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

Abstract

The invention belongs to the technical field of radio wave propagation, and particularly discloses a numerical simulation method for propagation characteristics before and after atmospheric breakdown of high-power microwaves. The electron fluid model comprises a Maxwell equation set, an electron density continuity equation, an electron fluid momentum conservation equation and an electron fluid energy equation, and the evolution process of an electromagnetic field, electron density and electron energy before and after high-power microwave atmospheric breakdown can be calculated by solving the improved electron fluid model. According to the method, a more accurate transport coefficient is adopted according to different atmospheric pressures and initial electron densities, so that the simulation precision can be greatly improved; according to the method, a three-dimensional electromagnetic propagation problem can be converted into a quasi-two-dimensional problem, so that the simulation time is greatly shortened, and the computer memory is saved.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic field calculation technology, specifically relating to a numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown. Background Technology

[0002] In recent years, with breakthroughs in pulsed power technology, especially advancements in key technologies such as high-energy-density capacitor arrays, solid-state semiconductor switching devices, and magnetic compression generators, the radiated power of high-power microwave (HPM) sources has reached the gigabyte (GW) level. When high-power microwaves propagate through the atmosphere, due to their high energy, they accelerate seed electrons in the gas to collide with neutral particles in an avalanche-like manner, ionizing and generating a large number of free electrons. Once the electron density rises sharply to a certain concentration, microwave breakdown occurs.

[0003] During atmospheric breakdown and plasma formation, high-power microwaves are strongly reflected and absorbed, affecting their atmospheric propagation. In electronic countermeasures, the core damage mechanism of high-power microwave pulses (HPM) lies in the instantaneous emission of a narrow pulse microwave beam with peak power in the gigawatt range, penetrating the electromagnetic shielding system of the target equipment and injecting electromagnetic energy into the electronic system via front / rear gate coupling. When the power density in the target area exceeds the dielectric breakdown threshold, a dielectric breakdown effect is triggered in a very short time. Through the combined effects of thermal accumulation and overvoltage breakdown, irreversible damage occurs to sensitive components such as semi-radio frequency front-ends and conductor devices. This physical process involves complex atmospheric propagation dynamics and nonlinear electromagnetic coupling effects. While the coupled energy can burn out sensitive components of radar or communication equipment, it is crucial to ensure that the pulse power density exceeds the breakdown threshold of the target area. Therefore, studying the propagation of high-power microwaves before and after atmospheric breakdown is of great significance for antenna design and power threshold estimation.

[0004] Currently, numerical simulation methods for high-power microwave atmospheric breakdown have formed a comprehensive technical system encompassing microscopic particle dynamics and macroscopic multi-field coupling. The particle simulation-Monte Carlo collision (PIC-MCC) method, the time-domain spectral method, and the finite-difference time-domain (FDTD) method are among the mainstream approaches. PIC-MCC combines particle tracking and Monte Carlo statistical methods to simulate the collision process between electrons and gas molecules, including ionization, excitation, and elastic collisions. By solving the Newton-Lorentz and Poisson equations, it can accurately describe the dynamic evolution of plasma; however, this method has extremely low computational efficiency. The time-domain spectral method is suitable for accurate simulation of complex structures, but its computational efficiency is also lower than that of the FDTD method. The FDTD method does not require matrix solving, has low memory usage, and is suitable for dynamically simulating the breakdown threshold variation with pulse parameters such as amplitude and pulse width; however, it is difficult to simulate three-dimensional high-power microwave atmospheric breakdown and has a low computational speed.

[0005] Therefore, it is necessary to propose a method that can quickly simulate the propagation before and after atmospheric breakdown of three-dimensional high-power microwaves. Summary of the Invention

[0006] The purpose of this invention is to propose a numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown. This method simplifies the original three-dimensional problem into a quasi-two-dimensional problem based on the finite-difference time-domain method of rotating bodies, thereby reducing computation time and the demand for computer memory. The method of this invention also ignores the effects of electron diffusion and Lorentz force, and uses the empirical electron fluid energy equation to replace the electron energy conservation equation to solve for electron energy, thereby further improving computational efficiency.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

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

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

[0010] Step 2. Set the atmospheric propagation parameters of the high-power microwave, including the waveform, amplitude, frequency, propagation time of the high-power microwave, as well as the ambient air pressure and initial electron density;

[0011] Step 3. Initialize the plane wave source excitation based on the waveform, amplitude, and frequency of the high-power microwave; set the total number of simulation steps based on the propagation time of the high-power microwave; and initialize the parameters and transport coefficients of the electrofluid model based on the ambient air pressure.

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

[0013] Step 5. Determine whether the current simulation step count has reached the total simulation step count. If the current simulation step count has not reached the total simulation step count, update the current simulation step count and proceed to step 6; if the current simulation step count has reached the total simulation step count, proceed to step 7.

[0014] Step 6. Calculate the root mean square value of the electric field based on the electric field strength obtained in Step 4, update the transport coefficient, save the electric field strength, magnetic field strength, electron density, electron velocity and electron energy of each point in space at the current time, and return to Step 4;

[0015] Step 7. Analyze the electric field strength, magnetic field strength, electron density, electron velocity 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.

[0016] Furthermore, based on the numerical simulation method for the propagation characteristics of high-power microwave atmospheric breakdown before and after the above-mentioned atmospheric breakdown, this invention also proposes a computer device, which includes a memory and one or more processors.

[0017] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the numerical simulation method for the propagation characteristics of high-power microwave atmospheric breakdown before and after described above.

[0018] The present invention has the following advantages:

[0019] As described above, this invention discloses a numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown. This method employs the finite-difference time-domain method of rotating bodies to solve an improved electron fluid model, transforming the computational domain from three-dimensional space to a two-dimensional plane. Only the electromagnetic problem on the two-dimensional rotationally symmetric plane needs to be solved to obtain the magnitude of the spatial electromagnetic field. By transforming a three-dimensional variable problem into a two-dimensional variable problem, computer memory is significantly saved and computation speed is improved. This invention also improves the electron fluid model for high-power microwave atmospheric breakdown by replacing the electron energy conservation equation with an empirical electron fluid energy equation to solve for electron energy, neglecting the effects of electron diffusion and the Lorentz force, thus reducing the complexity of the model and further improving computational efficiency. This invention is applicable to simulating the propagation characteristics of high-power microwaves before and after atmospheric breakdown under different atmospheric pressures and electron densities. By setting different microwave waveforms, amplitudes, and frequencies, the evolution of electron density, electron energy, and microwave electric field before and after high-power microwave atmospheric breakdown can be obtained, thereby meeting engineering application requirements. Attached Figure Description

[0020] Figure 1 This is a flowchart of a numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the simulation structure in an embodiment of the present invention.

[0022] Figure 3 This is a graph showing the evolution of electron density during the high-power microwave atmospheric breakdown process in an embodiment of the present invention.

[0023] Figure 4 This is a diagram showing the electric field propagation along the r direction during the high-power microwave atmospheric breakdown process in an embodiment of the present invention.

[0024] Figure 5This is a diagram showing the electric field propagation along the φ direction during the high-power microwave atmospheric breakdown process in an embodiment of the present invention.

[0025] Figure 6 This is a diagram showing the evolution of electron energy during the high-power microwave breakdown of the atmosphere in an embodiment of the present invention. Detailed Implementation

[0026] Example 1

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0028] This invention provides a numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown. The method is based on the rotating body finite-difference time-domain (BOR-FDTD) method, solving an improved electron fluid model based on empirical formulas, specifically the empirical electron fluid energy equation. This electron fluid model includes Maxwell's equations, the electron density continuity equation, the electron fluid momentum conservation equation, and the electron fluid energy equation, enabling the calculation of the evolution of the electromagnetic field, electron density, and electron energy before and after high-power microwave atmospheric breakdown. This invention employs more accurate transport coefficients based on different atmospheric pressures and initial electron densities, significantly improving simulation accuracy. Furthermore, this method transforms the three-dimensional electromagnetic propagation problem into a quasi-two-dimensional problem, greatly reducing simulation time and saving computer memory.

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

[0030] Step 1. Establish a framework for a rotating body finite-difference time-domain method suitable for high-power microwave propagation, which includes plane wave excitation, total field-scattered field, boundary conditions, spatial interval and time step, and connection boundary.

[0031] Figure 2 The simulation structure diagram designed for this invention is shown below:

[0032] The maximum value of the connection boundary in the r direction is N. r_SF_max The maximum value of the connecting boundary in the z-direction is N. z_SF_max The minimum value in the z-direction connecting the boundaries 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 iterative formula, as shown in formulas (1) to (4). Then, the electromagnetic intensity and magnetic field intensity at the one-dimensional node are projected onto the connecting boundary N using the equivalence principle through projection and interpolation. r_SF_max N z_SF_max Nz_SF_min superior.

[0034]

[0035] Where j is the symbol for one-dimensional node coordinates, n is the symbol for simulation steps, 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 a simulation step, the magnetic field strength is calculated first, followed by 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. Similarly, 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, and '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] These represent the electric field intensity in the r and φ directions, respectively, at the previous simulation step number and the current node coordinates.

[0038] These represent the current simulation step number and the electric field intensity at the current node coordinates in the r and φ directions, respectively.

[0039] These represent the electric field intensity in the r and φ directions, respectively, at the previous simulation step number and the coordinates of the next node.

[0040] These represent the previous simulation step number and the magnetic field strength in the r and φ directions at the current node coordinates, respectively.

[0041] These represent the current simulation step number and the magnetic field strength in the r and φ directions at the coordinates of the previous node, respectively.

[0042] These represent the current simulation step number and the magnetic field strength at the current node coordinates in the r and φ directions, respectively.

[0043] ε0 and μ0 are the permittivity and permeability of air, respectively.

[0044] Spatial interval d r d z d r Let d be the size of the spatial grid in the r direction. z The size of the spatial grid in the z-direction.

[0045] Time step d t More stringent stability conditions need to be met. t <δ / (2*c), where c is the speed of light, and δ is taken as d.r and d z The smaller value in, i.e., δ = min{d r ,d z}, min{·} represents taking the minimum value.

[0046] Boundary conditions include convolutionally perfectly matched layer (CPML) absorbing boundary conditions for electromagnetic waves and hydrodynamic upstream and downstream boundary conditions for electron density and electron fluid velocity. CPMLs are applied in the r and z directions of the computational space, with a total of 20 CPML layers.

[0047] Step 2. Set the atmospheric propagation parameters for the high-power microwave, including the waveform, amplitude, frequency, propagation time of the high-power microwave, as well as the ambient air pressure and initial electron density.

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

[0049] The amplitude of high-power microwaves is defined by the parameter amp, which is measured in volts.

[0050] The frequency of high-power microwaves is defined by the parameter ω, which is measured in radians per second.

[0051] The propagation time of high-power microwaves is defined by the parameter timeDom, which is measured in seconds.

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

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

[0054] Step 3. Initialize the plane wave source excitation in Step 1 according to the waveform, amplitude and frequency of the high-power microwave set in Step 2. Set the total number of simulation steps according to the propagation time of the high-power microwave set in Step 2. Initialize the parameters β and transport coefficient of the electrofluid model according to the ambient air pressure set in Step 2.

[0055] The initialization of the sinusoidal plane wave source excitation is expressed as:

[0056]

[0057] The initialization of the Gaussian pulse plane wave source excitation is expressed as:

[0058]

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

[0060]

[0061] Total number of simulation steps n max Divide the propagation time timeDom by the time step d t get.

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

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

[0064] Among them, E rms This represents the root mean square value of the electric field, with units of V / cm; V c The collision rate represents the transport coefficient.

[0065] The transport coefficient needs to be initialized based on atmospheric pressure. The formula for 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] Among them, V i V represents the ionization rate, which is the transport coefficient. a The adhesion rate represents the transport coefficient.

[0070] Step 4. Solve the improved electron fluid model using the finite-difference time-domain method of rotating bodies, which includes Maxwell's equations, the electron density continuity equation, the electron fluid momentum conservation equation, and the electron fluid energy equation, to calculate the electric field strength, magnetic field strength, electron density, electron velocity, and electron energy at each point in space at the current time.

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

[0072]

[0073] J = -qN e ν (11)

[0074]

[0075] in, The symbols for curl calculation are: E represents electric field strength, B represents magnetic flux density, t represents time, H represents magnetic field strength, J represents current density, D represents electric flux density, and q and N represent electric flux density. e m e 、ν、T e These represent the electron's charge, density, mass, velocity, and energy, respectively.

[0076] Formulas (9) and (10) are Maxwell's equations for high-power microwave propagation. Formula (11) represents the current formed by the movement of free electrons in the atmosphere. Formula (12) is the electron density continuity equation neglecting the influence of plasma diffusion. Formula (13) is the electron fluid momentum conservation equation neglecting the influence of magnetic field and plasma diffusion. Formula (14) is an empirical electron fluid energy equation that replaces the electron energy conservation equation to solve for electron energy.

[0077] The partial differential equations of the improved electron fluid model, solved using the finite-difference time-domain method for rotating bodies, are as follows:

[0078]

[0079]

[0080] Among them, E r E φ E z The electric field intensities H in the r, φ, and z directions are respectively. r H φ H z ν represents the magnetic field strength in the r, φ, and z directions, respectively. r ν φ ν z Let εr be the electron fluid velocities in the r, φ, and z directions, respectively; let ε0 and μ0 be the air dielectric constant and permeability, respectively; let R be the distance in the r direction; and let m be the mode number of the finite-difference time-domain method for rotating bodies.

[0081] When solving the partial differential equations of the electron fluid model using the finite-difference time-domain method for spinning bodies, the electron velocity ν is considered. r ν φ ν z respectively with electric field strength E r E φ E zThe electrons are placed in the same grid space and the electric field strength is calculated first, followed by the electron velocity, within the same time interval. The specific calculation process is as follows:

[0082] Solving equations (15), (16), and (17) yields the electric field intensity E at each point in space at the current time. r E φ E z .

[0083] Solving equations (18), (19), and (20) yields the magnetic field strength H at each point in space at the current time. r H φ H z .

[0084] Solving equations (22), (23), and (24) yields the electron velocity ν. r ν φ ν z .

[0085] Solving formula (21) yields the electron density N. e .

[0086] Solving formula (14) yields the electron energy T. e .

[0087] Step 5. Determine if the current simulation step count has reached the total simulation step count n. max .

[0088] If the current simulation step count has not reached the total simulation step count n max If the current simulation step count is reached, then update the current simulation step count and proceed to step 6. Updating the current simulation step count involves incrementing its value by one. If the current simulation step count reaches the total simulation step count n... max Then proceed to step 7.

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

[0090] The specific steps for updating the transport coefficient are:

[0091] First, calculate the root mean square value of the electric field E based on the electric field value. rms :

[0092]

[0093] Where T represents the period of the high-power microwave.

[0094] Based on 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. 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, an amplitude of 6e was simulated. 6 V, a high-power microwave with a frequency of 2.85 GHz sinusoidal wave, undergoes atmospheric breakdown under ambient air pressure and an initial electron density of 10. Figures 3 to 6 The graphs show the evolution of electron density, electric field in the r-direction, electric field in the φ-direction, and average electron energy from 0 to 10 ns. It can be seen that during the breakdown process, the electron density gradually increases and then tends to equilibrium. During this process, a large amount of electromagnetic waves are absorbed and reflected, accompanied by a gradual decrease in average electron energy. In other words, after atmospheric breakdown, the energy of high-power microwaves drops significantly, severely affecting their propagation characteristics.

[0106] Example 2

[0107] This embodiment 2 describes a computer device that includes a memory and one or more processors.

[0108] The memory stores executable code, which, when executed by the processor, implements the steps of the numerical simulation method for the propagation characteristics of high-power microwave atmospheric breakdown before and after in Embodiment 1 above.

[0109] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0110] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown, characterized in that, Includes the following steps: Step 1. Establish the framework of the finite-difference time-domain method for high-power microwave propagation of rotating bodies, which includes plane wave source excitation, total field-scattered field, boundary conditions, spatial interval and time step, and connection boundary; Step 2. Set the atmospheric propagation parameters of the high-power microwave, including the waveform, amplitude, frequency, propagation time of the high-power microwave, as well as the ambient air pressure and initial electron density; Step 3. Initialize the plane wave source excitation based on the waveform, amplitude, and frequency of the high-power microwave; set the total number of simulation steps based on the propagation time of the high-power microwave; and initialize the parameters and transport coefficients of the electrofluid model based on the ambient air pressure. Step 4. Solve the improved electron fluid model using the finite-difference time-domain method of rotating bodies, which includes Maxwell's equations, the electron density continuity equation, the electron fluid momentum conservation equation, and the electron fluid energy equation, to calculate the electric field strength, magnetic field strength, electron density, electron velocity, and electron energy at each point in space at the current time. Step 5. Determine whether the current simulation step count has reached the total simulation step count. If the current simulation step count has not reached the total simulation step count, update the current simulation step count and proceed to step 6. If the current simulation step count reaches the total simulation step count, proceed to step 7; Step 6. Calculate the root mean square value of the electric field based on the electric field strength obtained in Step 4, update the transport coefficient, save the electric field strength, magnetic field strength, electron density, electron velocity and electron energy of each point in space at the current time, and return to Step 4; Step 7. Analyze the electric field strength, magnetic field strength, electron density, electron velocity 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.

2. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 1, characterized in that, In step 1, The maximum value of the connection boundary in the r direction is N. r_SF_max The maximum value of the connecting boundary in the z-direction is N. z_SF_max The minimum value in the z-direction connecting the boundaries is N. z_SF_min ; The plane wave source excitation and the total field-scattered field are realized by setting up a one-dimensional BOR-FDTD iterative formula as shown in formulas (1) to (4), and then using the equivalence principle, the electromagnetic intensity and magnetic field intensity at the one-dimensional node are projected onto the connecting boundary N through projection and interpolation methods. r_SF_max N z_SF_max N z_SF_min superior; Where ε0 and μ0 represent the air dielectric constant and permeability, respectively; j is the symbol for the one-dimensional node coordinates; the superscript n is the symbol for the simulation step number; and the subscripts r_inc and φ_inc represent the components of the plane wave source excitation in the r and φ directions, respectively. These represent the electric field intensity in the r and φ directions, respectively, at the previous simulation step number and the current node coordinates. These represent the current simulation step number and the electric field intensity at the current node coordinates in the r and φ directions, respectively. These represent the electric field intensity in the r and φ directions, respectively, at the previous simulation step number and the coordinates of the next node. These represent the magnetic field strength in the r and φ directions, respectively, at the previous simulation step number and the current node coordinates. These represent the current simulation step number and the magnetic field strength in the r and φ directions at the coordinates of the previous node, respectively. These represent the current simulation step number and the magnetic field strength at the current node coordinates in the r and φ directions, respectively. Spatial interval d r and d z d r Let d be the size of the spatial grid in the r direction. z 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{·} represents taking the minimum value.

3. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 1, characterized in that, In step 1, Boundary conditions include convolutionally perfectly matched layer (CPML) absorption boundary conditions for electromagnetic waves and hydrodynamic upstream and downstream boundary conditions for electron density and electron velocity. CPML is applied in the r and z directions of the computation space, and there are a total of 20 layers of CPML.

4. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 2, characterized in that, Step 2 specifically involves: The waveform of high-power microwaves is defined by the parameter pulseSetting. pulseSetting=1 represents a Gaussian pulse, pulseSetting=2 represents a sinusoidal modulated Gaussian pulse, and pulseSetting=3 represents a sine wave. The amplitude value of high-power microwaves is defined by the parameter amp; The frequency of high-power microwaves is defined by the parameter ω; The propagation time of high-power microwaves is defined by the parameter timeDom; The ambient air pressure p is set to the atmospheric pressure measured before the high-power microwave propagation; The initial electron density is the environmental value before high-power microwave propagation.

5. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 4, characterized in that, Step 3 specifically involves: The initialization of the sinusoidal plane wave source excitation is expressed as: The initialization of the Gaussian pulse plane wave source excitation is expressed as: The initialization of the sinusoidal modulated Gaussian pulse plane wave source excitation is expressed as: Total number of simulation steps n max Divide the propagation time timeDom by the time step d t get; The parameter β of the electron fluid model is initialized based on the high-power microwave frequency and ambient air pressure. The formula for parameter β is: β=E rms / (1+ω 2 / V c 2 ) 0.5 p (5) Among them, E rms V represents the root mean square value of the electric field; c The collision rate represents the transport coefficient; The transport coefficient is initialized based on the ambient air pressure p. The formula for the transport coefficient is as follows: V i =5.14×10 11 exp(-73×β -0.44 )p (6) V a =7.6×10 -4 b 2 / (β+218) 2 p (7) V c =5×10 9 [β / (β+8)] 0.5 p (8) Among them, V i V represents the ionization rate, which is the transport coefficient. a The adhesion rate represents the transport coefficient.

6. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 5, characterized in that, In step 4, the improved electron fluid model is expressed as: J=-qN e n (11) in, The symbols for curl calculation are: E represents electric field strength, B represents magnetic flux density, t represents time, H represents magnetic field strength, J represents current density, D represents electric flux density, and q and N represent electric flux density. e m e 、ν、T e These represent the electron's charge, density, mass, velocity, and energy, respectively. Formulas (9) and (10) are Maxwell's equations for high-power microwave propagation. Formula (11) represents the current formed by the movement of free electrons in the atmosphere. Formula (12) is the electron density continuity equation neglecting the influence of plasma diffusion. Formula (13) is the electron fluid momentum conservation equation neglecting the influence of magnetic field and plasma diffusion. Formula (14) is the empirical electron fluid energy equation for solving electron energy by replacing the electron energy conservation equation.

7. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 6, characterized in that, In step 4, the partial differential equations of the improved electron fluid model are solved using the finite-difference time-domain method for rotating bodies: Among them, E r E φ E z The electric field intensities H in the r, φ, and z directions are respectively. r H φ H z ν represents the magnetic field strength in the r, φ, and z directions, respectively. r ν φ ν z denoted as r, φ, and z, respectively, where R is the distance in the r direction and m is the mode number of the finite-difference time-domain method for rotating bodies.

8. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 7, characterized in that, In step 4 When solving the partial differential equations of the electron fluid model using the finite-difference time-domain method for spinning bodies, the electron velocity ν is considered... r ν φ ν z respectively with electric field strength E r E φ E z They are placed in the same grid space location respectively; Solving equations (15), (16), and (17) yields the electric field intensity E at each point in space at the current time. r E φ E z ; Solving equations (18), (19), and (20) yields the magnetic field strength H at each point in space at the current time. r H φ H z ; Solving equations (22), (23), and (24) yields the electron velocity ν. r ν φ ν z ; Solving formula (21) yields the electron density N. e ; Solving formula (14) yields the electron energy T. e .

9. The numerical simulation method for the propagation characteristics of high-power microwaves before and after atmospheric breakdown according to claim 8, characterized in that, The process of updating the transport coefficient in step 6 is as follows: Solve for the root mean square value of the electric field E based on the electric field value. rms : Where T represents the period of the high-power microwave; Based on the root mean square value of the electric field E rms Solving for parameter β, the formula for solving parameter β is obtained from formulas (5) and (8): The parameter β of the electronic fluid model is obtained by solving formula (26); 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 .

10. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that... When the processor executes the executable code, it implements the steps of the numerical simulation method for the propagation characteristics of high-power microwave atmospheric breakdown before and after as described in any one of claims 1 to 9.

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