A method, system, device and medium for inverting electron density based on stimulated electromagnetic radiation characteristics of a hypersonic target wake

Abstract

A method, system, device and medium for inverting electron density based on stimulated electromagnetic radiation characteristics of a hypersonic target wake, the method comprising: signal acquisition, signal processing, peak value screening, and inversion result obtaining; the system, device and medium are used to implement a method for inverting electron density based on stimulated electromagnetic radiation characteristics of a hypersonic target wake; the present application can achieve the effect of inverting the electron density distribution in the plasma without directly contacting the target by analyzing the stimulated electromagnetic radiation signal, can solve the problems of interference of the probe method on the fluid field, temperature sensitivity, limited measurement range and high cost of the laser interference method, has the non-invasive electron density measurement capability, and high sensitivity, and can have high sensitivity inversion effect without disturbing the target fluid.

Description

Technical Field

[0001] This invention relates to the field of wake electron density inversion technology, and in particular to a method, system, device and medium for inverting electron density based on the stimulated electromagnetic radiation characteristics of hypersonic target wakes. Background Technology

[0002] Hypersonic targets generate ions and electrons during high-speed travel, forming a plasma sheath at the head and a wake plasma downstream. Experimental studies often require measuring electron density in the wake. In wind tunnel experiments, researchers use probes to detect localized electron density. An electrostatic probe is a thin metal wire, with the exception of the working portion at the tip, the rest is covered with an insulating material such as ceramic or glass. Probe measurements require a size that matches the plasma parameters, satisfying the condition that it is much smaller than the mean free path of electrons and ions. The measurement environment also has specific requirements, including the absence of a strong magnetic field around the probe and a mean free path of the plasma greater than the probe size. When the probe is inserted into a hypersonic flow field, it collects charged particles from the plasma. By applying different bias voltages to the probe, different currents are obtained, and finally, a current-voltage curve is plotted to diagnose the wake plasma.

[0003] The spacecraft carries ionospheric detection instruments, which infer electron density distribution by measuring the characteristics of the ionosphere around the spacecraft, including the phase and frequency of signals.

[0004] A similar technique is laser interferometry, which utilizes the interaction between a laser beam propagating in a wake plasma and electrons in the flow field, causing a change in the refractive index and thus altering the optical path. By comparing the changes in the interference pattern, the electron density distribution can be deduced.

[0005] However, electrostatic probes typically have a certain disturbance effect on the plasma. In their paper "Numerical Simulation of Langmuir Probe Absorption Ion Current Theory in Plasma Sheath" (Li Wenqiu, Wang Gang, Xiang Dong & Su Xiaobao. Numerical Simulation of Langmuir Probe Absorption Ion Current Theory in Plasma Sheath. Journal of Vacuum Science and Technology 36, 1271-1278, doi:10.13922 / j.cnki.cjovst.2016.11.10(2016).), Li Wenqiu, Wang Gang, Xiang Dong & Su Xiaobao proposed that while obtaining the current-probe bias voltage (IV) characteristic curve along with the electrostatic probe's intrusion into the plasma, this technique itself is also... An inaccurate technique with inherent interference characteristics; Wang Qiu, Huang Jiandong, Nie Chunsheng, Zhao Wei & Yu Xilong, in "Research on Electrostatic Probe Testing Technology of Electron Density in High Enthalpy Flow" (Wang Qiu, Huang Jiandong, Nie Chunsheng, Zhao Wei & Yu Xilong. Research on Electrostatic Probe Testing Technology of Electron Density in High Enthalpy Flow. Science in China: Technological Sciences 46, 500-508 (2016).), proposed that the probe should ideally be located in the free flow region of collision-free molecular flow; otherwise, the probe theory needs to consider its own influence on the flow effect and make corresponding corrections. However, the above two technical solutions require free electrons in the plasma to flow onto the probe, which may affect the plasma during measurement. The location of the probe in the flow field of hypersonic targets is limited, and it will seriously interfere with the structure of the wake field, thus making the measurement results inaccurate. High temperature environments have a certain impact on electrostatic probes. Due to the material of the probe, temperature changes may cause changes in the probe's resistance, thus affecting the accuracy of current measurement. The surface characteristics of the electrostatic probe may affect the measurement results, especially when there is an electric field gradient or electric field eddy current between the plasma and the probe.

[0006] Laser interferometry is limited to transparent media, requiring the target to have good transparency; otherwise, it will be absorbed. Laser interferometry also demands high precision and stability from optical components, including the laser modulation and detection system, which may increase the difficulty and cost of experiments. Xiong Youde, Yu Tao, Xue Tao & Wu Jie, in "Advances in the Measurement of Hypersonic / Hypersonic Flows by Focused Laser Differential Interferometry" (Xiong Youde, Yu Tao, Xue Tao & Wu Jie. Advances in the Measurement of Hypersonic / Hypersonic Flows by Focused Laser Differential Interferometry. Experimental Fluid Mechanics 36, 9-20 (2022)), demonstrated measurement results with an effective measurement range of only about 8 mm for the laser interferometer, illustrating its limited measurement range. Hopkins, KJ, Porat, H., McIntyre, TJ, Wheatley, V. & Veeraragavan, A, in "Measurements and analysis of hypersonic tripped boundary layer turbulence"...

[0007] (Hopkins, KJ, Porat, H., McIntyre, TJ, Wheatley, V. & Veeraragavan, A. Measurements and analysis of hypersonic tripped boundary layer turbulence. Experiments in Fluids 62, 1-12 (2021).) proposed that laser interferometry equipment has high-precision detection performance, but at the same time, it requires the use of high-quality materials and precision-machined instruments for manufacturing and calibration, so high cost is an unavoidable problem. However, the above scheme may require multi-point or multi-angle measurement methods for electron density measurement in large-scale flow fields. Therefore, the measurement range of laser interferometry is usually limited. Summary of the Invention

[0008] To overcome the shortcomings of the prior art, the present invention aims to provide a method, system, device, and medium for inverting electron density based on the stimulated electromagnetic radiation characteristics of hypersonic target wakes. By analyzing stimulated electromagnetic radiation signals, the invention achieves the effect of inverting the electron density distribution in plasma without direct contact with the target. The present invention can solve the problems of interference with the fluid field and temperature sensitivity of the probe method, as well as the limited measurement range and high cost of the laser interferometry method. It has non-invasive electron density measurement capability and high sensitivity, and can achieve a highly sensitive inversion effect without interfering with the target fluid.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes the following steps:

[0011] Step 1: Obtain the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma;

[0012] Step 2: Process the stimulated electromagnetic radiation signal obtained in Step 1 to obtain the wavenumber spectrum of the stimulated radiation signal;

[0013] Step 3: Perform peak filtering on the wavenumber spectrum of the stimulated emission signal obtained in Step 2 to obtain the wavenumber of the stimulated emission signal;

[0014] Step 4: Using the wavenumber of the stimulated emission signal obtained in Step 3, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result.

[0015] The method for obtaining the stimulated electromagnetic radiation signal in step 1 includes obtaining it through calculation or through experimentation;

[0016] The stimulated electromagnetic radiation signal is obtained through calculations, including theoretical calculations using the Zakharov or Vlasov models.

[0017] Specifically, the experiment involved emitting an incident electromagnetic wave into the wake plasma and receiving it through a receiving antenna to obtain the stimulated electromagnetic radiation signal.

[0018] Step 2 specifically involves: expanding the stimulated electromagnetic radiation signal obtained in step 1 using Fourier transform to obtain the Langmuir wavenumber spectrum <|E(k)|. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 >, that is, the spatial average of local high-frequency electric field intensity and the spatial average of ion perturbation.

[0019] Step 3 specifically involves:

[0020] Step 3.1, respectively, the Langmuir wavenumber spectrum <|E(k)| obtained in Step 2. 2 >and ion acoustic wavenumber spectrum<| n (k)| 2 The value of > corresponds to the wave number;

[0021] Step 3.2, use the maximum peak value screening method to analyze the Langmuir wavenumber spectrum <|E(k)| corresponding to the values ​​in Step 3.1. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 Peak selection was performed to obtain the Langmuir wavenumber spectrum <|E(k)|. 2 >excited signal wavenumber and ion acoustic wavenumber spectrum<|n(k)| 2 > the stimulated signal wavenumber.

[0022] Step 4 specifically involves:

[0023] Step 4.1, using the Langmuir wavenumber spectrum <|E(k)| obtained in step 3.2 2 > the stimulated signal wavenumber, construct the Langmuir wave dispersion relation:

[0024]

[0025] In the formula, i represents the imaginary unit, ω0 represents the angular frequency of the incident electromagnetic wave, ω1 represents the angular frequency of the high-frequency Langmuir wave, k0 represents the wave number of the incident electromagnetic wave, k1 represents the wave number of the high-frequency Langmuir wave, and ν e (k1) represents the electron collision frequency, which is related to the Langmuir wavenumber; ΔΩ represents the normalized difference between the incident wave angular frequency and the target plasma frequency; |E (0)| represents the electric field intensity of the incident wave, ν i Indicates the ion collision frequency;

[0026] Step 4.2, using the ion acoustic wavenumber spectrum <|n(k)| obtained in step 3.2 2 >The stimulated signal wavenumber is used to construct the dispersion relation of the ion acoustic wave:

[0027]

[0028] In the formula, ω2 represents the angular frequency of the low-frequency ion acoustic wave, and c s ν represents the propagation speed of ion acoustic waves, k2 represents the wavenumber of low-frequency ion acoustic waves, i represents the imaginary unit, and ν represents the propagation speed of ion acoustic waves. i Indicates the ion collision frequency;

[0029] Step 4.3: Using the Langmuir wave dispersion relation obtained in Step 4.1 and the ion acoustic wave dispersion relation obtained in Step 4.2, construct the three-wave coupling resonance relation:

[0030] ω0=ω1+ω2

[0031] k0 = k1 + k2

[0032] In the formula, ω0 represents the incident electromagnetic wave angular frequency, ω1 represents the high-frequency Langmuir wave angular frequency, ω2 represents the low-frequency ion acoustic wave angular frequency, k0 represents the wave number of the incident electromagnetic wave, k1 represents the high-frequency Langmuir wave wave number, and k2 represents the low-frequency ion acoustic wave wave number.

[0033] Step 4.4: Using the relationships from steps 4.1, 4.2, and 4.3, construct equations to obtain the relationship between Langmuir wave, ion acoustic wave wavenumber, and plasma frequency:

[0034]

[0035] In the formula, ω p T represents the plasma frequency of the target. e T represents electron temperature. i The ion temperature is represented by M, the ion mass by m, the electron mass by k1, and the wavenumber of the high-frequency Langmuir wave.

[0036] Step 4.5: Use the relationship between Langmuir wave, ion acoustic wave wavenumber and plasma frequency obtained in step 4.4 to invert the electron density of the hypersonic target wake.

[0037] A system for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes:

[0038] Signal acquisition module: Acquires the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma;

[0039] Signal processing module: processes the stimulated electromagnetic radiation signal acquired by the signal acquisition module to obtain the wavenumber spectrum of the stimulated radiation signal;

[0040] Peak filtering module: Performs peak filtering on the wavenumber spectrum of the stimulated emission signal obtained by the signal processing module to obtain the wavenumber of the stimulated emission signal;

[0041] Inversion Result Acquisition Module: Using the wavenumber of the stimulated emission signal obtained by the peak screening module, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result.

[0042] A device for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes:

[0043] Memory: Used to store the computer program for implementing the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of hypersonic target wakes;

[0044] Processor: Used to implement the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake when executing the computer program.

[0045] A computer-readable storage medium:

[0046] The computer-readable storage medium stores a computer program that, when executed by a processor, enables a method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] 1. In step 1 of this invention, the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma is obtained, which has the advantage of a large monitoring range compared with the existing laser interferometry technology.

[0049] 2. The signal processing method in step 2 of this invention is performed on an algorithmic basis. Compared with existing laser interferometry, it has the advantages of stability and anti-interference, and will not affect the interference image due to minor vibrations.

[0050] 3. Step 3 of this invention analyzes the wavenumber spectrum, which has the advantage of easily removing noise compared with time domain analysis.

[0051] 4. In step 4 of this invention, the electron density inversion technique is used to obtain the inversion result, which has the advantage of being non-contact compared with existing probe techniques.

[0052] 5. The inversion method of the present invention can invert the electron density distribution in the hypersonic target wake plasma within a range of 20-80m. Compared with laser interferometry, the measurement range is significantly improved. The non-contact inversion measurement method provided by the present invention, compared with electrostatic probe, is free from direct contact measurement methods and does not need to interfere with the target plasma. It has the advantages of wide measurement range and non-contact.

[0053] In summary, compared with the prior art, the present invention can solve the problems of interference with the fluid field and temperature sensitivity of the probe method, as well as the limited measurement range and high cost of the laser interferometry. It has non-invasive electron density measurement capability and high sensitivity, and can achieve highly sensitive inversion results without interfering with the target fluid. Attached Figure Description

[0054] Figure 1 This is a flowchart of the method of the present invention.

[0055] Figure 2 This is a geometric model diagram of the hypersonic target wake plasma obtained through simulation in an embodiment of the present invention.

[0056] Figure 3 This is a hypersonic target wake plasma target electron number density distribution map provided in the embodiments of the present invention.

[0057] Figure 4 This is a schematic diagram of the dispersion function and three-wave coupling inversion theory provided in the embodiment of the present invention.

[0058] Figure 5 These are the Langmuir wave and ion acoustic wave wavenumber spectra provided in the embodiments of the present invention.

[0059] Figure 6 This is the true value map of the target plasma electron number density provided in the embodiments of the present invention.

[0060] Figure 7 This is a graph showing the inversion results of the Langmuir wavenumber provided in an embodiment of the present invention.

[0061] Figure 8 This is a graph showing the inversion result of the ion acoustic wavenumber provided in an embodiment of the present invention. Detailed Implementation

[0062] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0063] See Figure 1 A method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes the following steps:

[0064] Step 1: Obtain the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma;

[0065] Methods for obtaining stimulated electromagnetic radiation signals include obtaining them through calculation or through experimentation;

[0066] The stimulated electromagnetic radiation signal is obtained through calculations, including theoretical calculations using the Zakharov or Vlasov model. The Zakharov model contains two-fluid equations that describe the coupling process between the incident wave and the plasma wave. The frequency of the incident electromagnetic wave must be higher than the frequency of the wake plasma.

[0067] If stimulated emission signals are obtained through experiments, incident electromagnetic waves are emitted into the wake plasma. The incident frequency and wake plasma are required to be consistent with those in the following embodiment. Finally, the stimulated electromagnetic radiation signals are obtained by receiving them through a receiving antenna.

[0068] Compared with existing laser interferometry techniques, this method has the advantage of a larger monitoring range.

[0069] Step 2: Process the stimulated electromagnetic radiation signal obtained in Step 1 to obtain the wavenumber spectrum of the stimulated radiation signal, specifically as follows:

[0070] The stimulated electromagnetic radiation signal obtained in step 1 is expanded in wavenumber using Fourier transform to obtain the Langmuir wavenumber spectrum <|E(k)|. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 >, that is, the spatial average of local high-frequency electric field intensity and the spatial average of ion perturbation.

[0071] The signal processing in step 2 is performed on an algorithmic basis. Compared with existing laser interferometry techniques, it has the advantages of stability and anti-interference, and will not be affected by minor vibrations.

[0072] Step 3: Perform peak filtering on the wavenumber spectrum of the stimulated emission signal obtained in Step 2 to obtain the wavenumber of the stimulated emission signal. See [link to relevant documentation]. Figure 5 Specifically:

[0073] Step 3.1, respectively, the Langmuir wavenumber spectrum <|E(k)| obtained in Step 2. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 The value of > corresponds to the wave number;

[0074] Step 3.2, use the maximum peak value screening method to analyze the Langmuir wavenumber spectrum <|E(k)| corresponding to the values ​​in Step 3.1. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 Peak selection was performed to obtain the Langmuir wavenumber spectrum <|E(k)|. 2>excited signal wavenumber and ion acoustic wavenumber spectrum<|n(k)| 2 The stimulated signal wavenumber is the wavenumber of the signal. The wavenumber spectrum is in the form of strips with a few secondary peaks. The wavenumber corresponding to the maximum value of the spectral line is the stimulated signal wavenumber.

[0075] Step 3 involves analyzing the wavenumber spectrum, which has the advantage of easily removing noise compared to time-domain analysis.

[0076] Step 4: Using the wavenumber of the stimulated emission signal obtained in Step 3, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result, specifically:

[0077] Step 4.1, using the Langmuir wavenumber spectrum <|E(k)| obtained in step 3.2 2 > the stimulated signal wavenumber, construct the Langmuir wave dispersion relation:

[0078]

[0079] In the formula, i represents the imaginary unit, ω0 represents the angular frequency of the incident electromagnetic wave, ω1 represents the angular frequency of the high-frequency Langmuir wave, k0 represents the wave number of the incident electromagnetic wave, k1 represents the wave number of the high-frequency Langmuir wave, and ν e (k1) represents the electron collision frequency, which is related to the Langmuir wavenumber; ΔΩ represents the normalized difference between the incident wave angular frequency and the target plasma frequency; |E (0) | represents the electric field intensity of the incident wave, ν i Indicates the ion collision frequency;

[0080] Step 4.2, using the ion acoustic wavenumber spectrum <|n(k)| obtained in step 3.2 2 >The stimulated signal wavenumber is used to construct the dispersion relation of the ion acoustic wave:

[0081]

[0082] In the formula, ω2 represents the angular frequency of the low-frequency ion acoustic wave, and c s ν represents the propagation speed of ion acoustic waves, k2 represents the wavenumber of low-frequency ion acoustic waves, i represents the imaginary unit, and ν represents the propagation speed of ion acoustic waves. i Indicates the ion collision frequency;

[0083] Step 4.3: Using the Langmuir wave dispersion relation obtained in Step 4.1 and the ion acoustic wave dispersion relation obtained in Step 4.2, construct the three-wave coupling resonance relation:

[0084] ω0=ω1+ω2

[0085] k0 = k1 + k2

[0086] In the formula, ω0 represents the incident electromagnetic wave angular frequency, ω1 represents the high-frequency Langmuir wave angular frequency, ω2 represents the low-frequency ion acoustic wave angular frequency, k0 represents the wave number of the incident electromagnetic wave, k1 represents the high-frequency Langmuir wave wave number, and k2 represents the low-frequency ion acoustic wave wave number.

[0087] Step 4.4: Using the relationships from steps 4.1, 4.2, and 4.3, construct equations to obtain the relationship between Langmuir wave, ion acoustic wave wavenumber, and plasma frequency:

[0088]

[0089] In the formula, ω p T represents the plasma frequency of the target. e T represents electron temperature. i The ion temperature is represented by M, the ion mass by m, the electron mass by k1, and the wavenumber of the high-frequency Langmuir wave.

[0090] Step 4.5: Use the relationship between Langmuir wave, ion acoustic wave wavenumber and plasma frequency obtained in step 4.4 to invert the electron density of the hypersonic target wake.

[0091] In step 4, the inversion results are obtained using electron density inversion technology, which has the advantage of being non-contact compared with existing probe technology.

[0092] A system for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes:

[0093] Signal acquisition module: Acquires the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma;

[0094] Signal processing module: processes the stimulated electromagnetic radiation signal acquired by the signal acquisition module to obtain the wavenumber spectrum of the stimulated radiation signal;

[0095] Peak filtering module: Performs peak filtering on the wavenumber spectrum of the stimulated emission signal obtained by the signal processing module to obtain the wavenumber of the stimulated emission signal;

[0096] Inversion Result Acquisition Module: Using the wavenumber of the stimulated emission signal obtained by the peak screening module, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result.

[0097] A device for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake includes:

[0098] Memory: Used to store the computer program for implementing the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of hypersonic target wakes;

[0099] Processor: Used to implement the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake when executing the computer program.

[0100] A computer-readable storage medium:

[0101] The computer-readable storage medium stores a computer program that, when executed by a processor, enables a method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake.

[0102] The application effects of the present invention will be described in detail below with reference to the embodiments.

[0103] Step 1: Use the Zakharov model to obtain the stimulated electromagnetic radiation excited in the wake plasma by the pumping electromagnetic wave;

[0104] In this embodiment, a blunt cone target wake plasma with a Mach number of 18 is selected as the inversion target. The geometric parameters of the blunt cone model are as follows: Figure 2 The device is 2.011m long, with a 1m base length and an 8° blunt cone head with a radius of 0.25m. The electron density of the flow field is calculated using CFD (Computational Fluid Dynamics) simulation. The electron density details of the flow field are shown below. Figure 3 As shown, the electron density exhibits a distribution characteristic symmetrical about the central axis of the aircraft model, with the density decreasing the further away from the bottom of the aircraft. The Zakharov model is used to describe the interaction between the pumping electromagnetic wave and the target plasma. The incident wave perturbs the target plasma, exciting low-frequency ion acoustic waves and high-frequency Langmuir acoustic waves, as shown... Figure 4 As shown. The model equations are as follows:

[0105]

[0106]

[0107] In the formula, i represents the imaginary unit, E(x,t) is the total high-frequency field, n is the density perturbation of ions, n0 represents the total number of ions, and v s Let ε0 represent the ion sound velocity, ε0 represent the dielectric constant, and <> and || represent the spatial mean and absolute value, respectively. θ j =k j x-ω j t(j=0,1,2), ω j It is a complex number, k j It is a real number. It is θ j The conjugate of complex numbers.

[0108] The stimulated electromagnetic radiation signal is obtained by solving the Zakharov equation to solve for the interaction between the incident electromagnetic wave and the plasma.

[0109] Step 2: Process the stimulated electromagnetic radiation signal obtained in Step 1 to obtain the wavenumber spectrum of the stimulated radiation signal;

[0110] The stimulated emission signal obtained in step 1 is processed to obtain the Langmuir wavenumber spectrum <|E(k)|. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 The wavenumber spectra of the processed high-frequency and low-frequency signals are as follows: Figure 5 As shown, the horizontal axis of the spectrum represents the corresponding wavenumber, and the vertical axis represents the signal intensity. The two spectra show that the wavenumbers of both signals are concentrated at k = 28.023, but there are also mixed waves distributed around them. After cleaning, they are removed to obtain the peak wavenumber.

[0111] Step 3: Perform peak filtering on the wavenumber spectrum of the stimulated emission signal obtained in Step 2 to obtain the wavenumber of the stimulated emission signal, such as... Figure 5 As shown, specifically:

[0112] Step 3.1, respectively, the Langmuir wavenumber spectrum <|E(k)| obtained in Step 2. 2 > and ion acoustic wavenumber spectrum <|n(k)| 2 The value of > corresponds to the wave number;

[0113] Step 3.2, use the maximum peak value screening method to analyze the Langmuir wavenumber spectrum <|E(k)| corresponding to the values ​​in Step 3.1. 2 > and ion acoustic wavenumber spectrum<|n(k| 2 Peak selection was performed to obtain the Langmuir wavenumber spectrum <|E(k)|. 2 >excited signal wavenumber and ion acoustic wavenumber spectrum<|n(k)| 2 The stimulated signal wavenumber is the wavenumber of the signal. The wavenumber spectrum is in the form of strips with a few secondary peaks. The wavenumber corresponding to the maximum value of the spectral line is the stimulated signal wavenumber.

[0114] Step 4: Using the wavenumber of the stimulated emission signal obtained in Step 3, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result, specifically:

[0115] Depend on Figure 4 It can be seen that stimulated electromagnetic radiation is excited through three-wave coupled resonance within the target plasma, and the three-wave coupled resonance relationship is as follows:

[0116] ω0=ω1+ω2

[0117] k0 = k1 + k2

[0118] In the formula, ω0, ω1, ω2 represent the angular frequencies of the incident electromagnetic wave, the high-frequency Langmuir wave, and the low-frequency ion sound wave, respectively, and k0, k1, k2 represent the wave numbers of the incident electromagnetic wave, the high-frequency Langmuir wave, and the low-frequency ion sound wave, respectively.

[0119] By substituting E and n obtained in step 1 into the Zakharov equation and eliminating the low-frequency term n, the dispersion relation of the high-frequency Langmuir wave can be obtained. Similarly, the dispersion relation of the low-frequency example sound wave can be obtained as follows:

[0120]

[0121]

[0122] Based on the signal wavenumber obtained in step 2, the relationship between wavenumber and frequency can be obtained. By combining this with the resonance relationship, the relationship between wavenumber and plasma frequency can be obtained:

[0123]

[0124] Where, ω p For the target plasma frequency, T e It is the electron temperature, T i M represents the ion temperature, M represents the ion mass, and m represents the electron mass.

[0125] The above equation shows that the Langmuir wavenumber is related to the plasma frequency, and the electron number density can be inverted given the incident wave.

[0126] Figure 5 Taking the results shown as an example, after obtaining k1 = 28.023, the target plasma frequency ω can be obtained through wavenumber calculation using the formula above. p =1.136×10 8 rad / s, and thus the electron number density distribution n e =4.056×10 12 / m 3 Applying this theory to all plasma micro-elements within the target range yields the inversion results for these targets.

[0127] like Figure 3 As shown, the wake plasma within a range of 20m to 80m from the bottom of the blunt cone target and within 1m from the central axis is taken as the research target. The true value of the electron number density of the target flow field is as follows: Figure 6 As shown, the horizontal axis represents the distance from the bottom of the aircraft, and the vertical axis represents the width of the contrail. Figure 7 , Figure 8 The inversion results of this embodiment have the same meaning as... Figure 6Similarly, the results show that the electron number density distribution of the target wake plasma can be accurately obtained within the effective range.

[0128] To evaluate performance, the normalized root mean square error of the electron number density is defined as follows:

[0129]

[0130] Where, n e反 n is the electron density inversion value. e真 δ represents the true value of the electron density, and N represents the total number of infinitesimal elements within the effective inversion region; the error of the example is δ = 0.0549.

[0131] In summary, this method offers high resolution, achieving an accuracy of 0.1m × 0.1m in this embodiment, enabling high-resolution inversion; it is non-invasive, requiring no physical contact with the object being measured, which is crucial for applications where the object remains unaffected; and it has a wide range, accurately reflecting up to 100m in this embodiment. 2 The invention measures the electron density distribution of the wake within a certain range. Therefore, compared with existing technologies, this invention can solve the problems of interference with the fluid field and temperature sensitivity of probe methods, as well as the limited measurement range and high cost of laser interferometry. It has non-invasive electron density measurement capabilities and high sensitivity, and can achieve highly sensitive inversion results without disturbing the target fluid.

Claims

1. A method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake, characterized in that, Includes the following steps: Step 1: Obtain the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma; Step 2: Process the stimulated electromagnetic radiation signal obtained in Step 1 to obtain the wavenumber spectrum of the stimulated radiation signal; Step 3: Perform peak filtering on the wavenumber spectrum of the stimulated emission signal obtained in Step 2 to obtain the wavenumber of the stimulated emission signal; Step 4: Using the wavenumber of the stimulated emission signal obtained in Step 3, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result; Step 2 specifically involves expanding the stimulated electromagnetic radiation signal obtained in step 1 using Fourier transform to obtain the Langmuir wavenumber spectrum. ion acoustic wavenumber spectrum That is, the spatial average of local high-frequency electric field intensity and the spatial average of ion perturbation; Step 3 specifically involves: Step 3.1, respectively, the Langmuir wavenumber spectra obtained in Step 2 are... ion acoustic wavenumber spectrum The value corresponds to the wavenumber; Step 3.2: Use the maximum peak value screening method to analyze the Langmuir wavenumber spectra obtained from the numerical values ​​in Step 3.1 after matching the wavenumbers. ion acoustic wavenumber spectrum Peak selection was performed to obtain the Langmuir wavenumber spectrum. Excited signal wavenumber and ion acoustic wavenumber spectrum The stimulated signal wavenumber.

2. The method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake according to claim 1, characterized in that, The method for obtaining the stimulated electromagnetic radiation signal in step 1 includes obtaining it through calculation or through experimentation; The stimulated electromagnetic radiation signal is obtained through calculations, including theoretical calculations using the Zakharov or Vlasov models. Specifically, the experiment involved emitting an incident electromagnetic wave into the wake plasma and receiving it through a receiving antenna to obtain the stimulated electromagnetic radiation signal.

3. The method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Utilize the Langmuir wavenumber spectrum obtained in Step 3.

2. The Langmuir wave dispersion relation is constructed based on the stimulated signal wavenumber: In the formula, Represents the imaginary unit. Indicates the angular frequency of the incident electromagnetic wave. Indicates the high-frequency Langmuir wave angular frequency. The wave number represents the incident electromagnetic wave. Indicates the wavenumber of the high-frequency Langmuir wave. This indicates the electron collision frequency, which is related to the Langmuir wavenumber. This represents the normalized difference between the incident wave angular frequency and the target plasma frequency. Indicates the electric field intensity of the incident wave. Indicates the ion collision frequency; Step 4.2, using the ion acoustic wavenumber spectrum obtained in step 3.

2. The dispersion relation of ion acoustic waves is constructed by determining the stimulated signal wavenumber: In the formula, This indicates the angular frequency of the low-frequency ion acoustic wave. This represents the propagation speed of ion sound waves. Indicates the wavenumber of low-frequency ion acoustic waves. Represents the imaginary unit. Indicates the ion collision frequency; Step 4.3: Using the Langmuir wave dispersion relation obtained in Step 4.1 and the ion acoustic wave dispersion relation obtained in Step 4.2, construct the three-wave coupling resonance relation: In the formula, Indicates the angular frequency of the incident electromagnetic wave. Indicates the high-frequency Langmuir wave angular frequency. This indicates the angular frequency of the low-frequency ion acoustic wave. The wave number represents the incident electromagnetic wave. Indicates the wavenumber of the high-frequency Langmuir wave. Indicates the wavenumber of low-frequency ion acoustic waves; Step 4.4: Using the relationships from steps 4.1, 4.2, and 4.3, construct equations to obtain the relationship between Langmuir wave, ion acoustic wave wavenumber, and plasma frequency: In the formula, Indicates the plasma frequency of the target. Indicates electron temperature, Indicates ion temperature. Indicates ion mass. Indicates electron mass, Indicates the wavenumber of the high-frequency Langmuir wave; Step 4.5: Use the relationship between Langmuir wave, ion acoustic wave wavenumber and plasma frequency obtained in step 4.4 to invert the electron density of the hypersonic target wake.

4. A system for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake, used to implement the method of claim 1, characterized in that, include: Signal acquisition module: Acquires the stimulated electromagnetic radiation signal excited by the incident electromagnetic wave in the wake plasma; Signal processing module: processes the stimulated electromagnetic radiation signal acquired by the signal acquisition module to obtain the wavenumber spectrum of the stimulated radiation signal; Peak filtering module: Performs peak filtering on the wavenumber spectrum of the stimulated emission signal obtained by the signal processing module to obtain the wavenumber of the stimulated emission signal; Inversion Result Acquisition Module: Using the wavenumber of the stimulated emission signal obtained by the peak screening module, the electron number density of the target plasma is inverted through the dispersion relation to obtain the inversion result.

5. A device for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake, characterized in that, include: Memory: for storing a computer program for implementing the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake as described in any one of claims 1-3; Processor: Used to implement, when executing the computer program, a method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake, as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the method for inverting electron density based on the stimulated electromagnetic radiation characteristics of a hypersonic target wake, as described in any one of claims 1-3.

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