A method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence

Abstract

The present invention relates to a method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence. Based on the power spectrum of the refractive index fluctuations of anisotropic plasma turbulence and the Rytov approximation theory, the long-term beam broadening and scintillation index of Gaussian beams in anisotropic plasma turbulence are solved. Two anisotropy factors are introduced to parameterize the anisotropic characteristics of the turbulence unit in the horizontal and vertical directions. The long-term beam broadening and scintillation index are simulated, and ultimately the propagation characteristic data of Gaussian beams in anisotropic hypersonic plasma turbulence are obtained. This method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence overcomes the shortcomings of the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence, making the wave propagation problem in hypersonic plasma turbulence not only based on isotropy, but also providing a theoretical basis for subsequent electromagnetic wave propagation problems in plasma turbulence.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic wave technology, and in particular relates to a method for calculating the propagation characteristics of a Gaussian beam in anisotropic hypersonic plasma turbulence. Background Art

[0002] Over the years, as aerospace engineering and military defense have significantly increased their importance in various countries, scientists have increasingly extensively researched hypersonic vehicles. A plasma sheath forms on the surface of high-speed aircraft. Hypersonic flow field experiments have demonstrated the presence of severe turbulence within this sheath. Hypersonic plasma turbulence causes random jitter in the amplitude and wavefront phase of electromagnetic waves, leading to signal distortion and severe disruption of relay communications between the aircraft and the ground, resulting in the "blackout" phenomenon. Therefore, studying the interaction between hypersonic plasma turbulence and optical waves is crucial, providing a theoretical foundation and basis for addressing this "blackout" problem.

[0003] Light waves exhibit numerous properties in atmospheric turbulence, such as beam drift, beam spread, arrival angle fluctuations, and scintillation index. Similarly, light waves exhibit numerous properties in hypersonic plasma turbulence. Previous studies have focused on non-Kolmogorov power spectra. The broadening and scintillation index of Gaussian beams in anisotropic plasma turbulence will fill this gap in research on anisotropic plasma turbulence. Yang Shaofei et al. proposed an anisotropic power spectrum of refractive index fluctuations in hypersonic plasma turbulence. Based on this anisotropic plasma turbulence power spectrum, and using the Rytov approximation and other approximations, they derived the broadening and scintillation index of Gaussian beams in turbulent plasma media.

[0004] In summary, there are many theoretical foundations for the study of atmospheric turbulence, and some work has also been done based on the non-Kolmogorov power spectrum of plasma turbulence, but there is little research on the propagation of light and electromagnetic waves in anisotropic plasma turbulence. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence in order to solve the above problems, so as to obtain the propagation characteristics of electromagnetic waves in anisotropic hypersonic plasma turbulence.

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

[0007] A method for calculating the propagation characteristics of a Gaussian beam in anisotropic hypersonic plasma turbulence comprises the following steps:

[0008] Step S1, obtaining the anisotropic hypersonic plasma turbulence refractive index fluctuation power spectrum Φ(κ) and introducing two anisotropy factors, using the two anisotropy factors to parameterize the anisotropic characteristics of the turbulence unit in the horizontal and vertical directions, and obtaining the refractive index fluctuation power spectrum Φ(κ) containing the two anisotropy factors x ,κ y );

[0009] Step S2: Obtain the long-term beam width W of the Gaussian beam in the turbulent medium based on the Rytov approximation theory. e , the calculation formula is:

[0010]

[0011] in, L represents the distance the light beam travels along the propagation axis, k represents the wave number, Λ is the beam parameter, and the calculation formula for T is:

[0012]

[0013] Where ξ is the normalized path coordinate, and ξ = 1-z / L;

[0014] Step S3: The refractive index fluctuation power spectrum Φ(κ x ,κ y ) coordinate system conversion calculation to obtain the calculated data Φ(q,0) and substitute it into the calculation formula T, use the confluent hypergeometric function U(a; c; z) to solve T, substitute T into the long-term beam broadening calculation formula of Gaussian beam in turbulent medium, and obtain the long-term beam broadening data W containing two anisotropic parameters after calculation e , where the calculation formula T of the calculation data Φ(q,0) is substituted into:

[0015]

[0016] Where C1=8π 2 k 2 L,

[0017] Step S4: Obtain the scintillation index of the Gaussian beam in the turbulent medium based on the Rytov approximation theory Will Decompose into two integrals, radial and axial and Among them, the scintillation index of Gaussian beam in turbulent medium is The expressions of radial and axial integrals are:

[0018]

[0019]

[0020]

[0021] Where ρ represents the distance from the beam center in the plane orthogonal to the z-axis, Θ is the beam parameter, I0(x)=J0(ix) is the modified Bessel function;

[0022] Step S5: Set the flicker index Simplified into two integrals: radial and axial and And substitute the anisotropic refractive index fluctuation power spectrum Φ(q,0) into the simplified radial and axial integrals respectively and The calculated flicker index is obtained after calculation Flicker Index The expression is:

[0023]

[0024] Step S6: Based on the anisotropy parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index A simulation model was constructed to obtain the distribution curves of beam broadening and scintillation index, and based on the distribution curves of long-term beam broadening and scintillation index, the propagation characteristic data of Gaussian beams in anisotropic hypersonic plasma turbulence were obtained.

[0025] As a further optimization solution of the present invention, the expression of the anisotropic hypersonic plasma turbulent refractive index fluctuation power spectrum Φ(κ) in step S1 is:

[0026]

[0027] in, ξ x and ξ y are the anisotropy parameters in the horizontal and vertical directions, is the variance of the refractive index fluctuation, L0 is the outer scale of turbulence, κ0 = 2π / l0, l0 is the inner scale of turbulence, m = 4-D, D is the fractal dimension, a = 475(κ0) 2.683 ;

[0028] The power spectrum of refractive index fluctuation Φ(κ) with two anisotropy factors x ,κ y ) is:

[0029]

[0030] As a further optimization solution of the present invention, the expression of the beam parameter Θ in step S4 is:

[0031]

[0032] in,

[0033]

[0034]

[0035]

[0036] W0 is the beam width, R0 is the phase front curvature radius, and Θ0=1.

[0037] As a further optimization scheme of the present invention, the anisotropic refractive index fluctuation power spectrum Φ(q,0) is substituted into the radial and axial integrals respectively. and The flicker index is obtained by calculation, which specifically includes the following steps:

[0038] Step S5.1: Simplify the radial integral using approximation Among them, the approximate formula is:

[0039]

[0040]

[0041] Among them, the radial integral The simplified expression is:

[0042]

[0043] Step S5.2: Simplify the radial integral Decompose into two integrals and Calculate and substitute the power spectrum Φ(q,0) into the calculation to obtain the radial integral of the scintillation index and in,

[0044]

[0045]

[0046] Step S5.3: Simplify the axial component using approximation and decomposed into two integrals and Substituting the power spectrum Φ(q,0) into the calculation, the axial integral of the scintillation index is obtained and in,

[0047]

[0048]

[0049] Step S5.4: Combine the radial component and the axial component of the scintillation index to obtain the calculated scintillation index. Flicker Index The expression is:

[0050]

[0051] As a further optimization solution of the present invention, the anisotropic parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index Construct a simulation model, specifically, with anisotropic parameter ξ x , transmission distance L, refractive index fluctuation variance The horizontal axis is combined with the long-term beam broadening W e , logarithm of flicker index A simulation model is constructed for the vertical axis, and the long-term beam broadening and scintillation index of the Gaussian in hypersonic plasma turbulence are simulated respectively to obtain the distribution curves of the beam broadening and scintillation index.

[0052] The beneficial effects of the present invention are:

[0053] Based on the power spectrum of the refractive index fluctuation of anisotropic plasma turbulence and the Rytov approximation theory, the present invention solves the long-term beam broadening and scintillation of a Gaussian beam in anisotropic plasma turbulence, introduces two anisotropy factors to parameterize the anisotropic characteristics of the turbulence unit in the horizontal and vertical directions, simulates the long-term beam broadening and scintillation index, and ultimately obtains the propagation characteristic data of the Gaussian beam in anisotropic hypersonic plasma turbulence. This makes up for the shortcomings of the propagation characteristics of the Gaussian beam in anisotropic hypersonic plasma turbulence, makes the wave propagation problem in hypersonic plasma turbulence not only based on isotropy, and provides a theoretical basis for subsequent electromagnetic wave propagation problems in plasma turbulence. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is the overall flow chart of the present invention;

[0055] Figure 2Schematic diagram of the Gaussian beam broadening model in anisotropic plasma turbulence in the present invention;

[0056] Figure 3 is the simulation anisotropy parameter ξ of the present invention x The relationship between Gaussian beam width and transmission distance L at different times;

[0057] Figure 4 is a diagram showing the relationship between Gaussian beam broadening and transmission distance L when the internal scale l0 is different in the simulation of the present invention;

[0058] Figure 5 The simulated refractive index fluctuation power spectrum of the present invention When the Gaussian beam broadening is different from the anisotropy parameter ξ x relationship diagram;

[0059] Figure 6 The Gaussian beam broadening and anisotropy parameter ξ are different when the outer scale L0 of the simulation is different. x relationship diagram;

[0060] Figure 7 is the simulation anisotropy parameter ξ of the present invention x At different times, the scintillation index of the Gaussian beam is related to the variance of the refractive index fluctuation relationship diagram;

[0061] Figure 8 The scintillation index and refractive index fluctuation variance of the Gaussian beam when the outer scale l0 of the present invention is different relationship diagram;

[0062] Figure 9 The scintillation index and anisotropy parameter ξ of the Gaussian beam when the outer scale l0 of the simulation is different x relationship diagram;

[0063] Figure 10 is the variance of the simulated refractive index fluctuation of the present invention When different, the scintillation index of the Gaussian beam is related to the anisotropy parameter ξ x relationship diagram. DETAILED DESCRIPTION

[0064] 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.

[0065] Example 1

[0066] like Figures 1 to 2As shown, a method for calculating the propagation characteristics of a Gaussian beam in anisotropic hypersonic plasma turbulence includes the following steps:

[0067] Step S1, obtaining the anisotropic hypersonic plasma turbulence refractive index fluctuation power spectrum Φ(κ) and introducing two anisotropy factors, using the two anisotropy factors to parameterize the anisotropic characteristics of the turbulence unit in the horizontal and vertical directions, and obtaining the refractive index fluctuation power spectrum Φ(κ) containing the two anisotropy factors x ,κ y );

[0068] Among them, according to the experimental results of the hypersonic flow field, the von Kármán spectrum model is modified to obtain the expression of the power spectrum of the anisotropic hypersonic plasma turbulent refractive index fluctuation. The expression of the power spectrum of the anisotropic hypersonic plasma turbulent refractive index fluctuation Φ(κ) is:

[0069]

[0070] in, ξ x and ξ y are the anisotropy parameters in the horizontal and vertical directions, is the refractive index fluctuation variance, L0 is the outer scale of turbulence, κ0 = 2π / l0, l0 is the inner scale of turbulence, m = 4-D, D is the fractal dimension, and from the results of hypersonic experiments, we know that a = 475(κ0) 2.683 ;

[0071] Among them, the relationship between L0 and l0 is:

[0072]

[0073] Among them, the Rayleigh number R e =5.06×10 3 / m;

[0074] Using the Markov approximation method and assuming that the power spectrum of the refractive index fluctuation of the hypersonic plasma turbulence is delta-correlated at any pair of points along the propagation direction, the spatial wave number vector k can be ignored. z , the refractive index fluctuation power spectrum Φ(κ x ,κ y ) is:

[0075]

[0076] Step S2: Obtain the long-term beam width W of the Gaussian beam in the turbulent medium based on the Rytov approximation theory. e , the calculation formula is:

[0077]

[0078] in, L represents the distance the beam travels along the propagation axis, k represents the wave number, and Λ is the beam parameter;

[0079] According to the Rytov approximation theory, the expression of T is obtained:

[0080]

[0081] Because Lκ 2 / k<<1, after simplifying it using geometric optics approximation, the calculation formula of T is:

[0082]

[0083] Where ξ is the normalized path coordinate, and ξ = 1-z / L;

[0084] Step S3: The refractive index fluctuation power spectrum Φ(κ x ,κ y ) coordinate system conversion calculation to obtain the calculation data Φ(q,0) and substitute the calculation data Φ(q,0) into the calculation formula T. Using the confluent hypergeometric function U(a; c; z), substitute the obtained calculation formula T into the long-term beam broadening calculation formula of the Gaussian beam in the turbulent medium. After calculation, the long-term beam broadening data W containing two anisotropic parameters is obtained. e , where the calculation formula T of the calculation data Φ(q,0) is substituted into:

[0085]

[0086] Where C1=8π 2 k 2 L,

[0087] Specifically, the stretched coordinate system of the anisotropic refractive index fluctuation power spectrum is transformed into an isotropic coordinate system, and the power spectrum is written in the form of Φ(q,0).

[0088]

[0089]

[0090] Where θ represents the angle between q and the x-axis, and the power spectrum is written as:

[0091]

[0092] Substituting Φ(q,0) into T, we get:

[0093]

[0094] C1=8π 2 k 2 L,

[0095] Using the second kind of confluent hypergeometric function U(a; c; z),

[0096]

[0097] Write T as:

[0098]

[0099] in,

[0100] because Using similarity:

[0101]

[0102] Finally, the expression containing the anisotropy factor T is obtained:

[0103]

[0104] Step S4: Obtain the scintillation index of the Gaussian beam in the turbulent medium based on the Rytov approximation theory After decomposition, obtain radial and axial integrals and Among them, the scintillation index of Gaussian beam in turbulent medium is The expressions of radial and axial integrals are:

[0105]

[0106]

[0107]

[0108]

[0109] Where ρ represents the distance from the beam center in the plane orthogonal to the z-axis, Θ is the beam parameter, I0(x)=J0(ix) is the modified Bessel function;

[0110] The expression of the beam parameter Θ is:

[0111]

[0112] in,

[0113]

[0114]

[0115]

[0116] W0 is the beam width, R0 is the phase front curvature radius, and Θ0=1.

[0117] Step S5: Set the flicker index Divided into two integrals, radial and axial and And substitute the anisotropic refractive index fluctuation power spectrum Φ(q,0) into the simplified radial and axial integrals respectively and The calculated flicker index is obtained after calculation Flicker Index The expression is:

[0118]

[0119] Among them, the anisotropic refractive index fluctuation power spectrum Φ(q,0) is substituted into the simplified radial and axial integrals respectively. and The flicker index is obtained by calculation, which specifically includes the following steps:

[0120] Step S5.1: Simplify the radial integral using approximation Among them, the approximate formula is expressed as:

[0121]

[0122]

[0123] Among them, the radial integral The simplified expression is:

[0124]

[0125] Step S5.2: Simplify the radial integral Further decomposed into two integrals and Substituting the power spectrum Φ(q,0) into the calculation, we can obtain the radial integral of the scintillation index: and in,

[0126]

[0127]

[0128] Step S5.3: Simplify the axial component using approximation and decomposed into two integrals and Substituting the power spectrum Φ(q,0) into the calculation, we can obtain the axial component of the scintillation index. and Specifically, because Will It can be expressed approximately as:

[0129]

[0130] but and becomes:

[0131]

[0132]

[0133] Substituting the refractive index fluctuation power spectrum into and The final result is:

[0134]

[0135]

[0136] Step S5.4: Combine the radial component and the axial component of the scintillation index to obtain the calculated scintillation index. Flicker Index The expression is:

[0137]

[0138] Step S6: Based on the anisotropy parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index A simulation model was constructed to obtain the distribution curves of beam broadening and scintillation index, and based on the distribution curves of beam broadening and scintillation index, the propagation characteristic data of Gaussian beam in anisotropic hypersonic plasma turbulence was obtained.

[0139] Among them, based on the anisotropy parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index Construct a simulation model, specifically, with anisotropic parameter ξ x , transmission distance L, refractive index fluctuation variance The horizontal axis is combined with the long-term beam broadening W e , logarithm of flicker index A simulation model is constructed for the vertical axis, and the long-term beam broadening and scintillation index of the Gaussian in hypersonic plasma turbulence are simulated respectively to obtain the distribution curves of the beam broadening and scintillation index.

[0140] In order to make the distribution curve of the scintillation index more obvious, the logarithm of the scintillation index is calculated, and this distribution curve is used to better study the influence of hypersonic plasma turbulence on the Gaussian beam.

[0141] Experimental Example 1

[0142] Experimental simulation conditions

[0143] The parameters of plasma turbulence are as follows: Gaussian beam, beam width W0 = 0.01 m, wave number k = 1.25 × 10 5 / m, refractive index fluctuation variance Anisotropy parameter ξ y =1, turbulent outer scale L0 = 0.3m, Reynolds number R e =5.06×10 3 / m.

[0144] Experimental results analysis

[0145] In the first simulation experiment, the present invention is used to simulate and calculate the Gaussian beam broadening distribution in anisotropic plasma turbulence.

[0146] The results are as follows Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As shown, from the comparison of the four figures, it can be seen that the long-term beam broadening decreases with the increase of the anisotropy parameter, and decreases with the increase of the inner scale, the decrease of the variance of the refractive index fluctuation and the increase of the outer scale.

[0147] This shows that increasing the anisotropy of turbulence can reduce the turbulence effect, thereby weakening the influence of turbulence on Gaussian beams.

[0148] Simulation experiment 2: The present invention is used to simulate the Gaussian beam scintillation index in anisotropic plasma turbulence. The results are as follows: Figure 7 、 Figure 8 、 Figure 9 and Figure 10 As shown in the figure, it can be seen from the comparison of the four figures that the scintillation index decreases with the increase of turbulence anisotropy, and decreases with the increase of outer scale and the decrease of refractive index fluctuation variance.

[0149] This phenomenon shows that the larger the outer scale of the plasma turbulence, the smaller the impact of the turbulence on the Gaussian beam, the larger the variance of the refractive index fluctuation, the more complex the turbulent microstructure, and the stronger the scattering effect on the Gaussian beam.

[0150] 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 variations and improvements are possible within the scope of the present invention, as would be apparent to those skilled in the art. These variations and improvements are fully encompassed within the scope of the present invention.

Claims

1. A method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence, characterized in that: The following steps are involved: Step S1, obtaining the anisotropic hypersonic plasma turbulence refractive index fluctuation power spectrum Φ(κ) and introducing two anisotropy factors, using the two anisotropy factors to parameterize the anisotropic characteristics of the turbulence unit in the horizontal and vertical directions, and obtaining the refractive index fluctuation power spectrum Φ(κ) containing the two anisotropy factors x ,κ y ); Step S2: Obtain the long-term beam width W of the Gaussian beam in the turbulent medium based on the Rytov approximation theory. e , the calculation formula is: in, L represents the distance the light beam travels along the propagation axis, k represents the wave number, Λ is the beam parameter, and the calculation formula for T is: Where ξ is the normalized path coordinate, and ξ = 1-z / L; Step S3: The refractive index fluctuation power spectrum Φ(κ x ,κ y ) coordinate system conversion calculation to obtain the calculated data Φ(q,0) and substitute Φ(q,0) into the calculation formula T, using the confluent hypergeometric function U(a; c; z), and substitute the obtained T into the long-term beam broadening calculation formula of Gaussian beam in turbulent medium, and calculate the long-term beam broadening data W containing two anisotropic parameters e , where the calculation formula T of the calculation data Φ(q,0) is substituted into: Where C1=8π 2 k 2 L, Step S4: Obtain the scintillation index of the Gaussian beam in the turbulent medium based on the Rytov approximation theory After decomposition, obtain radial and axial integrals and Among them, the scintillation index of Gaussian beam in turbulent medium is The expressions of radial and axial integrals are: Where ρ represents the distance from the beam center in the plane orthogonal to the z-axis, Θ is the beam parameter, I0(x)=J0(ix) is the modified Bessel function; Step S5: Set the flicker index Simplified into two integrals: radial and axial and And substitute the anisotropic refractive index fluctuation power spectrum Φ(q,0) into the simplified radial and axial integrals respectively and The calculated flicker index is obtained after calculation Flicker Index The expression is: Step S6: Based on the anisotropy parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index Build a simulation model to obtain the distribution curves of beam broadening and scintillation index, and based on the distribution curves of beam broadening and scintillation index, obtain the propagation characteristic data of Gaussian beams in anisotropic hypersonic plasma turbulence; The expression of the anisotropic hypersonic plasma turbulence refractive index fluctuation power spectrum Φ(κ) in step S1 is: in, ξ x and ξ y are the anisotropy parameters in the horizontal and vertical directions, is the variance of the refractive index fluctuation, L0 is the outer scale of turbulence, κ0 = 2π / l0, l0 is the inner scale of turbulence, m = 4-D, D is the fractal dimension, a = 475(κ0) 2.683 ; The power spectrum of refractive index fluctuation Φ(κ) with two anisotropy factors x ,κ y ) is:

2. The method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence according to claim 1, characterized in that: The expression of the beam parameter Θ in step S4 is: in, W0 is the beam width, R0 is the phase front curvature radius, and Θ0=1.

3. The method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence according to claim 1, characterized in that: Substitute the anisotropic refractive index fluctuation power spectrum Φ(q,0) into the simplified radial and axial integrals respectively and The flicker index is obtained by calculation, which specifically includes the following steps: Step S5.1: Simplify the radial integral using approximation Among them, the approximate expression is: Among them, the radial integral The simplified expression is: Step S5.2: Simplify the radial integral Decompose into two integrals and Substituting the power spectrum Φ(q,0) into the calculation, we can obtain the radial integral of the scintillation index: and in, Step S5.3: Simplify the axial component using approximation and decomposed into two integrals and Substituting the power spectrum Φ(q,0) into the calculation, we can obtain the axial component of the scintillation index. and in, Step S5.4: Combine the radial component and the axial component of the scintillation index to obtain the calculated scintillation index. Flicker Index The expression is:

4. The method for calculating the propagation characteristics of Gaussian beams in anisotropic hypersonic plasma turbulence according to claim 1, wherein: The anisotropy parameter ξ x , transmission distance L, refractive index fluctuation variance and the long-term beam broadening W e , logarithm of flicker index Construct a simulation model, specifically, with anisotropic parameter ξ x , transmission distance L, refractive index fluctuation variance The horizontal axis is combined with the long-term beam broadening W e , logarithm of flicker index A simulation model is constructed for the vertical axis, and the long-term beam broadening and scintillation index of the Gaussian in hypersonic plasma turbulence are simulated respectively to obtain the distribution curves of the beam broadening and scintillation index.

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