A method for plasma parameter reconstruction based on improved SOM algorithm

Abstract

The present invention relates to a method for plasma parameter reconstruction based on an improved SOM algorithm, comprising: obtaining the relative dielectric constant of a plasma target body to be reconstructed, obtaining the real part and the imaginary part of the relative dielectric constant of the plasma target body; using the real part and the imaginary part of the relative dielectric constant of the plasma target body to reconstruct plasma parameters, the plasma parameters including electron density and collision frequency; using the electron density reconstruction value to normalize the collision frequency reconstruction value, to obtain the normalized collision frequency reconstruction value. The present invention can reconstruct plasma parameters with high precision; the present invention can normalize the collision frequency with the electron density reconstruction value, thereby obtaining a high-precision collision frequency reconstruction value; the present invention can reconstruct plasma parameters with monochromatic electromagnetic waves, can avoid direct contact with plasma, and can also reconstruct plasmas with different electron densities through multiple frequencies.

Description

Technical Field

[0001] The invention relates to the technical field of inverse scattering applications, in particular to a plasma parameter reconstruction method based on an improved SOM algorithm. Background Art

[0002] In daily life, the application scope of plasma is becoming more and more extensive. The high-temperature parts of lightning and flames are plasma. In the field of aerospace, plasma has important application prospects in spacecraft reentry communications and "blackout" phenomena. The reconstruction of plasma characteristic parameters is an important issue that needs to be solved in the study of plasma technology applications. Therefore, it is of great significance to study how to efficiently and accurately reconstruct plasma parameters.

[0003] High-precision plasma diagnosis is the premise of plasma technology research. At present, the theory and research methods of plasma diagnosis are relatively mature. According to whether the diagnostic equipment goes deep into the plasma, the diagnostic methods are divided into two types: interventional and non-intrusive. The interventional method is to insert the test probe into the plasma to obtain some plasma parameters. The commonly used probe method is the Langmuir probe method, which obtains the IV curve of the measuring probe by inserting it into the plasma, and then obtains the plasma parameters. The advantages of this method are simple structure and low cost, but the material of the probe will affect the measurement of the parameters. When encountering high temperature, the probe will be damaged and then contaminate the plasma. In severe cases, it will also cause inaccurate diagnostic results. This interventional diagnostic method will pollute the plasma environment and is only suitable for plasmas with lower temperatures. In recent years, some researchers have studied the characteristics of different types of microwave probes on plasma parameters, and compared microwave probes using numerical methods. However, the influence of the probe on the reconstruction of plasma parameters cannot be avoided.

[0004] The non-invasive method does not directly contact the plasma, but only infers the plasma parameters through the received plasma radiation data or the interaction between electromagnetic waves and plasma. Non-invasive diagnostic methods have a wider range of applications. Common methods include laser interferometry, microwave method and spectroscopy. In the 20th century, researchers proposed spectroscopy, which uses spectra to invert parameters such as plasma electron density and temperature. However, the data processing of spectroscopy is more complicated, modeling is required for calculation, and the inversion accuracy is low, so it can only be used as a preliminary reference. In 1966, some researchers used the plasma phenomenon generated by laser phenomena and used an interferometer to diagnose the plasma. The biggest disadvantage of this method is that there is a large human error, resulting in low inversion accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a method for analyzing the real and imaginary parts of the relative dielectric constant of a plasma through an improved SOM algorithm, reconstructing the electron density and the collision frequency using the real and imaginary parts, and normalizing the collision frequency using the reconstructed value of the electron density, thereby obtaining a high-precision collision frequency inversion value, which greatly expands the scope of application of the plasma parameter reconstruction method based on the improved SOM algorithm.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for plasma parameter reconstruction based on an improved SOM algorithm, the method comprising the following steps in order:

[0007] (1) Obtaining the relative dielectric constant ε of the plasma target to be reconstructed r , obtain the real part of the relative dielectric constant ε′ of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr ;

[0008] (2) Using the real part ε′ of the relative dielectric constant of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr , and the electron density reconstruction value is obtained and collision frequency reconstruction value υ r ;

[0009] (3) Using electron density to reconstruct values Normalized collision frequency reconstruction value υ r , get the normalized collision frequency reconstruction value v en .

[0010] The step (1) specifically refers to:

[0011] The relative dielectric constant of the plasma target is:

[0012]

[0013] Where ω is the electromagnetic wave frequency; υ is the true value of the collision frequency; ω p is the plasma oscillation angular frequency.

[0014] q e is the electron charge, ε 0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of the electron density; the real part of the relative dielectric constant of the plasma target is obtained as follows:

[0015]

[0016] In the formula, ε′ r is the real part of the relative dielectric constant of the plasma target;

[0017] The imaginary part of the relative dielectric constant of the plasma target is obtained as:

[0018]

[0019] In the formula, ε″ r is the imaginary part of the relative dielectric constant of the plasma target;

[0020] The relative dielectric constant of the plasma target to be reconstructed is obtained by the iterative solution method of the SOM algorithm, and the real part ε′ of the relative dielectric constant of the reconstructed plasma target is obtained. pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr .

[0021] The step (2) specifically refers to:

[0022] The expression of the true value of the collision frequency is as follows:

[0023]

[0024] Where ω is the frequency of the electromagnetic wave, ε′ r is the real part of the relative dielectric constant of the plasma target, ε″ r is the imaginary part of the relative dielectric constant of the plasma target;

[0025] The expression of the true value of electron density is as follows:

[0026]

[0027] In the formula, ω p is the plasma oscillation angular frequency, q e is the electron charge, ε 0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of electron density;υ is the true value of collision frequency;

[0028] The calculation formula of the collision frequency reconstruction value is as follows:

[0029]

[0030] In the formula, ε′ pr is the real part of the reconstructed plasma relative dielectric constant, ε″ pr is the imaginary part of the relative dielectric constant of the reconstructed plasma target;

[0031] The calculation formula of the electron density reconstruction value is as follows:

[0032]

[0033] In step (3), the electron density reconstruction value Normalized collision frequency reconstruction value υ r , the calculation formula is as follows:

[0034]

[0035] In the formula, υ en is the normalized collision frequency reconstruction value, is the electron density reconstruction value, υ r Reconstruct values ​​for collision frequency.

[0036] It can be seen from the above technical scheme that the beneficial effects of the present invention are: first, the present invention can reconstruct plasma parameters with high precision; second, the present invention can use the reconstructed value of electron density to normalize the collision frequency, so as to obtain a high-precision reconstruction value of the collision frequency; third, the present invention can avoid direct contact with the plasma and expand the reconstruction range. The present invention can use monochromatic electromagnetic waves to reconstruct plasma parameters, avoid direct contact with the plasma, and can also reconstruct plasmas with different electron densities through multiple frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of the method of the present invention;

[0038] Figure 2 This is the electron density reconstruction result diagram at different electromagnetic wave frequencies;

[0039] Figure 3 This is a comparison diagram before and after the reconstruction of the collision frequency using electron density normalization;

[0040] Figure 4 This is the reconstruction result of the collision frequency under different electromagnetic wave frequencies after normalization. DETAILED DESCRIPTION

[0041] like Figure 1 As shown, a method for plasma parameter reconstruction based on an improved SOM algorithm comprises the following steps in sequence:

[0042] (1) Obtaining the relative dielectric constant ε of the plasma target to be reconstructed r , obtain the real part of the relative dielectric constant ε′ of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr ;

[0043] (2) Using the real part ε′ of the relative dielectric constant of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr , and the electron density reconstruction value is obtained and collision frequency reconstruction value υ r ;

[0044] (3) Using electron density to reconstruct values Normalized collision frequency reconstruction value υ r , and obtain the normalized collision frequency reconstruction value υ en .

[0045] The step (1) specifically refers to:

[0046] The relative dielectric constant of the plasma target is:

[0047]

[0048] Where ω is the electromagnetic wave frequency; υ is the true value of the collision frequency; ω p is the plasma oscillation angular frequency.

[0049] q e is the electron charge, ε 0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of the electron density; the real part of the relative dielectric constant of the plasma target is obtained as follows:

[0050]

[0051] In the formula, ε′ r is the real part of the relative dielectric constant of the plasma target;

[0052] The imaginary part of the relative dielectric constant of the plasma target is obtained as:

[0053]

[0054] In the formula, ω″ r is the imaginary part of the relative dielectric constant of the plasma target;

[0055] The relative dielectric constant of the plasma target to be reconstructed is obtained by the iterative solution method of the SOM algorithm, and the real part ε′ of the relative dielectric constant of the reconstructed plasma target is obtained. pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr .

[0056] The step (2) specifically refers to:

[0057] By transforming equations (2) and (3), the true value expression of the collision frequency is obtained as shown below:

[0058]

[0059] Where ω is the frequency of the electromagnetic wave, ε′ r is the real part of the relative dielectric constant of the plasma target, ε″ r is the imaginary part of the relative dielectric constant of the plasma target;

[0060] By transforming equations (2) and (3), the true value expression of the electron density is obtained as shown below:

[0061]

[0062] In the formula, ω p is the plasma oscillation angular frequency, q e is the electron charge, ε 0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of electron density; v is the true value of collision frequency;

[0063] From formula (3), we can see that when the electron density is constant, the imaginary part of the relative dielectric constant has a nonlinear relationship with the collision frequency, that is, corresponding to a certain imaginary part ε″ r , two different collision frequencies can be obtained by the inversion method. In order to overcome the nonlinear problem caused by the plasma characteristics and obtain the unique reconstruction value of the collision frequency, the equations (2) and (3) are replaced by Substitute it into equation (5) as a whole. Therefore, the real and imaginary parts of the dielectric constant can be calculated using the SOM algorithm, and then the unique reconstructed value of the collision frequency can be obtained.

[0064] The calculation formula of the collision frequency reconstruction value is as follows:

[0065]

[0066] In the formula, ε′ pr is the real part of the reconstructed plasma relative dielectric constant, ε″ pr is the imaginary part of the relative dielectric constant of the reconstructed plasma target;

[0067] The calculation formula of the electron density reconstruction value is as follows:

[0068]

[0069] In step (3), the electron density reconstruction value Normalized collision frequency reconstruction value vr , the calculation formula is as follows:

[0070]

[0071] In the formula, v en is the normalized collision frequency reconstruction value, is the electron density reconstruction value, v r Reconstruct values ​​for collision frequency.

[0072] The results of plasma parameter reconstruction based on the traditional SOM algorithm are poor, especially the reconstruction of collision frequency. The reconstruction results can be seen in the attached Figure 3 In (b), there are many noise points and the reconstruction effect is poor. The present invention improves the SOM algorithm and proposes a plasma parameter reconstruction based on the improved SOM algorithm, wherein the improvement refers to using the reconstructed electron density to normalize the collision frequency, and finally achieving high-precision reconstruction of the collision frequency.

[0073] The following combination Figures 1 to 4 The present invention is further described.

[0074] The simulation model used in the present invention is the classic Austrian model, which consists of a central ring (with inner and outer radii of 0.3m and 0.6m respectively) and two disks (with inner and outer radii of 0.2m respectively). Both the ring and the disk are composed of uniform plasma.

[0075] The electromagnetic wave frequencies of the present invention are 200MHz, 400MHz, 800MHz, 1.6GHz, 2GHz, and the number of iterations is 100 times. The electron density reconstruction results are as follows: Figure 2 shown.

[0076] While increasing the electron density, the incident frequency was adjusted to keep the relative dielectric constant between 0.8 and 0.01i. Figure 2 The inversion result can clearly show the reconstructed value of the plasma electron density. The reason for the poor reconstruction effect of the collision frequency is that the real component of the relative dielectric constant of the background medium tends to 1 after inversion, which will cause the denominator in equation (6) to be approximately 0, and the collision frequency will eventually have an extreme value. Therefore, the reconstructed value of the collision frequency needs to be normalized using the electron density.

[0077] like Figure 3As shown, (a) is the true value of the collision frequency, (b) is the unnormalized reconstructed value of the collision frequency, and (c) is the reconstructed value of the collision frequency after normalization using the electron density. It can be clearly seen from the three comparison figures that there are many noises in (b), the imaging effect is poor, and only the approximate outline of the medium can be reconstructed, and the imaging error is large; while the imaging effect of the normalized (c) is significantly improved, the redundant noises are shielded, and it is closer to the true value (a), further reflecting the advantage of normalized high-precision reconstruction.

[0078] like Figure 4 As shown, (a) to (e) are the true values ​​of the collision frequency, and (f) to (j) are the normalized reconstructed values ​​of the collision frequency; among them, the electromagnetic wave frequencies from left to right are 200MHz, 400MHz, 800MHz, 1.6GHz, and 2GHz, respectively, and the number of iterations is 100 times. It can be clearly seen from the reconstructed results that the normalized collision frequency has no unnecessary noise and the imaging clarity is high.

[0079] The present invention can reconstruct the collision frequency with high precision. The reconstruction result after normalization is more accurate mainly because the electron density obtained by SOM at the background domain pixel point is very small relative to the plasma domain. Normalization factor It can effectively attenuate the extreme collision frequency that appears in the background medium.

[0080] To further illustrate the reconstruction effect of the present invention, the error of the parameter reconstruction value of the medium target can be calculated, and the error calculation formula is as follows:

[0081]

[0082] Where Re is the error of the reconstructed value, a represents the row of image pixels, b represents the column of image pixels, M is the total number of rows and columns, and Y is r is the plasma parameter reconstruction value, Y t is the true value of plasma parameters.

[0083] The comparison of the errors between the true and reconstructed values ​​of the plasma parameters calculated above is shown in Table 1.

[0084] Table 1 Comparison of plasma target errors

[0085] f / GHz 0.2 0.4 0.8 1.6 2 <![CDATA[N e ]]> 0.0268 0.0268 0.0267 0.0267 0.0265 υ 0.2757 0.2758 0.2757 0.2759 0.2758 <![CDATA[υ en ]]> 0.0574 0.0575 0.0574 0.0573 0.0572

[0086] In Table 1, f is the frequency of the electromagnetic wave; it can be seen from Table 1 that the present invention can reconstruct plasma parameters, electron density and collision frequency with high precision, which proves that the present invention has a good plasma diagnostic effect.

[0087] In summary, the present invention mainly reconstructs the plasma parameters: electron density and collision frequency by utilizing the dielectric constant of the plasma target. In order to be closer to the actual situation, the present invention adds 10% Gaussian white noise during simulation. The effectiveness of the present invention is proved by simulation results and error analysis. In addition, in the presence of Gaussian noise, the present invention has the advantages of fast convergence speed and strong anti-noise performance.

Claims

1. A method for plasma parameter reconstruction based on an improved SOM algorithm, characterized in that: The method comprises the following steps in order: (1) Obtaining the relative dielectric constant ε of the plasma target to be reconstructed r , obtain the real part of the relative dielectric constant ε′ of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr ; (2) Using the real part ε′ of the relative dielectric constant of the reconstructed plasma target pr , and the imaginary part ε″ of the relative dielectric constant of the reconstructed plasma target pr , and the electron density reconstruction value is obtained and the collision frequency reconstruction value v r ; (3) Using electron density to reconstruct values Normalized collision frequency reconstruction value v r , and obtain the normalized collision frequency reconstruction value v en ; The step (1) specifically refers to: The relative dielectric constant of the plasma target is: Where ω is the frequency of the electromagnetic wave; υ is the true value of the collision frequency; ε p is the plasma oscillation angular frequency; q e is the electron charge, ε0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of the electron density; the real part of the relative dielectric constant of the plasma target is obtained as follows: In the formula, ε′ r is the real part of the relative dielectric constant of the plasma target; The imaginary part of the relative dielectric constant of the plasma target is obtained as: In the formula, ε″ r is the imaginary part of the relative dielectric constant of the plasma target; The relative dielectric constant of the plasma target to be reconstructed is obtained by the iterative solution method of the SOM algorithm, and the real part ε′ of the relative dielectric constant of the reconstructed plasma target is obtained. pr , and the imaginary part ε′ of the relative dielectric constant of the reconstructed plasma target p ' r ; The step (2) specifically refers to: The expression of the true value of the collision frequency is as follows: Where ω is the frequency of the electromagnetic wave, ε′ r is the real part of the relative dielectric constant of the plasma target, ε″ r is the imaginary part of the relative dielectric constant of the plasma target; The expression of the true value of electron density is as follows: In the formula, ω p is the plasma oscillation angular frequency, q e is the electron charge, ε0 is the vacuum dielectric constant, m e is the mass of the electron, N e is the true value of electron density;υ is the true value of collision frequency; The calculation formula of the collision frequency reconstruction value is as follows: In the formula, ε′ pr is the real part of the reconstructed plasma relative dielectric constant, ε″ pr is the imaginary part of the relative dielectric constant of the reconstructed plasma target; The calculation formula of the electron density reconstruction value is as follows:

2. The method for plasma parameter reconstruction based on the improved SOM algorithm according to claim 1, characterized in that: In step (3), the electron density reconstruction value Normalized collision frequency reconstruction value v r , the calculation formula is as follows: In the formula, v en is the normalized collision frequency reconstruction value, is the electron density reconstruction value, v r Reconstruct values ​​for collision frequency.

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