CN116681019A - Method for researching electromagnetic wave transmission characteristics of plasmas based on equivalent circuit model - Google Patents

Abstract

The invention discloses a research method of plasma electromagnetic wave transmission characteristics based on an equivalent circuit model, relates to the technical field of microwave circuits, and solves the problems that an algorithm is complex and the transmission characteristics of plasma cannot be truly reflected in the prior art; the method comprises the following steps: establishing an initial plasma equivalent circuit model according to an electromagnetic transmission characteristic curve obtained by a moment method; determining an electromagnetic transmission characteristic curve obtained by an equivalent circuit method of plasma of an equivalent circuit model; comparing an electromagnetic transmission characteristic curve obtained by a moment method with an electromagnetic transmission characteristic curve obtained by an equivalent circuit method to determine the parameter optimal value of a circuit element in an equivalent circuit model; determining the transmission characteristic of electromagnetic waves in the plasma according to the optimal value of the parameter; the method and the device realize the conversion of the complex field transmission problem in the plasma into the circuit calculation problem, reveal the transmission mechanism of the electromagnetic wave in the plasma through the distribution of the equivalent circuit model, reduce the calculation difficulty and rapidly and accurately analyze the transmission characteristic of the electromagnetic wave.

Description

Research Method of Electromagnetic Wave Transmission Characteristics of Plasma Based on Equivalent Circuit Model

technical field

The invention relates to the technical field of microwave circuits, in particular to a research method of plasma electromagnetic wave transmission characteristics based on an equivalent circuit model.

Background technique

With the development of hyper-vehicles, the plasma surrounding hyper-vehicles provides a prerequisite for the realization of plasma stealth of hyper-vehicles. The development of plasma-based stealth technology will provide a new solution for the stealth of superb aircraft. The mechanism of plasma cloaking is mainly refraction cloaking and absorption cloaking. Refractive stealth means that non-uniform plasma has different refractive indices, which will deviate the direction of electromagnetic wave echo, so that the radar cannot receive the echo. Absorption stealth means that the plasma absorbs the energy of electromagnetic waves, the movement of particles is intensified, and finally converted into heat energy through collisions. As a traditional wave-absorbing material, plasma has a good absorption effect on low-frequency electromagnetic waves. When electromagnetic waves enter the plasma medium, reflection, refraction, and absorption will occur, thereby greatly weakening the echo intensity and avoiding radar detection. Therefore, plasma is widely used. Used in the preparation of absorbing materials. The use of plasma in stealth technology has the advantages of wide absorption frequency band, good absorption effect, and insensitivity to the incident direction.

The research on plasma is mainly divided into theoretical research, numerical research and experimental research. Among them, the theoretical research method refers to the direct calculation and solution of Maxwell's equations; the goal of numerical research is to solve the wave equation. With the development of computer technology, numerical simulation methods have been popularized, mainly including WKB (Wentzel Kramers Brillouin) method and scattering matrix method , Monte Carlo-based particle network simulation method and time-domain finite difference method; experimental research refers to the use of plasma generation devices and electromagnetic wave measurement devices to build an experimental environment for experiments.

Theoretical research is based on Maxwell's equations to establish an ideal plasma wave equation. This research method is relatively complicated and cannot truly reflect the transmission characteristics of plasma, and usually there is no analytical solution; , to solve the wave equation of the plasma wave equation, this method depends on certain hardware and software resources, the accuracy of the numerical model needs to be further verified, and the physical meaning is not intuitive; the experimental method also has certain limitations for plasma research , For example, the construction of the experimental device is complex and costly.

Contents of the invention

The present invention provides a method for researching the transmission characteristics of plasma electromagnetic waves based on an equivalent circuit model, which effectively solves the problem in the prior art that the algorithm is complex and cannot truly reflect the transmission characteristics of the plasma, and further realizes that the plasma The complex field transmission problem in the system is transformed into a circuit calculation problem. Through the distribution of the equivalent circuit model, the transmission mechanism of electromagnetic waves in the plasma is revealed, which greatly reduces the difficulty of calculation, and can quickly and accurately analyze the transmission characteristics of electromagnetic waves.

The invention provides a method for researching the transmission characteristics of plasma electromagnetic waves based on an equivalent circuit model, the method comprising:

According to the electromagnetic transmission characteristic curve obtained by the method of moments, the initial plasma equivalent circuit model is established;

Determining the electromagnetic transmission characteristic curve obtained by the equivalent circuit method of the plasma of the equivalent circuit model;

Comparing the electromagnetic transmission characteristic curve obtained by the method of moments with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and determining the optimal value of the parameters of the circuit components in the equivalent circuit model;

According to the optimal value of the parameter, the transmission characteristic of the electromagnetic wave in the plasma is determined.

In a possible implementation manner, the establishment of the initial plasma equivalent circuit model and the determination of the electromagnetic transmission characteristic curve obtained by the plasma equivalent circuit method of the equivalent circuit model include:

Analyzing the transmission characteristics of the electromagnetic transmission characteristic curve obtained by the method of moments, and determining the equivalent circuit model according to the transmission characteristics;

Obtaining the transmission matrix of the equivalent circuit model, and using the conversion relationship between the transmission matrix and the scattering matrix to determine the electromagnetic transmission characteristic curve obtained by the equivalent circuit method of the equivalent circuit model.

In a possible implementation manner, the transmission matrix is expressed as:

Wherein, A, B, C, and D represent the matrix values in the transmission matrix, A and B represent the values of the first row of the transmission matrix in turn, and C and D represent the second row of the transmission matrix in turn The value of , N represents the number of multiplications, and T _i represents the transmission matrix of the i-th component, which is specifically expressed as:

in, Z _i represents the impedance of the i-th capacitor; Y _i represents the admittance of the i-th inductance.

In a possible implementation manner, the impedance of the capacitor is specifically expressed as: The admittance of the inductor is specifically expressed as: /> Among them, C _i represents the value of the i-th capacitor; L _i represents the value of the i-th inductor.

In a possible implementation manner, the conversion relationship between the transmission matrix and the scattering matrix is specifically expressed as:

Among them, Z ₀ represents the characteristic impedance of free space.

In a possible implementation, the objective function of the genetic algorithm is expressed as:

Wherein, y ₁ represents the electromagnetic transmission characteristic curve obtained by the moment method, y ₂ represents the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, f represents the electromagnetic transmission characteristic curve obtained by the moment method and the equivalent circuit method obtained The distance between the electromagnetic transmission characteristic curves.

In a possible implementation, the electromagnetic transmission characteristic curve obtained by the method of moments is compared with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method to determine the Optimal values of parameters, including:

Based on the genetic algorithm, inversion calculation is performed according to the electromagnetic transmission characteristic curve obtained by the method of moments, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and the parameter range of circuit components, and it is judged whether the objective function can converge. And the difference is less than or equal to the threshold, determine the judgment result;

If the judgment result is yes, then output the optimal value of the parameter, and the optimal value of the parameter is within the parameter range of the circuit component;

If the judgment result is no, modify the parameter range or adjust the structure of the equivalent circuit model, so that the objective function converges and the difference is less than or equal to the threshold;

Output the optimal value of the parameter.

In a possible implementation manner, the adjusting the structure of the equivalent circuit model so that the objective function converges and the difference is less than or equal to the threshold, specifically includes:

increasing the number of circuit components in the equivalent circuit model, and judging whether the objective function converges and the difference is less than or equal to the threshold;

When the objective function converges and the difference is less than or equal to the threshold, the optimal value of the parameter is output.

In a possible implementation manner, the determining the transmission characteristics of the electromagnetic wave in the plasma according to the optimal value of the parameter includes:

Calculating multiple electron vibration angular frequencies corresponding to multiple electron densities;

Obtaining the plurality of electron vibration angular frequencies respectively, and determining a plurality of electromagnetic transmission characteristic curves obtained by the method of moments;

Obtaining the electromagnetic transmission characteristic curve obtained by the equivalent circuit method by using the equivalent circuit;

Each time, the genetic algorithm is used to inversely calculate one of the electromagnetic transmission characteristic curves obtained by the method of moments, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and the parameter range of circuit components, until multiple sets of parameters are obtained. value of merit;

According to the change rules between the optimal values of the plurality of groups of parameters and the plurality of electronic vibration angular frequencies, the characteristics of the plasma are analyzed to obtain the analysis results.

In a possible implementation manner, the electronic vibration angular frequency is specifically expressed as:

Wherein, N _e represents electron density, e represents electron charge, e=1.6×10 ^-9 C, and me _represents electron mass.

One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

The present invention adopts a method for researching the transmission characteristics of plasma electromagnetic waves based on an equivalent circuit model. The method includes: establishing an initial plasma equivalent circuit model based on the electromagnetic transmission characteristic curve obtained by the method of moments, and Calculate the electromagnetic transmission characteristic curve obtained by the equivalent circuit method using the effective circuit model, and simply and intuitively correspond the electromagnetic transmission characteristic curve obtained by the moment method to the corresponding circuit for characteristic research; compare the electromagnetic transmission characteristic curve obtained by the moment method with Compare the electromagnetic transmission characteristic curves obtained by the equivalent circuit method, determine the optimal value of the parameters of the circuit components in the equivalent circuit model, convert the material characteristics into the connection mode and specific parameter values of the circuit components, and master the mapping between the two relationship, which greatly simplifies the model, omits the complex intermediate calculation process, conducts simple and efficient analysis of the plasma, and improves the efficiency of calculation and analysis; effectively solves the problem of complex algorithms in the prior art and cannot truly reflect the plasma The problem of transmission characteristics, and then realizes the transformation of complex problems into simple circuit connection problems, and then performs characteristic analysis, which greatly reduces the difficulty of calculation, and can quickly and accurately analyze the transmission characteristics of electromagnetic waves.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments of the present invention or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a flow chart of the steps of the research method of the plasma electromagnetic wave transmission characteristics based on the equivalent circuit model provided by the present invention;

Fig. 2 is a schematic diagram of the relationship between the plasma medium and electromagnetic waves provided by the present invention;

Fig. 3 is the electromagnetic transmission characteristic curve that the method of moments provided by the present invention obtains;

Fig. 4 is the schematic diagram of equivalent circuit model provided by the present invention;

Fig. 5 is the comparison diagram of the electromagnetic transmission characteristic curve obtained by the equivalent circuit method and the electromagnetic transmission characteristic curve obtained by the moment method in the equivalent circuit model provided by the present invention;

6 is a schematic diagram of an equivalent circuit model provided by the present invention;

Fig. 7 is a comparison diagram of the electromagnetic transmission characteristic curve obtained by the equivalent circuit method provided by the present invention and the electromagnetic transmission characteristic curve obtained by the moment method;

Fig. 8 is the variation of the transmission parameter curve with the plasma thickness in the equivalent circuit provided by the present invention;

Fig. 9 shows the variation of the transmission parameter curve with the plasma density in the equivalent circuit provided by the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Apparently, the described embodiments are some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

The research on plasma is mainly divided into theoretical research, numerical research and experimental research. Among them, the theoretical research method refers to the direct calculation and solution of Maxwell's equations; the goal of numerical research is to solve the wave equation. With the development of computer technology, numerical simulation methods have been popularized, mainly including WKB (Wentzel Kramers Brillouin) method and scattering matrix method , Monte Carlo-based particle network simulation method and time-domain finite difference method; experimental research refers to the use of plasma generation devices and electromagnetic wave measurement devices to build an experimental environment for experiments. For the research method of plasma technology, the theoretical research is to establish the ideal plasma wave equation based on Maxwell's equations. This kind of research method is relatively complicated, and cannot truly reflect the transmission characteristics of plasma, and usually there is no analytical solution; numerical research refers to solving the wave equation of the plasma wave equation through methods such as finite difference in time domain, which depends on certain Hardware and software resources, the accuracy of the numerical model need to be further verified, and the physical meaning is not intuitive; through the experimental method, plasma research also has certain limitations, such as the complexity and high cost of the experimental device.

The present invention provides a method for researching plasma electromagnetic wave transmission characteristics based on an equivalent circuit model. As shown in FIG. 1 , the method includes the following steps S101 to S103.

When the electromagnetic wave hits the plasma as an incident wave, part of it will be output from the incident end in the form of reflected waves, and the other part will pass through the plasma medium and become transmitted waves after interacting with the plasma, as shown in Figure 2.

S101, according to the electromagnetic transmission characteristic curve obtained by the method of moments, establish an initial plasma equivalent circuit model, and calculate the electromagnetic transmission characteristic curve obtained by the equivalent circuit method according to the equivalent circuit model, in a specific implementation provided by the present invention In the example, the electromagnetic transmission characteristic curve obtained by the method of moments is based on the electromagnetic simulation software, the frequency range of the simulation is set to 0-30Ghz, the boundary conditions are set as structural units in the x and y directions, and open space in the z direction. Create a custom material, select the 'drude' model in the dispersion model, use the plasma frequency formula, set the parameters 'Epsiloninfinity' to '1.0', 'Plasma frequency' to '5.63e10', 'Collision frequency' to '1e6', Complete material creation. Create a plasma structural unit model using the material you just defined. The periodic length of the structural unit in the x and y directions is 10 mm, and the thickness in the z direction is 15 mm. After the modeling is completed, set the electromagnetic wave to be vertically incident from the 'Zmax' direction and run the simulation. The electromagnetic transmission characteristic curve obtained by the moment method is shown in Fig. 3 .

In a possible implementation manner, an initial plasma equivalent circuit model is established, and an electromagnetic transmission characteristic curve obtained by an equivalent circuit method is calculated according to the equivalent circuit model, including the following steps (1)-(2).

(1) Analyze the transmission characteristics of the electromagnetic transmission characteristic curve obtained by the moment method, and determine the equivalent circuit model according to the transmission characteristics.

In a specific embodiment of the present invention, it is analyzed that the plasma structure has good attenuation of low-frequency components of electromagnetic waves, and at the same time has good permeability to high-frequency components of waves. The curve characteristics are very similar to high-pass filters, and the cut-off frequency Around 7GHz. Combined with the passive LC filter design method, the equivalent circuit unit structure is determined, as shown in Figure 4, and the overall equivalent circuit model is built using the unit circuit. It should be noted that the second-order two-port network provided by the present invention is initially set based on the ideas involved from simple to complex, and it does not mean that the equivalent circuit can only be constructed from the second-order two-port network .

Save the electromagnetic transmission characteristic curve obtained by the moment method as the frequency value of 1003 frequency points, and the electromagnetic transmission characteristic curve value obtained by the moment method corresponding to each frequency point, and import the electromagnetic transmission characteristic curve value obtained by the moment method into In MATLAB, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method is calculated through the microwave network theory, and the plasma surface can be equivalent to a two-port network.

(2) Obtain the transmission matrix of the equivalent circuit model, and use the conversion relationship between the transmission matrix and the scattering matrix to determine the electromagnetic transmission characteristic curve obtained by the equivalent circuit method of the equivalent circuit model. The transmission matrix is specifically expressed as:

Among them, A, B, C, and D represent the matrix values in the transfer matrix, A and B represent the values of the first row of the transfer matrix in turn, C and D represent the values of the second row of the transfer matrix in turn, and N represents the accumulated The number of times of multiplication, T _i represents the transfer matrix of the i-th component, specifically expressed as:

in, Z _i represents the impedance of the i-th capacitor; Y _i represents the admittance of the i-th inductance.

The impedance of a capacitor is specifically expressed as: The admittance of the inductor is specifically expressed as: /> Among them, C _i represents the value of the i-th capacitor; L _i represents the value of the i-th inductor.

Specifically when calculating:

Specifically in a specific embodiment provided by the present invention, as shown in Figure 4, it is a second-order circuit, when n=2, N=1, that is:

The conversion relationship between the transmission matrix and the scattering matrix is specifically expressed as:

Among them, A, B, C, and D represent the matrix values in the transmission matrix, A and B respectively represent the values of the first row of the transmission matrix, C and D represent the values of the second row of the transmission matrix respectively, and Z ₀ represents is the characteristic impedance of free space.

In a specific embodiment, specific values of A, B, C, and D are expressed as values at corresponding positions in the matrix T above. The cascading characteristics of the transmission matrix can quickly and conveniently connect the discontinuous parts in the equivalent circuit.

S102. Comparing the electromagnetic transmission characteristic curve obtained by the method of moments with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and determining optimal values of parameters of the circuit components in the equivalent circuit model. In a specific embodiment provided by the present invention, the optimal value of the parameters is solved according to the genetic algorithm. The objective function of the genetic algorithm is expressed as:

Among them, _y1 represents the electromagnetic transmission characteristic curve obtained by the moment method, _y2 represents the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, f represents the electromagnetic transmission characteristic curve obtained by the moment method and the electromagnetic transmission characteristic obtained by the equivalent circuit method distance between curves. .

In a possible implementation, based on the genetic algorithm, the electromagnetic transmission characteristic curve obtained by the moment method is compared with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method to determine the optimal parameters of the circuit components in the equivalent circuit model. The merit value includes the following steps S201 to S204.

S201, based on the genetic algorithm, perform inversion calculation according to the electromagnetic transmission characteristic curve obtained by the method of moments, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and the parameter range of circuit components, and judge whether the objective function can be converged and the difference is less than or Equal to the threshold value, determine the judgment result.

S202. If the judgment result is yes, output the optimal value of the parameter, and the optimal value of the parameter is within the parameter range of the circuit component.

S203. If the judgment result is negative, modify the parameter range or adjust the structure of the equivalent circuit model, so that the objective function converges and the difference is less than or equal to the threshold.

S204, outputting the optimal value of the parameter.

In the inversion calculation of the component values in the initial circuit using the genetic algorithm, the specific genetic algorithm refers to simulating the process of biological evolution to optimize the objective function, and to find the minimum value of the objective function. The genes of organisms produce offspring individuals through selective cross-mutation. In the genetic algorithm, according to similar rules, the genotype corresponds to the variable combination in the algorithm, and each generation produces the most adaptable individual through selection, crossover, and mutation, and the individual in the final population is the target solution.

Set the parameters of the genetic algorithm. The Population size parameter represents the number of individuals in each generation. A larger value of this parameter range can increase the probability of jumping out of the local optimal solution, but at the same time it will increase the calculation time of the algorithm. After debugging The preferred setting is 50. Value range (Bounds), the parameter range can specify the upper and lower limits of each variable in all populations, represented by a matrix with two rows and two columns, the first row of the matrix is the lower limit of the five independent variables, and the second row is the independent variable The upper limit of , here is set to [1*10 ^-15 1*10 ^-10 ; 100*10 ^-15 100*10 ^-10 ], corresponding to the value range of components C1 and L1 in the equivalent circuit model. The initial range (Initial range) is used to specify the value range of the variables in the initial population. It is different from the meaning of Bounds. This parameter only limits the initial population. After knowing the approximate range of the optimal solution, adjusting the parameter reasonably can make it easier to approach the optimal Solution, here it is set to [1*10 ^-15 1*10 ^-10 ; 100*10 ^-15 100*10 ^-10 ]. The selection function parameter can define how to select parents from the population to generate the offspring population. Here, the selection is set to Roulette (roulette selection). This method is easy to converge and should not fall into a local optimal solution. The mutation method is set to Gaussian (Gaussian form). The Stopping criteria setting (Stopping criteria) is used to specify the stopping condition of the algorithm iteration, preferably setting the maximum number of generations to 200.

After the above parameters are set, and other parameters use the default settings, the genetic algorithm can be run. Judging whether the objective function can converge, if yes, output the values of components C1 and L1, if not, modify the parameter range or adjust the structure of the equivalent circuit model.

In a possible implementation manner, the structure of the equivalent circuit model is adjusted so that the objective function converges and the difference is less than or equal to a threshold, which specifically includes the following steps S301 to S302.

S301. Increase the number of circuit components in the equivalent circuit model, and determine whether the objective function converges and the difference is less than or equal to a threshold.

S302. When the objective function converges and the difference is less than or equal to the threshold, output the optimal value of the parameter.

When the structure of the equivalent circuit model is wrong, the value of the objective function cannot be reduced to the allowable range of the error. At this time, we need to adjust the structure of the equivalent circuit in time. Common problems are as follows:

(1) When the objective function value cannot be reduced to an acceptable range, the circuit structure cannot be adjusted blindly. For the first time, it is necessary to rule out that the objective function value cannot be reduced because the algorithm converges to the local optimum in advance. Try empirically tuning the genetic algorithm hyperparameters and increasing the number of trials to rule out chance results. When there is a large difference in the results no matter how you adjust the algorithm parameters, you can consider adjusting the structure of the circuit model.

(2) The number of components in the equivalent circuit is too small. Here, the passive LC analog filter is considered. When the order of the passive LC filter is not enough, the analog filter is difficult to approach the ideal filter. The specific performance is equivalent The electromagnetic transmission characteristic curve obtained by the circuit method is too gentle than that obtained by the moment method. At this time, the order of the LC filter should be increased, that is, the equivalent circuit units shown in Figure 4 are repeatedly cascaded.

(3) When the number of components in the equivalent circuit is too large, the transmission parameter curve of the circuit model will experience unstable jumps due to the resonance between different components. Some of the two curves differ greatly. At the same time, because the number of components corresponds to the number of independent variables of the genetic algorithm, when there are too many components, the iteration speed of the algorithm will be slow, and it is easy to fall into a local optimal solution.

In a specific embodiment provided by the present invention, when it is a second-order equivalent circuit, the comparison diagram of the electromagnetic transmission characteristic curve obtained by the equivalent circuit method and the electromagnetic transmission characteristic curve obtained by the moment method is shown in Figure 5 At this time, considering that the second-order circuit is not enough to simulate the plasma with this thickness due to insufficient circuit order, the circuit order of the equivalent circuit model is increased. The adjusted equivalent circuit is shown in Figure 6, including: inductors L1, L2, and capacitors C1, C2, and C3. When the value of the objective function falls within the allowable range of error, the equivalent circuit is not necessarily correct. It is also necessary to substitute the results obtained by the genetic algorithm into the circuit calculation, draw the electromagnetic transmission characteristic curve obtained by the equivalent circuit method for verification, and then Compared with the electromagnetic transmission characteristic curve obtained by the method of moments, as shown in Figure 7, when the fitting effect of the two curves is good and there is only a small difference in details, the equivalent circuit model can be considered to be valid.

S103. Determine the transmission characteristics of the electromagnetic wave in the plasma according to the optimal value of the parameter. According to the optimal value of the parameter, determining the transmission characteristic of the electromagnetic wave in the plasma includes the following steps S401 to S404.

S401. Calculate multiple electron vibration angular frequencies corresponding to multiple electron densities, respectively. The angular frequency of electron vibration is specifically expressed as:

Among them, N _e represents electron density, e represents electron charge, e=1.6×10 ^-9 C, me _represents electron mass, ε ₀ is expressed as a constant, ε ₀ =8.85×10 ^-12 (F/m).

S402. Obtain a plurality of electron vibration angular frequencies respectively, and determine a plurality of electromagnetic transmission characteristic curves obtained by the method of moments.

S403, using the equivalent circuit to obtain the electromagnetic transmission characteristic curve obtained by the equivalent circuit method.

S404, each time using the genetic algorithm to perform inversion calculation on one of the electromagnetic transmission characteristic curve obtained by the method of moments, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method, and the parameter range of circuit components, until multiple sets of optimal values of parameters are obtained .

S405, analyzing the characteristics of the plasma according to the variation rules between the optimal values of multiple groups of parameters and the multiple electron vibration angular frequencies, and obtaining the analysis results.

In the specific embodiment provided by the present invention, the thickness of the plasma is respectively taken as 6mm, 9mm, 12mm, 15mm, and 18mm, and the input parameter range is changed in turn, and the transmission parameter curve is calculated by electromagnetic, and the electromagnetic transmission characteristic curve obtained by the equivalent circuit method is derived. . As shown in Fig. 8, it is observed that the change range of the transmission parameter curve is not much larger than that when the plasma frequency is adjusted, but the shape of the curve in the transition section changes greatly. At the beginning, as the thickness increases, the transmission characteristic curve changes significantly when the thickness is in the range of 6mm to 12mm. When the thickness changes from 12mm to 18mm, the transmission characteristic curve does not change significantly. There is a large overshoot near the cutoff frequency. The characteristic curve of the analog filter, that is, the "cutoff frequency" gradually increases with the increase of thickness at first, and then the trend of change weakens. The corresponding equivalent circuit model component values are extracted by genetic algorithm. The structure of the equivalent circuit model and the variation of the component values with the thickness of the plasma are obtained. According to the analysis results, it can be seen that when the plasma thickness changes from 6 mm to 18 mm, the values of capacitor C1 and inductor L1 gradually decrease, and the values of capacitor C2, inductor L2, and capacitor C3 also show a downward trend as a whole.

In a specific embodiment provided by the present invention, the plasma electron density is respectively taken as 1*10 ¹⁷ , 2.5*10 ¹⁷ , 5*10 ¹⁷ , and 7.5*10 ¹⁷ , and the electron vibration angular frequency is calculated according to the above formula, Obtained respectively: 1.78*10 ¹⁰ , 2.82*10 ¹⁰ , 3.98*10 ¹⁰ , 4.88*10 ¹⁰ , 5.63*10 ¹⁰ , change the range of input parameters in turn, combine the electromagnetic transmission characteristic curve obtained by the method of moments, and derive the equivalent circuit method The obtained electromagnetic transmission characteristic curve is shown in FIG. 9 , and the corresponding equivalent circuit model component values are extracted by genetic algorithm. The variation of the component value with the electron density of the plasma is obtained. According to the analysis results, it can be seen that when the electron density changes from 1*10 ¹⁷ to 2.5*10 ¹⁷ , the values of the components change greatly, and then with the increase of the electron density, the values of the components change slightly. From the perspective of the entire circuit, the variation range of the values of the inductors L1 and L2 is relatively small, and the variation range of the values of the capacitors C1, C2 and C3 is relatively large. Since the values of the components in the equivalent circuit model are negatively correlated with the electron density of the plasma as a whole, the equivalent circuit model can be used to predict the changes in the structural parameters of the plasma.

The angular frequency of electronic vibration is negatively correlated with the relative permittivity, and the relative permittivity is specifically expressed as:

in, ω _pt =0, v represents the plasma collision frequency.

Therefore, the electron density of the plasma is negatively correlated with the relative permittivity of the plasma. The real part of the relative permittivity indicates how much electrical energy is stored in the material from the external electric field, and the imaginary part indicates how much electrical energy is dissipated in the material to the external electric field. When the plasma electron density becomes larger, the relative permittivity decreases, that is, the energy exchange between the plasma material and the outside world decreases, and correspondingly in the equivalent circuit, the values of capacitance and inductance decrease. Therefore, the electron density of the plasma is negatively correlated with the equivalent circuit element values.

The present invention uses the simple and intuitive method of circuit to analyze complex electromagnetic wave and field problems, which is much easier than solving complex equations. On the one hand, numerical calculation methods require hardware and software resources with certain computing power. On the other hand, the information we need is not the distribution of electromagnetic fields in the entire space. For example, in this invention, we only focus on the plasma in a certain frequency band. Transmission characteristics, that is, the transmission parameter curve, at this time, the equivalent circuit model can be used to achieve the purpose simply and efficiently. Compared with the prior art, the present invention has the following advantages: clear physical meaning, simple and efficient, and its complex calculation and simulation process can be omitted when studying plasma transmission or reflection characteristics. It provides a new way to quickly analyze the properties of plasma dielectric materials. At the same time, when the equivalent circuit model is used to study the plasma and the metasurface at the same time, the circuit bridges the two, which facilitates the exploration of the wave-absorbing mechanism of the composite structure of the plasma and the artificial metamaterial. The plasma equivalent circuit model in the present invention is simple, consisting only of capacitors and inductors, and the overall circuit structure is composed of circuit structural units, which belong to the repeated superposition of simple structures, and the calculation difficulty and model complexity are greatly reduced.

The various implementations in this specification are described in a progressive manner, the same or similar parts of the various implementations can be referred to each other, and each implementation focuses on the differences from other implementations. All or part of the present invention may be used in numerous general purpose or special purpose computer system environments or configurations. Examples: personal computers, server computers, handheld or portable devices, tablet-type devices, mobile communication terminals, multiprocessor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, including A distributed computing environment for any of the above systems or devices, etc.

The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the present invention; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be described in the foregoing embodiments Modifications to the technical solutions, or equivalent replacement of some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the present invention.

Claims (10)

1. A research method of plasma electromagnetic wave transmission characteristics based on an equivalent circuit model is characterized by comprising the following steps:

establishing an initial plasma equivalent circuit model according to an electromagnetic transmission characteristic curve obtained by a moment method, and calculating the electromagnetic transmission characteristic curve obtained by an equivalent circuit method according to the equivalent circuit model;

comparing the electromagnetic transmission characteristic curve obtained by the moment method with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method to determine the parameter optimal value of the circuit components in the equivalent circuit model;

and determining the transmission characteristic of the electromagnetic wave in the plasma according to the optimal value of the parameter.

2. The method of claim 1, wherein said establishing an initial plasma equivalent circuit model and calculating an equivalent circuit derived electromagnetic transmission characteristic from said equivalent circuit model comprises:

analyzing the transmission characteristic of the electromagnetic transmission characteristic curve obtained by the moment method, and determining the equivalent circuit model according to the transmission characteristic;

and acquiring a transmission matrix of the equivalent circuit model, and determining an electromagnetic transmission characteristic curve obtained by an equivalent circuit method of the equivalent circuit model by utilizing a conversion relation between the transmission matrix and a scattering matrix.

3. The method of claim 2, wherein the transmission matrix is expressed as:

wherein A, B, C, D represents matrix values in the transmission matrix, A and B are respectively and sequentially represented as values of a first row of the transmission matrix, C and D are respectively and sequentially represented as values of a second row of the transmission matrix, N represents multiplication times, T _i The transmission matrix of the ith component is shown as follows:

wherein ,Z _i representing the impedance of the ith capacitor; y is Y _i Indicating the admittance of the ith inductance.

4. A method according to claim 3, characterized in that the impedance of the capacitor is expressed in particular as:the admittance of the inductance is specifically expressed as: /> wherein ,C_i Representing the value of the ith capacitance; l (L) _i Representing the value of the i-th inductance.

5. A method according to claim 3, characterized in that the transformation relationship between the transmission matrix and the scattering matrix is expressed in particular as:

wherein ,Z₀ Expressed as the characteristic impedance of free space.

6. The method of claim 1, wherein the objective function of the genetic algorithm is expressed as:

wherein ,y₁ Representing the electromagnetic transmission characteristic curve obtained by the moment method, y ₂ And f represents the distance between the electromagnetic transmission characteristic curve obtained by the moment method and the electromagnetic transmission characteristic curve obtained by the equivalent circuit method.

7. The method of claim 6, wherein comparing the electromagnetic transmission characteristic curve obtained by the moment method with the electromagnetic transmission characteristic curve obtained by the equivalent circuit method to determine the parameter optimal value of the circuit component in the equivalent circuit model comprises:

based on a genetic algorithm, carrying out inversion calculation according to the electromagnetic transmission characteristic curve obtained by the moment method, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method and the parameter range of the circuit component, judging whether the objective function can be converged and the difference is smaller than or equal to the threshold value, and determining a judging result;

if the judging result is yes, outputting the parameter optimal value, wherein the parameter optimal value is in the parameter range of the circuit component;

if the judgment result is negative, modifying the parameter range or adjusting the structure of the equivalent circuit model to enable the objective function to be converged and the difference to be smaller than or equal to the threshold value;

outputting the parameter optimal value.

8. The method according to claim 7, wherein said adjusting the structure of the equivalent circuit model to converge the objective function with a difference less than or equal to the threshold value comprises:

increasing the number of circuit components in the equivalent circuit model, and judging whether the objective function converges and the difference is smaller than or equal to the threshold value;

and outputting the parameter optimal value when the objective function converges and the difference is smaller than or equal to the threshold value.

9. The method of claim 1, wherein determining the transmission characteristics of the electromagnetic waves in the plasma based on the parameter optimum values comprises:

respectively calculating a plurality of electronic vibration angular frequencies corresponding to the plurality of electronic densities;

respectively acquiring the plurality of electronic vibration angular frequencies, and determining a plurality of electromagnetic transmission characteristic curves obtained by the moment method;

acquiring an electromagnetic transmission characteristic curve obtained by the equivalent circuit method by utilizing the equivalent circuit;

inverting and calculating the electromagnetic transmission characteristic curve obtained by one moment method, the electromagnetic transmission characteristic curve obtained by the equivalent circuit method and the parameter range of the circuit components by using a genetic algorithm each time until a plurality of groups of parameter optimal values are obtained;

and carrying out characteristic analysis on the plasmas according to the change rule between the optimal values of the multiple groups of parameters and the multiple electronic vibration angular frequencies to obtain an analysis result.

10. The method according to claim 9, characterized in that said electronic oscillation angular frequency is expressed in particular as:

wherein ,N_e Represents electron density, e represents electron quantity, e=1.6x10 ^-9 C，m _e Representing the electron mass.