Numerical simulation method for propagation characteristics of high power microwave before and after atmospheric breakdown

Abstract

The application belongs to the technical field of wave propagation, and particularly discloses a numerical simulation method for propagation characteristics before and after high-power microwave atmospheric breakdown, which is based on a rotational body time-domain finite difference method to solve an electron fluid model improved based on an empirical formula, the electron fluid model including a Maxwell equation set, an electron density continuity equation, an electron fluid momentum conservation equation and an electron fluid energy equation, and the evolution processes of electromagnetic fields, electron densities and electron energies before and after high-power microwave atmospheric breakdown can be calculated by solving the improved electron fluid model. According to different atmospheric pressures and initial electron densities, the application adopts more accurate transport coefficients, so that the simulation precision can be greatly improved; and the application can also convert a three-dimensional electromagnetic propagation problem into a quasi-two-dimensional problem, so that the simulation time can be greatly shortened and the computer memory can be saved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic field calculation, and particularly relates to a numerical simulation method for propagation characteristics before and after high-power microwave atmospheric breakdown. BACKGROUND

[0002] In recent years, with the breakthrough progress of pulse power technology, especially the progress of key technologies such as high-energy-density capacitor array, solid-state semiconductor switch device and magnetic compression generator, the radiation power of a high-power microwave (HPM) source has reached the GW level. When the high-power microwave propagates in the atmosphere, due to the high energy carried by the high-power microwave, seed electrons and neutral particles in the gas will have an avalanche collision, ionization and generate a large number of free electrons, and the electron density will rise sharply to a certain concentration, which will cause microwave breakdown.

[0003] During the formation of the plasma in the atmospheric breakdown, the high-power microwave will be strongly reflected and absorbed, which will affect the atmospheric propagation of the high-power microwave. The core damage mechanism of the HPM in electronic countermeasures is to penetrate the electromagnetic shielding system of the target device through a narrow pulse microwave beam with a GW-level peak power, and inject electromagnetic energy into the internal part of the electronic system through the front door / coupling path. When the power density of the target area exceeds the dielectric breakdown threshold, the dielectric breakdown effect will be caused in a very short time, and through the double effects of heat accumulation and overvoltage breakdown, irreversible damage will occur to sensitive elements such as the semi-radio front end and the conductor device. This physical process involves complex atmospheric propagation dynamics and nonlinear electromagnetic coupling effects, and through the coupling energy, the sensitive elements of the radar or communication device are burned, but it is necessary to ensure that the pulse power density exceeds the breakdown threshold of the target area, so the research on the propagation before and after the atmospheric breakdown of the high-power microwave has great significance for the design of the antenna and the power threshold.

[0004] At present, the numerical simulation method for the atmospheric breakdown of the high-power microwave has formed a comprehensive technical system from the micro-particle dynamics to the macro multi-field coupling, and the particle simulation-Monte Carlo collision PIC-MCC method, the time-domain spectral element method and the finite-difference time-domain FDTD method are relatively mainstream methods. The PIC-MCC combines the particle tracking and the Monte Carlo statistical method, simulates the collision process of the electron and the gas molecule including ionization, excitation and elastic collision, and can accurately describe the dynamic evolution of the plasma by solving the Newton-Lorentz equation and the Poisson equation, but the calculation efficiency of the method is extremely low. The time-domain spectral element method is suitable for accurate simulation of complex structures, but the calculation efficiency is also lower than that of the FDTD method. The FDTD method does not need to solve the matrix, has low memory occupation, and is suitable for dynamic simulation of the breakdown threshold with the change of the pulse parameters such as the amplitude and the pulse width, but it is difficult to simulate the three-dimensional atmospheric breakdown of the high-power microwave, and the calculation rate is low.

[0005] Therefore, it is necessary to provide a method capable of quickly simulating three-dimensional high-power microwave propagation before and after atmospheric breakdown. SUMMARY

[0006] The present application aims to provide a numerical simulation method for the propagation characteristics of high-power microwave before and after atmospheric breakdown, which simplifies the original three-dimensional problem to quasi-two-dimensional problem based on the time-domain finite difference method of rotating body, so as to reduce the calculation time and the demand for computer memory, and the method of the present application also ignores the influence of electron diffusion and Lorentz force, and uses the empirical electron fluid energy equation to replace the electron energy conservation equation to solve the electron energy, thereby further improving the calculation efficiency.

[0007] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0008] A numerical simulation method for the propagation characteristics of high-power microwave before and after atmospheric breakdown, comprising the following steps:

[0009] Step 1. Establishing the framework of the time-domain finite difference method of rotating body for high-power microwave propagation, which includes plane wave source excitation, total field-scattered field, boundary condition, spatial interval and time step, and connecting boundary;

[0010] Step 2. Setting the atmospheric propagation parameters of high-power microwave, including the waveform, amplitude, frequency, propagation time of high-power microwave, and environmental pressure and initial electron density;

[0011] Step 3. Initializing the plane wave source excitation according to the waveform, amplitude and frequency of high-power microwave, setting the total simulation step number according to the propagation time of high-power microwave, and initializing the parameters and transport coefficients of the electron fluid model according to the environmental pressure;

[0012] Step 4. Solving the improved electron fluid model using the time-domain finite difference method of rotating body, which includes Maxwell's equations, electron density continuity equation, electron fluid momentum conservation equation and electron fluid energy equation, to calculate the electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy at each point in the space at the current time;

[0013] Step 5. Judging whether the current simulation step number reaches the total simulation step number, if the current simulation step number does not reach the total simulation step number, updating the current simulation step number and going to step 6; if the current simulation step number reaches the total simulation step number, going to step 7;

[0014] Step 6. Calculating the root mean square value of electric field according to the electric field intensity obtained in step 4, updating the transport coefficients, saving the electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy at each point in the space at the current time, and returning to step 4;

[0015] Step 7. Analyzing the electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy of each point in the space within the propagation time to obtain the evolution result of the high-power microwave propagation before and after the atmospheric breakdown.

[0016] In addition, on the basis of the numerical simulation method for the propagation characteristics before and after the atmospheric breakdown of the high-power microwave, the present application further provides a computer device comprising a memory and one or more processors.

[0017] The memory stores executable codes, and the processor executes the executable codes to implement the steps of the numerical simulation method for the propagation characteristics before and after the atmospheric breakdown of the high-power microwave.

[0018] The present application has the following advantages:

[0019] As described above, the present application provides a numerical simulation method for the propagation characteristics before and after the atmospheric breakdown of the high-power microwave, which solves the improved electron fluid model by using the rotating body finite difference time domain method, converts the calculation region from three-dimensional space to two-dimensional plane, and only needs to solve the electromagnetic problem on the two-dimensional rotationally symmetric plane to obtain the size of the space electromagnetic field. By converting the three-dimensional variable problem into a two-dimensional variable problem, the computer memory can be greatly saved, and the operation speed can be improved. The present application method also improves the electron fluid model for the atmospheric breakdown of the high-power microwave, uses the empirical electron fluid energy equation to replace the electron energy conservation equation to solve the electron energy, ignores the effects of electron diffusion and Lorentz force, reduces the complexity of the model, and further improves the calculation efficiency. The present application method is suitable for simulating the propagation characteristics before and after the atmospheric breakdown of the high-power microwave under different atmospheric pressures and electron densities. By setting different microwave waveforms, amplitudes and frequencies, the evolution process of the electron density, electron energy and microwave electric field before and after the atmospheric breakdown of the high-power microwave can be obtained, thereby meeting the engineering application requirements. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The flowchart of the numerical simulation method for the propagation characteristics before and after the atmospheric breakdown of the high-power microwave in the embodiment of the present application.

[0021] Figure 2 The simulation structure schematic diagram in the embodiment of the present application.

[0022] Figure 3 The electron density evolution diagram of the atmospheric breakdown process of the high-power microwave in the embodiment of the present application.

[0023] Figure 4 The electric field propagation diagram in the r direction of the atmospheric breakdown process of the high-power microwave in the embodiment of the present application.

[0024] Figure 5A φ direction electric field propagation diagram of a high-power microwave breakdown atmospheric process in an embodiment of the present application.

[0025] Figure 6 An electron energy evolution diagram of a high-power microwave breakdown atmospheric process in an embodiment of the present application. DETAILED DESCRIPTION

[0026] Embodiment 1

[0027] The present application is further described below in conjunction with the accompanying drawings and specific embodiments:

[0028] The present application provides a numerical simulation method for propagation characteristics before and after high-power microwave atmospheric breakdown, and the method is based on a BOR-FDTD method for solving an electron fluid model improved based on an empirical formula, i.e., an empirical electron fluid energy equation, and the electron fluid model includes a Maxwell equation set, an electron density continuity equation, an electron fluid momentum conservation equation, and an electron fluid energy equation, and can calculate the evolution processes of electromagnetic fields, electron density, and electron energy before and after high-power microwave atmospheric breakdown. According to different atmospheric pressures and initial electron densities, the method uses more accurate transport coefficients, which can greatly improve the simulation accuracy; at the same time, the method converts a three-dimensional electromagnetic propagation problem into a quasi-two-dimensional problem, which can greatly shorten the simulation time and save computer memory.

[0029] As shown in Figure 1 , the numerical simulation method for propagation characteristics before and after high-power microwave atmospheric breakdown specifically includes the following steps:

[0030] Step 1. Establish a framework of a BOR-FDTD method suitable for high-power microwave propagation, which includes a plane wave excitation, a total field-scattered field, a boundary condition, a spatial interval and a time step, and a connection boundary.

[0031] Figure 2 The simulation structure designed by the present application is specifically as follows:

[0032] The maximum value of the connection boundary in the r direction is N r_SF_max , the maximum value of the connection boundary in the z direction is N z_SF_max , and the minimum value of the connection boundary in the z direction is N z_SF_min .

[0033] The plane wave source excitation and the total field-scattered field are realized by setting a one-dimensional BOR-FDTD iteration formula, as shown in formulas (1) to (4), and then the electromagnetic intensity and the magnetic field intensity on the one-dimensional node are projected to the connection boundaries N r_SF_max , N z_SF_max , and Nz_SF_min Up.

[0034]

[0035] where j is the one-dimensional node coordinate symbol, n is the simulation step symbol, and the subscripts r_inc and φ_inc represent the components of the plane wave source excitation in the r and φ directions, respectively.

[0036] In one simulation step, the magnetic field strength is calculated first, and then the electric field strength. The superscript n represents the electric field strength of the previous simulation step, and n+1 represents the electric field strength of the current simulation step. The superscript n-0.5 represents the magnetic field strength of the previous simulation step, and n+1 represents the magnetic field strength of the current simulation step. In one-dimensional node coordinates, j represents the electric field strength of the current node coordinate, j+1 represents the electric field strength of the next node coordinate, j-0.5 represents the magnetic field strength of the previous node coordinate, and j+0.5 represents the magnetic field strength of the current node coordinate.

[0037] E_r_n_j and E_φ_n_j represent the electric field strengths in the r and φ directions, respectively, of the previous simulation step and the current node coordinate.

[0038] E_r_n_j and E_φ_n_j represent the electric field strengths in the r and φ directions, respectively, of the current simulation step and the current node coordinate.

[0039] E_r_n_j and E_φ_n_j represent the electric field strengths in the r and φ directions, respectively, of the previous simulation step and the next node coordinate.

[0040] H_r_n_j and H_φ_n_j represent the magnetic field strengths in the r and φ directions, respectively, of the previous simulation step and the current node coordinate.

[0041] H_r_n_j and H_φ_n_j represent the magnetic field strengths in the r and φ directions, respectively, of the current simulation step and the previous node coordinate.

[0042] H_r_n_j and H_φ_n_j represent the magnetic field strengths in the r and φ directions, respectively, of the current simulation step and the current node coordinate.

[0043] ε0 and μ0 are the air dielectric constant and magnetic permeability, respectively.

[0044] Spatial interval d r , d z , d r is the size of the spatial grid in the r direction, d z is the size of the spatial grid in the z direction.

[0045] Time step d t A more stringent stability condition d t < δ / (2*c) must be satisfied, where c is the speed of light, and δ takes dr and d z the smaller one, i.e. δ = min{d r ,d z}, min{·} means taking the minimum value.

[0046] The boundary conditions include the convolutional perfect matched layer (CPML) absorbing boundary condition for electromagnetic wave and the fluid dynamics upstream and downstream boundary conditions for electron density and electron fluid velocity. The CPML is added in the r direction and the z direction of the calculation space, and the CPML is 20 layers in total.

[0047] Step 2. Set the atmospheric propagation parameters of high power microwave, which include the waveform, amplitude, frequency, propagation time of high power microwave, and environmental air pressure and initial electron density.

[0048] The waveform of high power microwave is defined by the parameter pulseSetting, pulseSetting = 1 represents Gaussian pulse, pulseSetting = 2 represents sinusoidal modulated Gaussian pulse, and pulseSetting = 3 represents sinusoidal wave.

[0049] The amplitude value of high power microwave is defined by the parameter amp, and the unit is volt.

[0050] The frequency of high power microwave is defined by the parameter ω, and the unit is radian per second.

[0051] The propagation time of high power microwave is defined by the parameter timeDom, and the unit is second.

[0052] The environmental air pressure is the atmospheric pressure measured before the propagation of high power microwave, which is set by the parameter p, and the unit of p is millimeter of mercury.

[0053] The initial electron density is the environmental value before the propagation of high power microwave.

[0054] Step 3. Initialize the plane wave source excitation of step 1 according to the waveform, amplitude and frequency of high power microwave set in step 2, set the total simulation step number according to the propagation time of high power microwave set in step 2, and initialize the parameters β and transport coefficient of the electron fluid model according to the environmental air pressure set in step 2.

[0055] The initialization expression of sinusoidal wave plane wave source excitation is:

[0056]

[0057] The initialization expression of Gaussian pulse plane wave source excitation is:

[0058]

[0059] The initialization expression of sinusoidal modulated Gaussian pulse plane wave source excitation is:

[0060]

[0061] Total simulation steps n max Divided by the time step d t Get.

[0062] The parameter β of the electron fluid model needs to be initialized according to the high-power microwave frequency and the ambient air pressure, and the formula of the parameter β is:

[0063] β = E rms / (1+ω 2 / V c 2 ) 0.5 p (5)

[0064] Wherein, E rms represents the root mean square value of the electric field, and the unit is V / cm; V c represents the collision rate of the transport coefficient.

[0065] The transport coefficient needs to be initialized according to the atmospheric pressure, and the formula of the transport coefficient is:

[0066] V i = 5.14 × 10 11 exp(-73 × β -0.44 )p (6)

[0067] V a = 7.6 × 10 -4 β 2 / (β+218) 2 p (7)

[0068] V c = 5 × 10 9 [β / (β+8)] 0.5 p (8)

[0069] Wherein, V i represents the ionization rate of the transport coefficient, and V a represents the adhesion rate of the transport coefficient.

[0070] Step 4. The improved electron fluid model is solved by using the rotating body finite difference time domain method, which includes Maxwell equation set, electron density continuity equation, electron fluid momentum conservation equation and electron fluid energy equation, to calculate the electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy of each point in the space at the current time.

[0071] The improved electron fluid model is represented as:

[0072]

[0073] J = - q N e v (11)

[0074]

[0075] wherein, denotes the rotation calculation symbol, E denotes the electric field intensity, B denotes the magnetic flux density, t denotes time, H denotes the magnetic field intensity, J denotes the current density, D denotes the electric flux density, q, N e , m e , v, T e respectively denote the charge, density, mass, velocity and energy of the electron.

[0076] Equation (9) and equation (10) are the Maxwell equations for high-power microwave propagation, equation (11) represents the current formed by the movement of free electrons in the atmosphere, equation (12) is the continuity equation of electron density ignoring the influence of plasma diffusion, equation (13) is the electron fluid momentum conservation equation ignoring the influence of the magnetic field and plasma diffusion, and equation (14) is an empirical electron fluid energy equation for solving the electron energy instead of the electron energy conservation equation.

[0077] The partial differential equations of the improved electron fluid model solved by the rotating body finite difference time domain method are as follows:

[0078]

[0079]

[0080] wherein, E r , E φ , E z are the electric field intensities in the r, φ and z directions respectively, H r , H φ , H z are the magnetic field intensities in the r, φ and z directions respectively, v r , v φ , v z are the electron fluid velocities in the r, φ and z directions respectively, ε0 and μ0 are the air dielectric constant and magnetic permeability respectively, R is the distance in the r direction, and m is the mode number of the rotating body finite difference time domain method.

[0081] When solving the partial differential equations of the electron fluid model by the rotating body finite difference time domain method, the electron velocities v r , v φ , v z are respectively multiplied by the electric field intensities E r , E φ , E zPut in the same grid space position, and in the same time interval, first calculate the electric field intensity, and then calculate the electron velocity. The specific calculation process is as follows:

[0082] Solve formula (15), formula (16), formula (17) to get the electric field intensity E of each point in the space at the current time r , E φ , E z .

[0083] Solve formula (18), formula (19), formula (20) to get the magnetic field intensity H of each point in the space at the current time r , H φ , H z .

[0084] Solve formula (22), formula (23), formula (24) to get the electron velocity v r , v φ , v z .

[0085] Solve formula (21) to get the electron density N e .

[0086] Solve formula (14) to get the electron energy T e .

[0087] Step 5. Determine whether the current simulation step number reaches the total simulation step number n max .

[0088] If the current simulation step number does not reach the total simulation step number n max , update the current simulation step number and go to step 6, wherein the operation of updating the current simulation step number is to add one to the value of the current simulation step number. If the current simulation step number reaches the total simulation step number n max , go to step 7.

[0089] Step 6. Calculate the root mean square value of the electric field according to the electric field intensity obtained in step 4, update the transport coefficient, save the electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy of each point in the space at the current time, and return to step 4.

[0090] The specific steps of updating the transport coefficient are as follows:

[0091] First, solve the root mean square value of the electric field E rms according to the electric field value:

[0092]

[0093] Wherein, T represents the period of high power microwave.

[0094] According to the root mean square value of the electric field Erms Solving for parameter β, the formula for solving parameter β is obtained from formulas (5) and (8):

[0095]

[0096] The parameter β of the electron fluid model is obtained by solving formula (26).

[0097] Substitute the obtained parameter β into formulas (6), (7), and (8) to calculate the ionization rate V of the transport coefficient. i Adhesion rate V a and collision rate V c .

[0098] Save the electron density, electric field strength in the r direction, electric field strength in the φ direction, and electron energy at each point in space at the current time into the data files obre.dat, obEr.dat, obEphi.dat, and obUe.dat respectively.

[0099] Step 7. Analyze the electron density, electric field strength in the r direction, electric field strength in the φ direction, and electron energy at each point in space during the propagation time to obtain the evolution results of high-power microwave propagation before and after atmospheric breakdown.

[0100] Step 7 specifically includes:

[0101] Step 7.1. As Figure 3 As shown, after saving the obre.dat data file, open the Origin plotting software, import the data into worksheet book1, select the "line graph" option, and obtain the electron density evolution graph of high-power microwave atmospheric propagation.

[0102] Step 7.2. Figure 4 As shown, after saving the obEr.dat data file, open the Origin plotting software, import the data into worksheet book2, select the "line graph" option, and obtain the electric field intensity evolution graph in the r direction of high-power microwave atmospheric propagation.

[0103] Step 7.3. As Figure 5 As shown, after saving the obEphi.dat data file, open the Origin plotting software, import the data into worksheet book3, select the "line graph" option, and obtain the evolution graph of electric field intensity in the φ direction of high-power microwave atmospheric propagation.

[0104] Step 7.4. Figure 6 As shown, after saving the obUe.dat data file, open the Origin plotting software, import the data into worksheet book4, select the "line graph" option, and obtain the electron energy evolution graph of high-power microwave atmospheric propagation.

[0105] In this embodiment, the high-power microwave with amplitude of 6e 6 V, frequency of 2.85Ghz sine wave, in the process of atmospheric breakdown with ambient pressure, initial electron density of 10. Figures 3 to 6 The evolution diagrams of electron density, electric field in r direction, electric field in φ direction, and average electron energy from 0 to 10ns are shown in FIG. 2, FIG. 3, FIG. 4, and FIG. 5, respectively. It can be seen from the diagrams that the electron density will gradually increase and then tend to be balanced in the process of breakdown, in which electromagnetic wave is absorbed and reflected in large quantities, and the average electron energy gradually decreases, that is, the energy of high-power microwave will greatly decrease after atmospheric breakdown, which seriously affects the propagation characteristics.

[0106] Embodiment 2

[0107] This embodiment 2 describes a computer device, which comprises a memory and one or more processors.

[0108] The executable code is stored in the memory, and when the processor executes the executable code, the steps of the numerical simulation method of the propagation characteristics of high-power microwave before and after atmospheric breakdown in the above embodiment 1 are implemented.

[0109] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described here.

[0110] Of course, the above description is only for the preferred embodiments of the present application, and the present application is not limited to the above-mentioned embodiments. It should be noted that any person skilled in the art, under the guidance of this specification, can make all equivalent replacements, obvious modifications, and fall within the scope of the present application.

Claims

1. A method for numerical simulation of propagation characteristics of high power microwaves before and after atmospheric breakdown, characterized in that, The method comprises the following steps: Step 1. establishing a framework of the rotation body finite-difference time-domain method for high-power microwave propagation, which comprises a plane wave source excitation, a total field-scattered field, a boundary condition, a space interval and a time step, and a connection boundary; Step 2. setting atmospheric propagation parameters of the high-power microwave, which comprise a waveform, an amplitude, a frequency, a propagation time of the high-power microwave, and an environmental air pressure and an initial electron density; Step 3. initializing the plane wave source excitation according to the waveform, the amplitude and the frequency of the high-power microwave, setting a total simulation step number according to the propagation time of the high-power microwave, and initializing parameters and transport coefficients of an electron fluid model according to the environmental air pressure; Step 4. solving the improved electron fluid model by using the rotation body finite-difference time-domain method, which comprises a Maxwell equation set, an electron density continuity equation, an electron fluid momentum conservation equation and an electron fluid energy equation, and calculating electric field intensity, magnetic field intensity, electron density, electron velocity and electron energy at each point in a space at a current time; Step 5. judging whether the current simulation step number reaches the total simulation step number, if not, updating the current simulation step number and returning to step 6; if the current simulation step number reaches the total simulation step number, returning to step 7; Step 6. calculating a root mean square value of the electric field according to the electric field intensity obtained in step 4, updating the transport coefficients, saving the electric field intensity, the magnetic field intensity, the electron density, the electron velocity and the electron energy at each point in the space at the current time, and returning to step 4; Step 7. analyzing the electric field intensity, the magnetic field intensity, the electron density, the electron velocity and the electron energy at each point in the space within the propagation time, and obtaining evolution results of the high-power microwave propagation before and after atmospheric breakdown.

2. The method of claim 1, wherein, In the step 1, The maximum value of the connection boundary in the r direction is N r_SF_max The maximum value of the connection boundary in the z direction is N z_SF_max The minimum value of the connection boundary in the z direction is N z_SF_min ; The plane wave source excitation and the total field-scattered field implementation are achieved by setting one-dimensional BOR-FDTD iteration formulas as shown in formulas (1) to (4), and then projecting and interpolating the electromagnetic intensity and magnetic field intensity on the one-dimensional nodes to the connecting boundary N r_SF_max , N z_SF_max , N z_SF_min ; wherein ε0 and μ0 represent air permittivity and permeability respectively, j is a one-dimensional node coordinate symbol, the superscript n is a simulation step number symbol, and the subscripts r_inc and φ_inc represent components of the plane wave source excitation in the r and φ directions respectively; Ei, Ei+1, Ei+2, Ei+3, Ei+4, Ei+5, Ei+6, Ei+7, Ei+8, Ei+9, Ei+10, Ei, Ei+1, Ei+2, Ei+3, Ei+4, Ei+5, Ei+6, Ei+7, Ei+8, Ei+9, Ei+ Ei, Ei+1, Ei+2, Ei+3, Ei+4, Ei+5, Ei+6, Ei+7, Ei+8, Ei+9, Ei+10, Ei r and φ direction magnetic field strength of the previous simulation step, respectively; Bx, By, Bz represent the magnetic field strength in the r and φ direction of the last node coordinate; Bx, By, Bz represent the magnetic field strength in the r and φ direction of the current node coordinates, respectively; Spatial interval d r and d z , d r is the size of the spatial grid in the r direction, d z is the size of the spatial grid in the z direction; Time step d t Satisfying stability condition d t < δ / (2*c), where c is the speed of light, δ = min{d r < d z}, min{·} means taking the minimum value.

3. The method of claim 1, wherein, In the step 1, The boundary condition comprises a convolution perfect matched layer (CPML) absorbing boundary condition for electromagnetic waves and fluid mechanics upstream and downstream boundary conditions for the electron density and the electron velocity; The CPML is added in the r direction and the z direction of the calculation space, and the CPML has 20 layers.

4. The method of claim 2, wherein, The step 2 is specifically: The waveform of the high-power microwave is defined by a parameter pulseSetting, pulseSetting=1 represents a Gaussian pulse, pulseSetting=2 represents a sinusoidal modulated Gaussian pulse, and pulseSetting=3 represents a sinusoidal wave; The amplitude value of the high-power microwave is defined by a parameter amp; The frequency of the high-power microwave is defined by a parameter ω; The propagation time of the high-power microwave is defined by a parameter timeDom; The environmental air pressure p is set as an atmospheric pressure measured before the high-power microwave propagation; The initial electron density is an environmental value before the high-power microwave propagation.

5. The method of numerical simulation of high-power microwave atmospheric breakdown pre-and post-propagation characteristics according to claim 4, characterized in that, The step 3 is specifically: The sinusoidal wave plane wave source excitation initialization is represented as: The Gaussian pulse plane wave source excitation initialization is represented as: The sinusoidal modulated Gaussian pulse plane wave source excitation initialization is represented as: Total number of simulation steps n max Divided by the time step d t Obtained; According to the high-power microwave frequency and the ambient pressure, a parameter β of the electron fluid model is initialized, and the parameter β is expressed by a formula: β = E rms (1 + ω 2 / V c 2 ) 0.5 p (5) where Ε rms represents the electric field root mean square value; V c represents the collision rate of the transport coefficient; According to the ambient pressure p, a transport coefficient is initialized, and the transport coefficient is expressed by a formula: V i = 5.14 x 10 11 exp(-73 x β -0.44 p (6) V a = 7.6 x 10 -4 β 2 / (β+218) 2 p (7) V c = 5 x 10 9 [β / (β+8)] 0.5 p (8) where V i represents the ionization rate of the transport coefficient, V a represents the sticking rate of the transport coefficient.

6. The method of numerical simulation of high-power microwave atmospheric breakdown pre-and post-propagation characteristics according to claim 5, characterized in that, In the step 4, the improved electron fluid model is expressed by: J = - qN e v (11) wherein, denotes the curl operator, E denotes the electric field intensity, B denotes the magnetic flux density, t denotes time, H denotes the magnetic field intensity, J denotes the current density, D denotes the electric flux density, q, N e , m e , v, T e denote the charge, density, mass, velocity and energy of an electron, respectively; The formula (9) and the formula (10) are Maxwell equations of high-power microwave propagation, the formula (11) represents a current formed by free electron movement in the atmosphere, the formula (12) is an electron density continuity equation ignoring plasma diffusion, the formula (13) is an electron fluid momentum conservation equation ignoring the magnetic field and the plasma diffusion, and the formula (14) is an empirical electron fluid energy equation for solving electron energy instead of an electron energy conservation equation.

7. The method of claim 6, wherein the method is a numerical simulation method of high-power microwave atmospheric breakdown pre-and post-propagation characteristics, characterized in that, In the step 4, a partial differential equation of the improved electron fluid model solved by using a rotating body finite difference time domain method is: where E r , E φ , E z are the electric field intensity in r, φ, z directions, respectively, H r , H φ , H z are the magnetic field intensity in r, φ, z directions, respectively, v r , v φ , v z are the electron fluid velocity in r, φ, z directions, respectively, R is the distance in r direction, and m is the mode number of the time domain finite difference method for the rotating body.

8. The method of numerical simulation of high-power microwave atmospheric breakdown pre-and post-propagation characteristics according to claim 7, characterized in that, In the step 4, When solving the partial differential equations of the electron fluid model by the time-domain finite-difference method, the electron velocity v r , v φ , and v z are respectively placed at the same grid space position as the electric field intensity E r , E φ , and E z ​ Solving formula (15), formula (16), formula (17) obtains the electric field intensity E of each point in the space at the current time r , E φ , E z ; Solving formula (18), formula (19), formula (20) obtains the magnetic field intensity H of each point in the space at the current time r , H φ , H z ; Solving equation (22), equation (23), equation (24) obtains the electron velocity v r , φ , z ; Solving equation (21) gives the electron density N e ; Solving equation (14) gives the electron energy T e .

9. The method of numerical simulation of high-power microwave atmospheric breakdown pre-and post-propagation characteristics according to claim 8, characterized in that, In the step 6, a process of updating the transport coefficient is specifically as follows: Solving the electric field root mean square value E from the electric field value rms : Wherein, T represents a period of the high-power microwave. According to the root mean square value of the electric field E rms The parameter β is solved according to the formula (5) and the formula (8). The parameter β of the electron fluid model is obtained by solving the formula (26); The solved parameter β is substituted into formula (6), formula (7) and formula (8) to sequentially obtain ionization rate V i , adhesion rate V a and collision rate V c .

10. A computer device comprising a memory and one or more processors, the memory having stored therein executable code, the computer device characterized in that, The processor executes the executable code, and the steps of the numerical simulation method of the high-power microwave propagation characteristics before and after the atmospheric breakdown are realized according to any one of claims 1 to 9.

Images