Plasma sheath electromagnetic scattering calculation method based on equivalent reflectivity model

Abstract

The invention provides a plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model, and relates to the technical field of electromagnetic simulation, and the method comprises the steps: sampling a plasma flow field, and obtaining the electromagnetic parameter data of plasma; based on the electromagnetic parameter data of the plasma, the equivalent reflectivity on the surface element is calculated through an analytical method, and an equivalent reflectivity model is constructed; calculating scattering characteristics of the plasma sheath by using an equivalent reflectivity model and an improved physical optical method to obtain a radar scattering sectional area; whether the radar scattering sectional area converges is judged, if not, the number of plasma sampling layers is increased, sampling is conducted again, if yes, the radar scattering sectional area serves as an electromagnetic scattering result, and electromagnetic scattering calculation of the plasma sheath is completed. The problems of high resource consumption and low speed of plasma sheath electromagnetic scattering calculation are solved.

Description

Technical Field

[0001] The present invention 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 is formed at the front of the vehicle. The intense friction between the vehicle and the air causes the air around the vehicle to dissociate and ionize, forming a high-temperature plasma sheath. The plasma sheath will attenuate, reflect, and scatter electromagnetic waves, thereby interfering with the vehicle's communications and radar detection, and even causing communication interruptions, resulting in a "black barrier" phenomenon. In the process of analyzing the mechanism of the "black barrier" phenomenon, electromagnetic computing can flexibly and efficiently model and numerically solve electromagnetic problems, becoming a powerful tool for analyzing the interaction between electromagnetic waves and plasma.

[0003] In recent years, a number of numerical algorithms for solving the coupling between electromagnetic waves and plasma have emerged at home and abroad. These algorithms can be mainly divided into two categories. One is the full-wave numerical calculation method, such as the finite difference time domain (FDTD), finite element method (FEM), volume integral equation (VIE), volume surface integral equation (VSIE) and finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA, FE-BI). These methods all require volume segmentation in the plasma region, which leads to high consumption of computing resources, especially when solving large-scale targets.

[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 plasma sheath electromagnetic scattering calculation method based on the equivalent reflectivity model provided by the present invention solves the problems of large resource consumption and slow speed in the plasma sheath electromagnetic scattering calculation.

[0006] In order to achieve the above-mentioned invention object, 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 and an improved physical optics method to calculate the scattering characteristics of the plasma sheath and obtain the radar scattering cross section;

[0010] S4: Determine whether the radar scattering cross-section area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar scattering cross-section 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 respectively:

[0012]

[0013] μ i =μ 0 ;

[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, ε 0 is the dielectric constant in free space, μ 0 represents the magnetic permeability in free space.

[0015] Further, 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, an equivalent reflectivity on a surface element of the plasma sheath 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 in the medium for a distance d, n represents the nth layer of the 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 medium n, d represents the distance electromagnetic waves propagate in the medium, μ n Represents the relative magnetic permeability of medium n, μ 0 is the magnetic permeability in free space, ε 0 is 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 represents the equivalent reflectivity on the plasma sheath surface element, R n-1,n R represents the reflectivity of the interface between the nth medium and the n-1th 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 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 is the incident magnetic field, r 0 represents the center position vector of the region, W represents the vector from the incident direction to the outgoing direction, Indicates the incident direction, Rv Represents the reflectivity of each surface element in the equivalent reflectivity model.

[0031] The beneficial effects of the present invention are as follows: the plasma on each facet is sampled, and then the equivalent reflectivity under the multilayer medium is calculated according to the electromagnetic parameters of the sampling points, and finally the equivalent reflectivity model is input into the non-uniform plasma physical optics method to calculate the scattering result, so as to complete the electromagnetic scattering calculation of the plasma sheath, thereby greatly accelerating the speed of simulating the electromagnetic scattering characteristics of the plasma sheath.

[0032] (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 facets is not considered, which can reduce the amount of calculation and resource consumption;

[0033] (2) Using physical optics to solve electromagnetic simulation problems of non-uniform plasma flow fields greatly improves computational efficiency compared to full-wave methods and enables rapid evaluation of the scattering characteristics of hypersonic vehicles;

[0034] (3) For the face elements divided by the physical optics method, the equivalent reflectivity of each face element is calculated separately. By deriving the equivalent reflectivity formula of multi-layer dielectric coated metal, an equivalent reflectivity model of hypersonic vehicle is constructed. Finally, the improved physical optics method (Improved PO) is used to calculate the scattering characteristics of the model, which greatly improves the speed of electromagnetic scattering calculation of plasma sheath. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0036] Figure 1 is an exemplary flow chart of a plasma sheath electromagnetic scattering calculation method based on an equivalent reflectivity model according to some embodiments of this specification;

[0037] Figure 2 is an exemplary schematic diagram of a 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 this specification;

[0039] Figure 4 is an exemplary schematic diagram of the dissection result of a plasma-clad aircraft according to some embodiments of the present specification;

[0040] Figure 5 is an exemplary schematic diagram of the distribution of electron density maps 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 shown in some embodiments of this specification. DETAILED DESCRIPTION

[0042] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0043] Example

[0044] Figure 1 is an exemplary flow chart of a plasma sheath electromagnetic scattering calculation method 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] The plasma flow field is the flow state of ionized gas under the action of an external electric field or electromagnetic field. For example, the plasma flow field may include a plasma sheath constructed by the aircraft model RAMC, where the RAMC is a blunt cone target with a head radius of 0.1524m, a body length of 1.29m, and a side 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, Figure 5 The figure shows the distribution of electron density obtained by CFD calculation of the flow field, which is at a flight altitude of 76km, a temperature of 195.5K, and a flight speed of 27.3 Mach. The high-density plasma around the aircraft is mainly concentrated at the head, and as the plasma diffuses, the plasma density gradually decreases from the middle to the tail of the aircraft, showing a large plasma density span and very uneven density distribution.

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

[0050] In some embodiments, Figure 2 As shown, the processor can take 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 taken 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 =μ 0 ;

[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, ε 0 is the dielectric constant in free space, μ 0 represents the magnetic permeability in free space.

[0055] S2: Based on the electromagnetic parameter data of plasma, the equivalent reflectivity on the surface element is calculated by analytical method, and the 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, Figure 3 As shown, the processor can deduce the influence of the coating medium on the backscattering amplitude of the electromagnetic wave based on the electromagnetic wave propagation characteristics in the three-layer structure of air-medium-metal target, and construct an equivalent reflectivity model. Specifically, the processor can obtain the equivalent reflectivity model based on the reflection and transmission of the electromagnetic wave at the interface between the air and the coating medium, and the multiple reflections and transmissions of the electromagnetic wave that penetrates into the medium between the air-medium interface and the metal surface.

[0058] In some embodiments, when the amplitude is E 0 When a plane wave is incident on the plasma sheath, the resulting reflected field expression can be:

[0059]

[0060] Among them, E 0 represents the plane wave incident amplitude, R +It represents the reflectivity of electromagnetic waves when they are incident from air to medium, R- represents the reflectivity when electromagnetic waves are incident from medium to air, T + It represents the refractive index of electromagnetic waves incident from air to the medium, T - Represents the refractive index when the electromagnetic wave is incident from the medium to the air, R PEC 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 of 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 the air is c The expression can be:

[0067]

[0068] In some embodiments, the processor can obtain the reflectivity of the dielectric interface through calculation based on the electromagnetic parameter data of the plasma; use the reflectivity of the dielectric 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 surface.

[0069] In some embodiments, the expression of the reflectivity of the medium interface can be:

[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 in the medium for a distance d, n represents the nth layer of the medium, η nrepresents the wave impedance in medium n, λ represents the wavelength of electromagnetic wave, ε n represents the relative dielectric constant of medium n, d represents the distance electromagnetic waves propagate in the medium, μ n Represents the relative magnetic permeability of medium n, μ 0 is the magnetic permeability in free space, ε 0 is the dielectric constant in free space.

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

[0075]

[0076] Among them, R v represents the equivalent reflectivity on the plasma sheath surface element, R n-1,n R represents the reflectivity of the interface between the nth medium and the n-1th 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, Figure 4 As shown in the figure, the segmentation results of the plasma-envelope vehicle 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 zero.

[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] Where R represents the distance from the radar to 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 expression of the Gordon model may be:

[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 of 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 is the incident magnetic field, r 0 represents the center position vector of the region, W represents the vector 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 scattering cross-section area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar scattering cross-section 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, when the residual r n <10 -3 When , the algorithm considers that RCS converges; otherwise, it does not converge.

[0100] In some embodiments, the processor may compare the results obtained by Improved PO with the results of FE-BI-MLFMA, which uses volume meshing to simulate the electromagnetic scattering characteristics of the RAMC model with inhomogeneous plasma sheathing, 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 dissection model Equivalent reflectivity model Unknowns 2216651 86416 Memory 125.6GB 2.5GB time 14h20m 100s

[0103] In some embodiments, Figure 6 As shown in the figure, the single-station RCS results of FE-BI-MLFMA and Improved PO methods are shown. Theta, or θ, represents the angle of horizontal incidence, and the average error between the two is 3.9116 dB. The error is within an acceptable range, verifying the accuracy of the equivalent reflectivity model. Table 1 shows the numerical performance comparison of different methods for the inhomogeneous plasma model. The equivalent reflectivity model is significantly better than the volume segmentation model in terms of unknowns, memory, and time, which illustrates the high efficiency of the equivalent reflectivity model.

[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 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 greatly improves computational efficiency compared to full-wave methods and enables rapid evaluation of the scattering characteristics of hypersonic vehicles;

[0107] (3) For the face elements divided by the physical optics method, the equivalent reflectivity of each face element is calculated separately. By deriving the equivalent reflectivity formula of multi-layer dielectric coated metal, an equivalent reflectivity model of hypersonic vehicle is constructed. Finally, the improved physical optics method (Improved PO) is used to calculate the scattering characteristics of the model, which greatly improves the speed of electromagnetic scattering calculation of 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, the equivalent reflectivity on the surface element is calculated by an analytical method, and an equivalent reflectivity model is constructed; S3: using the equivalent reflectivity model and an improved physical optics method to calculate the scattering characteristics of the plasma sheath and obtain the radar scattering cross section; S4: Determine whether the radar scattering cross-section area converges. If not, increase the number of plasma sampling layers and return to S1 for resampling. If converged, use the radar scattering cross-section 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: m i =μ0; 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.

3. The plasma sheath electromagnetic scattering calculation method based on the equivalent reflectivity model according to claim 1 is characterized in that: The S2 includes: Based on the electromagnetic parameter data of the plasma, the reflectivity of the medium interface is obtained by calculation; Using the reflectivity of the medium interface, an equivalent reflectivity on a surface element of the plasma sheath is obtained by calculation; The equivalent reflectivity model is obtained by integrating the equivalent reflectivities of all facets on the plasma sheath surface.

4. The method for calculating electromagnetic scattering of a plasma sheath based on an equivalent reflectivity model according to claim 3, characterized in that: The expression of the reflectivity of the medium interface is: 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 in the medium for a distance d, n represents the nth layer of the 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 medium n, d represents the distance electromagnetic waves propagate in the medium, μ n represents the relative magnetic permeability of medium n, μ0 represents the magnetic permeability in free space, and ε0 represents the dielectric constant in free space.

5. The method for calculating electromagnetic scattering of a plasma sheath based on an equivalent reflectivity model according to claim 3, characterized in that: The expression of the equivalent reflectivity on the surface element of the plasma sheath is: Among them, R v represents the equivalent reflectivity on the plasma sheath surface element, R n-1,n R represents the reflectivity of the interface between the nth medium and the n-1th 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.

6. The plasma sheath electromagnetic scattering calculation method based on the equivalent reflectivity model according to claim 1 is characterized in that: The expression of the radar cross section is: 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.

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