A simulation method based on time-varying plasma sheath identification technology

Abstract

The present invention discloses a simulation method based on time-varying plasma sheath identification technology, including: establishing a spatial electromagnetic field simulation model and a flow field simulation model, and using a mixture of tetrahedrons and hexahedrons to mesh the two models respectively, to obtain the structural information of the two models, including the unit information and node information of the tetrahedrons and hexahedrons; mapping the node information of the flow field model area corresponding to the aircraft to the corresponding position of the electromagnetic field model area, and obtaining the plasma parameters corresponding to each unit of the electromagnetic field model; using the time domain discontinuous Galerkin method to solve the scattering problem, and obtain the echo signal under the influence of plasma; constructing a compensation factor by measuring the plasma density, and compensating the echo signal under the influence of plasma; and determining the target position information through the simulation results of the above steps. The simulation results of the present invention indicate that the coherent accumulation result has a peak at the position where the target is located, and the coherent performance has been significantly improved.

Description

Technical Field

[0001] The invention belongs to the field of analysis of plasma sheath and target recognition problems, in particular to a simulation method based on time-varying plasma sheath recognition technology. Background Art

[0002] According to existing literature, there are few studies on the recognition of targets covered by plasma at home and abroad. Therefore, the research on ISAR imaging and target recognition of targets covered by plasma sheath is carried out under the background of national defense construction and the demand for aerospace information security. By obtaining the influence of plasma on the electric field of the target far zone and comparing it with ISAR imaging, the influence of plasma sheath on ISAR imaging can be obtained.

[0003] At present, there are few articles published abroad on the recognition of sheathed plasma targets, and domestic research is also in its infancy. The impact of plasma on imaging has not been studied in depth. So far, there is no clear definition and method for the recognition of sheathed plasma targets. In this context, it is of great significance to study the recognition technology of hypersonic targets sheathed with plasma sheaths. Summary of the invention

[0004] The purpose of the present invention is to provide a simulation method based on time-varying plasma sheath identification technology to realize the identification of sheathed plasma targets, the coherence performance is significantly improved, and the information of the target location can be obtained.

[0005] The technical solution to achieve the purpose of the present invention is: a simulation method based on time-varying plasma sheath identification technology, comprising the following steps:

[0006] Establish a spatial electromagnetic field simulation model and a flow field simulation model, and use a mixture of tetrahedrons and hexahedrons to discretize the two models, respectively, to obtain the structural information of the two models, including the unit information of tetrahedrons and hexahedrons and the node information;

[0007] Map the node information of the flow field model area corresponding to the aircraft to the corresponding position of the electromagnetic field model area, and find out the plasma parameters corresponding to each unit of the electromagnetic field model;

[0008] The time-domain discontinuous Galerkin method is used to solve the scattering problem and obtain the echo signal under the influence of plasma;

[0009] By measuring the plasma density, a compensation factor is constructed to compensate for the echo signal under the influence of plasma;

[0010] The target position information is determined through the simulation results of the above steps.

[0011] Furthermore, the node information of the flow field model includes temperature, electron density, pressure and mass fraction of each gas on the original flow field tetrahedral grid.

[0012] Furthermore, the mesh discretization uses ANSYS to mesh the model, distinguishes the plasma area from other areas by assigning different material numbers, and finds the corresponding aircraft mesh according to the material number.

[0013] Furthermore, the plasma parameters corresponding to each unit are:

[0014]

[0015] ν c (i,j,k)=5.2e18·n e (i,j,k)·kk·T(i,j,k) (1.2)

[0016]

[0017] Where i, j, k are the coordinates of the flow field point in the X, Y, and Z directions, T represents the temperature at the flow field point, kk is the Boltzmann constant, ω p and ν c are the plasma frequency and collision frequency, n e is the electron density, ε r is the relative dielectric parameter of plasma.

[0018] Furthermore, the method of solving the scattering problem by using the time domain discontinuous Galerkin method to obtain the echo signal under the influence of plasma specifically includes:

[0019] Step 3-1, constructing a plasma scattering problem equation system, performing Galerkin method test, unknown quantity expansion and vector identity transformation on the equation system to obtain a new equation system;

[0020] Step 3-2, substitute the upwind flux into the new set of equations to obtain the near-field value;

[0021] Step 3-3, after calculating the near-field value, set an extrapolation surface in the scattered field, calculate the surface current and surface magnetic current on the extrapolation surface, and then calculate the current moment and magnetic current moment from the surface current and surface magnetic current to obtain the electric field value of the time-domain far field, and perform Fourier transform on the time-domain far-field value to obtain the object RCS;

[0022] Step 3-4, obtain the radar echo under the influence of the plasma sheath.

[0023] Furthermore, the step 3-1 specifically includes:

[0024] The equations for the plasma scattering problem are constructed as follows:

[0025]

[0026]

[0027]

[0028] Where E is the electric field strength in V / m, H is the magnetic field strength in A / m, ε is the dielectric constant in F / m, μ is the magnetic permeability in Ω / m, ε0 is the vacuum dielectric constant, ε ∞ is the dielectric constant at infinity, which is 1, ε Drude is the plasma dielectric constant, is the Nabla operator;

[0029] Substitute the dielectric constant into the first equation (1.4):

[0030]

[0031]

[0032]

[0033] make: The system of equations is written as:

[0034]

[0035] The Galerkin test is performed on formula (1.8), and the test basis function is N i , using the vector identity for formula (1.8) and Gauss's theorem The new set of equations is:

[0036]

[0037]

[0038]

[0039] Among them, S is the outer surface of the solution area, e n is the normal component of the outer surface, Ω is the solution area, and Δt is the time step.

[0040] Furthermore, the near-field value is:

[0041]

[0042] Among them, the parameters parameter

[0043] The matrix element expressions are as follows:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In the formula, Y = 1 / Z represents the intrinsic admittance, the superscript "+" represents the information of the adjacent body, and no superscript represents the information of the body. represents intrinsic impedance;

[0052] Formula (1.12) is written in DGTD semi-discrete form as:

[0053]

[0054] In the formula, represent the test basis function and the expanded basis function of the electric field respectively; They represent the test basis function and expanded basis function of the magnetic field respectively.

[0055] Furthermore, the step 3-3 specifically includes:

[0056] According to the equivalent principle, the surface current and surface magnetic current on the extrapolated surface are:

[0057]

[0058] Where, E(r,t) is the near field value;

[0059] The current moment and magnetic current moment calculated from the surface current and surface magnetic current are:

[0060]

[0061] In the formula, r represents the position vector of the field point, r′ represents the position vector of the equivalent source, and α represents the angle between the two vectors; r′cosα is:

[0062]

[0063] Time domain far-field electric field component E θ and for:

[0064]

[0065]

[0066] The object RCS is:

[0067]

[0068] Where F{·} represents the Fourier transform, and It represents the two components of the far-field electric field value, E inc (r, t) represents the incident electric field.

[0069] Furthermore, the radar echo under the influence of the plasma sheath in step 3-4 is:

[0070]

[0071] Where T1 and T2 are the transmission coefficients of the radar signal in the transmission and reception periods, respectively. T1(Ne(t-τ), fr(t)) represents the effect of the time-varying plasma sheath in the transmission period, which is a function of Ne(t) and fr(t). T2(Ne(t-τ), fr(t)) is the effect of the time-varying plasma sheath in the reception period. τ is the electron density time interval of the transmission coefficients T1 and T2. r is the instantaneous frequency of the transmitting cycle and the receiving cycle.

[0072] Furthermore, the compensated radar echo is:

[0073]

[0074] in is the phase of the transmission coefficient T1, is the phase of the transmission coefficient T2.

[0075] Compared with the prior art, the present invention has the following significant advantages: 1) a corresponding compensation factor constructed by the electron density of the plasma sheath is introduced, and the echo is well compensated by compensating the phase, the coherence performance is significantly improved, and the information of the target location can be obtained; 2) the target recognition result of the hypersonic aircraft is more accurate; 3) the gap in the current imaging technology can be filled by combining the plasma-coated target with the inverse synthetic aperture radar imaging technology; 4) the monitoring and identification of stealth targets in the air is also an urgent and very meaningful task, and the research on plasma target recognition technology is also bound to be an important part of the research on anti-stealth technology, which has important significance and value; 5) in turn, it can also provide relevant experience for realizing the plasma stealth of target objects in engineering.

[0076] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Flowchart for obtaining the target far-zone electric field.

[0078] Figure 2 This is a diagram showing the effect of the plasma sheath on the signal.

[0079] Figure 3 This is the time-varying plasma sheath electron density distribution diagram.

[0080] Figure 4 Schematic diagram of the coherence results under the influence of the plasma sheath.

[0081] Figure 5 This is the coherent integration result after compensation.

[0082] Figure 6 This is a diagram of the scattering area division based on the time-domain discontinuous Galerkin method analysis. DETAILED DESCRIPTION

[0083] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0084] In one embodiment, in combination Figure 1 , provides a simulation method based on time-varying plasma sheath identification technology, comprising the following steps:

[0085] Step 1, establish a spatial electromagnetic field simulation model and a flow field simulation model, and use a mixture of tetrahedrons and hexahedrons to discretize the meshes of the two models to obtain the structural information of the models, including the unit information and node information of the tetrahedrons and hexahedrons;

[0086] Step 2, establish a two-dimensional and three-dimensional model diagram of the aircraft covered with the plasma sheath, obtain the node information of the flow field, map the node information of the flow field area to the corresponding position of the electromagnetic field model area, and calculate the plasma parameters corresponding to each unit;

[0087] Step 3, using the time domain discontinuous Galerkin method to solve the scattering problem and obtain the echo signal under the influence of plasma;

[0088] Step 4, constructing a compensation factor by measuring the plasma density to compensate for the echo signal under the influence of the plasma;

[0089] Without any compensation, the radar echo is severely distorted and the coherent integration has no peak. If the electron density is well measured, then through compensation, the echo is well compensated and the coherent integration result has a peak at the location of the target.

[0090] The node information of the flow field described in step 2 includes the temperature, electron density, pressure, mass fraction of each gas on the tetrahedral grid of the original flow field. The plasma parameters corresponding to each unit are obtained, and the equation is:

[0091]

[0092] ν c (i,j,k)=5.2e18·n e (i,j,k)·kk·T(i,j,k) (1.2)

[0093]

[0094] Where i, j, k are the flow field point numbers in the X, Y, and Z directions, T represents the temperature at the flow field point, kk is the Boltzmann constant, ω p and ν c are the plasma frequency and collision frequency, ω is the electron density, n e is the electron density, ε r is the relative dielectric parameter of plasma. The above parameters are all functions of the coordinates i, j, k corresponding to the flow field points.

[0095] After obtaining the node information of the flow field, the model is meshed in ANSYS. The plasma area is distinguished from other areas by assigning different material numbers. The aircraft mesh to which it belongs is found according to the material number. At this time, tetrahedral mesh discretization is used to map the node information of the flow field area to the corresponding position of the electromagnetic field model area, and the plasma parameter ω corresponding to each unit is obtained. p and ν c , substituting into formula (1.3), the dielectric parameters of each unit can be obtained.

[0096] The described method of solving the scattering problem using the time-domain discontinuous Galerkin method is as follows:

[0097]

[0098]

[0099]

[0100] Where E is the electric field strength in V / m, H is the magnetic field strength in A / m, ε is the dielectric constant in F / m, μ is the magnetic permeability in Ω / m, ε0 is the vacuum dielectric constant, ε ∞ is the dielectric constant at infinity, which is 1, ε Drude is the plasma dielectric constant, It is the Nabla operator.

[0101] Substitute the dielectric constant into the first equation (1.4):

[0102]

[0103]

[0104]

[0105] make: The system of equations can be written as:

[0106]

[0107] The Galerkin test is performed on formula (1.8), and the test basis function is N i , using the vector identity for formula (1.8) and Gauss's theorem The system of equations becomes:

[0108]

[0109]

[0110]

[0111] Among them, S is the outer surface of the solution area, e n is the normal component of the outer surface, Ω is the solution area, Δt is the time step, the surface integral of the above formula is for the introduction of the first-order absorbing boundary condition, discontinuity means that adjacent units do not share the information of the basis function, and the unknown quantity is defined on each unit. The DGTD method ensures the continuity of the field between adjacent units by introducing numerical fluxes. Common numerical fluxes include central flux, upwind flux and penalty flux.

[0112] Step 3-1, perform Galerkin test, unknown quantity expansion, and vector identity transformation on the equation system (1.8);

[0113] Step 3-2, substitute the headwind flux (1.12) shown below into (1.9) (1.10) in step 2-1;

[0114] Generally speaking, the calculation accuracy of the upwind flux is higher. The continuity of the field between adjacent units in the present invention is given by the upwind flux condition, which is specifically defined as follows:

[0115]

[0116] In the formula represents intrinsic impedance, Y=1 / Z represents intrinsic admittance, the superscript “+” represents the information of the adjacent body, and no superscript represents the information of the main body.

[0117] Using the upwind flux to ensure the continuity of adjacent units, substituting into the above formula (1.12) we can get:

[0118]

[0119] And expand the electric and magnetic fields using hexahedral stacked vector basis functions:

[0120]

[0121] Substituting (1.14) into (1.13), we obtain:

[0122]

[0123] The above equation is expanded using the central difference at time n:

[0124]

[0125]

[0126]

[0127] Finally, we get:

[0128]

[0129] in,

[0130] The matrix element expressions are as follows:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138] Finally written in DGTD semi-discrete form:

[0139]

[0140] In the formula, represent the test basis function and the expanded basis function of the electric field respectively; They represent the test basis function and expanded basis function of the magnetic field respectively.

[0141] Since the numerical method of this patent adopts DGTD, the units are discontinuous and independent from each other. ee and T hh Represents the interaction between the bulk basis functions and the bulk basis functions. When the global matrix on the left side of the equal sign is formed, the global matrix is ​​a block diagonal matrix because there is no interaction between the bulk basis functions and the adjacent bulk basis functions.

[0142] Step 3-3: Substitute the near field value (1.20) obtained from the above formula for e n+1 Substituting the result into the following formula,

[0143] After calculating the near-field value, an extrapolation surface is set in the scattering field. The electric field value of the far field can be obtained by calculating the surface current and surface magnetic current on the extrapolation surface, and then calculating the current moment and magnetic current moment from the surface current and surface magnetic current.

[0144] The equivalent current and magnetic current on the extrapolated surface are derived from the equivalent principle:

[0145]

[0146] E(r,t) is the near-field electric field value. When calculating the radar cross section, it is necessary to set the elevation angle θ and azimuth angle in the spherical coordinate system. The values ​​of these two angles determine the far-field observation direction.

[0147] The current moment N and magnetic current moment L are obtained by the following formula:

[0148]

[0149] In the above formula, r represents the position vector of the field point, r' represents the position vector of the equivalent source, and α represents the angle between the two vectors. Then r'cosα in the above formula is:

[0150]

[0151] Time domain far-field electric field component E θ and It can be obtained according to the following formula:

[0152]

[0153]

[0154] like Figure 6 As shown, the time-domain discontinuous Galerkin method for analyzing scattering problems divides the calculation area into the total field area and the scattered field area. The outermost layer is surrounded by ABC, and the division range of each area is shown in the figure: the middle part is the scatterer, TF represents the total field area, SF represents the scattered field area, CB represents the total field-scattering field boundary, OB represents the extrapolation surface, and the outermost layer ABC is the absorbing boundary condition used to truncate the entire calculation area.

[0155] The formula for RCS is:

[0156]

[0157] The Fourier transform represented by the above formula F{·} is and It represents the two components of the far-field electric field value, E inc (r, t) represents the incident electric field.

[0158] The obtained time-domain far-field value is Fourier transformed and then substituted into the above formula to obtain the object RCS.

[0159] Combination Figure 2 , step 3-4 obtains the radar echo model under the influence of the plasma sheath:

[0160] It should be noted that the plasma sheath is time-varying and changes with spatial position. The distribution of electron density from the surface of the aircraft to the free space is different from the distribution from the free space to the surface of the aircraft. In addition, for the time-varying plasma sheath, the electron density value changes with time. When the radar transmit signal passes through the time-varying plasma sheath, its electron density is different from the time-varying electron density of the plasma sheath when the radar receive signal passes through the time-varying plasma sheath. Therefore, the transmission coefficients in the transmitting period and the receiving period are different. The influence of the time-varying plasma sheath on the transmitting period and the receiving period of the radar signal should be described by two different functions. The single-pulse radar echo model under the time-varying plasma sheath is derived:

[0161]

[0162] Where T1(Ne(t-τ), fr(t)) represents the effect of the time-varying plasma sheath in the transmission period, which is a function of Ne(t) and fr(t). T2(Ne(t-τ), fr(t)) is the effect of the time-varying plasma sheath in the receiving period. T1 and T2 are the transmission coefficients of the radar signal in the transmission and receiving periods, respectively. fr(t) is the instantaneous frequency required to calculate T1 and T2. T1 and T2 are the key to the single-pulse radar echo model under the time-varying plasma sheath, which is derived as follows.

[0163] Electron density is an important parameter for calculating the transmission coefficient T. Since the time interval between the transmission and reception of the radar signal is τ, the time interval for calculating the electron density of the transmission coefficients T1 and T2 is τ. Therefore, in (1.28), the electron density of the transmission period T1 is:

[0164]

[0165] The time span of the electron density is:

[0166]

[0167] The electron density of the receiving period transmission coefficient T2 is

[0168]

[0169] The time span of the electron density is:

[0170]

[0171] The instantaneous frequency f of the transmitting cycle and the receiving cycle r It is another important parameter for calculating the transmission coefficient. The instantaneous frequency of the radar signal at time t is:

[0172]

[0173] in is the phase of the radar echo s(t) without plasma influence.

[0174]

[0175]

[0176] After obtaining the electron density and instantaneous frequency, the transmission coefficients T1 and T2 can be calculated, and then the radar echo under the influence of the plasma sheath can be obtained:

[0177]

[0178] The step 4 constructs a compensation factor by measuring the plasma density to compensate the echo signal under the influence of the plasma; including:

[0179] Step 4-1, Figure 3 It is a schematic diagram of the time-varying electron density of the plasma sheath. By obtaining the electron density, a compensation factor can be constructed to compensate for the echo affected by the plasma.

[0180] When a time-varying plasma sheath appears, the coherent integration results change and the target detection performance decreases. This section analyzes the coherent integration results of the time-varying plasma sheath, laying the foundation for studying the influence of the time-varying plasma sheath on the target detection performance, and deriving the multi-pulse radar echo under the time-varying plasma sheath: For the above formula (1.36)

[0181] Demodulation can be obtained:

[0182]

[0183] in t m =(m-1)T p It's slow time

[0184] Substituting the slow time into equation (1.37):

[0185]

[0186] After the matched filter:

[0187]

[0188] The pulse compression result is:

[0189]

[0190] In the above formula Represents convolution. For hypersonic vehicles, due to their hypersonic characteristics, distance offset will occur, and distance correction is required. Ignoring the influence of acceleration, a first-order Keystone transform is performed to convert Substituting into the above formula, we can get:

[0191]

[0192] Step 4-2 obtains the compensated radar echo.

[0193] Compensation method of plasma sheath in radar echo: The time-varying plasma sheath can cause severe intra-pulse modulation and inter-pulse modulation, resulting in pulse compression failure and degraded coherence performance. This is a tricky problem because the time-varying plasma sheath affects not only the Doppler dimension (slow time) but also the range dimension (fast time). Analysis shows that the phase change caused by the time-varying plasma sheath is the main reason for the degradation of hypersonic airborne target detection performance. Based on the measured electron density, the compensated radar echo can be written as:

[0194]

[0195] in is the phase of the transmission coefficient T1, is the phase of the transmission coefficient T2.

[0196] Figure 4 It is the coherent integration result of the electromagnetic wave passing through the plasma sheath. When the electron density of the plasma sheath is time-varying, it will cause time-varying amplitude attenuation and phase shift. Time-varying amplitude attenuation and phase shift will distort the radar signal and cause intra-pulse modulation. The distorted echo does not match the matched filter. The peak disappears and the side lobe increases abnormally, resulting in range dispersion and peak disappearance. When the signal passes through the time-varying plasma sheath, the electron density changes differently. Due to the different transmission coefficients, the amplitude and phase are also different, which will lead to inter-pulse modulation. The target-enveloping plasma will lead to a decrease in recognition performance. In the absence of any compensation, the coherent accumulation has no peak.

[0197] Figure 5 This is the coherent integration result after compensating for the time-varying plasma density. It can be seen from the figure that the echo is well compensated. The simulation results show that the coherent accumulation result has a peak at the location of the target, and the coherent performance has been significantly improved.

[0198] The present invention combines the theory of electromagnetic wave propagation in plasma, proposes the influence of plasma on spatial resolution, then studies the identification of targets covered with plasma, analyzes the influence of the presence or absence of plasma on the identification of high-definition targets, and finally estimates the phase error of the plasma sheath and compensates for it, and finally verifies the correctness of the method through simulation results.

[0199] It should be pointed out that the methods involved in the present invention that are not elaborated in detail all adopt well-known methods, such as establishing a space electromagnetic field simulation model and a flow field simulation model, meshing the two models, establishing a two-dimensional and three-dimensional model of an aircraft covered with a plasma sheath, etc., which will not be repeated here.

[0200] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A simulation method based on time-varying plasma sheath identification technology, characterized in that: The following steps are involved: Establish a spatial electromagnetic field simulation model and a flow field simulation model, and use a mixture of tetrahedrons and hexahedrons to discretize the two models, respectively, to obtain the structural information of the two models, including the unit information of tetrahedrons and hexahedrons and the node information; Map the node information of the flow field model area corresponding to the aircraft to the corresponding position of the electromagnetic field model area, and find out the plasma parameters corresponding to each unit of the electromagnetic field model; The time-domain discontinuous Galerkin method is used to solve the scattering problem and obtain the echo signal under the influence of plasma; By measuring the plasma density, a compensation factor is constructed to compensate for the echo signal under the influence of plasma; Determine the target position information through the simulation results of the above steps; The plasma parameters corresponding to each unit are: v c (i,j,k)=5.2e18·n e (i,j,k)·kk·T(i,j,k)(1.2) Where i, j, k are the coordinates of the flow field point in the X, Y, and Z directions, T represents the temperature at the flow field point, kk is the Boltzmann constant, ω p and v c are the plasma frequency and collision frequency, n e is the electron density, ε r is the relative dielectric parameter of plasma; The method of solving the scattering problem by using the time domain discontinuous Galerkin method to obtain the echo signal under the influence of plasma specifically includes: Step 3-1, constructing a plasma scattering problem equation system, performing Galerkin method test, unknown quantity expansion and vector identity transformation on the equation system to obtain a new equation system; Step 3-2, substitute the upwind flux into the new set of equations to obtain the near-field value; Step 3-3, after calculating the near-field value, set an extrapolation surface in the scattered field, calculate the surface current and surface magnetic current on the extrapolation surface, and then calculate the current moment and magnetic current moment from the surface current and surface magnetic current to obtain the electric field value of the time-domain far field, and perform Fourier transform on the time-domain far-field value to obtain the object RCS; Step 3-4, obtaining the radar echo under the influence of the plasma sheath; The compensated echo signal is: in is the phase of the transmission coefficient T1, is the phase of the transmission coefficient T2.

2. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The node information of the flow field model includes the temperature, electron density, pressure and mass fraction of each gas on the original flow field tetrahedral grid.

3. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The mesh discretization uses ANSYS to mesh the model, distinguishes the plasma area from other areas by assigning different material numbers, and finds the corresponding aircraft mesh according to the material number.

4. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The step 3-1 specifically includes: The equations for the plasma scattering problem are constructed as follows: Where E is the electric field strength in V / m, H is the magnetic field strength in A / m, ε is the dielectric constant in F / m, μ is the magnetic permeability in Ω / m, ε0 is the vacuum dielectric constant, ε ∞ is the dielectric constant at infinity, which is 1, ε Drude is the plasma dielectric constant, is the Nabla operator; Substitute the dielectric constant into the first equation (1.4): make: The system of equations is written as: The Galerkin test is performed on formula (1.8), and the test basis function is N i , using the vector identity for formula (1.8) and Gauss's theorem The new set of equations is: Among them, S is the outer surface of the solution area, e n is the normal component of the outer surface, Ω is the solution area, and Δt is the time step.

5. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The near field values ​​are: Among them, the parameters parameter The matrix element expressions are as follows: In the formula, Y = 1 / Z represents the intrinsic admittance, the superscript "+" represents the information of the adjacent body, and no superscript represents the information of the body. represents intrinsic impedance; Formula (1.12) is written in DGTD semi-discrete form as: In the formula, represent the test basis function and the expanded basis function of the electric field respectively; They represent the test basis function and expanded basis function of the magnetic field respectively.

6. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The step 3-3 specifically includes: According to the equivalent principle, the surface current and surface magnetic current on the extrapolated surface are: Where, E(r, t) is the near field value; The current moment and magnetic current moment calculated from the surface current and surface magnetic current are: In the formula, r represents the position vector of the field point, r′ represents the position vector of the equivalent source, and α represents the angle between the two vectors; r′cosα is: Time domain far-field electric field component E θ and for: The object RCS is: Where F{·} represents the Fourier transform, and It represents the two components of the far-field electric field value, E inc (r, t) represents the incident electric field.

7. The simulation method based on time-varying plasma sheath identification technology according to claim 1 is characterized in that: The radar echo under the influence of the plasma sheath in step 3-4 is: Where T1 and T2 are the transmission coefficients of the radar signal in the transmission and reception periods, respectively. T1(Ne(t-τ), fr(t)) represents the effect of the time-varying plasma sheath in the transmission period, which is a function of Ne(t) and fr(t). T2(Ne(t-τ), fr(t)) is the effect of the time-varying plasma sheath in the reception period. τ is the electron density time interval of the transmission coefficients T1 and T2, and f r is the instantaneous frequency of the transmitting cycle and the receiving cycle.

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