Method for calculating electromagnetic scattering field of moving plasma target based on dgtd

Abstract

The application belongs to the field of electromagnetic field calculation, and discloses a method for calculating electromagnetic scattering field of moving plasma target based on DGTD. The method firstly models the target to obtain a model file; then calculates the space and time components in the moving coordinate system by using Lorentz transformation formula, and introduces incident wave into the moving coordinate system; then iterates electromagnetic field in combination with the moving plasma model, calculates the near-field data under the moving coordinate system, and inversely transforms the near-field data by using Lorentz transformation to obtain the near-field data under the laboratory coordinate system, and extrapolates to obtain the laboratory coordinate system, Fourier transforms the time-domain incident electromagnetic field to obtain the frequency-domain value, and then solves to obtain the single-station radar scattering cross section (RCS) of the target under the laboratory coordinate system. The application can better fit complex models, is more flexible in the treatment of multi-scale problems, can effectively improve the numerical dispersion phenomenon, and can simulate moving targets with higher speed.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of electromagnetic field calculation, and particularly relates to a method for calculating electromagnetic scattering field of a moving plasma target based on DGTD. BACKGROUND

[0002] When a hypersonic vehicle is working, it rubs against the surrounding environment to create a high-temperature and high-pressure environment, thereby generating a thin layer of plasma on the surface of the vehicle, and the electromagnetic characteristics of the thin layer of plasma will seriously affect the communication, detection and identification functions of the vehicle.

[0003] At present, numerical methods for studying electromagnetic scattering characteristics of high-speed moving targets have developed rapidly at home and abroad. The relativistic numerical simulation methods for electromagnetic characteristics of high-speed moving targets mainly include a relative boundary condition (RBC) method based on relativity and a Loretz-FDTD method. However, the above methods are limited by the regularity of the grid, and when solving multi-scale problems and high-precision simulation, the requirements for computing time and computing resources are very high; and the FDTD method is second-order accuracy, and for high-precision requirements, the computing time and computing resources are often sacrificed to obtain high precision.

[0004] Therefore, it is necessary to provide a method for calculating electromagnetic scattering field of a moving plasma target based on DGTD to solve the above technical problems in the prior art. SUMMARY

[0005] The application aims to provide a method for calculating electromagnetic scattering field of a moving plasma target based on DGTD, which is based on a Loretz-DGTD algorithm formed by combining a time-domain discontinuous Galerkin (DGTD) with a Lorentz transformation and a shift operator, so as to improve the efficiency and resource utilization of electromagnetic scattering calculation of moving plasma and improve the numerical dispersion phenomenon.

[0006] To achieve the above-mentioned purpose, the application provides the following technical scheme:

[0007] The method for calculating electromagnetic scattering field of a moving plasma target based on DGTD comprises the following steps:

[0008] Step 1, modeling the plasma target in a laboratory coordinate system to obtain a model file; the model file includes a spatial grid component of the target model, a region boundary of the target model, a maximum cell size in different regions and a label of a region to which a cell belongs, and also contains a total number of cells and coordinates of each point for reading by a main program;

[0009] Step 2, obtaining spatial and time components in a moving coordinate system by using a Lorentz transformation formula in combination with the target spatial grid component in the model file parameters and a time component in the running parameters;

[0010] Step 3, using modulated Gaussian pulses as incident waves, and introducing incident waves into the moving coordinate system;

[0011] Step 4, first, based on the weak solution form of Maxwell's curl equation and numerical flux, combined with high-order basis functions and time integration strategy, the electromagnetic field in the moving coordinate system is solved; then combined with the moving plasma model, the electromagnetic field is iterated, and the near-field data in the moving coordinate system is calculated;

[0012] Step 5, the near-field data in the moving coordinate system is subjected to inverse Lorentz transformation to obtain the near-field data in the laboratory coordinate system;

[0013] Step 6, the near-field data obtained in step 5 is extrapolated to obtain the laboratory coordinate system, and the time-domain incident electromagnetic field is subjected to Fourier transform to obtain its frequency domain value; then the single-station radar scattering cross section RCS of the target in the laboratory coordinate system is solved;

[0014] Step 7, the Sears-Hacck model is introduced into the main program and calculated, and the data results are processed to obtain the RCS curve of the target at different speeds.

[0015] Compared with the prior art, the present application has the following beneficial effects:

[0016] As described above, the electromagnetic scattering field calculation method of the moving plasma target based on DGTD provided by the present application solves the electromagnetic scattering characteristics of the high-speed moving plasma target by combining Lorentz transformation and time-domain discontinuous Galerkin method, not only makes up for the shortcomings of FDTD in modeling complex models due to regular grid, but also greatly improves the efficiency and resource utilization of the electromagnetic scattering calculation of the moving plasma, and can better fit complex models and handle multi-scale problems more flexibly. At the same time, the numerical dispersion of the method is low, which can effectively improve the numerical dispersion phenomenon and simulate higher speed moving targets. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows.

[0018] Figure 1 The flow chart of the electromagnetic scattering field calculation method of the moving plasma target based on DGTD in the embodiments of the present application;

[0019] Figure 2 The schematic diagram of the two coordinate systems subjected to Lorentz transformation provided in the embodiments of the present application;

[0020] Figure 3 The center profile diagram of the target calculated in the embodiments of the present application;

[0021] Figure 4 This is a radar cross section (RCS) diagram of the target in an embodiment of the present invention;

[0022] Figure 5 for Figure 4 A magnified view of a section at point A in the middle;

[0023] Figure 6 for Figure 4 A magnified view of a section at point B in the middle;

[0024] Figure 7 The image shows the radar cross section (RCS) of the target calculated by the method of this invention and the FDTD method. Detailed Implementation

[0025] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0026] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Example 1

[0028] like Figure 1 As shown in the figure, this embodiment describes a method for calculating the electromagnetic scattering field of a moving plasma target based on DGTD. This method is based on the Lorentz-DGTD algorithm, which combines discontinuous Galerkin time-domain (DGTD) with Lorentz transformation and shift operator. This method greatly improves the efficiency and resource utilization of electromagnetic scattering calculations for moving plasmas and effectively mitigates numerical dispersion phenomena. The method includes the following steps:

[0029] Step 1: Model the plasma target in the laboratory coordinate system K and obtain the .msh file of the model.

[0030] The plasma target in the stationary coordinate system (i.e., the laboratory coordinate system) was modeled in Gmesh using the Python language, resulting in a modeling program. After running the modeling program, a model file .msh was output.

[0031] The model file (.msh) includes the spatial mesh components of the target model, the region boundaries of the target model, the maximum element size in different regions, and the label of the region to which the element belongs. It also contains the total number of elements and the coordinates of each point for the main program to read.

[0032] Wherein, the spatial grid components in x, y, z directions are dx, dy, dz.

[0033] Step 2, combine the target spatial grid components in the model file parameters and the time components in the running parameters, and use the Lorentz transformation formula to obtain the spatial and time components in the moving coordinate system K'.

[0034] As shown in Figure 2 , the target and the moving coordinate system K' have the same speed size v and the moving angle θ v and

[0035] In this embodiment, v = 0.1c, c is the speed of light in vacuum, and the moving angle is Therefore, according to the relativity covariance, the electromagnetic scattering problem of the moving plasma in the laboratory coordinate system K can be converted to the moving coordinate system K' for solving.

[0036] The transformation relationship of the spatial and time components between the laboratory coordinate system K and the moving coordinate system K' is obtained by the spatial steps (spatial grid components) dx, dy, dz in x, y, z directions in the laboratory coordinate system K and the time component Δt set in the main program, and is as follows:

[0037]

[0038] Wherein, dx, dy, dz represent the spatial components in x, y, z directions in the laboratory coordinate system K; dx', dy', dz' represent the spatial components in x, y, z directions in the moving coordinate system K'; dt represents the time component in the laboratory coordinate system K, dt' represents the time component in the moving coordinate system K'; v x , v y , v z are the components of the moving speed v of the target in x, y, z directions, respectively; β = v / c, c is the speed of light in vacuum; represents the unit vector of the scattering direction, represents the unit vector of the speed.

[0039] represents the unit vector in x, y, z directions, respectively, as shown in formula (5).

[0040]

[0041] Wherein, θ v represents the angle between the moving speed in the laboratory coordinate system K and the positive half of the z axis; represents the angle between the projection of the moving direction in the laboratory coordinate system K to the xoy plane and the positive half of the x axis.

[0042] Step 3: Use a modulated Gaussian pulse as the incident wave to introduce the incident wave into the moving coordinate system K′.

[0043] Since there is relative motion between the laboratory coordinate system K and the moving coordinate system K′, it is necessary to convert the incident electromagnetic wave to the moving coordinate system K′ for calculation based on the principles of relativity.

[0044] The formula for the principle of phase invariance of electromagnetic waves is:

[0045]

[0046] In the formula, ω i It is the angular frequency of the electromagnetic wave in the stationary coordinate system, k. i0 Let θ be the wave vector. i and The incident wave direction angle is denoted as .

[0047] Based on the principle of phase invariance of electromagnetic waves, the transformation relationship of electromagnetic wave frequency, amplitude and incident plane wave vector in the moving coordinate system K′ is obtained (Formula (6)).

[0048]

[0049] Where, ω i E0, k i These are the angular frequency, amplitude, and wave vector of an electromagnetic wave in a stationary coordinate system; a i Let a be the unit vector of the incident wave vector. v φ is the unit vector of the target velocity; φ is the angle between the polarization direction of the incident electromagnetic wave and the velocity. Let β be the Lorentz factor, where β = |v| / c.

[0050] In this embodiment, a modulated Gaussian pulse is used as the incident wave, and the expression of the incident wave in the stationary coordinate system is shown in formula (7).

[0051]

[0052] Among them, E i (t) represents the incident wave in the stationary coordinate system; t0 is a constant representing the waveform delay time; τ is a constant that determines the width of the Gaussian pulse. After introducing this Gaussian pulse into the moving coordinate system K′, the expression is transformed into formula (8).

[0053]

[0054] in, |E'0| is the amplitude, refer to the second formula (6).

[0055] Step 4. Iteration of electromagnetic field based on moving plasma model to calculate the near-field data in moving coordinate system K'.

[0056] Firstly, the electromagnetic field in moving coordinate system is solved based on the weak form of Maxwell curl equation and numerical flux, combined with high-order basis function and time integration strategy, as follows.

[0057] Step 4.1.1, Maxwell curl equation is:

[0058]

[0059] Wherein, ε represents the dielectric coefficient of medium, μ represents the magnetic permeability, H represents the magnetic field intensity, E represents the electric field intensity, σ e represents the electrical conductivity, σ h represents the magnetic permeability loss coefficient.

[0060] This embodiment is based on the weak form of Maxwell curl equation and numerical flux, combined with high-order basis function and time integration strategy to solve the electromagnetic field. When the result (the solution of Maxwell curl equation, i.e. the solution of about equal to) is a non-strict solution of electromagnetic field, it is brought into the left end of Maxwell curl equation, and the result will not be zero (the solution of about equal to is brought into the original equation, and the result of the original equation is not 0, there will be floating, defined as the residual r and r1, recorded as:

[0061]

[0062] The weighted residual R and R1 are obtained by multiplying the weight function N points with r and r1, and integrating along the region τ:

[0063]

[0064] Wherein, the weight function N refers to the unit basis function; m=1, 2, 3, …, M, M is the total number of calculation regions; q=1, 2, …, Q, Q is the total number of unit basis functions.

[0065] Step 4.1.2, let R and R1 be zero, combined with vector equation The weak form of Maxwell curl equation is obtained:

[0066]

[0067] Wherein, τ m represents the space wrapped by the unit, represents the vector basis function of the unit, m represents the mth unit, q' represents the label of the basis function (the value is 1 to 6, i.e. six edges of a tetrahedron), n represents the outer normal vector of the tetrahedron face, and the area integral Flux of the product of the tangential component of the electric field, the tangential component of the magnetic field and the tangential component of the basis function along the surface of the element.

[0068] In this embodiment, the area integral in the weak form of Maxwell's curl equation is extended to the concept of numerical flux, so the weak form of Maxwell's equation with numerical flux can be derived as:

[0069]

[0070] where E m+ and H m+ denote the electromagnetic field of the adjacent element, E m and H m denote the electromagnetic field of the current element; M s and J s denote the surface electromagnetic current at the interface of the adjacent element. and represent the jump and dissipation factors respectively under different numerical flux conditions.

[0071] Step 4.1.4, the time-domain step formula of Maxwell's equation is further calculated from the weak form of Maxwell's equation with numerical flux:

[0072]

[0073] where α h , β h , α e , β e are coefficients; M, S, F κe , F κh , G vh , G ve are coefficient matrices; M sκ,n , M sν,n+1 / 2 , J sκ,n+1 / 2 , J sv,n are the surface electromagnetic currents of the adjacent element.

[0074] Step 4.1.5, the constitutive parameters of plasma and other dispersive media vary with frequency, which can be expressed as:

[0075] D = ε(ω)E (9)

[0076] B = μH

[0077] In the formula, D is the electric displacement vector, ε(ω) is the dielectric constant of the dispersive medium, ω is the angular frequency, B is the magnetic induction intensity, and μ is the magnetic permeability of the medium.

[0078] Considering plasma and other dispersive media, Maxwell's equation containing the constitutive relation can be written as:

[0079]

[0080] where μ represents the magnetic permeability, σ h represents the magnetic permeability loss coefficient, σ e represents the electrical conductivity.

[0081] Because the target and the moving coordinate system remain relatively static, the time-domain stepping formula of the magnetic field H' in the moving coordinate system is derived from formula (10) as follows:

[0082]

[0083] where α h , β h are coefficients, M, S, F κe and G vh are coefficient matrices, M sκ,n , J sv,n are electromagnetic currents of adjacent unit surfaces, and m+ represents adjacent units.

[0084] The time-domain stepping formula of the electric displacement vector D' in the moving coordinate system is derived from the second formula of formula (10) as follows:

[0085]

[0086] where M, S, F κe and G ve are coefficient matrices, J sκ,n+1 / 2 is an electromagnetic current of an adjacent unit surface, m+ represents adjacent units, and Δt is dt.

[0087] The electromagnetic modeling of the moving plasma in this embodiment combines the principle of relativity to construct a plasma model that is relatively static in the moving coordinate system. Taking the Drude model as an example, the relative dielectric coefficient in the moving coordinate system can be expressed as:

[0088]

[0089] where ε(ω') is the relative dielectric coefficient in the moving coordinate system, ω' is the angular frequency in the moving coordinate system, ε0 is the vacuum dielectric constant, ε ∞ is a constant representing the relative dielectric constant when the frequency is infinite, v c is the plasma collision frequency, and ω p is the plasma frequency.

[0090] This embodiment is based on the shift operator method to solve the electromagnetic scattering problem of the target, and therefore formula (13) can be expressed in the form of a rational fraction:

[0091]

[0092] where p'n , q' n represent the coefficients of the numerator and denominator, respectively.

[0093] Finally, according to the conversion operator between the time domain and the frequency domain The time domain iterative formula of the electric field E' in the moving coordinate system can be obtained as follows:

[0094]

[0095] In the formula, ε0 is the vacuum permittivity; a0, a1, b0, b1, and b2 represent the coefficients of the formula transformation, which change with the parameter settings; m represents a unit, m' represents a unit in the moving coordinate system; and n represents a time step.

[0096] Then, the electromagnetic field is iterated in combination with the moving plasma model to calculate the near-field data in the moving coordinate system, and the iteration steps are as follows:

[0097] Step 4.2.1, preprocessing, that is, calculating the unit coefficient matrix.

[0098] Step 4.2.2, setting the initial field value of the electromagnetic field to zero.

[0099] Step 4.2.3, when n = 0 (time 0), the magnetic field H' is calculated using formula (11), and the electric displacement vector D' is calculated using formula (12).

[0100] Step 4.2.4, the electric field E' is calculated using formula (15).

[0101] Step 4.2.5, when n → n + 1, repeat steps 4.2.3 and 4.2.4 until the iteration is completed.

[0102] Step 5, performing inverse Lorentz transformation on the near-field data in the moving coordinate system K' to obtain the near-field data in the laboratory coordinate system K.

[0103] The formula for performing inverse Lorentz transformation on the electromagnetic field in the moving coordinate system K' to transform the electromagnetic field value into the laboratory coordinate system K is as follows:

[0104]

[0105] In the formula, E' || , E' ⊥ , H' || , H' ⊥ are the horizontal and vertical components of the near-field field value in the moving coordinate system relative to the target moving direction, and c is the speed of light in a vacuum.

[0106] Step 6, extrapolating the near-field data obtained in step 5 to obtain the near-field data in the stationary coordinate system E s(f) the time domain incident electromagnetic field E i (t) performing Fourier transform to obtain its frequency domain value E i (f); and then solving the equation (17) to obtain the monostatic radar cross section (RCS) of the target in the laboratory coordinate system K.

[0107]

[0108] Step 7, importing the Sears-Hacck model shown in the program (main program) and calculating, and obtaining the RCS curve of the target at different speeds by processing the data results, as shown in Figure 3 . Figure 4 .

[0109] As can be seen from Figure 4 , due to the different speeds, the RCS of the moving target is shifted in frequency. When the speed is 0.1c and the positive direction along the x-axis, the frequency is shifted by 0.1Ghz and 0.24Ghz to the low frequency at the frequencies of 1.15Ghz and 2.6Ghz respectively; when the speed is 0.1c and the negative direction along the x-axis, the frequency is shifted by 0.13Ghz and 0.28Ghz to the high frequency at the frequencies of 1.15Ghz and 2.6Ghz respectively. Figure 4 The results are consistent with the Doppler effect. Therefore, by combining the Lorentz transformation and the DGTD method, the electromagnetic characteristics of the moving plasma target are solved, and the electromagnetic scattering characteristics of the high-speed moving plasma can be effectively calculated.

[0110] As shown in Figure 7 , when the 1m ideal metal ball is used in the method of the embodiment, the discrete size is 0.1m, and the discrete size is 0.05m in the FDTD method; the comparison of the RCS shows that the fitting of the method of the embodiment and the Mie theory solution is better. Therefore, the embodiment greatly improves the efficiency and resource utilization of the calculation of the electromagnetic scattering of the moving plasma, and can better fit the complex model, and the processing of the multi-scale problem is more flexible. At the same time, the method of the embodiment can effectively improve the numerical dispersion phenomenon. When the target moving speed is 0.3c, the RCS of the target can still be calculated by the method of the embodiment, and the electromagnetic field value is ensured not to diverge.

[0111] The method of the embodiment includes but is not limited to the time-varying moving plasma ball, plasma cylinder, cone, etc., for example, it can also include complex shape dispersive medium targets, such as the combination of cone and hemisphere, and missile models with non-uniform plume, etc.

[0112] The embodiments of the present application are only used to illustrate the technical solutions of the present application and not to limit, for those skilled in the art, it can be understood that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the present application, the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for calculating electromagnetic scattering field of a moving plasmonic target based on DGTD, characterized in that, The method comprises the following steps: Step 1, modeling the plasma target in the laboratory coordinate system to obtain a model file; the model file comprises a spatial grid component of the target model, a regional boundary of the target model, a maximum unit size in different regions and a label of the region to which the unit belongs, and further comprises a total number of units and coordinates of each point for reading by a main program; Step 2, combining the target spatial grid component in the model file parameter and the time component in the running parameter, and using the Lorentz transformation formula to obtain the spatial and time components in the moving coordinate system; Step 3, using a modulated Gaussian pulse as an incident wave, and introducing the incident wave into the moving coordinate system; Step 4, firstly, solving the electromagnetic field in the moving coordinate system based on a weak solution form and numerical flux of Maxwell's curl equation, and combining a high-order basis function and a time integration strategy; and then, combining a moving plasma model to perform iteration on the electromagnetic field and calculating near-field data in the moving coordinate system; Step 5, performing inverse Lorentz transformation on the near-field data in the moving coordinate system to obtain near-field data in the laboratory coordinate system; Step 6, extrapolating the near-field data obtained in step 5 to obtain the laboratory coordinate system, and performing Fourier transformation on the time-domain incident electromagnetic field to obtain a frequency-domain value thereof; Then, the target single-station radar scattering cross section RCS in the laboratory coordinate system is solved; Step 7, importing the Sears-Hacck model into the main program and performing calculation, and processing the obtained data to obtain an RCS curve of the target at different speeds.

2. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, In step 1, a modeling program is obtained by modeling the plasma target in the laboratory coordinate system in Gmesh through Python language, and the modeling program outputs a model file.msh after running.

3. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, In step 2, the transformation relationship between the spatial and time components of the laboratory coordinate system K and the moving coordinate system K' is obtained from the spatial grid components dx, dy and dz in the x, y and z directions of the laboratory coordinate system K and the time component Δt set in the main program. Since the target has the same velocity magnitude v and the motion angle θ as the moving coordinate system K' v ′and Therefore, v = 0.1c is defined, where c is the speed of light in a vacuum; In step 3, the transformation relationship of the frequency, amplitude and incident plane wave vector of the electromagnetic wave in the moving coordinate system K' is obtained according to the phase invariance principle of the electromagnetic wave. wherein dx, dy, dz represent the spatial components in the x, y, z directions in the laboratory coordinate system K; dx', dy', dz' represent the spatial components in the x, y, z directions in the moving coordinate system K'; dt represents the time component in the laboratory coordinate system K, dt' represents the time component in the moving coordinate system K'; v x , v y , v z are the components of the target's moving speed v in the x, y, z directions, respectively; β = v / c, c is the speed of light in vacuum; represents the unit vector of the scattering direction, represents the unit vector of the velocity; respectively, denote the unit vectors in the x, y, z directions, respectively, and are given by: where θ v denotes the angle between the velocity of the motion and the positive half-axis of the z-axis in the laboratory coordinate system K; denotes the angle between the projection of the direction of the motion onto the xoy plane and the positive half-axis of the x-axis in the laboratory coordinate system K.

4. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, Then, a modulated Gaussian pulse is used as an incident wave, and the expression of the incident wave in the laboratory coordinate system is: In step 4, the specific steps for solving the electromagnetic field in the moving coordinate system are as follows: where ω i , E0, k i are the angular frequency, amplitude and wave vector of the electromagnetic wave in the laboratory frame, respectively; a i is the unit vector of the incident wave vector, a v is the unit vector of the target velocity; φ is the angle between the polarization direction of the incident electromagnetic wave and the velocity; is the Lorentz factor, where β = |v| / c; B is the magnetic induction strength; Step 4.1.1, based on the weak solution form and numerical flux of Maxwell's curl equation, and combining a high-order basis function and a time integration strategy to solve the electromagnetic field, when the result is a non-strict solution of the electromagnetic field, the result is not zero, which is defined as the residual r and r1; then, the weighted residual R and R1 are obtained by multiplying the weight function N points with r and r1 and integrating along the region τ; where E i (t) represents the incident wave in the laboratory coordinate system; t0is a constant, representing the waveform delay time; τ is a constant, which determines the Gaussian pulse width; after introducing this Gaussian pulse into the moving coordinate system K', the expression is: wherein, |E'0| is the amplitude.

5. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, Step 4.1.2, setting R and R1 to zero, and combining the vector equation ▽·(A×B)=B·(▽×A)-A·(▽×B) to obtain the weak solution form of Maxwell's curl equation; Step 4.1.3, the weak solution form of Maxwell's curl equation is obtained, and the weak solution form of Maxwell's equation containing numerical flux is obtained; ​ ​ Step 4.1.4, the time-domain step formula of Maxwell equation is calculated from the weak solution form of Maxwell equation containing numerical flux; Step 4.1.5, the constitutive parameters of plasma vary with frequency, which is expressed as: In the formula, D is the electric displacement vector, ε(ω) is the dielectric constant of the dispersive medium, ω is the angular frequency, B is the magnetic induction intensity, and μ is the magnetic permeability of the medium; The Maxwell equation considering the constitutive relation of plasma is: where μ represents magnetic permeability, σ h represents the magnetic permeability loss coefficient, σ e represents electrical conductivity; Since the target and the moving coordinate system remain relatively stationary, the time-domain step formula of the magnetic field H' in the moving coordinate system is: where α h , β h are coefficients, M, S, F κe , G vh are coefficient matrices, M sκ,n , J sv,n are the electromagnetic currents of the adjacent cells, and m+denotes the adjacent cell. The time-domain step formula of the electric displacement vector D' in the moving coordinate system is: where M, S, F κe and G ve are coefficient matrices, J sκ,n+1 / 2 is the electromagnetic flow of the adjacent unit surface, m+ represents the adjacent unit, and Δt is dt; The electromagnetic modeling of moving plasma combines the principle of relativity to construct a plasma model that is relatively stationary in the moving coordinate system. The relative dielectric coefficient of the plasma in the moving coordinate system can be expressed as: where ε(ω') is the relative dielectric constant of the moving coordinate system; ω' is the angular frequency of the moving coordinate system; ε0 is the vacuum dielectric constant; ε ∞ is a constant, representing the relative dielectric constant at infinite frequency; v c is the plasma collision frequency; ω p is the plasma frequency; Based on the shift operator method to solve the electromagnetic scattering problem of the target, the relative dielectric coefficient is expressed in the form of a rational fraction: In the formula, p' n ,q' n These represent the coefficients of the numerator and denominator, respectively. Finally, according to the conversion operator between the time domain and the frequency domain, the time-domain iterative formula of the electric field E' in the moving coordinate system is obtained as: In the formula, ε0 is the vacuum dielectric constant; a0, a1, b0, b1 and b2 represent the coefficients of the formula transformation, which change with the parameter settings; m represents the unit, m' represents the unit in the moving coordinate system; n represents the time step.

6. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 5, wherein, In the step 4, the specific steps of iterating the electromagnetic field and calculating the near-field data in the moving coordinate system are as follows: Step 4.2.1, calculate the unit coefficient matrix; Step 4.2.2, set the initial field value of the electromagnetic field to zero; Step 4.2.3, when n=0, calculate the magnetic field H' and the electric displacement vector D'; where n=0 represents the time 0; Step 4.2.4, calculate the electric field E'; Step 4.2.5, when n→n+1, repeat steps 4.2.3 and 4.2.4 until the iteration is completed.

7. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, In the step 5, the electromagnetic field in the moving coordinate system K' is subjected to inverse Lorentz transformation to transform the electromagnetic field value into the laboratory coordinate system K: wherein E | | ⊥ | | ⊥ are the horizontal and vertical components of the near-field field value with respect to the target motion direction in the moving coordinate system, and c is the speed of light in vacuum.​​​​​ 8. The DGTD-based method of computing the electromagnetic scattering fields of a moving plasmonic target of claim 1, wherein, In the step 6, the formula for calculating the monostatic radar scattering cross section RCS of the target in the laboratory coordinate system is obtained as: where E s (f) is the laboratory coordinate system, E i (f) is the time domain incident electromagnetic field E i (t) is the frequency domain value obtained by Fourier transform.

Images