Plasma electron density distribution microwave diagnosis method based on particle swarm optimization

Abstract

The invention discloses a plasma electron density distribution microwave diagnosis method based on a particle swarm algorithm, and the method comprises the steps: measuring the phase of an electromagnetic wave without / with plasma through a phase interference principle, obtaining actually-measured phase interference data, calculating an electron density mean value according to the actually-measured phase interference data, and carrying out the calculation of the electron density mean value; generating a plurality of different initial electron density distributions, and then performing multi-order fitting on the initial electron density distributions to obtain an electron density distribution fitting formula; fitting coefficients in the fitting formula serve as particles of a particle swarm algorithm, and an initial population is generated; according to the initial population, plasma electron density distribution is obtained through iterative solution by means of the particle swarm algorithm, phase interference data, corresponding to the electron density distribution, of particles are calculated through a ray tracing method in iteration and serve as analog phase interference data, and the particle fitness is calculated according to the analog phase interference data and actually-measured phase interference data. According to the invention, the electron density distribution diagnosis precision and the resource utilization rate in the strong refraction scene are effectively improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of plasma parameter measurement, and particularly relates to a microwave diagnosis method for plasma electron density distribution based on a particle swarm algorithm. BACKGROUND

[0002] In the research and industrial application of plasma physics, the accurate diagnosis of the plasma electron density distribution is of great importance. Since 1961, researchers have theoretically analyzed the plasma with uniform distribution, parabolic distribution and improved parabolic form, and proposed a method for reconstructing the parabolic electron density distribution by using the refractive angle measurement and fitting formula. Later, the research of Vest et al. pointed out that when using laser interference fringes to diagnose the refractive index distribution of the target, the strong refraction has little effect on the reconstruction result. In 1983, G.J. Tallents solved the refractive angle and the electron density distribution with a parabolic distribution form by using holographic laser interference, but this kind of scheme, although having strict theoretical derivation, is difficult to be directly applied to the microwave band and implemented in experiments.

[0003] At present, as a non-invasive and stable method, microwave diagnosis has been widely used in the field of plasma diagnosis. Microwave diagnosis technology mainly includes microwave interference method, microwave reflection method, cavity method or waveguide method and microwave diffraction method. Among them, the microwave reflection method, the cavity method and the waveguide method can achieve good diagnostic accuracy under certain conditions, but for large-size, wide-parameter-range plasma generating devices, the design of the diagnostic method is limited by the selection of the diagnostic frequency, the electromagnetic wave refraction error in the process of electron density distribution diagnosis, the phase whole cycle ambiguity and other problems, and it is difficult to achieve better diagnostic accuracy. The microwave interference method is based on the interaction between electromagnetic waves and plasma to diagnose the mean value and spatial distribution of the electron density. However, the cutoff effect and refraction phenomenon of electromagnetic wave interaction with plasma require the use of higher diagnostic frequency. However, with the increase of diagnostic frequency, the phase sensitivity is limited by the hardware system and is reduced, thereby limiting the diagnostic accuracy of the microwave interference method. In recent years, although researchers have made certain progress in using the microwave interference method to diagnose the plasma electron density distribution, when facing large-scale, large-parameter-gradient axisymmetric plasma, the existing microwave interference method is affected by the strong refraction of electromagnetic waves, and its diagnostic accuracy is limited. In addition, many of these methods need to adjust the angle of the receiving device or design a special lens antenna to complete the diagnosis of the plasma electron density distribution, which not only increases the cost, but also increases the complexity of operation. SUMMARY

[0004] In order to solve the above problems existing in the prior art, the present application provides a microwave diagnosis method for plasma electron density distribution based on a particle swarm algorithm.

[0005] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The plasma electron density distribution microwave diagnostic method provided by the present invention based on particle swarm optimization includes:

[0007] The phase interference principle is used to measure the phase of the electromagnetic wave in the absence of plasma and in the presence of plasma, and the measured phase interference data are obtained;

[0008] The electron density mean at the plasma symmetry axis is calculated based on the measured phase interferometry data, and a plurality of initial electron density distributions with different electron density peaks and electron density distribution forms are generated based on the electron density mean, and a multi-order fitting is performed on the initial electron density distribution to obtain an electron density distribution fitting formula;

[0009] Using the fitting coefficients of the electron density distribution fitting formula as particles of the particle swarm algorithm to generate an initial population;

[0010] According to the initial population, the particle swarm algorithm is used to iteratively solve the plasma electron density distribution; wherein, during the iterative process, according to the electron density distribution fitting formula corresponding to the particle, the phase interference data under the corresponding electron density distribution is calculated by the ray tracing method as the simulated phase interference data, and the fitness of the particle is calculated based on the simulated phase interference data and the measured phase interference data.

[0011] Optionally, the calculating the fitness of the particle according to the simulated phase interference data and the measured phase interference data includes:

[0012] Calculating the fitness of the particle using a fitness function according to the simulated phase interference data and the measured phase interference data;

[0013] The fitness function is:

[0014]

[0015] in, is the I-th phase difference value in the measured phase interferometry data, φ I is the Ith phase difference value in the simulated phase interference data, the number of phase difference values ​​is N, A represents the weighting coefficient, a represents the starting position of the data in the weighting term, b represents the ending position of the data in the weighting term, 1≤a≤b≤N.

[0016] Optionally, in the process of iteratively solving the plasma electron density distribution using the particle swarm algorithm, the position of the particle is updated as follows:

[0017]

[0018] wherein g represents an index of iteration number, i represents an index of fitting coefficient, t i is the i-th fitting coefficient in a set of fitting coefficients corresponding to a particle, ω g represents an inertia factor of the g-th iteration, represents the fitting coefficient t i corresponding to a particle, c1 and c2 are preset acceleration factors, pbest i represents a local optimal solution, gbest i represents a global optimal solution, is t i , is the updated t i after the g-th iteration, and rand(·) represents a function of generating random numbers.

[0019] Optionally, the fitting formula according to the electron density distribution corresponding to the particle uses a ray tracing method to calculate phase interference data under the corresponding electron density distribution, and the method comprises the following steps.

[0020] According to the fitting formula of the electron density distribution, the electron density of each layer of the plasma is calculated, and according to the electron density, the complex permittivity and the real part of the complex refractive index of each layer of the plasma are calculated by using the relationship between the electron density and the complex permittivity.

[0021] According to the initial incident angle of the ray, the complex permittivity and the real part of the complex refractive index, the Snell complex refractive law and the geometric relationship of the ray path are used to calculate the refraction angle and the path length of the ray incident to each layer of the plasma.

[0022] According to the refraction angle and the path length, the phase shift integral of the ray along the propagation path is calculated by using the interference phase accumulation formula, and the phase interference data under the corresponding electron density distribution is obtained according to the phase shift integral and the phase of the electromagnetic wave in the absence of plasma.

[0023] Optionally, the calculation of the complex permittivity and the real part of the complex refractive index of each layer of the plasma according to the electron density by using the relationship between the electron density and the complex permittivity comprises the following steps.

[0024] According to the electron density, the complex permittivity of each layer of the plasma is calculated by using the relationship between the electron density and the complex permittivity, and the calculation method comprises the following steps.

[0025]

[0026] wherein ε r represents the complex permittivity, e represents the charge amount carried by an electron, m e represents the mass of an electron, ε0 represents the vacuum permittivity, j represents the complex unit, and n erepresents the electron density of the plasma, v e represents the collision frequency, ω represents the angular frequency of the electromagnetic wave;

[0027] The real part of the complex refractive index of each layer of the plasma is calculated based on the complex dielectric constant. The calculation method includes:

[0028]

[0029] in, represents the complex refractive index, n represents the real part of the complex refractive index, and y represents the imaginary part of the complex refractive index.

[0030] Optionally, calculating the phase shift integral of the ray along the propagation path using an interference phase accumulation formula according to the refraction angle and the path length includes:

[0031]

[0032] in, represents the phase shift integral of the ray along the propagation path, ε0 represents the dielectric constant of vacuum, M represents the number of layers of different media that the ray passes through, and n q represents the real part of the complex refractive index when propagating through the qth layer, l q represents the path length of the qth layer propagation, and k0 represents the constant of electromagnetic waves in a vacuum.

[0033] Optionally, the multi-order fitting is a fourth-order fitting.

[0034] Optionally, the electron density distribution forms include: linear distribution, Gaussian distribution and parabolic distribution.

[0035] Optionally, different methods for generating the electron density peak value include:

[0036] Twice the electron density average is taken as the initial electron density peak value, and different values ​​are randomly selected as the electron density peak value within the range of 0.5 times the initial electron density peak value to 1.5 times the initial electron density peak value.

[0037] The present invention provides a microwave diagnosis method for plasma electron density distribution based on particle swarm algorithm. First, the measured phase interference data of electromagnetic wave rays in the absence and presence of plasma are measured. Then, based on the calculated electron density mean at the plasma symmetry axis, multiple different initial electron density distributions are generated, and the fitting coefficient of the initial electron density distribution fitting formula is used as the initial population of the particle swarm algorithm. Then, based on the initial population, the particle swarm algorithm is used to iteratively solve to obtain the optimal electron density distribution result. In the iterative process, the ray tracing method is used to calculate the phase interference data under the electron density distribution corresponding to the particle as simulated phase interference data, and the fitness of the particle is calculated based on the simulated phase interference data and the measured phase interference data using the fitness function. The solution of the present invention generates an initial population based on the electron density mean obtained by traditional microwave interference diagnosis, and obtains the optimal electron density distribution through iterative solution by particle swarm algorithm. This overcomes the problem that the traditional plasma electron density distribution diagnosis method is limited in diagnostic accuracy due to the strong refraction of electromagnetic waves when facing large-scale, large parameter gradient axisymmetric plasmas, effectively improving diagnostic accuracy and resource utilization efficiency.

[0038] In addition, since the solution of the present invention only relies on phase interference data, it does not involve the measurement of refraction angle and does not require the design of special equipment. Moreover, the phase interference data can be directly and conveniently obtained in experiments and actual engineering applications. Therefore, the solution of the present invention effectively reduces the complexity of system design and the complexity of operation.

[0039] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 1 is a flow chart of a microwave diagnosis method for plasma electron density distribution based on a particle swarm optimization algorithm according to an embodiment of the present invention;

[0041] Figure 2 A schematic diagram of the process of a particle swarm algorithm in a microwave diagnosis method for plasma electron density distribution based on a particle swarm algorithm provided in an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of obtaining measured phase interference data using the phase interference principle in an embodiment of the present invention;

[0043] Figure 4 Schematic diagram of a plasma electromagnetic wave propagation model constructed using a ray tracing method in an embodiment of the present invention;

[0044] Figure 5 A schematic diagram of a simulation experiment of a microwave diagnosis method for plasma electron density distribution based on a particle swarm algorithm according to an embodiment of the present invention;

[0045] Figure 6 A schematic diagram of the diagnosis results of a simulation experiment of a microwave diagnosis method for plasma electron density distribution based on a particle swarm optimization algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0047] In order to achieve better plasma electron density distribution diagnosis accuracy and improve resource utilization efficiency in scenarios where electromagnetic waves are strongly refraction-affected, the present invention provides a plasma electron density distribution microwave diagnosis method based on particle swarm optimization. Figure 1 , the method comprises the following steps:

[0048] S10. Using the phase interference principle, the phases of the electromagnetic wave in the absence of plasma and in the presence of plasma are measured respectively to obtain measured phase interference data.

[0049] For details, see Figure 3 As shown, an electromagnetic wave transmitting source is set on one side of the plasma, and multiple receiving positions are set on the other side of the plasma. N measurement points are selected within the receiving position range, that is, measurement points with different values ​​of h, where h represents the distance from the receiving position to the horizontal symmetry axis of the plasma. Then, a vector network analyzer is used to measure the phase of the electromagnetic wave at the N measurement points when there is no plasma. and the phase when there is plasma The measured phase interferometry data is calculated That is, the phase difference between the presence and absence of plasma at each measurement point. Here, since the phase obtained by the vector network analyzer is between -180° and 180°, the following formula is used to calculate the measured phase interference data:

[0050]

[0051] in, is the I-th phase difference value in the measured phase interferometry data, that is, the measured phase interferometry data of the I-th measurement point, represents the phase of the I-th measurement point when there is plasma, It represents the phase of the I-th measurement point in the absence of plasma, and % represents the remainder operation.

[0052] S20. Based on the measured phase interference data, the mean electron density at the plasma symmetry axis is calculated, and based on the mean electron density, multiple electron density peaks and initial electron density distributions with different electron density distribution forms are generated, and the initial electron density distribution is subjected to multi-order fitting to obtain an electron density distribution fitting formula.

[0053] In this embodiment, first, based on the measured phase interference data at the position h=0 obtained in step S10, the formula Calculate the mean electron density at the plasma symmetry axis, where n e represents the electron density, f represents the electromagnetic wave frequency, d represents the diameter of the plasma, represents the measured phase interferometry data at position h = 0. Then, based on the electron density mean, different electron density peaks are selected, and then combined with different electron density distribution forms to generate multiple different initial electron density distributions. These different initial electron density distributions are then subjected to multi-order fitting to obtain their electron density distribution fitting formulas.

[0054] Exemplarily, the electron density distribution forms may include linear distribution, Gaussian distribution and parabolic distribution.

[0055] In one embodiment, the multi-order fitting may be a fourth-order fitting. Accordingly, when a fourth-order fitting is performed on the initial electron density distribution, the corresponding electron density distribution fitting formula may be expressed as:

[0056] n e (r) = t1 + t2r + t3r 2 +t4r 3 +t5r 4 ;

[0057] Among them, t1~t5 represent fitting coefficients, and r represents the distance between any position and the center of the circle.

[0058] In one embodiment, when selecting different electron density peak values ​​based on the electron density mean, the method for generating different electron density peak values ​​includes: taking 2 times the electron density mean as the initial electron density peak value, and randomly selecting different values ​​as the electron density peak value in the range of 0.5 times the initial electron density peak value to 1.5 times the initial electron density peak value.

[0059] S30. Using the fitting coefficients of the electron density distribution fitting formula as particles of the particle swarm algorithm to generate an initial population.

[0060] Specifically, the fitting coefficients t1~t L They are all particles in the initial population of the particle swarm algorithm, where L is the fitting order.

[0061] It can be understood that by using real measured phase interferometer data to calculate the electron density mean, and then generating the initial electron density distribution based on the electron density mean, and using the fitting coefficient of the corresponding fitting formula as the initial parameter of the particle swarm algorithm, the particle swarm algorithm can achieve faster convergence speed.

[0062] S40. Based on the initial population, the particle swarm algorithm is used to iteratively solve the plasma electron density distribution; wherein, during the iteration process, according to the electron density distribution fitting formula corresponding to the particle, the phase interference data under the corresponding electron density distribution is calculated using the ray tracing method as the simulated phase interference data, and the fitness of the particle is calculated based on the simulated phase interference data and the measured phase interference data.

[0063] In this embodiment, see Figure 2 , according to the initial population, the particle swarm algorithm is used to iteratively solve the plasma electron density distribution, specifically including:

[0064] S401 , according to the electron density distribution fitting formula corresponding to the particle, using a ray tracing method to calculate phase interference data under the corresponding electron density distribution as simulated phase interference data.

[0065] Here, see Figure 4 As shown, the ray tracing model in the ray tracing method is a two-dimensional model, in which the plasma is set to a layered circular cross-section, and the plasma electron density of each layer is different. The electromagnetic wave source emits multiple rays along the plasma direction at the same time, and the rays reach the receiving position after passing through plasma layers with different parameters.

[0066] In this embodiment, for each particle in the particle swarm algorithm, the phase interference data under the corresponding electron density distribution is calculated using a ray tracing method according to the electron density distribution fitting formula corresponding to the particle, specifically including:

[0067] (1) According to the electron density distribution fitting formula, the electron density of each plasma layer is calculated, and based on the electron density, the complex dielectric constant and the real part of the complex refractive index of each plasma layer are calculated using the relationship between electron density and complex dielectric constant.

[0068] Here, according to a set of fitting coefficients corresponding to the particle, the electron density distribution fitting formula corresponding to the particle can be determined, such as: n e (r) = t1 + t2r + t3r 2 +t4r 3 +t5r 4 , so that the electron density of different layers of the plasma can be obtained. Then, using the relationship between electron density and complex dielectric constant, the complex dielectric constant and the real part of the complex refractive index of each layer of the plasma can be calculated.

[0069] Then, based on the electron density, the complex dielectric constant and the real part of the complex refractive index of each layer of the plasma are calculated using the relationship between electron density and complex dielectric constant, including:

[0070] Based on the electron density, the complex dielectric constant of each layer of the plasma is calculated using the relationship between electron density and complex dielectric constant. The calculation methods include:

[0071]

[0072] Among them, ε r represents the complex dielectric constant, e represents the charge carried by electrons, m e represents the electron mass, ε0 represents the vacuum dielectric constant, j represents the complex unit, n e represents the electron density of the plasma, v e represents the collision frequency, ω represents the angular frequency of the electromagnetic wave;

[0073] Then, the real part of the complex refractive index of each layer of the plasma is calculated based on the complex dielectric constant of each layer of the plasma. The calculation method includes:

[0074]

[0075] in, represents the complex refractive index, n represents the real part of the complex refractive index, and y represents the imaginary part of the complex refractive index.

[0076] In this embodiment, when calculating the complex dielectric constant, the collision frequency is set to a fixed value because the collision frequency has little effect on the phase.

[0077] (2) According to the initial incident angle of the ray, the complex dielectric constant and the real part of the complex refractive index, the refraction angle and path length of the ray incident on each layer of the plasma are calculated using Snell's law of complex refraction and the geometric relationship of the ray path.

[0078] Here, for the refraction angle of the ray incident on each layer of the plasma, as Figure 4 As shown in Figure 1, when an electromagnetic wave propagates from medium 1 into medium 2, the refraction angle can be solved using Snell's law of complex refraction:

[0079] n i sin(θ i )=n t sin(θ t );

[0080] y i sin(β i )=y t sin(β t );

[0081] Among them, n i represents the real part of the complex refractive index of medium 1, n t represents the real part of the complex refractive index of medium 2, y i represents the imaginary part of the complex refractive index of medium 1, yt represents the imaginary part of the complex refractive index of medium 2, θ i Represents the medium 1 and n i The relevant angle of incidence, θ t Represents medium 2 and n t The relevant refraction angle, β i Represents the medium 1 and y i The relevant angle of incidence, β t Represents medium 2 and y t The relevant refraction angle.

[0082] Because n i sin(θ i )=n t sin(θ t ) characterizes the phase change, and the phase change plays a decisive role in the diagnosis of the electron density distribution. Therefore, in this embodiment, only formula n is used. i sin(θ i )=n t sin(θ t ) to solve for the angle of refraction without considering the angle of refraction corresponding to the imaginary part of the complex refractive index.

[0083] In addition, for the path length of the ray incident on each layer of the plasma, as Figure 4 As shown in the figure, when the ray enters the first layer of the plasma with an initial incident angle α, its refraction angle β can be calculated. Assuming that the ray moves in a straight line in each layer of the plasma, the propagation path length l2 of the ray in the first layer can be calculated based on the trigonometric function relationship between the known refraction angle β, the radius of the first layer of the plasma, the radius of the second layer and the ray propagation path. Similarly, the refraction angle and path length of the ray in each layer of the plasma when it passes through the plasma can be known.

[0084] (3) According to the refraction angle and path length, the phase shift integral of the ray along the propagation path is calculated using the interference phase accumulation formula, and the phase interference data under the corresponding electron density distribution is obtained based on the phase shift integral and the phase of the electromagnetic wave in the absence of plasma.

[0085] It is known that the typical electric field equation for electromagnetic wave propagation is expressed as:

[0086]

[0087] in, represents the attenuation term, represents the phase shift term, k0 represents the propagation constant of electromagnetic waves in a vacuum, l represents the propagation path length of the ray, n represents the real part of the complex refractive index, y represents the imaginary part of the complex refractive index, represents the direction of the imaginary refraction angle, Represents the direction of the real part of the refraction angle, and E0 represents the electric field at the starting position of the electromagnetic wave propagation. Since the phase change of the ray along the propagation path depends on the phase shift term Therefore, the phase shift integral of the ray along the propagation path can be calculated based on the real part of the refractive index and the propagation path length of the ray.

[0088] Specifically, in step (3), the phase shift integral of the ray along the propagation path is calculated using the interference phase accumulation formula according to the refraction angle and the path length, including:

[0089]

[0090] in, represents the phase shift integral of the ray along the propagation path, M represents the number of layers of different media that the ray passes through, and n q represents the real part of the complex refractive index when propagating through the qth layer, l q represents the path length of the qth layer propagation, and k0 represents the constant of electromagnetic waves in a vacuum.

[0091] Therefore, for each particle, the ray tracing method is used to calculate the phase shift integral of the ray along the propagation trajectory at N measurement points under the electron density distribution corresponding to the particle. And according to the phase shift integral and the phase of the electromagnetic wave without plasma at N measurement points The same method as that used in step S10 to calculate the measured phase interference data is used to obtain the phase interference phase, and the phase interference data is used as the simulated phase interference data φ1 to φ N Among them, N measurement points and All are obtained in step S10.

[0092] S402: Calculate the fitness of the particle according to the simulated phase interference data and the measured phase interference data.

[0093] In this embodiment, for each particle, the fitness of the simulated phase interferometer data and the measured phase interferometer data of the particle is calculated using a fitness function, so that the difference between the electron density distribution corresponding to the particle and the actual electron density distribution can be evaluated. Here, the fitness of the particle is calculated based on the simulated phase interferometer data and the measured phase interferometer data, specifically including:

[0094] According to the simulated phase interference data and the measured phase interference data, the fitness of the particle is calculated using the fitness function, where the fitness function is:

[0095]

[0096] in, is the I-th phase difference value in the measured phase interferometer data, φ ITo simulate the I-th phase difference value in the phase interference data, the number of phase difference values ​​is N, A represents the weighting coefficient, a represents the starting position of the data in the weighting term, b represents the ending position of the data in the weighting term, and 1≤a≤b≤N.

[0097] In the above formula, the fitness function performs a weighted processing on the phase interferometer data at different measurement points. The fitness function consists of two terms: the first term is the sum of the squares of the differences between the simulated phase interferometer data and the measured phase interferometer data at each measurement point, and the second term is the weighting term, which calculates the sum of the squares of the differences between the simulated phase interferometer data and the measured phase interferometer data for measurement points a to b and multiplies it by the weighting coefficient. This allows the particle swarm algorithm to pay more attention to the phase interferometer data of measurement points a to b during the iteration process, thereby improving the reconstruction effect of the electron density distribution trend. Here, setting the weighting coefficient too large will lead to increased reconstruction errors at other measurement points, while setting it too small will not achieve the ideal electron density distribution reconstruction effect. Therefore, in practical applications, the weighting coefficient and the starting and ending positions of the data in the weighting term need to be selected after multiple tests to select the optimal parameters.

[0098] S403. Update the local optimal solution and the global optimal solution according to the calculated fitness, and then update the position of the particle.

[0099] Specifically, according to the minimum fitness among all particles, a set of fitting coefficients t1~t corresponding to the particle with the minimum fitness can be obtained. L This set of fitting coefficients is the optimal fitting coefficient for this iteration, i.e., the local optimal fitting coefficient. Furthermore, this minimum fitness is compared with the global minimum fitness (i.e., the historical minimum fitness up to the current iteration). If this minimum fitness is less than the global minimum fitness, the local optimal fitting coefficient is used as the global optimal fitting coefficient. Then, the linear decreasing weight method is used to update the fitting coefficients corresponding to the particles.

[0100] In this embodiment, in the process of iteratively solving the plasma electron density distribution using the particle swarm algorithm, the position of the particles is updated as follows:

[0101]

[0102] Among them, g represents the iteration index, i represents the index of the fitting coefficient, and t i is the i-th fitting coefficient in a set of fitting coefficients corresponding to the particle, ω g represents the inertia factor of the g-th iteration, Indicates the fitting coefficient t in the g-th iteration i The corresponding speed, c1 and c2 are the preset acceleration factors, pbest i Indicates the local optimal solution, gbest idenotes the global optimal solution, t g is the t of the gth iteration i , t g+1 is the updated t after the gth iteration i , rand(·) denotes generating a random number. Here, pbest i t g is the t of the gth iteration i , gbest i t g is the t of the gth iteration i .

[0103] Here, ω g can be calculated by the following formula:

[0104]

[0105] where G k denotes the maximum number of iterations of the particle swarm algorithm, ω ini denotes the initial inertia factor, ω end denotes the inertia factor when the iteration reaches the maximum evolution generation, ω ini and ω end are both preset values. It can be understood that ω g is a non-negative value, when ω g is larger, the global optimization ability of the particle swarm algorithm is strong, while the local optimization ability is weak. When ω g is smaller, the global optimization ability of the particle swarm algorithm is weak, while the local optimization ability is strong, therefore, through dynamic ω g a better optimization effect than a fixed value can be obtained.

[0106] S404, repeat steps S401-S403 to determine the plasma electron density distribution.

[0107] Specifically, in each iteration, the simulated phase interference data corresponding to each particle is obtained through step S401, the fitness of the particle is calculated through step S402, the global optimal solution and the position of the particle are updated through step S403, the above iteration and updating process is repeated until the iteration termination condition of the particle swarm algorithm is met, and the final electron density distribution fitting coefficient is obtained.

[0108] The particle swarm algorithm-based plasma electron density distribution microwave diagnosis method provided by the present application is further described below through simulation experiments.

[0109] (1) Simulation scene setting.

[0110] The simulation phase results of CST (Computer Simulation Technology, CST suite) simulation software are used as the measured phase interference data to verify the method of the application. In the simulation, a layered plasma cylinder with a radius of 100 mm is set. The positional relationship of the wave source, the plasma and the receiving position in the CST simulation experiment is as shown in Figure 5 The electromagnetic wave frequency is set to 29 GHz, 32 GHz, 35 GHz and 38 GHz, and the plasma electron density distribution is set to a Gaussian distribution n e (r)=na×exp(-(r×20) 2 ), wherein na is the electron density peak value, and the value is 1e18 m 3 , 4e18 m 3 and 8e18 m 3 , and the collision frequency v e =2 GHz.

[0111] (2) Simulation steps.

[0112] Step 1: According to the above settings, the phases of the electromagnetic wave in the absence of plasma and in the presence of plasma are obtained respectively according to the phase interference principle, and the measured phase interference data is calculated. Here, as shown in Figure 3 , ro represents the distance from the connecting line of the wave source and the receiving position to the center of the plasma cross section, and the sampling interval is 7.5 mm. In the range of ro=0 mm to ro=97.5 mm, N=14 position points are determined, thereby obtaining 14 measured phase interference data

[0113] Step 2: According to the measured phase interference data at h=0 (i.e. ro=0 mm), the average electron density is calculated, and the initial electron density peak value is 2 times the average electron density. Then, for the linear distribution, the Gaussian distribution and the parabolic distribution, 40 different electron density peak values are randomly selected in the interval of 0.5 times the initial electron density peak value to 1.5 times the initial electron density peak value, thereby obtaining 120 different initial electron density distributions. The electron density distribution fitting formula n e (r)=t1+t2r+t3r 2 +t4r 3 +t5r 4 is obtained by fitting the fourth order of the electron density distribution.

[0114] Step 3: The fitting coefficients of the 120 electron density distribution fitting formulas are used as particles of the particle swarm algorithm, thereby obtaining the initial population.

[0115] Step 4: Based on the initial population, the particle swarm algorithm is used to iteratively solve the plasma electron density distribution. In the iterative process, the ray tracing algorithm is used to calculate the phase interference data of the ray along the propagation path under the corresponding electron density distribution according to the electron density fitting formula corresponding to the particle, and 14 simulated phase interference results φ1~φ1 at the same position are obtained. 14 Then, based on the measured phase interference data and the simulated phase interference data, the fitness function is used to calculate the fitness of the particle. The local optimal solution and the global optimal solution are updated according to the calculated fitness, and then the position of the particle is updated. In the iterative process of this experiment, the fitness function is: c1 and c2 are both set to 0.5, ω ini =0.4,ω end =0.9, and the iteration termination condition is 100 iterations.

[0116] In the method of the present invention, the reconstruction accuracy of the algorithm is characterized by the deviation Dev, which is calculated as follows: Among them, n set (r) represents the set value of the electron density distribution.

[0117] (3)Simulation results.

[0118] Figure 6 The electron density distribution reconstruction results and diagnostic accuracy of this simulation experiment are shown, where (a), (c) and (e) are the electron density peaks of 1e18m 3 、4e18m 3 and 8e18m 3 , and the electron density distribution results obtained by the method of the present invention when the electromagnetic wave frequency is set to 29 GHz, 32 GHz, 35 GHz and 38 GHz, wherein the horizontal axis is the radius to the center of the circle, the vertical axis is the electron density, and the Set Value is the set value n of the electron density distribution set (r). (b), (d) and (f) are the deviations Dev corresponding to (a), (c) and (e) respectively. Figure 6 It can be seen that the invented method has achieved better plasma electron density distribution diagnosis accuracy, and as shown in Figure (f), when the electron density peak is 8e18m 3 When the electromagnetic wave frequency is 29 GHz, the deviation Dev is less than 0.05, which means that the method of the present invention can complete the electron density distribution diagnosis when the diagnostic frequency is only 1.2 times the plasma peak characteristic frequency.

[0119] The application provides a plasma electron density distribution microwave diagnosis method based on a particle swarm algorithm, which comprises the following steps: firstly, measuring the measured phase interference data of electromagnetic wave rays in the absence of plasma and in the presence of plasma; then, generating a plurality of different initial electron density distributions according to the calculated average electron density at the symmetry axis of the plasma, and taking the fitting coefficients of the initial electron density distribution fitting formula as the initial population of the particle swarm algorithm; and then, according to the initial population, the optimal electron density distribution result is obtained by using the particle swarm algorithm for iterative solution, wherein the phase interference data corresponding to the electron density distribution of the particle is calculated by using the ray tracing method in the iteration process as the simulated phase interference data, and the fitness of the particle is calculated by using the fitness function according to the simulated phase interference data and the measured phase interference data. The initial population is generated based on the average electron density obtained by the traditional microwave interference diagnosis, and the optimal electron density distribution is obtained by using the particle swarm algorithm for iterative solution, so that the problem that the diagnosis precision is limited by the strong refraction phenomenon of electromagnetic waves when the traditional plasma electron density distribution diagnosis method is used to diagnose the large-scale and large-parameter gradient axisymmetric plasma is overcome, and the diagnosis precision and resource utilization efficiency are effectively improved.

[0120] In addition, since the scheme of the application only relies on phase interference data, it does not involve the measurement of refraction angle and does not need to design special equipment, and the phase interference data can be directly and conveniently obtained in experiments and actual engineering applications, so that the complexity of system design and operation complexity are effectively reduced. In addition, since the scheme of the application only relies on phase interference data, it does not involve the measurement of refraction angle and does not need to design special equipment, and the phase interference data can be directly and conveniently obtained in experiments and actual engineering applications, so that the complexity of system design and operation complexity are effectively reduced.

[0121] It should be noted that the terms "first", "second", and the like are used to distinguish similar objects, and do not necessarily have to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the application described herein can be implemented in an order other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the application. Rather, they are only examples of devices and methods consistent with some aspects of the application.

[0122] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" etc. means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the specification.

[0123] Although the present application is described herein in conjunction with various embodiments, those skilled in the art, with the benefit of the drawings and the disclosure, can understand and implement other variations of the disclosed embodiments in the implementation of the claimed application. In the description of the present application, the word "comprising" does not exclude other components or steps, "a" or "one" does not exclude a plurality, and "plurality" means two or more, unless otherwise expressly specified. In addition, some measures are described in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0124] The above is a further detailed description of the present application in conjunction with specific preferred embodiments, and cannot be considered as limiting the specific implementation of the present application to these descriptions. For those skilled in the art, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be considered as falling within the scope of protection of the present application.

Claims

1. A microwave diagnostic method for plasma electron density distribution based on particle swarm optimization, characterized in that: include: The phase interference principle is used to measure the phase of the electromagnetic wave in the absence of plasma and in the presence of plasma, and the measured phase interference data are obtained; The electron density mean at the plasma symmetry axis is calculated based on the measured phase interferometry data, and a plurality of initial electron density distributions with different electron density peaks and electron density distribution forms are generated based on the electron density mean, and a multi-order fitting is performed on the initial electron density distribution to obtain an electron density distribution fitting formula; Using the fitting coefficients of the electron density distribution fitting formula as particles of the particle swarm algorithm to generate an initial population; According to the initial population, the particle swarm algorithm is used to iteratively solve the plasma electron density distribution; wherein, during the iterative process, according to the electron density distribution fitting formula corresponding to the particle, the phase interference data under the corresponding electron density distribution is calculated by the ray tracing method as the simulated phase interference data, and the fitness of the particle is calculated based on the simulated phase interference data and the measured phase interference data.

2. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: The calculating the fitness of the particle according to the simulated phase interference data and the measured phase interference data includes: Calculating the fitness of the particle using a fitness function according to the simulated phase interference data and the measured phase interference data; The fitness function is: in, is the I-th phase difference value in the measured phase interferometry data, φ I is the Ith phase difference value in the simulated phase interference data, the number of phase difference values ​​is N, A represents the weighting coefficient, a represents the starting position of the data in the weighting term, b represents the ending position of the data in the weighting term, 1≤a≤b≤N.

3. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: In the process of iteratively solving the plasma electron density distribution using the particle swarm algorithm, the particle position is updated as follows: Among them, g represents the iteration index, i represents the index of the fitting coefficient, and t i is the i-th fitting coefficient in a set of fitting coefficients corresponding to the particle, ω g represents the inertia factor of the g-th iteration, Indicates the fitting coefficient t in the g-th iteration i The corresponding speed, c1 and c2 are the preset acceleration factors, pbest i Indicates the local optimal solution, gbest i represents the global optimal solution, is t at the g-th iteration i , is the updated t after the g-th iteration i , rand(·) represents a function that generates random numbers.

4. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: The method of calculating the phase interference data under the corresponding electron density distribution using a ray tracing method according to the electron density distribution fitting formula corresponding to the particle includes: The electron density of each layer of the plasma is calculated according to the electron density distribution fitting formula, and the complex dielectric constant and the real part of the complex refractive index of each layer of the plasma are calculated according to the electron density and the relationship between the electron density and the complex dielectric constant; Calculate the refraction angle and path length of the ray incident on each layer of the plasma based on the initial incident angle of the ray, the complex dielectric constant and the real part of the complex refractive index using Snell's law of complex refraction and the geometric relationship of the ray path; According to the refraction angle and the path length, the phase shift integral of the ray along the propagation path is calculated using the interference phase accumulation formula, and the phase interference data under the corresponding electron density distribution is obtained based on the phase shift integral and the phase of the electromagnetic wave in the absence of plasma.

5. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 4, characterized in that: The method of calculating the complex dielectric constant and the real part of the complex refractive index of each layer of the plasma based on the electron density and the relationship between the electron density and the complex dielectric constant includes: According to the electron density, the complex dielectric constant of each layer of the plasma is calculated using the relationship between the electron density and the complex dielectric constant. The calculation method includes: Among them, ε r represents the complex dielectric constant, e represents the charge carried by electrons, and m e represents the electron mass, ε0 represents the vacuum dielectric constant, j represents the complex unit, n e represents the electron density of the plasma, v e represents the collision frequency, ω represents the angular frequency of the electromagnetic wave; The real part of the complex refractive index of each layer of the plasma is calculated based on the complex dielectric constant. The calculation method includes: in, represents the complex refractive index, n represents the real part of the complex refractive index, and y represents the imaginary part of the complex refractive index.

6. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 4, characterized in that: The step of calculating the phase shift integral of the ray along the propagation path using an interference phase accumulation formula according to the refraction angle and the path length includes: in, represents the phase shift integral of the ray along the propagation path, ε0 represents the dielectric constant of vacuum, M represents the number of layers of different media that the ray passes through, and n q represents the real part of the complex refractive index when propagating through the qth layer, l q represents the path length of the qth layer propagation, and k0 represents the constant of electromagnetic waves in a vacuum.

7. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: The multi-order fitting is a fourth-order fitting.

8. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: The electron density distribution forms include linear distribution, Gaussian distribution and parabolic distribution.

9. The plasma electron density distribution microwave diagnosis method based on particle swarm optimization according to claim 1, characterized in that: Different methods for generating the electron density peak include: Twice the electron density average is taken as the initial electron density peak value, and different values ​​are randomly selected as the electron density peak value within the range of 0.5 times the initial electron density peak value to 1.5 times the initial electron density peak value.

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