Plasma field three-dimensional chromatography reconstruction method based on microwave reflection and probe combined measurement

By combining microwave reflection and electrostatic probe measurement, with Gaussian process regression model and multi-view optical tomography technology, the problem of three-dimensional reconstruction of plasma sheath electron density in high-temperature and high-speed environment was solved, and high-precision electron density diagnosis and "black barrier" relief were achieved.

CN120703815APending Publication Date: 2025-09-26UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Patent Information

Application Number
CN202510762119.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-06-09
Publication Date
2025-09-26

AI Technical Summary

Technical Problem

Existing technologies make it difficult to achieve non-contact, high-precision three-dimensional structural reconstruction of the plasma sheath electron density in a high-temperature and high-speed environment. A single method has the problem of difficulty in balancing stability and accuracy in complex flow fields.

Method used

Microwave reflection and electrostatic probe joint measurement are used, combined with Gaussian process regression model and multi-view optical tomography technology, and multi-source data are integrated to reconstruct plasma parameters, achieving high-precision fitting and three-dimensional reconstruction of electron density.

Benefits of technology

It has achieved high-precision diagnosis of the plasma sheath during the re-entry of a hypersonic vehicle, breaking through the limitations of spatiotemporal resolution and reliability of traditional measurement methods, providing an electron density field with millimeter-level resolution, and alleviating the "black barrier" phenomenon.

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Abstract

The invention discloses a plasma field three-dimensional chromatography reconstruction method based on microwave reflection and probe combined measurement, which comprises the following steps: firstly setting the frequency of a microwave antenna and the measurement position of a probe, and then realizing high-precision combined diagnosis of electron density distribution by combining the global non-contact measurement advantage of a microwave reflection method and the local fine measurement capability of an electrostatic probe; and then realizing high-precision fitting of the electron density based on a physical constraint Gaussian process regression model, establishing a mapping relation between the electron density and an emission coefficient, and finally reconstructing a three-dimensional electron density field with millimeter-level resolution.
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Description

Technical Field

[0001] The present invention belongs to the technical field of electron density measurement, and more specifically, relates to a plasma field three-dimensional tomography reconstruction method based on combined microwave reflection and probe measurement. Background Art

[0002] During reentry, a hypersonic vehicle forms a layer of high-temperature ionized gas, known as a plasma sheath, around the vehicle. This plasma sheath contains a large number of free electrons, which can form a dielectric barrier on the vehicle's surface, causing the so-called "blackout" phenomenon. Therefore, to mitigate the blackout effect, it is essential to thoroughly understand the spatial distribution of the electron density in the reentry plasma sheath. Therefore, this paper proposes a three-dimensional plasma field reconstruction method using multi-view tomography based on microwave-probe combined diagnosis.

[0003] To obtain the electron density value of the plasma sheath, mainstream plasma electron density measurement technologies mainly include electrostatic probe method, microwave reflection method and optical emission spectroscopy diagnostic technology. The electrostatic probe method has high spatial resolution and can provide local and accurate electron density and electron temperature data, but its invasive nature and limited heat resistance face significant challenges in high-temperature and high-speed environments. The microwave reflection method has the advantages of non-contact and global detection, but its inversion accuracy is limited by measurement noise, boundary blur and reflection coefficient fitting accuracy, resulting in insufficient resolution of spatial details. Although optical tomography is widely used in two-dimensional image reconstruction, it is limited by the number of projection angles and the accessibility of imaging angles. When reconstructing three-dimensional structures in complex flow fields, it is difficult to strike a balance between stability and accuracy.

[0004] Currently, it is difficult to obtain the complete spatial distribution of the electron density in the reentry plasma sheath using a single method. A non-contact, high-precision electron density measurement solution capable of three-dimensional structure reconstruction in complex, dynamic, and extreme environments is still lacking.

[0005] Therefore, to overcome this problem, we introduced tomography technology to reconstruct plasma parameters. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a three-dimensional tomographic reconstruction method of the plasma field based on the combined measurement of microwave reflection and probe. By combining the overall electron density information obtained by microwave reflection diagnosis with the local precise information obtained by electrostatic probe measurement, the tomographic reconstruction algorithm is used to fuse multi-source data to obtain the three-dimensional distribution of the electron density inside the plasma sheath.

[0007] To achieve the above-mentioned object of the invention, the present invention provides a plasma field three-dimensional tomography reconstruction method based on combined microwave reflection and probe measurement, characterized by comprising the following steps:

[0008] (1) Set the microwave antenna frequency and probe measurement position;

[0009] (2) Obtaining the electron density distribution curve;

[0010] (3) Obtain the electron density of each measurement point;

[0011] (4) Constructing a Gaussian process regression model based on physical constraints to integrate microwave measurement and probe measurement results to achieve high-precision fitting of electron density;

[0012] (5) Reconstruct the three-dimensional emission coefficient field of the plasma using tomography;

[0013] (6) Reconstruct the three-dimensional electron density field of plasma.

[0014] The object of the invention of the present invention is achieved like this:

[0015] The present invention is based on a three-dimensional tomography reconstruction method of the plasma field using combined microwave reflection and probe measurement. First, the microwave antenna frequency and the probe measurement position are set. Then, the global non-contact measurement advantage of the microwave reflection method and the local fine measurement capability of the electrostatic probe are combined to achieve high-precision joint diagnosis of the electron density distribution. Then, a Gaussian process regression model based on physical constraints is used to achieve high-precision fitting of the electron density, and a mapping relationship between the electron density and the emission coefficient is established, ultimately reconstructing the three-dimensional electron density field with millimeter-level resolution.

[0016] At the same time, the plasma field three-dimensional tomography reconstruction method based on the combined measurement of microwave reflection and probe of the present invention also has the following beneficial effects:

[0017] (1) While ensuring measurement accuracy, the present invention fully integrates the global measurement advantages of microwave reflectometry and the high-resolution local measurement capabilities of electrostatic probes, and combines multi-view optical tomography to optimize three-dimensional reconstruction accuracy to obtain millimeter-level resolution of plasma electron density fields, thereby achieving high-precision joint diagnosis of electron density;

[0018] (2) The present invention breaks through the limitations of traditional single measurement methods in terms of temporal and spatial resolution and measurement reliability, and is suitable for plasma sheath diagnosis during the reentry of hypersonic aircraft. It helps to study and alleviate the "blackout" problem and provides an efficient and accurate measurement method for hypersonic aircraft communication "blackout" diagnosis and high-precision plasma measurement.

[0019] (3) The present invention constructs a multi-frequency microwave reflection system to extract the plasma electron density gradient distribution, and uses a high-temperature resistant electrostatic probe to obtain reference measurement values ​​at key locations to optimize the accuracy and stability of microwave measurements;

[0020] (4) The present invention constructs the three-dimensional distribution of the plasma emission spectrum through multi-view optical tomography technology, and uses a data-driven nonlinear inversion method to achieve optimal reconstruction of the electron density field under limited viewing angles, ensuring high reliability and high adaptability under complex measurement conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of the plasma field three-dimensional tomography reconstruction method based on the combined measurement of microwave reflection and probe according to the present invention;

[0022] Figure 2 This is a schematic diagram of the installation of the electrostatic probe;

[0023] Figure 3 It is a schematic diagram of a multi-view camera system. DETAILED DESCRIPTION

[0024] The following describes the specific embodiments of the present invention in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, such descriptions will be omitted here.

[0025] Example

[0026] In this embodiment, if Figure 1 As shown, the present invention provides a plasma field three-dimensional tomography reconstruction method based on combined microwave reflection and probe measurement, comprising the following steps:

[0027] (1) Set the microwave antenna frequency and probe measurement position;

[0028] Assume that the microwave antenna contains n transmitting frequencies, namely: f1, f2, ..., f i ,…,f n ; In order to eliminate interference, this embodiment requires multi-frequency data calibration, so the present invention sets 10 transmission frequencies;

[0029] Assume that the plasma reflects the received microwave signal vertically, and set N1 = 10 sampling points on the reflection path;

[0030] Configure two high-temperature electrostatically resistant probes, denoted as P1 and P2; Figure 2 As shown, the probe is connected to a DC bias power supply using a shielded twisted pair cable, with the anode end connected to the probe body and the cathode grounded and then connected to an external control circuit;

[0031] Place P1 and P2 at the same sampling point to collect electron current and ion current respectively;

[0032] In this embodiment, a high-temperature tolerant electrostatic probe is used to ensure that the probe's spatial position strictly matches the microwave measurement area. Reference values ​​are obtained at multiple measurement points along the microwave measurement path, providing accurate electron density, potential, and electron temperature data. To improve the stability of the probe measurement, a high-impedance low-noise amplifier is used for signal acquisition, combined with numerical filtering to remove high-frequency interference, resulting in a more accurate local electron density reference value.

[0033] (2) Obtaining the electron density distribution curve;

[0034] (2.1) The microwave antenna transmits microwave signals of different frequencies, which are vertically reflected by the plasma and then connected to the vector network analyzer to measure the reflection coefficient R of the microwave signals of different frequencies. i ;

[0035] (2.2) Invert the electron density based on the reflection coefficient;

[0036] (2.2.1) Inverse complex dielectric constant

[0037]

[0038] Where Z0 is the characteristic impedance of vacuum; Z in,i The frequency is f i The equivalent wave impedance of the microwave signal in the plasma; d is the plasma thickness, c is the speed of light in vacuum; ω i is the angular frequency of the microwave signal, ω i =2πf i ;

[0039] (2.2.2), let the imaginary part Real part Then solve for the electron density

[0040]

[0041] Where ε0 is the dielectric constant of vacuum, m e is the mass of the electron, E is the charge of the electron;

[0042] (2.2.3) The electron density inverted at all emission frequencies By fitting the double Gaussian distribution function, the electron density distribution curve is obtained:

[0043]

[0044] Where x is a variable representing the distance between the plasma and the microwave antenna; ξ is the measurement error; a1 and a2 are the two peak heights of the electron density curve of the double Gaussian distribution, b1 and b2 are the two peak positions, and c1 and c2 are the half-widths of the two peaks;

[0045] (3) Obtain the electron density of each measurement point;

[0046] (3.1) Probe P1 and needle P2 are placed at each sampling point in sequence to collect the electron current and ion current at different positions. The electron current collected at the jth sampling point is The ion current is

[0047] (3.2) Calculate the saturated ion current at each sampling point:

[0048]

[0049] in, represents the saturated ion current at the jth sampling point, represents the voltage difference between the two probes, V1 j 、 are the voltages of the two probes at the jth sampling point;

[0050] (3.3) Perform linear fitting on the saturated ion current at all sampling points to obtain a fitting curve, and then take the intercept of the fitting curve as the saturated ion current I i,sat ;

[0051] (3.4) Calculate the electron temperature at each sampling point based on the slope of the fitting curve at the origin.

[0052]

[0053] Where k is the Boltzmann constant, represents the slope of the fitting curve at the origin,

[0054] (3.5), combined with the electron temperature and saturation ion current Get the electron density at each sampling point:

[0055]

[0056] Among them, m i is the ion mass, A is the probe tip contact area, and k is the Boltzmann constant;

[0057] (4) Constructing a physically constrained Gaussian process regression model to fuse microwave and probe measurement results and achieve high-precision fitting of electron density;

[0058] (4.1) Based on physical constraints, a Gaussian process regression model is established with the electron density distribution function as the prediction target:

[0059]

[0060] in, represents the Gaussian process regression model, μ(x) is the mean function, and the electron density distribution curve n obtained by microwave inversion is selected. e (x) is the prior estimate; k(x,x′) is the covariance function, and x′ is the covariance of x;

[0061] (4.2), set the hyperparameter θ = (μ(x), k(x, x′));

[0062] (4.3) Set the minimization optimization objective function;

[0063]

[0064] Among them, n e (x i ; θ) represents the prediction of the Gaussian process regression model at position x under given model parameters θ j The electron density at x j represents the distance between the plasma and the jth sampling point, R(θ) is the regularization term to prevent overfitting, and λ represents the weighting coefficient;

[0065] (4.4), set the marginal log-likelihood function to optimize the hyperparameters;

[0066]

[0067] Where K is the covariance matrix and N is the number of sampling points;

[0068] (4.5) Taking the minimum objective function value as the optimization goal, the optimal hyperparameter θ is obtained by maximizing the marginal log-likelihood function;

[0069] (4.6) The electron density data measured by the electrostatic probe Used as a training sample for the Gaussian process, the optimal hyperparameter θ is then substituted into the electron density distribution represented by the Gaussian process regression model based on physical constraints to obtain the optimized electron density distribution

[0070]

[0071] Among them, μ′(x) is the mean function corrected based on microwave measurement, ρj is the weighting coefficient;

[0072] (5) Reconstruct the three-dimensional emission coefficient field of the plasma using tomography;

[0073] (5.1) Use a high-resolution spectrometer to pre-scan the plasma and obtain the wavelength with the strongest spectral line intensity in the plasma spontaneous radiation;

[0074] (5.2) According to the wavelength with the strongest spectral line intensity in the plasma spontaneous radiation, a filter suitable for the emission wavelength with this intensity is selected to establish a multi-view camera system consisting of 7 cameras, such as Figure 3 As shown, the cameras were installed on the outer wall of the experimental chamber, and measurements and images were taken through the observation window at the top of the chamber. To prevent the strong electromagnetic interference generated during the experiment from affecting the optical camera shooting and data transmission, the camera part, network cable, and power control line were wrapped with copper mesh;

[0075] (5.3) Use a multi-view camera system to obtain projection images of the plasma field at various angles. The size of the projection images obtained at each angle is 512×640.

[0076] (5.4), assuming that each pixel in the projection image corresponds to a projection ray, the projection image is regarded as the projection of the plasma field along the direction of the ray, so the plasma is sliced ​​into b plasma sections;

[0077] On each plasma section, the plasma section is divided into M grids along the camera optical axis, and the size of each grid is l x ; Divide it into N grids along the direction perpendicular to the optical axis, and the size of each grid is l y , and finally divide each plasma section into M×N voxels;

[0078] (5.5) Obtain the three-dimensional emission coefficient field I of the kth plasma section k , k=1,2,…,b;

[0079] (5.5.1) Based on the relationship between the three-dimensional field of the plasma and the projection obtained by the multi-view camera system, calculate the projection light intensity value p of each projection ray in the k-th plasma section j' :

[0080]

[0081] Among them, i' and j' are the number indexes of voxel and projection ray respectively, r i' is the expansion coefficient represented by the ith voxel in the plasma three-dimensional field, p j' is the projection intensity value of the j'th projection ray, w i'j'Represents the contribution value of the i'th voxel to the j'th projection ray;

[0082] (5.5.2) Select the sinc function as the grid basis function, and then obtain the projection matrix W based on the sinc function, where each element in the projection matrix W satisfies:

[0083]

[0084] Among them, (m i' ,n i' ) is the grid position corresponding to the i'th voxel, is the azimuth angle of the optical center of the camera to which the j'th projection ray belongs to the i'th voxel, t i'j' is the radial distance between the i'th voxel and the camera to which the j'th projection ray belongs; sec(·) and tan(·) are the cosecant function and tangent function operations in trigonometric functions, respectively;

[0085] (5.5.3) Establish the tomographic equation system W·R=P, where is the expansion coefficient matrix in the three-dimensional plasma field, R is the variable to be determined; P is the projection intensity matrix W is the projection matrix

[0086] (5.5.4), multi-criteria optimization objective function;

[0087]

[0088] Among them, z τ is the weight of the multi-objective optimization function, Φ τ (F) is a multi-objective joint optimization function, specifically:

[0089]

[0090] Among them, B i'i” is the element value of the corresponding position (i',i'') of matrix B, ψ is the set of voxels in the plasma slice that are not close to the boundary, E i” is the set of voxels adjacent to the boundary of the i'th voxel; V i” is the set of voxels adjacent to the vertex of the i'th voxel;

[0091] (5.5.5) Use a continuous-time Hopfield-based neural network to solve the multi-criteria optimization objective function and obtain the expansion coefficient matrix R in the three-dimensional plasma field;

[0092] (5.5.6) Calculate the three-dimensional emission coefficient field I of the kth plasma section based on the expansion coefficient matrix R and the projection matrix W. k ;

[0093]

[0094] (5.6) Traverse each plasma section, and then follow step (5.5) to obtain the three-dimensional emission coefficient field I = [I1, I2, ..., I k ,…,I b ] T ;

[0095] (6) Reconstruct the three-dimensional field of electron density of plasma;

[0096] (6.1) Use ray tracing to analyze the microwave reflection path of the probe and the angle of the incident camera to obtain the spatial coordinates of the probe at each sampling point;

[0097] (6.2), combined with the optimized electron density distribution And the three-dimensional emission coefficient field I, extract the emission coefficient I(x) corresponding to the spatial coordinates of the probe at each sampling point, and thus establish the plasma electron density along the microwave reflection path and the corresponding data set of emission coefficients I(x);

[0098] (6.3) Using plasma electron density The corresponding data set of the emission coefficient I(x) is used to fit the mathematical mapping model from the plasma field emission coefficient to the plasma field electron density, that is, Among them, g1, g2, g3 are fitting coefficients;

[0099] (6.4), substitute the emission coefficients in the three-dimensional emission coefficient field I into the mathematical mapping model T(I(x)→n e (x)), and the three-dimensional field n of the reconstructed plasma electron density is obtained e .

[0100] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A plasma field three-dimensional tomography reconstruction method based on combined microwave reflection and probe measurement, characterized in that: The following steps are involved: (1) Assume that the microwave antenna contains n transmitting frequencies, namely: f1, f2,…, f i ,…,f n ; Assume that the plasma reflects the received microwave signal vertically, and set N1 sampling points on the reflection path; Two high-temperature, electrostatically resistant probes, designated P1 and P2, are configured. P1 and P2 are placed at the same sampling point to collect electron current and ion current, respectively. (2) Obtaining the electron density distribution curve; (2.1) The microwave antenna transmits microwave signals of different frequencies, which are vertically reflected by the plasma and then connected to the vector network analyzer to measure the reflection coefficient R of the microwave signals of different frequencies. i ; (2.2) Invert the electron density based on the reflection coefficient; (2.2.1) Inverse complex dielectric constant Where Z0 is the characteristic impedance of vacuum; Z in,i The frequency is f i The equivalent wave impedance of the microwave signal in the plasma; d is the plasma thickness, c is the speed of light in vacuum; ω i is the angular frequency of the microwave signal, ω i =2πf i ; (2.2.2), let the imaginary part Real part Then solve for the electron density Where ε0 is the dielectric constant of vacuum, m e is the mass of the electron, E is the charge of the electron; (2.2.3) The electron density inverted at all emission frequencies By fitting the double Gaussian distribution function, the electron density distribution curve is obtained: Where x is a variable representing the distance between the plasma and the microwave antenna; ξ is the measurement error; a1 and a2 are the two peak heights of the electron density curve of the double Gaussian distribution, b1 and b2 are the two peak positions, and c1 and c2 are the half-widths of the two peaks; (3) Obtain the electron density of each measurement point; (3.1) Probe P1 and needle P2 are placed at each sampling point in sequence to collect the electron current and ion current at different positions. The electron current collected at the jth sampling point is The ion current is (3.2) Calculate the saturated ion current at each sampling point: in, represents the saturated ion current at the jth sampling point, represents the voltage difference between the two probes, V1 j 、 are the voltages of the two probes at the jth sampling point; (3.3) Perform linear fitting on the saturated ion current at all sampling points to obtain a fitting curve, and then take the intercept of the fitting curve as the saturated ion current I i,sat ; (3.4) Calculate the electron temperature at each sampling point based on the slope of the fitting curve at the origin. Where k is the Boltzmann constant, represents the slope of the fitting curve at the origin, (3.5), combined with the electron temperature and saturation ion current Get the electron density at each sampling point: Among them, m i is the ion mass, A is the probe tip contact area, and k is the Boltzmann constant; (4) Constructing a physically constrained Gaussian process regression model to fuse microwave and probe measurement results and achieve high-precision fitting of electron density; (4.1) Based on physical constraints, a Gaussian process regression model is established with the electron density distribution function as the prediction target: in, represents the Gaussian process regression model, μ(x) is the mean function, and the electron density distribution curve n obtained by microwave inversion is selected. e (x) is the prior estimate; k(x,x′) is the covariance function, and x′ is the covariance of x; (4.2), set the hyperparameter θ = (μ(x), k(x, x′)); (4.3) Set the minimization optimization objective function; Among them, n e (x i ; θ) represents the prediction of the Gaussian process regression model at position x under given model parameters θ j The electron density at x j represents the distance between the plasma and the jth sampling point, R(θ) is the regularization term to prevent overfitting, and λ represents the weighting coefficient; (4.4), set the marginal log-likelihood function to optimize the hyperparameters; Where K is the covariance matrix and N is the number of sampling points; (4.5) Taking the minimum objective function value as the optimization goal, the optimal hyperparameter θ is obtained by maximizing the marginal log-likelihood function; (4.6) The electron density data measured by the electrostatic probe Used as a training sample for the Gaussian process, the optimal hyperparameter θ is then substituted into the electron density distribution represented by the Gaussian process regression model based on physical constraints to obtain the optimized electron density distribution Among them, μ′(x) is the mean function corrected based on microwave measurement, ρ j is the weighting coefficient; (5) Reconstruct the three-dimensional emission coefficient field of the plasma using tomography; (5.1) Use a high-resolution spectrometer to pre-scan the plasma and obtain the wavelength with the strongest spectral line intensity in the plasma spontaneous radiation; (5.2) Based on the wavelength with the strongest spectral line intensity in the plasma spontaneous radiation, select a filter suitable for the emission wavelength with this intensity to establish a multi-view camera system consisting of q cameras; (5.3) Use a multi-view camera system to obtain projection images of the plasma field at various angles. The size of the projection image obtained at each angle is a×b. (5.4), assuming that each pixel in the projection image corresponds to a projection ray, the projection image is regarded as the projection of the plasma field along the direction of the ray, so the plasma is sliced ​​into b plasma sections; On each plasma section, the plasma section is divided into M grids along the camera optical axis, and the size of each grid is l x ; Divide it into N grids along the direction perpendicular to the optical axis, and the size of each grid is l y , and finally divide each plasma section into M×N voxels; (5.5) Obtain the three-dimensional emission coefficient field I of the kth plasma section k , k=1,2,…,b; (5.5.1) Based on the relationship between the three-dimensional field of the plasma and the projection obtained by the multi-view camera system, calculate the projection light intensity value p of each projection ray in the k-th plasma section j' : Among them, i' and j' are the number indexes of voxel and projection ray respectively, r i' is the expansion coefficient represented by the ith voxel in the plasma three-dimensional field, p j' is the projection intensity value of the j'th projection ray, w i'j' Represents the contribution value of the i'th voxel to the j'th projection ray; (5.5.2) Select the sinc function as the grid basis function, and then obtain the projection matrix W based on the sinc function, where each element in the projection matrix W satisfies: Among them, (m i' ,n i' ) is the grid position corresponding to the i'th voxel, is the azimuth angle of the optical center of the camera to which the j'th projection ray belongs to the i'th voxel, t i'j' is the radial distance between the i'th voxel and the camera to which the j'th projection ray belongs; sec(·) and tan(·) are the cosecant function and tangent function operations in trigonometric functions, respectively; (5.5.3) Establish the tomographic equation system W·R=P, where is the expansion coefficient matrix in the three-dimensional plasma field, R is the variable to be determined; P is the projection intensity matrix W is the projection matrix (5.5.4), multi-criteria optimization objective function; Among them, z τ is the weight of the multi-objective optimization function, Φ τ (F) is a multi-objective joint optimization function, specifically: Among them, B i'i” is the element value of the corresponding position (i',i'') of matrix B, ψ is the set of voxels in the plasma slice that are not close to the boundary, E i” is the set of voxels adjacent to the boundary of the i'th voxel; V i” is the set of voxels adjacent to the vertex of the i'th voxel; (5.5.5) Use a continuous-time Hopfield-based neural network to solve the multi-criteria optimization objective function and obtain the expansion coefficient matrix R in the three-dimensional plasma field; (5.5.6) Calculate the three-dimensional emission coefficient field I of the kth plasma section based on the expansion coefficient matrix R and the projection matrix W. k ; (5.6) Traverse each plasma section, and then follow step (5.5) to obtain the three-dimensional emission coefficient field I = [I1, I2, ..., I k ,…,I b ] T ; (6) Reconstruct the three-dimensional field of electron density of plasma; (6.1) Use ray tracing to analyze the microwave reflection path of the probe and the angle of the incident camera to obtain the spatial coordinates of the probe at each sampling point; (6.2), combined with the optimized electron density distribution And the three-dimensional emission coefficient field I, extract the emission coefficient I(x) corresponding to the spatial coordinates of the probe at each sampling point, and thus establish the plasma electron density along the microwave reflection path and the corresponding data set of emission coefficients I(x); (6.3) Using plasma electron density The corresponding data set of the emission coefficient I(x) is used to fit the mathematical mapping model from the plasma field emission coefficient to the plasma field electron density, that is, Among them, g1, g2, g3 are fitting coefficients; (6.4), substitute the emission coefficients in the three-dimensional emission coefficient field I into the mathematical mapping model T(I(x)→n e (x)), and the three-dimensional field n of the reconstructed plasma electron density is obtained e .

2. The plasma field three-dimensional tomography reconstruction method based on microwave reflection and probe combined measurement according to claim 1 is characterized in that: The probe is connected to a DC bias power supply using a shielded twisted pair cable, with an anode end connected to the probe body and a cathode connected to an external control circuit after being grounded.

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