Electromagnetic correction method for electron density distribution of plasma flow field

Abstract

The application relates to a plasma flow field electron density distribution electromagnetic correction method, and relates to the electromagnetic correction field, and comprises the following steps: simulating the electron density of a model surface, and taking the simulated flow field electron density distribution as a basic distribution; inverting a correction function through the RCS measurement result of an observation point; expanding the correction function at the original point into a Taylor series to obtain the correction function; multiplying the correction function and the basic distribution at any position to obtain the correction value of the electron density at the any position; and the optimal individual screened out by a genetic algorithm is the inversion correction result, so that the simulation result of the plasma flow field electron density distribution can be corrected after the known target shape, the simulation result of the plasma flow field electron density distribution, the change amount of the RCS of the target within a limited azimuth angle and a limited frequency point after being affected by the plasma, and the accuracy of the simulation result of the plasma electron density is further improved.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic correction technology, and in particular to an electromagnetic correction method for electron density distribution in a plasma flow field. Background Technology

[0002] When a target flies at high speeds (above approximately 4000 m / s) in a thin atmosphere, the surrounding air is compressed and ionized, forming a plasma flow field enveloping the target and affecting its electromagnetic scattering characteristics. The calculation of the electromagnetic scattering characteristics of the target enveloped by the plasma flow field is directly related to the electron density distribution within the plasma flow field. Due to current technological limitations, the simulation calculation uncertainty of the electron density in the plasma flow field typically exceeds one order of magnitude, making it difficult to support the high-precision simulation calculation requirements for the target's electromagnetic scattering characteristics.

[0003] Therefore, to address the above shortcomings, it is necessary to provide an electromagnetic correction method for the electron density distribution in a plasma flow field. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] The technical problem to be solved by this invention is how to correct the simulation results of electron density in plasma flow field and reduce the input error of electromagnetic scattering characteristic simulation calculation.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention provides an electromagnetic correction method for electron density distribution in a plasma flow field, comprising the following steps:

[0008] I. Simulate and calculate the electron density on the surface of the model, and use the simulated electron density distribution around the flow field as the basic distribution;

[0009] II. Using the RCS measurement results of the observation points, the correction function is inverted; the correction function is expanded into a Taylor series at the origin, resulting in the following correction function:

[0010]

[0011] The correction value of the electron density at any position is obtained by multiplying the correction function by the basic distribution at any position;

[0012] III. The optimal individual selected by the genetic algorithm is the result of the inversion correction.

[0013] As a further explanation of the present invention, preferably, the correction function Corr p () represents the ratio between the true value and the baseline value of the electron density at any location.

[0014] As a further explanation of the present invention, preferably, the N in the correction function is approximated by order 1 as follows:

[0015] Corr p (x′, y′, z′)=Corr p (0, 0, 0)+a1x′+b1y′+c1z′.

[0016] As a further explanation of the present invention, preferably, when using a genetic algorithm to perform parameter inversion on the plasma flow field, a corresponding objective cost function is first defined:

[0017]

[0018] Where I represents the number of frequency observation points;

[0019] This indicates that under a plasma flow field, the experimentally measured fixed observation angle (field point) is at frequency f. i RCS value at the location;

[0020] This indicates that, in the case of the physical body only, the fixed observation angle (field point) measured in the experiment is at frequency f. i RCS value at the location;

[0021] This indicates that under a plasma flow field, the simulation calculation at a fixed observation angle (field point) is at frequency f. i RCS value at the location;

[0022] This indicates that, in the case of only the physical entity, the fixed observation angle (field point) in the simulation calculation is at frequency f. i RCS value at the location;

[0023] The flow field distribution under plasma flow field conditions is calculated using the finite-difference time-domain method.

[0024] (III) Beneficial Effects

[0025] The above-described technical solution of the present invention has the following advantages:

[0026] This invention designs an electromagnetic correction method for the electron density distribution of a plasma flow field. This method, after knowing the target shape, the simulation results of the electron density distribution of the plasma flow field, and the change in RCS of the target under the influence of plasma within a finite azimuth angle and a finite frequency point, can correct the simulation results of the electron density distribution of the plasma flow field, thereby further improving the accuracy of the plasma electron density simulation results. Attached Figure Description

[0027] Figure 1This is a schematic diagram of the experimental layout of the present invention;

[0028] Figure 2 This is a comparison chart of the simulated electron density results of probe 1 of the present invention and the results of multiple measurements;

[0029] Figure 3 This is a comparison chart of the simulated electron density results of probe 2 and multiple measurement results of the present invention;

[0030] Figure 4 This is a comparison chart of the simulated electron density results of probe 3 of the present invention and the results of multiple measurements;

[0031] Figure 5 This is a comparison chart of the simulated electron density results of probe 4 of the present invention and the results of multiple measurements;

[0032] Figure 6 This is a comparison chart of the simulated electron density results of probe 5 of the present invention and the results of multiple measurements;

[0033] Figure 7 This is a comparison chart of the electron density inversion correction result of probe 1 and the measurement result of the present invention;

[0034] Figure 8 This is a comparison chart of the probe 2 electron density inversion correction results and the measurement results of the present invention;

[0035] Figure 9 This is a comparison chart of the probe 3 electron density inversion correction results and the measurement results of the present invention;

[0036] Figure 10 This is a comparison chart of the electron density inversion correction results of probe 4 and the measurement results of the present invention;

[0037] Figure 11 This is a comparison chart of the electron density inversion correction result of probe 5 and the measurement result of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] An electromagnetic correction method for electron density distribution in a plasma flow field is proposed. The physical parameter mesh of the plasma flow field is three-dimensionally discretized in space using a cubic mesh format in a Cartesian coordinate system. The simulated electron density distribution of the flow field is used as the base distribution, denoted as the distribution at point r′. The ratio between the true value and the fundamental value of the electron density at any location is denoted as the correction function Corr. p (r′). The correction function is retrieved from the RCS measurement at observation point r, and the correction value of the electron density at any location can be obtained by multiplying the correction function by the fundamental distribution at any location. Specifically, the following steps are included:

[0040] I. Simulate and calculate the electron density on the surface of the model, and use the simulated electron density distribution of the flow field around it as the basic distribution;

[0041] II. Using the RCS measurement results at the observation point, the correction function is inverted; in the flow field distribution calculation model, the stagnation point (probe 1) is defined as the origin; the correction function is expanded into a Taylor series at the origin, resulting in the correction function as follows:

[0042]

[0043] The higher the order N of the series, the more accurately the series fits the original function, but correspondingly, the number of parameters to be inverted increases. On the one hand, the amount of experimental data and the accuracy of simulation and measurement are insufficient to support high-precision inversion; on the other hand, the more parameters to be inverted, the greater the difficulty of inversion. Therefore, a first-order approximation is taken for the correction function, and the form of the correction function after taking the first-order approximation becomes:

[0044] Corr p (x′, y′, z′)=Corr p (0, 0, 0)+a1x′+b1y′+c1z′

[0045] The correction function is obtained by using a plasma flow field parameter inversion algorithm that combines genetic algorithm and plasma time-domain algorithm.

[0046] When using a genetic algorithm to perform parameter inversion on a plasma flow field, the first step is to define a corresponding objective cost function. Since the measured and simulated values ​​of the target body differ at different frequency points, the cost function is defined as the distance between the measured RCS change of the target under the influence of the plasma flow field and the simulated RCS change. The cost function formula is:

[0047]

[0048] Where I represents the number of frequency observation points;

[0049] This indicates that under a plasma flow field, the experimentally measured fixed observation angle (field point) is at frequency f. i RCS value at the location;

[0050] This indicates that, in the case of the physical body only, the fixed observation angle (field point) measured in the experiment is at frequency f. i RCS value at the location;

[0051] This indicates that under a plasma flow field, the simulation calculation at a fixed observation angle (field point) is at frequency f. i RCS value at the location;

[0052] This indicates that, in the case of only the physical entity, the fixed observation angle (field point) in the simulation calculation is at frequency f. i RCS value at the location;

[0053] The flow field distribution under plasma flow conditions is calculated using the finite-difference time-domain method. During the inversion iteration process, the parameter distribution of each individual plasma flow field is determined by the correction function Corr for that individual. p (r′) and the fundamental distribution of electron density It is obtained by multiplying the corresponding grid positions.

[0054] III. The optimal individual selected by the genetic algorithm is the result of the inversion correction.

[0055] To verify the feasibility of this correction method, such as Figure 1 As shown, the plasma flow field around the target was simulated using a high-enthalpy shock wind tunnel, and the electron density distribution was measured to verify the method.

[0056] like Figure 1 As shown, in the wind tunnel test section, a cross channel was established where high-enthalpy airflow and microwave beams are mutually compatible. Along the wind tunnel axis is the high-enthalpy flow channel, where the incoming flow can simulate flight conditions at an altitude of 50 km and a flow velocity of 15 Ma, generating corresponding high-temperature gas flow and plasma around the target. The entire test environment is generated within the wind tunnel, which has a microwave anechoic chamber. Detection windows are opened on the wind tunnel walls. Intersecting the airflow direction is the microwave channel, employing a single-station, single-antenna scattered echo measurement system. It consists of a conical lens antenna and a wave-transparent window. Within this channel, the antenna emits microwave signals to illuminate the flow field region as a plane wave, and the antenna receives the echoes from the flow field region.

[0057] The relative calibration method based on free-space reflection is used for measurement. Under the conditions of determined radar operating frequency, polarization, and operating mode, calibration is performed using a calibration body with known RCS resolution values ​​to complete the frequency response error calibration of the measurement system. The calibrated system can then perform precise RCS measurement of the target.

[0058] The target to be measured is a spherical column. Its dimensions are: 50mm radius at the head, 250mm height, and 50mm radius at the base; the material is aluminum. The electron density on the model surface is simulated and calculated using the Langmuir probe method. Five holes are drilled along the same meridian on the model surface. After installing Langmuir probes, a probe array is formed, arranged sequentially from the stationary point, to measure the electron density at each probe location. Probes 1-5 are located on the head hemisphere, with the angles between the line connecting the probe center and the spherical center and the model axis being 0°, 30°, 45°, 60°, and 90°, respectively. The probes are planar probes (φ5.5mm) made of copper. A high-temperature resistant quartz tube is used for insulation between the probes and the model. Ceramic adhesive is used to connect the probes to the model wall, with the probe surface overlapping the model wall. At the tail end of the model, a steel pipe connects it to the vacuum chamber wall.

[0059] The RCS of the spherical column and the plasma flow field at frequencies of 5.5 GHz, 9 GHz, 10 GHz, and 14 GHz were measured in four experiments. The electron density distribution at each probe was also measured over time. The RCS measurement results are shown in the table below.

[0060] Table 1 RCS Measurement Results

[0061] Measurement frequency (GHz) <![CDATA[Target body RCS (dBm 2 )]]> <![CDATA[Plasma sheath covering RCS (dBm 2 )]]> 5.5 -15.60 -17.04 9.0 -11.92 -12.55 10.0 -15.26 -15.94 14.0 -11.91 -11.88

[0062] The simulated electron density results and experimental measurement results at each probe were compared, and the comparison results are as follows: Figure 2-6 As shown.

[0063] The simulation results for electron density were corrected using the aforementioned correction method. The genetic algorithm parameters were selected as follows: the population size was set to 10, the maximum number of iterations to 20, and both the crossover and mutation probabilities were set to 0.4. The resulting electron density correction function was:

[0064] Corr p (x′, y′, z′)=0.038+0.28x′+0.00040y′+0.00030z′

[0065] The electron density distribution at each probe was corrected using the inverted electron density error coefficients, and then compared with the measurement results. The comparison results are as follows: Figure 7-11 As shown, it can be seen that after electromagnetic inversion correction, the difference between the simulation results and the measurement results is significantly reduced compared with before correction, and the method achieves a good inversion correction effect.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of electromagnetic modification of electron density distribution in a plasma flow field, characterized by: Comprising the following steps: I. Simulate the electron density of the model surface, and take the electron density distribution of the simulated flow field as the basic distribution; II. Invert the correction function through the RCS measurement results of the observation points; expand the correction function into a Taylor series at the origin to obtain the correction function: Obtain the correction value of the electron density at any position by multiplying the correction function and the basic distribution at any position; III. Define the corresponding target cost function: wherein denotes the number of frequency observation points; represents the experimentally measured RCS value at a fixed observation angle at frequency frequencies under the plasma flow field. RCS(f) represents the experimentally measured value of the RCS at a fixed observation angle at frequency f only for the case of the body; and RCS(f) represents the experimentally measured value of the RCS at a fixed observation angle at frequency f only for the case of the body; and RCS values at the frequency of 10 GHz for the fixed observation angle of 0° RCS values at the frequency of 10 GHz for the fixed observation angle of 0° represents the simulated calculated fixed observation angle RCS value at frequency frequencies only. According to the plasma flow field, the flow field distribution is calculated by the finite difference time domain method, and then the optimal individual selected by the genetic algorithm is the inversion correction result.

2. The method of claim 1, wherein the electromagnetic modification of the electron density distribution of a plasma flow field is characterized by: correction function is the ratio between the true value of the electron density at an arbitrary position and the base value.

3. The method of claim 2, wherein the electromagnetic modification of the electron density distribution of a plasma flow field is characterized by: In the correction function Taking the first order approximation, we have 。

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