Analysis method of electromagnetic wave propagation characteristics based on k-ε plasma turbulence model

Abstract

The present invention relates to a method for analyzing electromagnetic wave propagation characteristics based on a k-ε plasma turbulence model, comprising the following steps: S1. calculating the dielectric constant of plasma turbulence under a standard k-ε turbulence model based on the gas ionization Saha equation and the refractive index of the plasma; S2. calculating the propagation model of electromagnetic waves under different plasma turbulence parameters based on the dielectric constant and a transmission matrix method, and analyzing the electromagnetic wave propagation characteristics using the propagation model. The present invention solves the dielectric constant of plasma turbulence based on a calculation method for the propagation coefficient of dust plasma turbulence under a standard k-ε turbulence model, and on this basis, obtains the propagation coefficient of electromagnetic waves in plasma turbulence under the standard k-ε turbulence model by using the transmission matrix method, providing a theoretical basis for studying the problem of electromagnetic wave propagation in plasma turbulence.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic computing, and in particular relates to a method for analyzing electromagnetic wave propagation characteristics based on a k-ε plasma turbulence model. Background Art

[0002] During flight, hypersonic vehicles experience friction with the air, causing a sharp rise in temperature around the vehicle and leading to ionization of the gas, forming a plasma flow field. Influenced by the vehicle's aerodynamic shape and flight speed, this plasma flow field generates multiple vortex structures of varying shapes and sizes, known as plasma turbulence. These turbulent flows within the plasma flow field can significantly reflect and refract electromagnetic waves, absorbing their energy and disrupting their propagation, impacting communication performance and quality. Therefore, studying the propagation characteristics of electromagnetic waves and plasma turbulence is crucial for addressing communication challenges related to plasma turbulence.

[0003] Currently, researchers at home and abroad have focused their research on the propagation characteristics of electromagnetic waves in plasmas, primarily on the interaction between pure plasma and electromagnetic waves, or on the interaction between light and the turbulence of the plasma sheath. Understanding the mechanisms, laws, and characteristics of the interaction between electromagnetic waves and plasma turbulence remains unclear. Li Xiaoqing et al. conducted experimental research on the propagation characteristics of spherically aberrated beams in atmospheric turbulence.

[0004] The standard k-ε turbulence model is the most widely used model in plasma turbulence. Current research does not take into account the propagation of electromagnetic waves under this model, and there is too little research on the propagation characteristics of electromagnetic waves in plasma turbulence. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model in order to solve the above problems.

[0006] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0007] A method for analyzing electromagnetic wave propagation characteristics based on a k-ε plasma turbulence model comprises the following steps:

[0008] S1. Calculate the dielectric constant of plasma turbulence under the standard k-ε turbulence model based on the Saha equation for gas ionization and the refractive index of the plasma;

[0009] S2. Based on the dielectric constant and transmission matrix method, calculate the propagation model of electromagnetic waves under different plasma turbulence parameters, and use the propagation model to analyze the propagation characteristics of electromagnetic waves.

[0010] As a further optimization scheme of the present invention, the method for calculating the dielectric constant of plasma turbulence under the standard k-ε turbulence model based on the gas ionization Saha equation and the refractive index of the plasma in step S1 includes:

[0011] S101. Based on the expression of the Saha equation for gas ionization under the standard k-ε model, derive the electron density in plasma turbulence;

[0012] S102. Combine electron density and temperature fluctuations to calculate electron density fluctuations in plasma turbulence;

[0013] S103. Calculating the refractive index in the plasma turbulence based on the electron density fluctuation and the electron-neutral particle collision frequency;

[0014] S104. Using the property that the dielectric constant is approximately equal to the square of the refractive index, calculate the dielectric constant in plasma turbulence.

[0015] As a further optimization solution of the present invention, the electron density calculation formula in step S101 is as follows:

[0016]

[0017] Among them, n e is the electron density in the plasma turbulence, n0 is the total number of gas molecules, K B is the Boltzmann coefficient, h is the Planck coefficient, m e is the electron mass, T is the gas ionization temperature, E i is the ionization energy.

[0018] As a further optimization solution of the present invention, the electron density fluctuation formula in step S102 is:

[0019]

[0020] Among them, n' e is the electron density fluctuation, T' represents the temperature fluctuation;

[0021] From the above formula, we can see that the ratio of electron density fluctuation to average electron density is greater than the ratio of temperature fluctuation to average temperature, which can be expressed as follows:

[0022]

[0023] As a further optimization solution of the present invention, the refractive index calculation formula described in step S103 is:

[0024]

[0025] in,

[0026] n t is the refractive index in the plasma turbulence, v e represents the collision frequency of electron-neutral particles, ω represents the frequency of electromagnetic waves, ω p represents the plasma frequency, q is the charge, m e is the mass of electron, and ε0 is the dielectric constant in vacuum state.

[0027] As a further optimization solution of the present invention, the dielectric constant calculation formula described in step S104 is:

[0028]

[0029] where ε is the dielectric constant in plasma turbulence; n t is the refractive index in the plasma turbulence, j 2 =-1.

[0030] As a further optimization solution of the present invention, the method for calculating the propagation model of electromagnetic waves under different plasma turbulence parameters based on the dielectric constant and the transmission matrix method described in step S2 is:

[0031] S201. Calculate the propagation coefficient of electromagnetic waves through the dust plasma slab divided into n layers based on the dielectric constant:

[0032]

[0033] Where c is the speed of light in free space, ε r (m) is the kth m The complex dielectric constant of the layer, ω is the incident wave frequency;

[0034] S202. Calculate the total electric field of the electromagnetic wave passing through the dust plasma slab based on the propagation coefficient:

[0035]

[0036] Where R represents the amplitude of the reflected electric field and the amplitude of the incident electric field E y The ratio of the total reflection coefficient, T r The amplitude of the transmitted electric field and the incident electric field E y The total transmission coefficient of the ratio, They are the first layer incident area k0, the mth layer area k m , the last layer of transmission area k p The z component of the incident wave number, They are the first layer incident area k0, the mth layer area km , the last layer of transmission area k p The x component of the incident wave number, B m and C m are the amplitudes of the reflected and transmitted waves toward +z and -z of the mth layer, respectively;

[0037] S203. Combining the total electric field formula with the propagation matrix formula, we obtain:

[0038]

[0039] Combine the column matrix in region k0 with the column matrix in region k p The relationship between the column matrices in is rearranged as follows:

[0040]

[0041] Among them, S g is the total scattering matrix, When S g Expressed as S g =(S g1 ,S g2 ) form, and then convert the formula into a propagation model:

[0042]

[0043] Among them, S g1 and S g2 Respectively represent S g The first and second column vectors of ;

[0044] S204. Calculate the propagation coefficients of the electromagnetic wave based on the propagation model: the total reflection coefficient and the total projection coefficient, and analyze the electromagnetic wave propagation characteristics based on the propagation coefficients.

[0045] As a further optimization solution of the present invention, the total reflection coefficient and the total transmission coefficient are expressed in decibels: R dB =20log 10 (R),T dB =20log 10 (T r ).

[0046] The beneficial effects of the present invention are:

[0047] The present invention solves the dielectric constant of plasma turbulence based on the calculation method of the dust plasma turbulence propagation coefficient under the standard k-ε turbulence model, and on this basis solves the propagation coefficient of electromagnetic waves in plasma turbulence under the standard k-ε turbulence model through the transfer matrix method, providing a theoretical basis for studying the problem of electromagnetic wave propagation in plasma turbulence. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a method for calculating the propagation characteristics of electromagnetic waves in plasma turbulence under the standard k-ε turbulence model of the present invention.

[0049] Figure 2 This is a diagram of the electromagnetic wave propagation model of plasma turbulence obtained by the transmission matrix method of the present invention.

[0050] Figure 3 It is a schematic diagram of the influence of different turbulence numbers on the electromagnetic wave propagation characteristics simulated by the present invention.

[0051] Figure 4 It is a schematic diagram of the influence of different turbulence outer scales on the electromagnetic wave propagation characteristics simulated by the present invention.

[0052] Figure 5 This is a schematic diagram of the influence of different gas ionization temperatures on electromagnetic wave propagation characteristics simulated by the present invention. DETAILED DESCRIPTION

[0053] The present application is described in further detail below in conjunction with the accompanying drawings. It is necessary to point out that the following specific implementation methods are only used to further illustrate the present application and cannot be understood as limiting the scope of protection of the present application. Technicians in this field can make some non-essential improvements and adjustments to the present application based on the above application content.

[0054] Example 1

[0055] like Figure 1-2 As shown, a method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model includes the following steps:

[0056] S1. Calculate the dielectric constant of plasma turbulence under the standard k-ε turbulence model based on the Saha equation for gas ionization and the refractive index of plasma;

[0057] S101. Based on the expression of the Saha equation for gas ionization under the standard k-ε model, the electron density in plasma turbulence is obtained:

[0058]

[0059] Among them, n e is the electron density in the plasma turbulence, n0 is the total number of gas molecules, K B is the Boltzmann constant, h is the Planck coefficient, m e is the electron mass, T is the gas temperature, E i is the ionization energy;

[0060] S102. Use the Saha equation to combine electron density and temperature fluctuations to calculate the electron density fluctuations in plasma turbulence:

[0061]

[0062] Among them, n' e is the electron density fluctuation, T' represents the temperature fluctuation;

[0063] From the above formula, we can see that the ratio of electron density fluctuation to average electron density is greater than the ratio of temperature fluctuation to average temperature, which can be expressed as follows:

[0064]

[0065] Among them, the electron density is also affected by the outer scale of the turbulence and the number of turbulences, which in turn affects the refractive index in the plasma turbulence;

[0066] Before step S101, the presence of turbulence can be determined by using the Reynolds number formula:

[0067] Considering the change of Reynolds number in turbulent flow, the fluid density expression can be derived from the following formula:

[0068]

[0069]

[0070]

[0071] The fluid velocity expression is:

[0072]

[0073] The expression of Reynolds number can be obtained by the expression of fluid density and fluid velocity:

[0074]

[0075] in:

[0076]

[0077] Among them, T t is the stagnation pressure, τ is the static temperature, P is the stagnation pressure, ρ is the static pressure, R c represents the gas constant, γ is the ratio of specific heats, R1 is the gas coefficient, T1 is the stagnation pressure, M is the Mach number, T0 is the stagnation temperature of the plenum chamber, the subscript “0” refers to the plenum chamber conditions, and L is the turbulent outer scale;

[0078] S103. Calculate the refractive index in the plasma turbulence based on the electron density fluctuation and the electron-neutral particle collision frequency:

[0079]

[0080] in,

[0081] Among them, n t is the refractive index in the plasma turbulence, v e represents the collision frequency of electron-neutral particles, ω represents the frequency of electromagnetic waves, ω p represents the plasma frequency, q is the charge, m e is the mass of electron, ε0 is the dielectric constant in vacuum state;

[0082] S104. Using the property that the dielectric constant is approximately equal to the square of the refractive index, calculate the dielectric constant in plasma turbulence:

[0083]

[0084] where ε is the dielectric constant in plasma turbulence; n t is the refractive index in the plasma turbulence, j 2 =-1;

[0085] S2. Based on the dielectric constant and the transfer matrix method, the propagation model of electromagnetic waves under different plasma turbulence parameters is calculated, and the propagation characteristics of electromagnetic waves are analyzed using the propagation model;

[0086] S201. A plane electromagnetic wave is incident on a dust plasma slab from free space. The inhomogeneous dust plasma slab is divided into n layers, the first layer is the incident region (k0) and the last layer is the transmission region (k p ) are all free spaces, the kth m The propagation coefficient of a layer can be expressed as follows:

[0087]

[0088] Where c is the speed of light in free space, ε r (m) is the kth m The complex dielectric constant of the layer, ω is the incident wave frequency;

[0089] S202. Calculate the electromagnetic wave passing through the area (k0), (k m ) and (k p ) satisfies the formula:

[0090]

[0091] Where R represents the amplitude of the reflected electric field and the amplitude of the incident electric field E y The ratio of the total reflection coefficient, T r The amplitude of the transmitted electric field and the incident electric field E y The total transmission coefficient of the ratio, They are the first layer incident area k0, the mth layer area k m , the last layer of transmission area k p The z component of the incident wave number, They are the first layer incident area k0, the mth layer area k m , the last layer of transmission area k p The x component of the incident wave number, B m and C m are the amplitudes of the reflected and transmitted waves toward +z and -z of the mth layer, respectively;

[0092] S203. Combining the total electric field formula with the propagation matrix formula, we obtain:

[0093]

[0094] Among them, B1, C1, B n 、C n 、V p All are algebra used in calculations;

[0095] S203. The column matrix in region k0 can be combined with the column matrix in region k p The relationship between the column matrices in is rearranged as follows:

[0096]

[0097] Among them, S g is the total scattering matrix, When S g Expressed as S g =(S g1 ,S g2 ) form, and then convert the formula into a propagation model:

[0098]

[0099] Among them, S g1 and S g2 Respectively represent S g The first and second column vectors of the layered dielectric plate; the total reflection coefficient and total transmission coefficient can be expressed in decibels: R dB =20log 10 (R),T dB =20log 10 (T r );

[0100] S204. Calculate the propagation coefficients of the electromagnetic wave based on the propagation model: the total reflection coefficient and the total projection coefficient, and analyze the electromagnetic wave propagation characteristics based on the propagation coefficients.

[0101] Using the calculation method for the propagation characteristics of electromagnetic waves in plasma turbulence under the standard k-ε turbulence model obtained above, simulations were performed with the number of plasma turbulences, the outer scale of turbulence, and the gas ionization temperature as variables. By analyzing the curves, the influence of plasma turbulence parameters and gas ionization temperature on the propagation characteristics of electromagnetic waves was obtained:

[0102] The simulation results of the present invention can be further illustrated by the following experiments:

[0103] (1) Experimental simulation conditions

[0104] The constant parameters of dust plasma are selected as follows: plasma thickness is 1 cm, electron density is 10 18 m -3 , the incident angle is 0°.

[0105] (2) Analysis of experimental simulation results

[0106] Simulation experiment 1: The present invention is used to simulate the influence of different turbulence numbers on the propagation characteristics of electromagnetic waves in plasma turbulence, and the gas ionization temperature is selected as 3000K. The turbulence numbers are 0, 1, and 2 respectively; the results are as follows Figure 3 As shown in (a)(b).

[0107] Figure 3 The reflection and transmission coefficients for different turbulence numbers are calculated. Figure 3 As shown in (a), regardless of whether there is turbulence or not, the reflection coefficient of the plasma shows a regular oscillation and decreasing phenomenon as the frequency of the incident wave increases. This is due to the multiple reflections of the incident wave on the surface of the dielectric layer. Generally speaking, the more plasma turbulence there is, the greater the amplitude of the oscillation of the reflection coefficient of the electromagnetic wave will be. This is because the turbulent vortices in the plasma turbulence will interact with the electromagnetic waves, reflecting more electromagnetic waves, and it will be more difficult for electromagnetic waves to enter the plasma turbulence. Figure 3 As shown in (b), when the incident wave frequency is between 0 and 15 GHz, the transmission coefficient of turbulent plasma is greater than that of ordinary plasma, and the greater the number of turbulent flows within the plasma, the greater the transmission coefficient. This is because the increased turbulence, through the collision damping effect of electrons and other particles, promotes the conversion of electromagnetic wave energy into turbulent internal energy, severely hindering the Debye screening effect of electrons. As the incident wave frequency increases, the transmission coefficient gradually approaches 0 dB, indicating that in the range above 15 GHz, electromagnetic waves are almost completely transmitted, regardless of whether turbulence is present.

[0108] Simulation experiment 2: The present invention is used to simulate the influence of different turbulence outer scales on the propagation characteristics of electromagnetic waves in plasma turbulence. The gas ionization temperature is selected as 3000K and the number of turbulence is 1. The results are as follows: Figure 4 (a)(b).

[0109] Figure 4 The influence of different turbulence outer scales on electromagnetic wave propagation characteristics is given. Figure 4 As shown in (a), at 0-10GHz, the change in the size of the turbulence outer scale has no significant effect on the reflection coefficient of the electromagnetic wave. This is because the distance between the low-frequency incident wave and the turbulence cannot determine the reflection coefficient of the electromagnetic wave. As the frequency of the incident wave increases, the reflection coefficient of the electromagnetic wave shows an overall downward trend, and the amplitude of the oscillation shows a decreasing trend, which shows that high-frequency electromagnetic waves are not easily reflected. Figure 4 As shown in (b), when the incident wave frequency is between 0 and 15 GHz, the electromagnetic wave transmission coefficient increases as the outer scale of the turbulence increases. This is because the increase in the outer scale of the turbulence increases the interaction distance between the electromagnetic wave and the plasma turbulence. During electromagnetic wave transmission, the electric field of the electromagnetic wave inevitably accelerates free electrons. These accelerated electrons convert their energy into heat through collisions with other particles, further increasing energy attenuation. In other words, the increase in the outer scale of the turbulence increases the transmittance of the electromagnetic wave and strengthens the amplitude of the transmitted wave.

[0110] Simulation Experiment 3: Using the present invention to simulate the influence of different gas ionization temperatures on the propagation characteristics of electromagnetic waves in plasma turbulence, the outer scale of the turbulence is selected to be 1×10 -3 m, the number of turbulence is 1, and the results are as follows Figure 5 (a)(b).

[0111] Can Figure 5 The influence of different gas temperatures on the propagation characteristics of electromagnetic waves is given. Temperature fluctuations will affect the ionization process, and then affect the electron density, thus affecting the propagation characteristics of electromagnetic waves in plasma turbulence. Figure 5 As shown in (a), as the frequency of the incident wave increases, the reflection coefficient decreases and shows a periodic oscillation pattern. Due to the resonance between the evanescent wave in the dense plasma region and the standing wave in the boundary layer, many absorption peaks appear in the reflection coefficient curve. Overall, as the gas temperature increases, the reflection coefficient of the electromagnetic wave decreases. This is because the increase in gas temperature in turbulence increases the electron density, making it easier for electrons to collide with other particles, resulting in an increase in the total collision frequency in turbulence and a decrease in the reflection coefficient. Figure 5As shown in (b), for incident wave frequencies between 0 and 20 GHz, the transmission coefficient of electromagnetic waves increases with increasing gas temperature, but the increase is modest. This is because changing the gas temperature only alters the electron density distribution within the turbulent flow and has little effect on the transmission coefficient of the entire plasma. Furthermore, increasing gas temperature shifts the cutoff frequency toward higher frequencies.

[0112] The above-described embodiments merely illustrate several implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model, characterized in that: The following steps are involved: S1. Calculate the dielectric constant of plasma turbulence under the standard k-ε turbulence model based on the Saha equation for gas ionization and the refractive index of the plasma; S2. Based on the dielectric constant and the transmission matrix method, the propagation model of electromagnetic waves under different plasma turbulence parameters is calculated, and the propagation characteristics of electromagnetic waves are analyzed using the propagation model, specifically: S201. Calculate the propagation coefficient of electromagnetic waves through the dust plasma slab divided into n layers based on the dielectric constant: ； Where c is the speed of light in free space, ε r (m) It is k m The complex dielectric constant of the layer, ω is the incident wave frequency; S202. Calculate the total electric field of the electromagnetic wave passing through the dust plasma slab based on the propagation coefficient: ； Where R represents the amplitude of the reflected electric field and the amplitude of the incident electric field E y The ratio of the total reflection coefficient, T r The amplitude of the transmitted electric field is related to the incident electric field E y The total transmission coefficient of the ratio, They are the first layer incident area k0, the mth layer area k m , the last layer of transmission area k p The z component of the incident wave number, They are the first layer incident area k0, the mth layer area k m , the last layer of transmission area k p The x component of the incident wave number, B m and C m are the amplitudes of the reflected and transmitted waves toward +z and -z of the mth layer, respectively; S203. Combining the total electric field formula with the propagation matrix formula, we obtain: ； The area k Column matrix and region in 0 k p The relationship between the column matrices in is rearranged as follows: ； Among them, S g is the total scattering matrix, When S g Expressed as S g =(S g1 ,S g2 ) form, and then convert the formula into a propagation model: ； Among them, S g1 and S g2 Represents S g The first and second column vectors of ; S204. Calculate the propagation coefficients of the electromagnetic wave based on the propagation model: the total reflection coefficient and the total projection coefficient, and analyze the electromagnetic wave propagation characteristics based on the propagation coefficients.

2. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 1, characterized in that: The method for calculating the dielectric constant of plasma turbulence under the standard k-ε turbulence model according to the gas ionization Saha equation and the refractive index of the plasma in step S1 includes: S101. Based on the expression of the Saha equation for gas ionization under the standard k-ε model, derive the electron density in plasma turbulence; S102. Combine electron density and temperature fluctuations to calculate electron density fluctuations in plasma turbulence; S103. Calculating the refractive index in the plasma turbulence based on the electron density fluctuation and the electron-neutral particle collision frequency; S104. Using the property that the dielectric constant is approximately equal to the square of the refractive index, calculate the dielectric constant in plasma turbulence.

3. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 2, characterized in that: The electron density calculation formula in step S101 is as follows: ； Among them, n e is the electron density in the plasma turbulence, n0 is the total number of gas molecules, K B is the Boltzmann coefficient, h is the Planck coefficient, m e is the electron mass, T is the gas ionization temperature, E i is the ionization energy.

4. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 3, characterized in that: The electron density fluctuation formula in step S102 is: ； Among them, n' e is the electron density fluctuation, T' represents the temperature fluctuation; From the above formula, we can see that the ratio of electron density fluctuation to average electron density is greater than the ratio of temperature fluctuation to average temperature, which can be expressed as follows:

5. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 4, characterized in that: The refractive index calculation formula in step S103 is: ； in, ; ； Among them, n t is the refractive index in the plasma turbulence, v e represents the collision frequency of electron-neutral particles, ω represents the frequency of electromagnetic waves, ω p represents the plasma frequency, q is the charge, m e is the mass of electron, and ε0 is the dielectric constant in vacuum state.

6. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 5, characterized in that: The dielectric constant calculation formula in step S104 is: ； where ε is the dielectric constant in plasma turbulence; n t is the refractive index in the plasma turbulence, j 2 =-1.

7. The method for analyzing electromagnetic wave propagation characteristics based on the k-ε plasma turbulence model according to claim 6, characterized in that: The total reflection coefficient and total transmission coefficient are expressed in decibels: R dB =20log 10 (R),T dB =20log 10 (T r ).

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