Dust plasma parameter inversion method

Abstract

The present application relates to the technical field of plasma analysis, and discloses a dust plasma parameter inversion method, which comprises the following steps: firstly, measuring the attenuation coefficient of dust plasma to microwaves through experimental measurement; secondly, inversely deducing the dielectric coefficient and conductivity of dust plasma from the attenuation coefficient calculation formula; thirdly, substituting the deduced result into the dust plasma dielectric coefficient and conductivity calculation formula to obtain the electron concentration, dust particle concentration and dust particle radius in the dust plasma; and finally, verifying the reliability of the inversion result. The present application is based on the microwave transmission theory and experimental research of dust plasma, verifies and perfects the related theory, and proposes a measurement method of internal parameters of dust plasma, which has practical significance for further exploring the radio physics problems in dust plasma.

Description

Technical Field

[0001] This invention relates to the field of plasma analysis technology, specifically to a method for inverting dust plasma parameters. Background Technology

[0002] Dust plasma refers to plasma containing dust particles, also known as complex plasma. The charging and discharging effects of dust particles make its electromagnetic properties significantly different from those of ordinary plasma. Phenomena such as the strong attenuation of microwaves by solid rocket exhaust, mid-polar summer echoes in polar regions, the "communication blackout" during spacecraft re-entry into the atmosphere, and the instability of longitudinal waves in dust plasma all require explanation using theories related to dust plasma.

[0003] Based on the current state of research both domestically and internationally, theoretical research on electromagnetic wave propagation in dusty plasmas outnumbers experimental research. Experimental equipment and technologies for space-based dusty plasmas are not yet fully mature, and experimental costs are high. Existing ground-based experiments on microwave propagation in dusty plasmas only provide qualitative analyses of microwave propagation, with virtually no experimental verification of existing theories. This is primarily because methods for measuring the internal parameters of dusty plasmas are not yet fully developed. Current experiments can only measure electron concentration and electron temperature in dust-free plasmas using the Langmuir probe method and emission spectroscopy. However, effective methods for measuring internal parameters after the addition of dust particles have not yet been established. Therefore, a method for inverting dusty plasma parameters is needed for verification. Summary of the Invention

[0004] The purpose of this invention is to provide a method for inverting parameters of dust plasma. Based on the theory and experimental research of microwave transmission in dust plasma, this invention verifies and improves the relevant theories and proposes a method for measuring the internal parameters of dust plasma. This has practical significance for further exploring radio physics issues in dust plasma.

[0005] This invention is implemented as follows:

[0006] This invention provides a method for inverting dust plasma parameters; specifically, it is performed according to the following steps:

[0007] S1: The attenuation coefficient of the dust plasma to microwaves was measured by experiment; the charge number of dust particles in the dust plasma, and the charging current of electrons and ions to dust particles under unheated conditions are as shown in equations (1)-(2).

[0008]

[0009]

[0010] When the charging is balanced, it is as shown in equation (3);

[0011]

[0012] This leads to equation (4);

[0013]

[0014] Considering the conditions of electrical neutrality and the charge of dust particles; as shown in equations (5)-(6);

[0015]

[0016] If r d <<λ D ,r d / λ D →0, Then q d0 =Cφ d0 =r d φ d0 ;

[0017]

[0018] Using the International System of Units (SI), as shown in equation (7), substituting into the above equation and considering the electroneutrality condition, we can obtain equation (8);

[0019]

[0020]

[0021] S2: The dielectric constant and conductivity of the dust plasma are then derived from the attenuation coefficient calculation formula; since experiments have shown that the inversion results of the characteristic parameters of dust particles are basically consistent with the actual concentration and radius of the dust particles. The formulas for the attenuation coefficient and phase coefficient of microwaves propagating in the medium are shown in Equation (9) and Equation (10), respectively;

[0022]

[0023]

[0024] Where ω=2πf is the angular frequency of the electromagnetic wave, the speed of light c=3×10^8m / s, and the vacuum permittivity ε0=8.85×10^-12F / m, the conductivity σ and the relative permittivity ε can be obtained from equations (9) and (10). r For plasma, see equations (11)-(12);

[0025]

[0026]

[0027] If the microwaves pass through a plasma medium, the calculated values ​​are the plasma's conductivity and relative permittivity. According to plasma theory, the collision frequency ν can be obtained by combining equations (11) and (12). eff and plasma oscillation frequency ω pe The oscillation frequency has the following relationship with the electron concentration, as shown in equation (13);

[0028]

[0029] In equation (13), the basic electron charge e = 1.6 × 10^-19 C, and the electron mass m e = 9.1 × 10^-31 kg, from which the plasma electron concentration n can be obtained. e .

[0030] Furthermore, for dust plasma, equations (14)-(15) are used;

[0031]

[0032]

[0033] In the formula, ω=2πf is the microwave angular frequency; It is the electron plasma frequency, where e = 1.6 × 10⁻⁶. -19 C is the fundamental electron charge, n e and m e =9.1×10 -31 kg represents the electron concentration and electron mass, respectively; c = 3 × 10⁻⁶ 8 m / s is the speed of light in a vacuum, and ε0 is the vacuum permittivity.

[0034] Furthermore, the effective collision frequency between electrons and molecules is as shown in equation (16);

[0035]

[0036] In equation (16), κ B =1.38×10 -23 J.K. -1 It is the Boltzmann constant, T e It is the electronic temperature, σ n =5×10 -21 m 2 It is the effective collision cross section between electrons and molecules, N n =p / κ B T i The concentration of neutral molecules is p, where p is the plasma pressure in the chamber during the experiment, and T is the ion temperature. i The temperature in the experimental chamber was taken as approximately 350 K; ν chIt is the charging frequency (charge relaxation rate), which describes how quickly the surface charge of dust particles recovers to its equilibrium value, as shown in equation (17).

[0037]

[0038] In the formula, Z d It is the charge number of dust particles; It is the frequency of ion plasma, m i It is the mass of the ion; It is the thermal velocity of the ions. η ed =n e e 2 D / m e It is the charging response factor, a characteristic parameter of dust. It only depends on the dust particle concentration n d It is related to the size of the dust particles. Without dust, η ed =0, Equations (14) and (15) degenerate into formulas for calculating plasma conductivity and dielectric constant. When microwaves pass through a dust plasma medium, the conductivity and relative dielectric constant of the dust plasma calculated in ① are different. Due to the concentration of dust particles n added in the laboratory, ... d Much smaller than the electron concentration n e Assuming no effect on electron concentration and collision frequency, the charging response factor η can be calculated from equations (14) and (15). ed and charge relaxation rate ν ch Then, the product value of the characteristic parameters related to dust can be calculated by equation (16). Due to the clustering phenomenon of dust particles, the actual size differs greatly from the nominal value, and the dust particles exhibit a Gaussian distribution, so determining the radius and concentration is still somewhat difficult. A value of the product of dust concentration and radius can be obtained.

[0039] S3: Substitute the deduced results into the formulas for calculating the dielectric constant and conductivity of dust plasma to obtain the electron concentration, dust particle concentration, and dust particle radius in the dust plasma;

[0040] S4: Verify the reliability of the inversion results. The first method for verifying the reliability of the inversion results is to follow these steps.

[0041] S5: First, to determine the reliability of the electron concentration without the addition of dust particles, the electron concentration obtained by inversion is compared with the results measured by the Langmiur probe using the formulas for calculating the conductivity and dielectric constant of plasma.

[0042] S6: By comparison, errors that may occur during the measurement process can be eliminated.

[0043] Furthermore, in step S4, a second method for verifying the reliability of the inversion results is specifically performed according to the following steps;

[0044] S7: Add dust particles into the cavity, substitute the inversion results into the relevant formula to further invert the electron concentration in the dust plasma;

[0045] S8: Substitute the relevant parameters of the dust plasma into the theoretical formula of the dust plasma to calculate its attenuation to the incident microwave at this frequency;

[0046] S9: Compare with the measured values. If the two values ​​are roughly consistent across multiple frequency points, then the formulas for calculating the conductivity and dielectric constant of dust plasma can be determined.

[0047] Compared with the prior art, the beneficial effects of the present invention are: based on the theory and experimental research of microwave transmission in dust plasma, the relevant theories are verified and improved, and a method for measuring the internal parameters of dust plasma is proposed, which has practical significance for further exploring the radio physics problems in dust plasma;

[0048] This method can be used to measure the internal parameters of dust plasmas and provides important support for further research on microwave transmission laws in dust plasmas. Furthermore, the upper atmosphere (60-1000 km) of Earth is dominated by weakly ionized plasmas. Under similar conditions in the mesosphere of the polar regions, some areas become weakly ionized dust plasmas. The instability of weakly ionized dust plasmas is closely related to local climate change. Studying the relationship between the instability of weakly ionized dust plasmas and climate change requires understanding the internal parameters of the weakly ionized dust plasmas in these regions. This method can lay the foundation for future research in this field in terms of talent cultivation and technological reserves. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 The electron concentration n of this invention e =10 15 m -3 Dust particle concentration from 10 10 m -3 Increase to 10 14 m-3 A graph showing the change in the charge number of dust particles of different sizes over time;

[0052] Figure 3 The electron concentration of this invention is ne = 10. 16 m -3 Dust particle concentration from 10 10 m -3 Increase to 10 14 m -3 The change in the charge number of dust particles of different sizes over time;

[0053] Figure 4 The electron concentration of this invention is ne = 10. 17 m -3 Dust particle concentration from 10 10 m -3 Increase to 10 14 m -3 The change in the charge number of dust particles of different sizes at that time;

[0054] Figure 5 The radius r of the dust particle d =0.1µm, electron concentration n e 10 respectively 15 m -3 10 16 m -3 10 17 m -3 At that time, the number of dust particles with charge changes with the dust particle concentration;

[0055] Figure 6 The radius r of the dust particle d =0.2um, electron concentration n e 10 respectively 15 m -3 10 16 m -3 10 17 m -3 At that time, the number of dust particles with charge changes with the dust particle concentration;

[0056] Figure 7 The radius r of the dust particle d =0.5um, electron concentration n e 10 respectively 15 m -3 10 16 m -3 10 17 m -3 At that time, the number of dust particles with charge changes with the dust particle concentration;

[0057] Figure 8The radius r of the dust particle d =1µm, electron concentration n e 10 respectively 15 m -3 10 16 m -3 10 17 m -3 The change in the number of dust particles' charges with the dust particle concentration.

[0058] Figure 9 The radius r of the dust particle d =2µm, electron concentration n e 10 respectively 15 m -3 10 16 m -3 10 17 m -3 The graph shows the change in the number of dust particles by dust particle concentration.

[0059] Figure 10 The dust particle radius rd = 5 μm and the electron concentration ne is 10. 15 m-3, 10 16 m-3, 10 17 The graph showing the change in dust particle charge number with dust particle concentration at m-3;

[0060] Figure 11 The results are the inversion results of electron concentration and characteristic parameters of dust particles in weakly ionized dust plasma;

[0061] Figure 12 It is the absorption and attenuation of microwave power at different frequencies;

[0062] Figure 13 It is the change of microwave attenuation coefficient with frequency;

[0063] Figure 14 This is a theoretically calculated value of electron concentration;

[0064] Figure 15 These are characteristic parameters of dust particles. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] Please see Figure 1 This paper presents a method for inverting parameters of dust plasma. In this embodiment, after adding dust particles to ordinary plasma, the dust particles acquire a charge due to the charging effect. The charge of the dust particles affects the electron concentration in the dust plasma, reducing it, and also affects the charging frequency. When inverting parameters in dust plasma, considering the charging frequency, the inversion formula becomes extremely complex, increasing the difficulty of the inversion. To reduce the difficulty, some simplified mathematical models are proposed. To ensure good parameter inversion accuracy under the simplified mathematical models, it is necessary to analyze and study the charge number of dust particles in dust plasma under different parameter backgrounds and its influence on the electron concentration. The following is a study on the charge number of dust particles in dust plasma.

[0067] In this embodiment, without heating, the charging current of electrons and ions to dust particles is as shown in equations (1)-(2):

[0068]

[0069]

[0070] During charging balance, Substituting equations (1) and (2) into equation (3) yields equation (3); substituting this into the charging balance condition...

[0071]

[0072] Therefore, we get equation (4);

[0073]

[0074] Considering the condition of electrical neutrality, as shown in equation

[0075] And the charge of dust particles as shown in equations (5)-(6);

[0076]

[0077] In equation (5), if r d <<λ D ,r d / λ D →0, Then q d0 =Cφ d0 =r d φ d0 Thus, we get equation (6):

[0078]

[0079] Considering that dust particles are negatively charged, when using the International System of Units (SI), as shown in equation (7), substituting into the above equation and considering the condition of electroneutrality, we can obtain equation (8).

[0080]

[0081]

[0082] Based on equation (8), the electron concentration and the charge number of dust particles in equilibrium state can be obtained through programming.

[0083] like Figure 2 — Figure 10 The following are the results calculated from the nuclear charge number of dust particles under different parameter conditions.

[0084] In this embodiment, by Figure 2 — Figure 10 The results show that when the dust particle concentration varies from 10¹⁰ m⁻³ to 10¹² m⁻³, the number of dust particles is almost solely related to their radius. Furthermore, when the electron concentration is three orders of magnitude greater than the dust particle concentration, the reduction in electron concentration due to the addition of dust particles is negligible.

[0085] In actual measurements, ν eff =10 7 ν ch =10 9 ω1=4×10 9 At that time, the attenuation coefficient α1 = 1.65; ω1 = 4.2 × 10⁻⁶. 9 At that time, the attenuation coefficient α1 = 1.55; ε0 = 8.85 × 10 -12 c = 3 × 10 8 e = 1.6 × 10 -19 m e =3.1×10 -31By changing the characteristic parameter D of the dust particles, the n values ​​on both sides... e It varies with D. The electron concentration and dust particle characteristic parameters can be obtained from its focus. From the intersection point, the electron concentration n inside the experimental cavity can be determined. e =3.7×10 15 m -3 The dust characteristic parameter is D = 29.73, and the electron concentration measurement result is consistent with the Langmiur probe measurement in terms of order of magnitude. This is because the added dust particle concentration is low, and the dust particle radius is small (a few micrometers), therefore, the addition of dust particles has little effect on the electron concentration. This makes the electron concentration essentially unchanged after the addition of dust particles. The conductivity and dielectric constant of the weakly ionized dust plasma were calculated by substituting the relevant parameters derived from two similar frequency points into the formulas for calculating the conductivity and dielectric constant of the weakly ionized dust plasma. The attenuation of microwaves by the dust plasma at different frequency points was then calculated and compared with the measured values, showing good agreement.

[0086] In this embodiment, as Figures 12-15 When only dust particles are present in the chamber, microwave attenuation is not observed, which is determined by the main mechanism of microwave attenuation. In the experiment, charged particles (mainly electrons) first gain energy from the microwaves, and then transfer the energy gained from the microwaves to neutral molecules and dust particles through collisions and recharging. Charged particles act as energy "transporters" here, which is why microwave attenuation is difficult to observe when there are no charged particles. In the experiment, a relatively stable weakly ionized dust plasma was first generated under a pressure of 60.03 Pa and a discharge condition of 2 kW. Then, a continuously variable frequency microwave signal emitted by a vector network analyzer was passed through this weakly ionized dust plasma. Figure 2 This is the measurement result of microwave attenuation. The horizontal axis represents the frequency of the incident microwave, and the vertical axis represents the absorption attenuation of the incident microwave power. Figure 2 Substituting the measurement results into equation (6) yields the following result: Figure 3 The microwave attenuation coefficient is shown. (From...) Figure 2 and Figure 3 It can be seen that, under the same experimental conditions, when dust particles are added to the plasma, the attenuation of microwaves by the dust plasma is greater than that of the plasma itself.

[0087] In this embodiment, the measured attenuation coefficient and electron concentration ( Figure 12 and Figure 13 Substituting equations (1) and (2) and considering equations (6) to (7), the charging response factor η of the weakly ionized dust plasma can be calculated. ed and the characteristic parameter D of dust particles.

[0088] like Figure 15These are the experimentally measured and theoretically calculated values ​​of the dust particle characteristic parameters, both of which are of the same order of magnitude. Theoretical calculations also show that for dust plasma with constant dust particle size and concentration, the dust particle characteristic parameter D does not change with the incident microwave frequency, which is consistent with the actual situation.

[0089] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for inverting parameters of dust plasma, characterized in that: Follow these steps: S1: The attenuation coefficient of dust plasma to microwaves was measured experimentally; S2: The dielectric constant and conductivity of the dust plasma can then be derived from the attenuation coefficient calculation formula; S3: Substitute the deduced results into the formulas for calculating the dielectric constant and conductivity of dust plasma to obtain the electron concentration, dust particle concentration, and dust particle radius in the dust plasma; S4: Verify the reliability of the inversion results; In step S1, the charge number of dust particles in the dust plasma, and the charging current of electrons and ions to dust particles in the absence of heating are as shown in equations (1)-(2). Equation (1) Equation (2) When the charging is balanced, it is as shown in equation (3); Equation (3) This leads to equation (4); Equation (4) Considering the conditions of electrical neutrality and the charge of dust particles; as shown in equations (5)-(6); Equation (5) like ,but ; Equation (6) Using the International System of Units (SI), as shown in equation (7), substituting into the above equation and considering the electroneutrality condition, we can obtain equation (8). Equation (7) Equation (8); This refers to the electron concentration.

2. The method for inverting dust plasma parameters according to claim 1, characterized in that, In step S4, the first method for verifying the reliability of the inversion results is specifically performed according to the following steps; S5: First, to determine the reliability of the electron concentration without the addition of dust particles, the electron concentration obtained by inversion is compared with the results measured by the Langmiur probe using the formulas for calculating the conductivity and dielectric constant of plasma; S6: By comparison, errors that may occur during the measurement process can be eliminated.

3. The method for inverting dust plasma parameters according to claim 1, characterized in that, In step S4, the second method for verifying the reliability of the inversion results is specifically performed according to the following steps; S7: Add dust particles into the cavity, substitute the inversion results into the relevant formulas to further invert the electron concentration in the dust plasma; S8: Substitute the relevant parameters of the dust plasma into the theoretical formula of the dust plasma to calculate its attenuation to the incident microwave at this frequency; S9: Compare with the measured values. If the two values ​​are roughly consistent across multiple frequency points, then the formulas for calculating the conductivity and dielectric constant of dust plasma can be determined.

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