A numerical method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas

Abstract

The application belongs to the technical field of computational electromagnetics, and discloses a numerical calculation method for simulating electromagnetic wave propagation characteristics in time-varying plasma, which is a three-dimensional Newton-HIE-FDTD method for efficiently simulating electromagnetic wave propagation in time-varying plasma based on a mixed explicit-implicit finite-difference time-domain method and Newton's second law of motion. The method inherits the advantages of the Newton-ADE-FDTD method, accurately represents the time-varying electron density through the time derivative, and can accurately capture the rich dynamic characteristics of the time-varying plasma. On this basis, the method also integrates the advantages of the HIE-FDTD method, so that the time step of the algorithm is only restricted by the grid size in two directions. Compared with other simulation methods based on time-varying plasma, the method is more efficient in calculation, and is particularly suitable for the analysis and simulation of electromagnetic wave propagation characteristics in time-varying plasma.

Description

Technical Field

[0001] This invention belongs to the field of computational electromagnetics technology, specifically relating to a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas. Background Technology

[0002] In the study of time-varying plasma electromagnetic problems, the finite-difference time-domain (FDTD) method is an effective and commonly used numerical calculation method.

[0003] Currently, FDTD simulation research on time-varying plasmas mainly focuses on efficiently and accurately simulating their rapidly changing dielectric properties. Researchers have introduced methods such as auxiliary differential equations (ADE), piecewise linear recursive convolution (PLRC), and Z-transform to directly handle the transient constitutive relations of time-varying plasmas at the collision frequencies, achieving effective simulation of ionization processes, quenching processes, and the dynamic electromagnetic response of periodically modulated plasmas.

[0004] However, these methods still face the inherent limitations of the traditional FDTD framework: the time step is strictly constrained by the Courant-Friedrich-Levy (CFL) stability condition, making it difficult to simultaneously meet the high-resolution requirements of drastic changes in time-varying parameters and the efficiency of long-term simulation; at the same time, the traditional Yee mesh is prone to numerical dispersion and anisotropic errors when simulating the spatial distribution of rapidly changing plasma parameters, affecting the computational accuracy in complex time-varying scenarios.

[0005] To address these issues, recent research has introduced the Newton-ADE-FDTD method to analyze the electromagnetic properties of time-varying plasmas. This method, by incorporating the Newton-ADE-FDTD framework, distinguishes itself from the classical ADE-FDTD technique and demonstrates significant performance improvements in characterizing the dynamic features of time-varying electron density during plasma electromagnetic wave propagation. However, this method inherits the inherent limitations of the ADE-FDTD scheme, namely, the time step is still constrained by the CFL stability condition.

[0006] Therefore, it is necessary to propose a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas that weakens the stability condition of CFL, can further improve the simulation efficiency of the algorithm while maintaining high accuracy, and has high efficiency and effectiveness. Summary of the Invention

[0007] The purpose of this invention is to propose a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas. This method can accurately capture the dynamic characteristics of rapidly changing electrons in time-varying dispersive media, fully characterize their rich dynamic behavior, and weaken the CFL stability condition, so that the time step is only constrained by the grid size in two directions. This method is more efficient in computation and more suitable for simulating electromagnetic waves in time-varying plasmas.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasma includes the following steps:

[0010] Step 1. Input the model file;

[0011] Step 2. Initialize and set parameters;

[0012] Step 3. Update the entire computation region. Electric field components in the direction Magnetic field components and auxiliary components;

[0013] Step 4. Update the entire computation region. , Electric field components in the direction and and auxiliary components;

[0014] Step 5. Add incentive sources to Electric field components in the direction On the component coefficients;

[0015] Step 6. Update the entire computation region. , , Current density in the direction , ;

[0016] Step 7. Update the entire computation region. , Magnetic field components in the direction and and auxiliary components;

[0017] Step 8. Update the current iteration time step. The value is ;

[0018] Determine if the current iteration time step is equal to the preset total iteration time step; if yes, output the calculation results of electric field component, magnetic field component and current density; otherwise, go to step 3.

[0019] Furthermore, based on the numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasmas described above, this invention also proposes a computer device, which includes a memory and one or more processors.

[0020] The memory stores executable code, and when the processor executes the executable code, it implements the steps of the numerical calculation method for the electromagnetic wave propagation characteristics in simulated time-varying plasmas, as described above.

[0021] Furthermore, based on the numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasmas described above, this invention also proposes a computer-readable storage medium storing a program thereon; when executed by a processor, this program is used to implement the steps of the numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasmas described above.

[0022] The present invention has the following advantages:

[0023] As described above, this invention discloses a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas. This method can efficiently and rapidly simulate the propagation characteristics of electromagnetic waves in time-varying plasmas. It is a three-dimensional Newton-HIE-FDTD method based on the hybrid explicit-implicit finite-difference time-domain method (HIE-FDTD) and Newton's second law of motion, used for efficiently simulating the propagation of electromagnetic waves in time-varying plasmas. This invention's method has the advantages of the Newton-ADE-FDTD method in simulating time-varying plasmas. It accurately represents the time-varying electron density through the time derivative, thereby accurately capturing the rich dynamic characteristics of time-varying plasmas. It can not only characterize the dynamic behavior of electron motion under time-varying conditions but also effectively capture the dynamic characteristics of time-varying electron density, reflecting a more realistic dynamic change. The numerical calculation method for simulating electromagnetic wave propagation characteristics in time-varying plasma proposed in this invention also has the advantages of the HIE-FDTD method in three-dimensional dielectric layer modeling, namely, the elimination of the CFL condition in the direction of thinner structure, so that the time step is only constrained by the spatial dimensions in two directions, thereby improving cost-effectiveness. Compared with other simulation methods based on time-varying plasma, the method of this invention is more efficient in computation and is particularly suitable for the analysis and simulation of electromagnetic wave propagation characteristics in time-varying plasma. Attached Figure Description

[0024] Figure 1 This is a flowchart of a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasma in an embodiment of the present invention.

[0025] Figure 2When the time-varying electron density changes only slightly, the electric field components at the reflection observation point are calculated using the method of this invention and different FDTD methods. The time-domain waveform diagram.

[0026] Figure 3 When the time-varying electron density changes only slightly, the electric field components at the transmission observation point (i.e., the transmission observation point) are calculated using the method of this invention and different FDTD methods. The time-domain waveform diagram.

[0027] Figure 4 When the time-varying electron density varies greatly, the electric field components at the observation point of the reflected wave are calculated using the method of this invention and different FDTD methods. The time-domain waveform diagram.

[0028] Figure 5 When the time-varying electron density varies greatly, the electric field components at the transmission wave observation point are calculated using the method of this invention and different FDTD methods. The time-domain waveform diagram. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0030] Example 1

[0031] This invention proposes a numerical calculation method that can efficiently and rapidly simulate the propagation characteristics of electromagnetic waves in time-varying plasmas. The basic principle of this method is as follows: First, based on Newton's second law of motion and the equation of current density, Maxwell's equations and their auxiliary control equations satisfied by the electromagnetic field in time-varying plasmas (dispersive media) are derived; then, the time step of each electromagnetic field component is defined according to the traditional HIE-FDTD method, and the electric field components that need to be implicitly solved are obtained from this; finally, the implicit update equations of the electric field components are obtained by solving, thus completing the derivation of the Newton-HIE-FDTD method.

[0032] This invention proposes a Newton-HIE-FDTD method based on the Newton-ADE-FDTD method and combined with the HIE-FDTD method. This method retains the advantages of the original method while weakening the CFL stability condition, thereby further improving the simulation efficiency of the algorithm while maintaining high accuracy. It has high efficiency and effectiveness.

[0033] The method of this invention can accurately capture the dynamic characteristics of rapidly changing electrons in time-varying dispersive media and fully characterize their rich dynamic behavior. Because it incorporates the advantages of the HIE-FDTD method—namely, weakening the CFL stability condition and making the time step constrained only by the grid size in two directions—this method is more computationally efficient and suitable for simulating electromagnetic fields in time-varying plasmas compared to other simulation methods based on time-varying plasma structures.

[0034] Before introducing the specific steps of the method of the present invention, the theoretical derivation process of the method of the present invention will be explained first.

[0035] Before deriving the update equations for the electromagnetic field component coefficients, it is necessary to first know Maxwell's equations satisfied by the electromagnetic field in time-varying plasmas (dispersive media), as shown in the following equation:

[0036] (1)

[0037] in, Represents the gradient operator, Indicates magnetic field, Represents an electric field; The polarization current density, For time-varying electron density, Let be the collision frequency of the plasma. The dielectric constant in vacuum. Permeability, For the mass of electrons, It represents the amount of charge of an electron.

[0038] For the time-varying electron density in the third equation of formula (1), perform central difference discretization in the time domain and denote it as... ,Right now:

[0039] (2)

[0040] in, The number of iteration steps is electron density at that time The number of iteration steps is Electron density at that time.

[0041] To implement the Newton-HIE-FDTD method, electromagnetic field components are defined. , and current density components The current density is defined at half-time steps, while other components are defined at full-time steps. Therefore, after discretizing the third equation of formula (1) using the central difference, the updated equation for the current density is obtained as follows:

[0042] (3)

[0043] (4)

[0044] (5)

[0045] in, express In time ,space The value at; For time difference; , , Spatial label; , , They represent , , Spatial difference in direction; Including electric field components , , Magnetic field components , , Electric field auxiliary component Magnetic field auxiliary component Current density , , Electron density of time-varying plasma . , ,and .

[0046] Note that the current density update uses the electric field component that is unknown at the current time step, so the current density needs to be updated only after the electric field component update is completed.

[0047] Next, expanding from the first equation in formula (1), we get:

[0048] (6)

[0049] Expanding the above equation using the central difference within the SC-PML framework yields:

[0050] (7)

[0051] (8)

[0052] (9)

[0053] At this point, the current density component at the current time step appears in the equations for each electric field component, and the relationship between the two is known. (The electric field component...) Taking the solution as an example, substituting formula (3) into formula (7) yields:

[0054] (10)

[0055] Similarly, the update equations for other electric field components can be obtained:

[0056] (11)

[0057] (12)

[0058] However, in the electric field component and The update equation still contains unknowns at the current time step, therefore, it is initially determined that implicit updates are necessary. Here, we also use the electric field components... Taking the solution as an example, the auxiliary variable on the right side of the equation can be expanded into the following form:

[0059] (13)

[0060] (14)

[0061] (15)

[0062] The coefficients involved are:

[0063] (16)

[0064] in, Represents the relative permittivity. , and The SC-PML parameter is introduced to introduce the CFS factor.

[0065] Substituting formulas (13), (14), and (15) into formula (10), we can obtain the following result. Implicit update equation:

[0066] (17)

[0067] Similarly, we can obtain Implicit update equation:

[0068] (18)

[0069] Finally, by performing central difference discretization on the second equation in formula (1), the update equations for the magnetic field components can be obtained, thus completing the derivation of the update equations for each electromagnetic field component of the Newton-HIE-FDTD algorithm. The method proposed in this invention integrates the HIE-FDTD algorithm into the three-dimensional Newton-ADE-FDTD algorithm, thereby removing the constraint of the z-direction grid and making the z-direction grid no longer constrain the time step of the algorithm, thereby reducing the amount of computation and improving computational efficiency.

[0070] The above describes the theoretical derivation process of the method of this invention, mainly introducing the source of the derivation of the update equation. The following describes the engineering implementation process of the method of this invention, explaining steps 1 to 8 according to the execution order during actual simulation.

[0071] like Figure 1 As shown, the numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma includes the following steps:

[0072] Step 1. Input the model file.

[0073] In step 1 of this embodiment, the content of the input model file includes:

[0074] The computational region size is ,in x-axis Number of grids in the direction, y-axis Number of grids in the direction, Vertical coordinates The number of grids in the direction, with a spatial step size of .

[0075] Time step .

[0076] conductivity in vacuum magnetic permeability Dielectric constant .

[0077] SC-PML absorption boundary and related parameters , , ,in, The value is an integer, and the range of values ​​is [value missing]. , The range of values ​​is , The range of values ​​is .

[0078] Simulation calculation time .

[0079] Time-varying plasma parameters, including the electron density of the time-varying plasma. Collision frequency And the initial position of the time-varying plasma in the simulation space; the electron density of the time-varying plasma. The law of change follows:

[0080] .

[0081] in, Indicates the average electron density. . Indicates the rate of change of electron density. The range of values ​​is . The center frequency representing the time-varying electron density change is taken as a value. . This indicates the current simulation calculation time.

[0082] The observation points include incident observation points, reflection observation points, and transmission observation points.

[0083] The source parameters include two parameters that affect the Gaussian pulse waveform: the pulse occurrence time. and pulse width .

[0084] Step 2. Initialize and set parameters.

[0085] In this embodiment, step 2 specifically includes:

[0086] The initialization parameters include:

[0087] The electric field components of the entire computational region Magnetic field components and current density The electric field auxiliary components of the entire computational domain Magnetic field auxiliary component And the parameters of the SC-PML absorption boundary. and Initialize to 0; where ,and .

[0088] Parameters of the SC-PML absorbing boundary Initialize to 1.

[0089] The parameters to be set include:

[0090] Setting parameters for the SC-PML absorption boundary , , Specifically:

[0091] .

[0092] .

[0093] .

[0094] in, and This represents the conductivity distribution parameters of the SC-PML absorption boundary in the corresponding direction. according to To set, The range of values ​​is , , , The absorption effect at the boundary is best when the value is 4. , The wavelength of the source; Locations of PML layers and non-PML sections; The thickness of the PML absorption boundary; This represents the scale scaling parameter of the SC-PML absorbing boundary in the corresponding direction. It is an integer, and ; This represents the complex frequency shift parameter of the SC-PML absorbing boundary in the corresponding direction. .

[0095] Setting parameters for auxiliary variables in the SC-PML framework , , Specifically:

[0096] .

[0097] in, , , These are all parameters of the SC-PML absorption boundary with introduced CFL factor, and their values ​​affect the performance of the absorption boundary. This represents the relative permittivity.

[0098] By initializing the field quantities, auxiliary variables, and SC-PML related parameters, this step can establish a stable and consistent computational environment before the iteration begins, reducing the interference of numerical oscillation and boundary pseudo-reflections on the results, and demonstrating the improved stability and boundary absorption performance of the method of this invention.

[0099] Step 3. Update the entire computation region. Electric field components in the direction Magnetic field components And auxiliary components.

[0100] In this embodiment, step 3 specifically includes:

[0101] Update the calculation of the entire computational region Electric field components in the direction and electric field auxiliary components , and the entire computing region Magnetic field components in the direction and magnetic field auxiliary components , The specific update equation is as follows:

[0102] .

[0103] .

[0104] .

[0105] .

[0106] .

[0107] .

[0108] in, express In time ,space The value at; For time difference; , , Spatial label; , , They represent , , Spatial difference in direction; Including electric field components , , Magnetic field components , , Electric field auxiliary component Magnetic field auxiliary component Current density , , Electron density of time-varying plasma .

[0109] Represents time-varying electron density, , Indicates the number of iteration time steps. electron density at that time Indicates the number of iteration time steps. Electron density at that time; Represents unit charge. Indicates electron mass.

[0110] express In the x-direction The values ​​at each grid point express In the y-direction The values ​​at each grid point express In the z-direction The values ​​at each grid point; Including parameters of auxiliary variables under the SC-PML framework , , .

[0111] This step introduces time-varying electron density and its related physical parameters during the electric field update process, enabling the electric field evolution to synchronously reflect the time changes in plasma medium parameters. Compared to conventional methods that are only applicable to slowly varying media, the method of this invention can more accurately characterize the transient coupling effect between the electromagnetic field and the time-varying plasma, thereby improving the computational accuracy in rapidly changing scenarios.

[0112] Step 4. Update the entire computation region. , Electric field components in the direction and And auxiliary components.

[0113] In this embodiment, step 4 specifically includes:

[0114] Update the calculation of the entire computational region Electric field components in the direction and electric field auxiliary components , and the entire computing region Electric field components in the direction and electric field auxiliary components , The specific update equation is as follows:

[0115] .

[0116] .

[0117] .

[0118] .

[0119] .

[0120] .

[0121] In this step, the electric field components , Both methods employ implicit update, solving tridiagonal equations (using matrix operations) to simultaneously obtain the electric field components in a single iteration. , In space , and The values ​​at three locations are used to improve computational efficiency.

[0122] Step 5. Add a field source, i.e., add an excitation source to... Electric field components in the direction On the component coefficients.

[0123] In step 5 of this embodiment, add Electric field components in the direction The specific expression for the excitation source on the component coefficients is:

[0124] .

[0125] in, Represents the excitation source function, and For field source parameters, Affects the timing of pulse occurrence. It affects the pulse width.

[0126] Step 6. Update the entire computation region. , , Current density in the direction , .

[0127] In this embodiment, step 6 specifically includes:

[0128] Update the calculation of the entire computational region , , Current density in the direction The specific update equation is as follows:

[0129] .

[0130] .

[0131] .

[0132] In this step, the updated equation for the current density is obtained based on the constitutive relation satisfied by the time-varying plasma, and the time-varying electron density is cleverly embedded into the algorithm. This allows the algorithm to accurately capture the dynamic characteristics of the rapid changes in electrons in the time-varying dispersive medium and fully characterize its rich dynamic behavior.

[0133] Step 7. Update the entire computation region. , Magnetic field components in the direction and And auxiliary components.

[0134] In this embodiment, step 7 specifically includes:

[0135] Update the calculation of the entire computational region Magnetic field components in the direction and magnetic field auxiliary components , and the entire computing region Magnetic field components in the direction and magnetic field auxiliary components , The specific update equation is as follows:

[0136] .

[0137] .

[0138] .

[0139] .

[0140] .

[0141] .

[0142] By synchronously introducing auxiliary variables and combining them with SC-PML absorbing boundaries in the magnetic field update, this step can ensure that the magnetic field evolution and electric field update are kept in line, reduce non-physical reflections and numerical error accumulation at the boundary, thereby improving the overall stability and reliability of electromagnetic wave propagation simulation throughout the computational domain.

[0143] Step 8. Update the current iteration time step. The value is Then determine if the current iteration time step is equal to the preset total iteration time step; if so, output the electric field component. Magnetic field components and current density If the result is not found, proceed to step 3.

[0144] In addition, to verify the effectiveness of the method proposed in this invention, the following specific experiments are also provided:

[0145] Simulation calculations were performed on the propagation of electromagnetic waves in a time-varying homogeneous plasma dispersive medium.

[0146] The method and steps of this invention are implemented in such a way that the entire computational domain consists of 30×30×100 grids, and 10 layers of SC-PML absorbing boundaries are placed at the upper and lower boundaries in the z-direction to intercept and absorb electromagnetic waves; the grid size is... m; The time step of the Newton-HIE-FDTD method is set to... ps corresponds to the time stability condition satisfied by the HIE-FDTD algorithm in the limiting case. The speed of light in a vacuum is used. The simulation ran for a total of 10,000 time steps; for easier comparison and observation, 1,000 time steps were selected for observation and research. The time-varying plasma was placed in grids 51 to 70, with a thickness of 10 cm. A Gaussian pulse excitation source was applied in the x-direction, and its waveform was as follows:

[0147] .

[0148] in, ns, .

[0149] The electron density is expressed as a sinusoidal time-varying electron density change function, and its time-domain expression is:

[0150] .

[0151] Among them, average electron density for ; Let electron density be the rate of change over time. ; The center frequency of the time-varying electron density and the collision frequency. for Mrad / s.

[0152] To verify the accuracy and superiority of the proposed numerical calculation method, Newton-HIE-FDTD, compared to the traditional auxiliary differential equation finite-difference time-domain method (Traditional ADE-FDTD), Newton-ADE-FDTD, traditional bilinear transform finite-difference time-domain method (Traditional BT-FDTD), Newton-Bilinear Transform-Finite-Difference Time-Domain Method (Newton-BT-FDTD), and the traditional hybrid explicit-implicit finite-difference time-domain method (Traditional HIE-FDTD), two representative cases were considered. In the first case, the center frequency of the time-varying electron density change is... MHz corresponds to time-varying plasmas with relatively slow-changing electron density, while in the second case, MHz represents a plasma with a rapidly changing time-varying electron density.

[0153] Figure 2 and Figure 3 The reflected and transmitted waves at the 70 MHz time-varying electron density center frequency, calculated using different FDTD methods, are shown respectively. Represents the electric field components in the x-direction at different times. The values ​​at the observation points of reflection and transmission are shown. It can be seen that, under conditions of small changes in electron density, the reflected and transmitted waves calculated by the Newton-HIE-FDTD method proposed in this invention are in high agreement with various other FDTD methods. This high consistency among the results verifies the accuracy of the method.

[0154] Figure 4 and Figure 5 The results show the reflected and transmitted waves at the 720MHz time-varying electron density center frequency calculated using different FDTD methods. These results clearly demonstrate that the Newton-HIE-FDTD method proposed in this invention can capture rapid electron density changes more effectively than traditional FDTD methods, thereby improving calculation accuracy. This improvement is even more pronounced in cases of rapidly changing time-varying electron densities. Furthermore, it is observed that the results of the Newton-HIE-FDTD method proposed in this invention are in good agreement with the Newton-BT-FDTD and Newton-ADE-FDTD methods, indicating that the Newton-HIE-FDTD method proposed in this invention, like the other two methods, possesses high accuracy.

[0155] Example 2

[0156] This embodiment 2 describes a computer device that includes a memory and one or more processors.

[0157] The memory stores executable code, which, when executed by the processor, implements the steps of the numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasma in Embodiment 1 above.

[0158] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0159] Example 3

[0160] This embodiment 3 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a numerical calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasmas.

[0161] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0162] 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 calculation method for simulating the propagation characteristics of electromagnetic waves in time-varying plasma, characterized in that, Includes the following steps: Step 1. Input the model file; Step 2. Initialize and set parameters; Step 3. Update the entire computation region. Electric field components in the direction Magnetic field components and auxiliary components; Step 4. Update the entire computation region. , Electric field components in the direction and and auxiliary components; Step 5. Add incentive sources to Electric field components in the direction On the component coefficients; Step 6. Update the entire computation region. , , Current density in the direction , ; Step 7. Update the entire computation region. , Magnetic field components in the direction and and auxiliary components; Step 8. Update the current iteration time step. The value is ; Determine if the current iteration time step is equal to the preset total iteration time step; if yes, output the calculation results of electric field component, magnetic field component and current density; otherwise, go to step 3. Step 3 specifically involves: Update the calculation of the entire computational region Electric field components in the direction and electric field auxiliary components , and the entire computing region Magnetic field components in the direction and magnetic field auxiliary components , The specific update equation is as follows: ； ； ； ； ； ； in, express In time ,space The value at; For time difference; , , Spatial label; , , They represent , , Spatial difference in direction; Including electric field components , , Magnetic field components , , Electric field auxiliary component Magnetic field auxiliary component Current density , , Electron density of time-varying plasma ;in ,and ; Represents time-varying electron density, , Indicates the number of iteration time steps. electron density at that time Indicates the number of iteration time steps. Electron density at that time; Indicates the collision frequency; Indicates the time step; Represents unit charge. Indicates electron mass; It represents the dielectric constant in a vacuum; Indicates the spatial step size; Indicates the magnetic permeability in a vacuum; express In the x-direction The values ​​at each grid point express In the y-direction The values ​​at each grid point express In the z-direction The values ​​at each grid point; Including parameters of auxiliary variables under the SC-PML framework , , ; Step 4 specifically involves: Update the calculation of the entire computational region Electric field components in the direction and electric field auxiliary components , and the entire computing region Electric field components in the direction and electric field auxiliary components , The specific update equation is as follows: ； ； ； ； ； ； Step 6 specifically involves: Update the calculation of the entire computational region , , Current density in the direction The specific update equation is as follows: ； ； 。 2. The numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma according to claim 1, characterized in that, In step 1, the content of the input model file includes: The computational region size is ,in x-axis Number of grids in the direction, y-axis Number of grids in the direction, Vertical coordinates The number of grids in the direction, with a spatial step size of ; Time step ; conductivity in vacuum magnetic permeability Dielectric constant ; SC-PML absorption boundary and related parameters , , ; Simulation calculation time ; Time-varying plasma parameters, including the electron density of the time-varying plasma. Collision frequency And the initial position of the time-varying plasma in the simulation space; the electron density of the time-varying plasma. The law of change follows: ； in, Indicates the average electron density. Indicates the rate of change of electron density. The center frequency representing the time-varying electron density change, Indicates the current simulation calculation time; The observation points include incident observation points, reflection observation points, and transmission observation points; The source parameters include two parameters that affect the Gaussian pulse waveform: the pulse occurrence time. and pulse width .

3. The numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma according to claim 2, characterized in that, Step 2 specifically involves: The initialization parameters include: The electric field components of the entire computational region Magnetic field components and current density The electric field auxiliary components of the entire computational domain Magnetic field auxiliary component And the parameters of the SC-PML absorption boundary. and Initialize to 0; Parameters of the SC-PML absorbing boundary Initialize to 1; The parameters to be set include: Setting parameters for the SC-PML absorption boundary , , Specifically: ； ； ； in, and The conductivity distribution parameters represent the absorption boundary of SC-PML. The range of values ​​is , , , , The wavelength of the source; Locations of PML layers and non-PML sections; The thickness of the PML absorption boundary; This represents the scale-scaling parameter of the SC-PML absorbing boundary. It is an integer, and ; This represents the complex frequency shift parameter of the SC-PML absorption boundary. ; Setting parameters for auxiliary variables in the SC-PML framework , , Specifically: ； in, This represents the relative permittivity.

4. The numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma according to claim 3, characterized in that, In step 5, add Electric field components in the direction The specific expression for the excitation source on the component coefficients is: ； in, This represents the excitation source function.

5. The numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma according to claim 4, characterized in that, Step 7 specifically involves: Update the calculation of the entire computational region Magnetic field components in the direction and magnetic field auxiliary components , and the entire computing region Magnetic field components in the direction and magnetic field auxiliary components , The specific update equation is as follows: ； ； ； ； ； 。 6. 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 calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma as described in any one of claims 1 to 5.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the numerical calculation method for electromagnetic wave propagation characteristics in simulated time-varying plasma as described in any one of claims 1 to 5.

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