Method for calculating electromagnetic scattering of plasma sheath based on equivalent reflectivity model

Abstract

The application provides a plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model, and relates to the technical field of electromagnetic simulation. The method is to sample a plasma flow field to obtain electromagnetic parameter data of the plasma; based on the electromagnetic parameter data of the plasma, an equivalent reflectivity on a surface element is calculated through an analytical method to construct an equivalent reflectivity model; the scattering characteristics of the plasma sheath are calculated using an improved physical optics method by using the equivalent reflectivity model to obtain a radar scattering cross section; whether the radar scattering cross section converges is judged; if not, the number of plasma sampling layers is increased, and resampling is performed; if the radar scattering cross section converges, the radar scattering cross section is taken as an electromagnetic scattering result, and the electromagnetic scattering calculation of the plasma sheath is completed. The application solves the problems of large resource consumption and slow speed in the electromagnetic scattering calculation of the plasma sheath.

Description

Technical Field

[0001] This specification relates to the field of electromagnetic simulation technology, and in particular to a method for calculating electromagnetic scattering of a plasma sheath based on an equivalent reflectivity model. Background Art

[0002] When a hypersonic vehicle flies, a strong shock wave forms at the front of the vehicle. The intense friction between the vehicle and the air causes the surrounding air to dissociate and ionize, forming a high-temperature plasma sheath. This plasma sheath attenuates, reflects, and scatters electromagnetic waves, interfering with the vehicle's communications and radar detection, or even causing communication interruption and a "blackout" phenomenon. Electromagnetic computing can flexibly and efficiently model and numerically solve electromagnetic problems in the process of analyzing the mechanism of this "blackout" phenomenon, making it a powerful tool for analyzing the interaction between electromagnetic waves and plasma.

[0003] In recent years, a number of numerical algorithms for solving electromagnetic wave-plasma coupling have emerged both domestically and internationally. These algorithms can be broadly categorized into two main groups: full-wave numerical methods, such as the finite difference time domain (FDTD) method, the finite element method (FEM), the volume integral equation (VIE), the volume surface integral equation (VSIE), and the finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA, FE-BI). These methods all require volumetric partitioning within the plasma region, resulting in high computational resource consumption and, in particular, limited performance when solving large-scale objects.

[0004] Existing methods can calculate the equivalent reflectivity of a uniform medium-coated metal model, but it is difficult to calculate the equivalent reflectivity of a non-uniform medium-coated metal, such as the plasma flow field outside a hypersonic vehicle. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model, which solves the problems of high resource consumption and slow calculation speed of plasma sheath electromagnetic scattering.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model, comprising:

[0007] S1: Sampling the plasma flow field to obtain electromagnetic parameter data of the plasma;

[0008] S2: Based on the electromagnetic parameter data of the plasma, the equivalent reflectivity on the surface element is calculated by an analytical method, and an equivalent reflectivity model is constructed;

[0009] S3: Using the equivalent reflectivity model, an improved physical optics method is used to calculate the scattering characteristics of the plasma sheath to obtain the radar cross section;

[0010] S4: Determine whether the radar cross-sectional area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar cross-sectional area as the electromagnetic scattering result to complete the electromagnetic scattering calculation of the plasma sheath.

[0011] Furthermore, the electromagnetic parameter data of the plasma include dielectric constant and magnetic permeability, and their expressions are:

[0012]

[0013] μ i =μ0;

[0014] Among them, ε i represents the dielectric constant of plasma i, μ i represents the magnetic permeability of plasma i, ω p represents the plasma angular frequency, ω represents the incident frequency, υ eff represents the collision angular frequency, j represents the imaginary unit, ε0 represents the dielectric constant in free space, and μ0 represents the magnetic permeability in free space.

[0015] Furthermore, the S2 includes:

[0016] Based on the electromagnetic parameter data of the plasma, the reflectivity of the medium interface is obtained by calculation;

[0017] Using the reflectivity of the medium interface, the equivalent reflectivity on the plasma sheath surface element is obtained by calculation;

[0018] The equivalent reflectivity model is obtained by integrating the equivalent reflectivities of all facets on the plasma sheath surface.

[0019] Furthermore, the expression of the reflectivity of the medium interface is:

[0020]

[0021]

[0022]

[0023] Among them, R n,n+1 represents the reflectivity of the interface between the n+1th layer of medium and the nth layer of medium, η n+1 represents the wave impedance in medium n+1, j represents the imaginary unit, It represents the phase difference when the electromagnetic wave propagates a distance d in the medium, n represents the nth layer of medium, η n represents the wave impedance in medium n, λ represents the wavelength of electromagnetic wave, ε n represents the relative dielectric constant of the medium n, d represents the distance that the electromagnetic wave propagates in the medium, μ n represents the relative magnetic permeability of the medium n, μ0 represents the magnetic permeability in free space, and ε0 represents the dielectric constant in free space.

[0024] Furthermore, the expression of the equivalent reflectivity on the surface element of the plasma sheath is:

[0025]

[0026] Among them, R v R represents the equivalent reflectivity on the plasma sheath surface element, n-1,n R represents the reflectivity of the interface between the nth layer of medium and the n-1th layer of medium. n,n+1 represents the reflectivity of the interface between the n+1th layer of medium and the nth layer of medium, j represents the imaginary unit, It represents the phase difference when the electromagnetic wave propagates a distance d in the medium.

[0027] Furthermore, the expression of the radar cross section is:

[0028]

[0029]

[0030] Where σ represents the radar cross-sectional area, r represents the observation distance, and E i represents the incident electric field, E s represents the scattered field, j represents the imaginary unit, k represents the wave number in the coating medium, A represents the area of ​​the irradiated region, represents the normal vector, Indicates the emission direction, H i Represents the incident magnetic field, r0 represents the center position vector of the region, W represents the vector pointing from the incident direction to the outgoing direction, Indicates the incident direction, R v Represents the reflectivity of each surface element in the equivalent reflectivity model.

[0031] The beneficial effects of the present application are: sampling the plasma on each face element, then calculating the equivalent reflectivity under the multi-layer medium according to the electromagnetic parameters of the sampling points, finally inputting the equivalent reflectivity model into the non-uniform plasma physical optics method to calculate the scattering result, completing the electromagnetic scattering calculation of the plasma sheath, and greatly speeding up the simulation of the electromagnetic scattering characteristics of the plasma sheath.

[0032] (1) Each face element of the divided grid is calculated respectively, which can reflect the non-uniform characteristics of the plasma flow field; only the grid in the normal direction of the current face element is considered in the calculation process, and the mutual influence between the face elements is not considered, which can reduce the calculation amount and resource consumption;

[0033] (2) The physical optics method is used to solve the electromagnetic simulation problem of the non-uniform plasma flow field, which greatly improves the calculation efficiency compared with the full-wave method, and realizes the rapid evaluation of the scattering characteristics of the hypersonic vehicle;

[0034] (3) For the divided face element of the physical optics method, the equivalent reflectivity of each face element is calculated separately, the equivalent reflectivity formula of the multi-layer medium covering metal is derived, the equivalent reflectivity model of the hypersonic vehicle is constructed, and finally the improved physical optics method (Improved PO) is used to calculate the scattering characteristics of the model, which greatly improves the speed of the electromagnetic scattering calculation of the plasma sheath. BRIEF DESCRIPTION OF DRAWINGS

[0035] The present specification will be further illustrated in the form of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting, and in these embodiments, the same numbers represent the same structures, wherein:

[0036] Figure 1 is an exemplary flowchart of the plasma sheath electromagnetic scattering calculation method based on the equivalent reflectivity model according to some embodiments of the present specification;

[0037] Figure 2 is an exemplary schematic diagram of the plasma sheath according to some embodiments of the present specification;

[0038] Figure 3 is an exemplary schematic diagram of electromagnetic wave propagation in an air-medium-metal target three-layer structure according to some embodiments of the present specification;

[0039] Figure 4 is an exemplary schematic diagram of the division result of the plasma covering vehicle according to some embodiments of the present specification;

[0040] Figure 5 is an exemplary schematic diagram of the electron density map distribution according to some embodiments of the present specification;

[0041] Figure 6 It is an exemplary schematic diagram of the single-station RCS results of the FE-BI-MLFMA and Improved PO methods according to some embodiments of this specification. DETAILED DESCRIPTION

[0042] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0043] Example

[0044] Figure 1 This is an exemplary flow chart of a method for calculating electromagnetic scattering of a plasma sheath based on an equivalent reflectivity model according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process can be executed by a processor.

[0045] S1: Sample the plasma flow field to obtain the electromagnetic parameter data of the plasma.

[0046] A plasma flow field is the flow state of an ionized gas under the influence of an external electric or electromagnetic field. For example, a plasma flow field can include a plasma sheath constructed from a model aircraft called RAMC. The RAMC is a blunt-nosed cone target with a head radius of 0.1524 m, a length of 1.29 m, and a lateral half-angle of 9°.

[0047] In some embodiments, the processor may perform n-layer sampling on the plasma sheath to obtain electromagnetic parameter data of the plasma.

[0048] In some embodiments, as Figure 5 The figure shows the electron density distribution obtained through CFD flow field calculations at an altitude of 76 km, a temperature of 195.5 K, and a speed of Mach 27.3. The high-density plasma surrounding the vehicle is primarily concentrated at the head. As the plasma spreads, the plasma density gradually decreases from the middle to the tail of the vehicle, resulting in a wide range of plasma density and a very uneven density distribution.

[0049] The electromagnetic parameter data of the plasma is a parameter reflecting the electromagnetic characteristics of the plasma. For example, the electromagnetic parameter data of the plasma may include dielectric constant and magnetic permeability.

[0050] In some embodiments, as Figure 2As shown in FIG, the processor can select a sampling point every 30 mm in the normal direction outside the plasma sheath mesh with a thickness of 150 mm, and take 5 sampling points. The average value of the electromagnetic parameters of the four tetrahedral meshes closest to the sampling point is used as the electromagnetic parameter of this sampling point.

[0051] In some embodiments, the expressions of the dielectric constant and the magnetic permeability may be:

[0052]

[0053] μ i =μ0;

[0054] Among them, ε i represents the dielectric constant of plasma i, μ i represents the magnetic permeability of plasma i, ω p represents the plasma angular frequency, ω represents the incident frequency, υ eff represents the collision angular frequency, j represents the imaginary unit, ε0 represents the dielectric constant in free space, and μ0 represents the magnetic permeability in free space.

[0055] S2: Based on the electromagnetic parameter data of the plasma, the equivalent reflectivity on the surface element is calculated by analytical methods, and an equivalent reflectivity model is constructed.

[0056] The equivalent reflectivity model is a mathematical model used to obtain the equivalent reflectivity on each surface element of the plasma sheath.

[0057] In some embodiments, as Figure 3 As shown, the processor can derive the effect of the coating medium on the electromagnetic wave backscattering amplitude based on the electromagnetic wave propagation characteristics in the three-layer structure of air-dielectric-metal target, and construct an equivalent reflectivity model. Specifically, the processor can derive the equivalent reflectivity model based on the reflection and transmission of electromagnetic waves at the interface between air and the coating medium, and the multiple reflections and transmissions between the air-dielectric interface and the metal surface caused by electromagnetic waves that penetrate the medium.

[0058] In some embodiments, when a plane wave with an amplitude of E0 is incident on the plasma sheath, the resulting reflected field expression can be:

[0059]

[0060] Where E0 represents the incident plane wave amplitude, R + Indicates the reflectivity of electromagnetic waves from air to medium, R- indicates the reflectivity of electromagnetic waves from medium to air, T + Represents the refractive index of electromagnetic waves incident from air to the medium, T - Represents the refractive index when electromagnetic waves are incident from the medium to the air, RPEC Represents the reflectivity of the metal, m represents the number of reflections, It represents the phase difference when the electromagnetic wave propagates a distance d in the medium.

[0061] In some embodiments, when a plane wave is incident perpendicular to the medium surface, the corresponding expressions for reflection coefficient and transmission coefficient can be:

[0062]

[0063]

[0064] R PEC =-1;

[0065] R + =-R - .

[0066] In some embodiments, the equivalent reflectivity R of the interface between the medium and air is c The expression can be:

[0067]

[0068] In some embodiments, the processor can obtain the reflectivity of the medium interface through calculation based on the electromagnetic parameter data of the plasma; use the reflectivity of the medium interface to obtain the equivalent reflectivity on the surface element of the plasma sheath through calculation; and obtain the equivalent reflectivity model by integrating the equivalent reflectivity on all surface elements of the plasma sheath.

[0069] In some embodiments, the reflectivity of the medium interface may be expressed as:

[0070]

[0071]

[0072]

[0073] Among them, R n,n+1 represents the reflectivity of the interface between the n+1th layer of medium and the nth layer of medium, η n+1 represents the wave impedance in medium n+1, j represents the imaginary unit, It represents the phase difference when the electromagnetic wave propagates a distance d in the medium, n represents the nth layer of medium, η n represents the wave impedance in medium n, λ represents the wavelength of electromagnetic wave, ε n represents the relative dielectric constant of the medium n, d represents the distance that the electromagnetic wave propagates in the medium, μ nrepresents the relative magnetic permeability of the medium n, μ0 represents the magnetic permeability in free space, and ε0 represents the dielectric constant in free space.

[0074] In some embodiments, the expression for the equivalent reflectivity on the plasma sheath surface element can be:

[0075]

[0076] Among them, R v R represents the equivalent reflectivity on the plasma sheath surface element, n-1,n R represents the reflectivity of the interface between the nth layer of medium and the n-1th layer of medium. n,n+1 represents the reflectivity of the interface between the n+1th layer of medium and the nth layer of medium, j represents the imaginary unit, It represents the phase difference when the electromagnetic wave propagates a distance d in the medium.

[0077] In some embodiments, as Figure 4 As shown in the figure, the segmentation results of the plasma-enclosed spacecraft are shown, and the equivalent reflectivity R on each surface element is v =E_R n-1,n .

[0078] S3: Using the equivalent reflectivity model, the improved physical optics method is used to calculate the scattering characteristics of the plasma sheath and obtain the radar scattering cross section.

[0079] The scattered field data is the data reflecting the electromagnetic scattering of the plasma sheath.

[0080] In some embodiments, the processor can construct the P0 current of the metal target based on the fact that an induced current can be excited in the area irradiated by the electromagnetic wave, while the induced current in the area not irradiated is 0.

[0081] In some embodiments, the expression of P0 current can be:

[0082]

[0083] Among them, J s (r′) represents the P0 current, and r′ represents the position vector.

[0084] In some embodiments, the processor may input the P0 current into a Stratton-Chu integral to obtain the far-field scattered field of the physical optics method.

[0085] In some embodiments, the expression of the far-field scattered field of the physical optics method can be:

[0086]

[0087] Among them, R represents the distance between the radar and the target, Indicates the incident direction.

[0088] In some embodiments, the processor can convert the far-field scattered field of the physical optics method into a semi-analytical form of line summation of the regional edge, and the calculation accuracy of this method is independent of the regional grid shape, number of edges and size, thereby obtaining a Gordon model.

[0089] In some embodiments, the Gordon model may be expressed as:

[0090]

[0091] Where T represents the projection length of W on the regional plane, represents the unit direction perpendicular to W on the plane of the region, a m represents the mth edge vector, m represents the edge vector number, M represents the total number of edge vectors, r m represents the edge center position vector; where,

[0092] In some embodiments, the processor may obtain the radar cross section when T=0 based on a Gordon model.

[0093] In some embodiments, the expression for radar cross section may be:

[0094]

[0095]

[0096] Where σ represents the radar cross-sectional area, r represents the observation distance, and E i is the incident electric field, E s represents the scattered field, j represents the imaginary unit, k represents the wave number in the coating medium, A represents the area of ​​the irradiated region, represents the normal vector, Indicates the emission direction, H i Represents the incident magnetic field, r0 represents the center position vector of the region, W represents the vector pointing from the incident direction to the outgoing direction, Indicates the incident direction, R v Represents the reflectivity of each surface element in the equivalent reflectivity model.

[0097] S4: Determine whether the radar cross-sectional area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar cross-sectional area as the electromagnetic scattering result to complete the electromagnetic scattering calculation of the plasma sheath.

[0098] The electromagnetic scattering result is a converged radar cross section result.

[0099] In some embodiments, the processor can iteratively calculate the scattered field, and when the residual r n <10 -3 When , the algorithm considers that RCS has converged; otherwise, it is considered not converged.

[0100] In some embodiments, the processor may compare the results obtained by the Improved PO with the results of the FE-BI-MLFMA method, which uses volume meshing to simulate the electromagnetic scattering characteristics of the RAMC model covered by non-uniform plasma, with a plane wave frequency of 3 GHz and a horizontal incidence angle range of θ∈[-90°,90°]. The single-station RCS of the RAMC aircraft under VV polarization is calculated, and the comparison results are shown in Table 1.

[0101] Table 1

[0102] method FE-BI-MLFMA Improved PO Model Body anatomy model Equivalent reflectivity model unknowns 2216651 86416 Memory 125.6GB 2.5GB time 14h20m 100s

[0103] In some embodiments, as Figure 6 Figure 2 shows the single-station RCS results for the FE-BI-MLFMA and Improved PO methods. Theta (θ) represents the angle of horizontal incidence, and the average error between the two methods is 3.9116 dB. This error is within an acceptable range, validating the accuracy of the equivalent reflectivity model. Table 1 compares the numerical performance of different methods for the inhomogeneous plasma model. The equivalent reflectivity model significantly outperforms the volumetric model in terms of unknowns, memory usage, and time consumption, demonstrating its high efficiency.

[0104] In some embodiments of the present specification, the plasma on each facet is sampled, and then the equivalent reflectivity under the multilayer medium is calculated based on the electromagnetic parameters of the sampling points. Finally, the equivalent reflectivity model is input into the inhomogeneous plasma physical optics method to calculate the scattering results, thereby completing the electromagnetic scattering calculation of the plasma sheath, which greatly speeds up the simulation of the electromagnetic scattering characteristics of the plasma sheath.

[0105] (1) Calculating each facet of the grid separately can reflect the non-uniform characteristics of the plasma flow field; during the calculation process, only the grid in the normal direction of the current facet is considered, and the mutual influence between the facets is not considered, which can reduce the amount of calculation and resource consumption;

[0106] (2) Using physical optics to solve electromagnetic simulation problems of non-uniform plasma flow fields, the computational efficiency is greatly improved compared to the full-wave method, and a rapid evaluation of the scattering characteristics of hypersonic vehicles is achieved;

[0107] (3) For the physical optics method, the equivalent reflectivity of each facet is calculated separately. The equivalent reflectivity formula of the multilayer medium coated with metal is derived, and the equivalent reflectivity model of the hypersonic vehicle is constructed. Finally, the improved physical optics method is used to calculate the scattering characteristics of the model, which greatly improves the speed of electromagnetic scattering calculation of the plasma sheath.

Claims

1. A plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model, characterized in that: include: S1: Sampling the plasma flow field to obtain electromagnetic parameter data of the plasma; S2: Based on the electromagnetic parameter data of the plasma, obtain the reflectivity of the medium interface through calculation; The expression of the reflectivity of the medium interface is: ； ； ； in, Indicates the Layer medium and the The reflectivity of the interface between the layers of dielectrics, Display medium The wave impedance in represents the imaginary unit, Indicates the distance electromagnetic waves propagate in a medium The corresponding phase difference is Indicates the Layer medium, Display medium The wave impedance in represents the wavelength of electromagnetic waves, Display medium The relative dielectric constant, It represents the distance that electromagnetic waves propagate in the medium. Display medium The relative magnetic permeability, represents the magnetic permeability in free space, represents the dielectric constant in free space; Using the reflectivity of the medium interface, the equivalent reflectivity on the plasma sheath surface element is obtained by calculation; The expression of the equivalent reflectivity on the surface element of the plasma sheath is: ； in, represents the equivalent reflectivity on the plasma sheath surface element, Indicates the Layer medium and the The reflectivity of the interface between the layers of dielectrics, Indicates the Layer medium and the The reflectivity of the interface between the layers of dielectrics, represents the imaginary unit, Indicates the distance electromagnetic waves propagate in a medium The corresponding phase difference when The equivalent reflectivity model is obtained by integrating the equivalent reflectivity of all facets on the plasma sheath surface. S3: Using the equivalent reflectivity model, an improved physical optics method is used to calculate the scattering characteristics of the plasma sheath to obtain the radar cross section; The expression of the radar cross section is: ； ； in, represents the radar cross section area, Indicates the observation distance, represents the incident electric field, represents the scattered field, represents the imaginary unit, represents the wave number in the coating medium, represents the area of ​​the irradiated region, represents the normal vector, Indicates the emission direction, represents the incident magnetic field, represents the region center position vector, represents the vector from the incident direction to the outgoing direction, , represents the incident direction, Represents the reflectivity of each surface element in the equivalent reflectivity model; S4: Determine whether the radar cross-sectional area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar cross-sectional area as the electromagnetic scattering result to complete the electromagnetic scattering calculation of the plasma sheath.

2. The plasma sheath electromagnetic scattering calculation method based on the equivalent reflectivity model according to claim 1 is characterized in that: The electromagnetic parameter data of the plasma include dielectric constant and magnetic permeability, and their expressions are: ； ； in, Indicates plasma The dielectric constant, Indicates plasma The magnetic permeability, represents the plasma angular frequency, represents the incident frequency, represents the collision angular frequency, represents the imaginary unit, represents the dielectric constant in free space, represents the magnetic permeability in free space.

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