ·n z ]=N charge [1,n i ·n j ·n k ]V[n i ·n j ·n k ,n x ·n y ·n z ]。 7. The lightweight determination method of microwave-loaded low-pressure discharge space potential according to claim 1 is characterized in that The electrostatic field generated by the space charge at (x, y, z) is expressed as: E S (x,y,z)=(E x (x,y,z),E y (x,y,z),E z (x,y,z)) in:

Images