A method for simulating signal transmission of a high-speed aircraft under influence of a plasma sheath

Abstract

A signal transmission simulation method of high-speed aircraft under the influence of plasma sheath, the present application relates to the field of wireless communication, in order to simulate the signal transmission problem of high-speed aircraft under the influence of plasma sheath. The present application firstly adopts double exponential model to simulate the electron density distribution of high-speed aircraft plasma sheath;Then the model is used to study the influence of plasma parameters on the attenuation, and the equivalent wave impedance method is used for layered analysis, and the plasma is layered according to the thickness, and the thickness of each layer is thin enough to ensure that the electromagnetic characteristics of the plasma in each layer are basically consistent;The influence of different plasma parameters, such as plasma collision frequency, on signal transmission attenuation is studied. The present application is suitable for simulating the influence of plasma sheath on electromagnetic wave.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology. Background Technology

[0002] High-speed aircraft possess numerous advantages, including high speed, high altitude, rapid response, and the ability to reach any region of the world in a short time. They hold significant importance for both military and civilian applications, attracting considerable attention from countries worldwide. However, when high-speed aircraft fly at extremely high speeds in the atmosphere, a plasma sheath forms on their surface. This sheath absorbs and reflects electromagnetic waves, severely impacting the amplitude and phase of communication signals, leading to deterioration or even interruption of communication quality. This is one of the biggest challenges currently facing high-speed aircraft.

[0003] To improve the telemetry, tracking, and control technology and communication capabilities of high-speed aircraft, it is necessary to establish channel conditions under the influence of a plasma sheath. Under these conditions, it is of great significance to realize a simulation method for signal transmission under the influence of a plasma sheath and obtain the plasma electron density distribution and signal attenuation sequence of the plasma sheath on the surface of the high-speed aircraft in the time domain. Summary of the Invention

[0004] This invention aims to address the signal transmission problem of high-speed aircraft under the influence of plasma sheaths, and thus provides a method for simulating signal transmission of high-speed aircraft under the influence of plasma sheaths.

[0005] The technical solution adopted in this invention is:

[0006] A method for simulating signal transmission of a high-speed aircraft under the influence of a plasma sheath, comprising the following steps:

[0007] Step 1: Establish the plasma sheath model, including: establishing the plasma electron density model, establishing the plasma frequency model, and establishing the plasma collision frequency model;

[0008] Step 2: Use a double exponential model to simulate the plasma sheath electron density distribution of a high-speed aircraft to obtain the plasma electron density distribution model.

[0009] Step 3: Modify the electron distribution model described in Step 2 to make it more consistent with the plasma electron density distribution in a real-world scenario;

[0010] Step 4: Using the equivalent wave impedance method, obtain the influence value of plasma electron density on signal transmission attenuation by combining the plasma electron density model established in Step 1 and the modified electron distribution model in Step 3.

[0011] Step 5: Using the equivalent wave impedance method, obtain the influence value of plasma collision frequency on signal transmission attenuation by combining the plasma collision frequency model established in Step 1 and the modified electron distribution model in Step 3.

[0012] Step 6: Use the equivalent wave impedance method to obtain the time-domain variation relationship of dynamic plasma sheath attenuation between the plasma frequency model established in Step 1 and the modified electron distribution model in Step 3.

[0013] Step 7: Take the influence value of plasma electron density on signal transmission attenuation obtained in Step 4, the influence value of plasma collision frequency on signal transmission attenuation obtained in Step 5, and the time-domain variation relationship of dynamic plasma sheath attenuation obtained in Step 6 as the signal transmission simulation results of a high-speed vehicle under the influence of plasma sheath, and complete a signal transmission simulation of a high-speed vehicle under the influence of plasma sheath.

[0014] Furthermore, in step one, the specific method for establishing the plasma electron density model is as follows: the plasma electron density is expressed using N... e (z) represents the number of electrons per unit volume. In the plasma generated on the surface of a high-speed aircraft, the plasma electron density is spatially non-uniform, and its variation depends on various factors such as the flight altitude, flight speed, and flight attitude of the high-speed aircraft. The plasma sheath electron density on the surface of the high-speed aircraft approximately follows a double exponential distribution in the low-altitude part and an approximately Gaussian distribution in the high-altitude part. The specific distribution model is selected according to the simulated transmission situation to complete the modeling.

[0015] Furthermore, in step one, the plasma frequency model established is specifically as follows:

[0016]

[0017] In the formula, N e (z,t) represents the electron density at a certain position at a certain moment; q e Represents the unit charge of an electron; ε0 is the dielectric constant in vacuum; m e Indicates electron mass.

[0018] Furthermore, in step one, the plasma collision frequency model established is specifically as follows:

[0019] v c =5.19×10 11 ·kTN e (z,t) (2)

[0020] In the formula, N e (z,t) represents the electron density at a certain position at a certain time; k is the Boltzmann constant; and T is the plasma temperature.

[0021] Furthermore, in step two, a double exponential function distribution model is used to simulate the electron density distribution of the plasma sheath on the surface of a high-speed aircraft during flight. The expression for the double exponential function distribution it satisfies is:

[0022]

[0023] In the formula, n emax The maximum electron density of the plasma; z 10 z1 represents the inflection point of the double exponential function; z2-z1 represents the thickness of the established plasma model; η1 represents the degree of change of the first part of the double exponential function; η2 represents the degree of change of the second part of the double exponential function.

[0024] The beneficial effects obtained by this invention are as follows:

[0025] 1. This invention can simulate the time-domain attenuation change of a signal after it passes through a plasma sheath;

[0026] 2. Compared to the traditional method of calculating electron density using chemical models, this simplifies the analysis process. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the plasma electron density with a double exponential distribution;

[0028] Figure 2 This is a schematic diagram of the plasma electron density after the correction of the double exponential distribution;

[0029] Figure 3 This is a schematic diagram of the layered structure of the plasma sheath;

[0030] Figure 4 This is a schematic diagram illustrating the principle of attenuation calculation based on the equivalent wave impedance method.

[0031] Figure 5 This is a schematic diagram illustrating the effect of collision frequency on attenuation;

[0032] Figure 6 This is a schematic diagram of the time-domain variation of dynamic plasma sheath decay. Detailed Implementation

[0033] This embodiment is described in conjunction with the figures and appendices. Figure 1-6The present invention will be described in further detail below. The signal transmission simulation method under the influence of a plasma sheath is proposed to solve the signal transmission problem of high-speed aircraft under the influence of a plasma sheath, and a numerical simulation method is provided. 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0034] Step 1: Establish the corresponding plasma sheath model. The plasma parameters involved in this invention mainly include: plasma density, plasma frequency, and plasma collision frequency.

[0035] Step 1: Establish a plasma electron density model. The plasma electron density commonly uses N0... e The electron density of a plasma is represented by the number of electrons per unit volume. Plasma electron density is not constant; in the plasma encountered by a high-speed aircraft, the variation in plasma electron density depends on various factors, such as the aircraft's altitude, speed, and attitude. The established plasma electron density model shows a non-uniform distribution in space. The electron density of the plasma sheath on the surface of the high-speed aircraft approximately follows a biexponential distribution in the low-altitude region, while in the high-altitude region, it approximately follows a Gaussian distribution.

[0036] Steps 1 and 2: Establishing a plasma frequency model. Plasma frequency generally refers to the plasma oscillation frequency, primarily the frequency at which microscopic particles such as electrons within the plasma oscillate after being subjected to some kind of disturbance. Generally, the angular frequency of plasma is:

[0037]

[0038] In the formula, q e N is the electron charge. e Let ε0 be the electron density of the plasma, ε0 be the vacuum permittivity, and m be the electron density of the plasma. e Given the electron mass, it can be seen that the plasma frequency depends only on the plasma electron density; therefore:

[0039]

[0040] Plasma frequency is one of the most fundamental parameters used to describe the characteristics of plasma. In the actual analysis process of this invention, plasma is treated as a special dispersive medium. When there are no particle collisions within the plasma, the refractive index of the plasma for electromagnetic waves is:

[0041]

[0042] In the formula, f represents the frequency of the transmitted electromagnetic wave. It can be seen that when f < f p At this time, electromagnetic waves cannot pass through the plasma; that is, only when f > f p Only when electromagnetic waves pass through the plasma can they propagate; therefore, the plasma frequency is also called the cutoff frequency.

[0043] Step 13: Establish a plasma collision frequency model. Plasma collision frequency refers to the frequency at which particles collide with each other in a plasma. In plasma, the motion of particles is greatly influenced by the interactions with surrounding particles; therefore, collision frequency is an important parameter of plasma properties. Plasma collision frequency refers to the number of times an electron collides with other particles per unit time. Generally, plasma collision frequency is related to electron density and temperature.

[0044] P = N e kT (4)

[0045] v c =5.19×10 11 ·P (5)

[0046] This shows that the higher the plasma electron density, the higher the plasma collision frequency.

[0047] Step 2: A double-exponential model is used to simulate the electron density distribution in the plasma sheath of a high-speed aircraft. Figure 1 The established plasma electron density model follows a double exponential function distribution n e (z) is:

[0048]

[0049] In the formula, n emax The highest electron density in the plasma; η1 and η2 are used to describe the trends of the first and second parts of the double exponential function, respectively, and then z is used. 10 The segmentation point of the double exponential function is represented by z2-z1; the plasma thickness can be calculated from z2-z1.

[0050] In this embodiment, the maximum electron density n is taken. emax =10 14 m -3 .

[0051] Step 3: Correct the electron distribution model described in Step 2 to better reflect the plasma electron density distribution in a real-world scenario. The double-exponential plasma electron distribution model established in Step 2 has a sharp peak point, but the electron distribution on the plasma sheath of a high-speed aircraft surface is smooth in reality. Therefore, the model established in Step 2 needs to be corrected. The correction method is to establish a steady-state value in the electron density distribution model to better describe the electron density distribution. The corrected plasma electron distribution model is shown below. Figure 2 As shown, the horizontal axis z represents the distance of this position from the surface of the aircraft; the vertical axis n e n represents electron density. emax This represents the maximum electron density value.

[0052] Step 4: Using the models proposed in Step 1 and Step 3, study the influence of plasma parameters on attenuation. Use the equivalent wave impedance method for layered analysis, and divide the plasma into layers according to thickness. The thickness of each layer is thin enough to ensure that the electromagnetic properties of the plasma are basically consistent in each layer.

[0053] Considering that the modified double-exponential plasma electron density distribution established in step three is nonlinear and complex to solve, the plasma sheath is modeled as N thin layers to facilitate analysis and calculation. The layered structure is as follows: Figure 3 As shown in the diagram. The electron density within each evenly distributed thin layer is also considered to be uniformly distributed. The electromagnetic wave attenuation value on each layer is calculated, and then summed N-1 times to obtain the total attenuation value. The specific implementation steps are as follows: Figure 4 As shown.

[0054] The parameters involved in this process are shown in the table below:

[0055] Table 1 Parameter Table

[0056]

[0057] Step 5: Following the method in Step 4, investigate the effect of plasma electron density on signal transmission attenuation;

[0058] In plasma, the differential form of Maxwell's equations is:

[0059]

[0060] in

[0061]

[0062]

[0063] Where E0 and H0 represent the peak values ​​of the electric and magnetic fields, respectively, we have:

[0064]

[0065] have:

[0066]

[0067] Electromagnetic waves propagate passively in plasma, therefore ρ = 0. We can obtain:

[0068]

[0069] The wave equation in plasma is:

[0070]

[0071] The plane wave expression can be obtained as follows:

[0072] E = E0e j(wt-kr) (14)

[0073] In the formula, The electromagnetic wave propagation coefficient is represented by μ. For simplicity, the influence of the magnetic medium is ignored for now. r =1

[0074] For ease of calculation, the relative permittivity ε of the plasma is now expressed as... r The form of splitting into real and imaginary parts:

[0075]

[0076] To study the propagation of electromagnetic waves in plasma, we can assume the electromagnetic wave propagation coefficient is:

[0077] k=(β-jα) (16)

[0078] In the formula, α is the attenuation constant of the electromagnetic wave propagating in the plasma in the plasma electron density model established in step three, and β represents the corresponding phase constant. Therefore, the expression for the electromagnetic wave in the plasma is:

[0079] E = E0e j[wt-(β-jα)r] (17)

[0080] Therefore, we can conclude that:

[0081]

[0082] Therefore, the attenuation constant α and the phase constant β are respectively:

[0083]

[0084]

[0085] The wave function of an electromagnetic wave can be represented as:

[0086]

[0087] In this embodiment, when the operating frequency ω within the fixed plasma is 12 × 10⁻⁶, 9 rad / s, 24×10 9 rad / s and 12×10 10 rad / s, fixed plasma electron density N e =10 10 cm -3 Then, the method described in steps three, four, and five is used to calculate the effect of collision frequency on attenuation. In this embodiment, the plasma collision frequency range is set to 10. 7 s -1 ~10 12 s -1 Within the range.

[0088] Depend on Figure 5 It can be seen that the collision frequency of the plasma has a significant impact on the transmission of electromagnetic waves within the plasma. As the plasma collision frequency increases, the attenuation value caused by the established signal transmission simulation first increases and then decreases. When the collision frequency is very high or very low, the attenuation value caused by the established signal transmission simulation is very small, and the peak attenuation is also related to the selected electromagnetic wave operating frequency.

[0089] This phenomenon occurs primarily because the attenuation of electromagnetic waves during transmission through plasma is mainly due to electrons within the plasma absorbing the energy of the electromagnetic waves and transferring that energy through collisions with other particles at high speeds, thus causing the electromagnetic waves to continuously attenuate. When the collision frequency of the plasma is very low, the plasma can be considered a lossless medium, and the attenuation effect on electromagnetic waves is minimal. When the collision frequency of the plasma is high, the kinetic energy of the electrons during collisions is high, resulting in a higher energy conversion efficiency for the electromagnetic waves.

[0090] Step 6: Based on the method in Step 5 and considering the influence of the actual flight attitude of the aircraft, obtain the time-domain variation of the dynamic plasma sheath attenuation.

[0091] In this embodiment, the high-speed aircraft is set at an altitude of 30km, and the carrier signal operating angular frequency is 12×10⁻⁶. 9 The plasma dynamics, measured in rad / s, caused by the dynamic changes during the flight of the high-speed aircraft, exhibit a sinusoidal variation, with the range limited to ±5°. The time-domain simulation results of plasma decay, obtained using the method in step four, are as follows: Figure 6 As shown. From Figure 6As can be seen, the attenuation change sequence caused by the established signal transmission simulation produces a periodic jitter, which can simulate the time-domain plasma attenuation.

[0092] Although the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary instances, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It should also be understood that features described in conjunction with individual embodiments can be used in other embodiments.

Claims

1. A method for simulating signal transmission of a high-speed aircraft under the influence of a plasma sheath, characterized by: It includes the following steps: Step 1: Establish the plasma sheath model, including: establishing the plasma electron density model, establishing the plasma frequency model, and establishing the plasma collision frequency model; the established plasma collision frequency model is specifically as follows: ； In the formula, The electron density at a specific location at a specific moment; k is the Boltzmann constant; T is the plasma temperature; Step 2: Use a double exponential model to simulate the electron density distribution of the plasma sheath of a high-speed aircraft to obtain the electron distribution model of the plasma electron density model; Step 3: Modify the electron distribution model described in Step 2 to make it more consistent with the plasma electron density distribution in a real-world scenario; Step 4: Using the equivalent wave impedance method, obtain the influence value of plasma electron density on signal transmission attenuation by combining the plasma electron density model established in Step 1 and the modified electron distribution model in Step 3. Step 5: Using the equivalent wave impedance method, obtain the influence value of plasma collision frequency on signal transmission attenuation by combining the plasma collision frequency model established in Step 1 and the modified electron distribution model in Step 3. Step 6: Use the equivalent wave impedance method to obtain the time-domain variation relationship of dynamic plasma sheath attenuation between the plasma frequency model established in Step 1 and the modified electron distribution model in Step 3. Step 7: Take the influence value of plasma electron density on signal transmission attenuation obtained in Step 4, the influence value of plasma collision frequency on signal transmission attenuation obtained in Step 5, and the time-domain variation relationship of dynamic plasma sheath attenuation obtained in Step 6 as the signal transmission simulation results of a high-speed vehicle under the influence of plasma sheath, and complete a signal transmission simulation of a high-speed vehicle under the influence of plasma sheath.

2. The method for simulating signal transmission of a high-speed aircraft under the influence of a plasma sheath according to claim 1, characterized in that... In step one, the specific method for establishing the plasma electron density model is: to use the plasma electron density... The electron density represents the number of electrons per unit volume. In the plasma generated on the surface of a high-speed aircraft, the plasma electron density is spatially non-uniform, and its variation depends on various factors such as the flight altitude, flight speed, and flight attitude of the high-speed aircraft. The plasma sheath electron density on the surface of the high-speed aircraft approximately follows a double exponential distribution in the low-altitude region, while in the high-altitude region, the plasma sheath electron density approximately follows a Gaussian distribution. A specific distribution model is selected based on the simulated transmission conditions to complete the modeling.

3. The method for simulating signal transmission of a high-speed aircraft under the influence of a plasma sheath according to claim 1, characterized in that... In step one, the plasma frequency model established is as follows: ； In the formula, It represents the electron density at a specific location at a specific moment; It represents the electron charge. The dielectric constant in a vacuum; The mass of an electron.

4. The method for simulating signal transmission of a high-speed aircraft under the influence of a plasma sheath according to claim 1, characterized in that... In step two, a double-exponential model is used to simulate the plasma sheath electron density distribution of a high-speed aircraft. The expression for the double-exponential function distribution of the plasma electron density is as follows: ； In the formula, This represents the maximum electron density of the plasma. These are the piecewise points of the double exponential function; The thickness of the plasma; This represents the steepness of the first segment of the double exponential function; This represents the steepness of the latter part of the double exponential function.

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