Simulation method and system for propagation characteristics of OAM vortex waves generated by antenna array

Abstract

The invention provides a simulation method and system for propagation characteristics of OAM vortex waves generated by an antenna array, and the method comprises the steps: carrying out the simulation of a single antenna through employing an FDTD time domain finite difference method, so as to verify the reliability of the modeling simulation of the antenna in Matlab through employing an FDTD algorithm; on the premise of conforming to the credibility, a first antenna array is designed, and modeling simulation is performed on the OAM wave generated by using the first antenna array, including: adding an ionized layer to the antenna array, adding an electron movement speed and a plasma change concentration parameter on the basis of analyzing the ionized layer by using a Durude model, and observing different characteristics of propagation of the OAM wave in the air and propagation of the OAM wave in an ionized layer to obtain a propagation rule of the OAM wave in the plasma.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio wave propagation and numerical simulation, and particularly relates to a simulation system for the propagation characteristics of OAM vortex waves generated by an antenna array. Background Art

[0002] The statements in this part merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] Currently, the two main electromagnetic simulation software in mainstream use are CST and HFSS, which are mainly used for electromagnetic design and analysis, especially in the design and optimization of high-frequency electronic devices (such as antennas, microwave devices, filters, etc.).

[0004] CST (Computer Simulation Technology) is an electromagnetic field simulation software developed by CST AG, which uses a variety of solvers (including time-domain, frequency-domain, and static solvers) to simulate different electromagnetic phenomena. HFSS (HighFrequency Structure Simulator) is an electromagnetic simulation software developed by ANSYS, which is particularly good at dealing with high-frequency electromagnetic problems. It mainly solves electromagnetic field problems based on the finite element method (FEM) and is widely used in fields such as antenna design, microwave components, filters, and waveguides.

[0005] However, if it is in the case of simulating the transmission of electromagnetic waves to the ionosphere, a simulation model of several tens of kilometers means that the electrical size of the simulation area is very large, and CST and HFSS are not very suitable for directly performing simulations on a scale of several tens of kilometers. Because they are based on FIT or FEM solvers, they are suitable for smaller computational domains and may encounter bottlenecks in memory and computing resources especially when dealing with large scales. Simulating an area of several tens of kilometers requires very fine grid division in space, which will result in a very large computational model, and thus requires a large amount of computing resources and memory. As the size of the computational domain increases, the computational complexity of electromagnetic solution also increases sharply, and it may require dozens or hundreds of computers for distributed computing, and the computing time will also increase significantly. In addition, the model may require a large amount of memory to store grids and calculation results.

[0006] The prior art discloses the paper "Research on the Propagation of Vortex Electromagnetic Waves in Plasmas - Zheng Han", which established a finite-difference time-domain method model in cylindrical coordinates, deduced the boundary absorption method in cylindrical coordinates, and on this basis calculated the propagation process of vortex electromagnetic waves in vacuum and plasmas, and simultaneously simulated the spatio-temporal evolution process of plasma density under the action of vortex electromagnetic waves.

[0007] The simulation results show that: when the vortex electromagnetic wave generated by the array antenna model propagates in vacuum, the shape of the vortex will not change; in the plasma medium, the propagation of the vortex wave still follows the linear theory. When the vortex electromagnetic wave encounters the plasma with the cut-off frequency, there will also be obvious reflection and standing waves will be generated; at the same time, the vortex wave can still maintain the vortex shape in the plasma; the linear effect of the vortex wave on the plasma makes the plasma also show a vortex state, which is consistent with the observations in the experiment.

[0008] However, an ideal current source is used in this article instead of generating the OAM wave through a simulation antenna. In practice, an antenna or antenna array must be used, and only the situation within a maximum height of 1 km is studied, without considering the actual propagation distance. Summary of the Invention

[0009] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a simulation system for the propagation characteristics of OAM vortex waves generated by an antenna array, which can observe the laws after it is transmitted to the ionosphere.

[0010] To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:

[0011] In the first aspect, a simulation method for the propagation characteristics of OAM vortex waves generated by an antenna array is disclosed, including:

[0012] Simulate a single antenna using the finite-difference time-domain (FDTD) method to verify the credibility of using the FDTD algorithm to model and simulate the antenna in Matlab;

[0013] On the premise of meeting the credibility, design the first antenna array and conduct modeling and simulation on using the first antenna array to generate OAM waves, including: adding an ionosphere to the antenna array, adding parameters of electron motion speed and plasma change concentration on the basis of analyzing the ionosphere using the Drude model, and conducting simulation analysis to observe the different characteristics of the OAM wave propagating in air and in the ionosphere.

[0014] As a further technical solution, conduct simulation using the finite-difference time-domain (FDTD) method, specifically including:

[0015] Define the basic parameters of the problem space, including the grid size and geometric structure;

[0016] Initialize the basic parameters of the problem space;

[0017] Determine whether to run the simulation. If not, output the 3D model of the problem space. If the simulation has been run, output the simulation results. If the simulation is run, initialize the relevant parameters of the FDTD simulation, enter the simulation, and start updating the magnetic field of this time step through the electric field of the previous time step, and update the electric field of this time step through the magnetic field of the previous time step;

[0018] Determine whether the time step has reached the preset value. If so, output the 3D model of the problem space. If the simulation has been run, output the simulation results. If not, enter again to start updating the magnetic field of this time step through the electric field of the previous time step until the time step reaches the preset value.

[0019] As a further technical solution, conduct modeling and simulation on using the first antenna array to generate OAM waves. The specific process includes:

[0020] Set the center point of the first antenna array at the origin;

[0021] The distance from any antenna to the origin is x(n), y(n), then the initial phase of antenna n is arctan{y(n) / x(n)}, and thus obtain the initial phase of the first antenna array;

[0022] Generate OAM waves through the first antenna array.

[0023] As a further technical solution, add the ionosphere to the antenna array. The simulation process of the Yagi antenna based on FDTD generating OAM waves transmitting in the ionosphere is as follows:

[0024] Use the first antenna array to generate OAM waves, and simulate its transmission in air and plasma with a gradually changing height at a set height. There are obvious differences between the radiation patterns of transmission in air and plasma;

[0025] Divide the plasma into multiple layers. As the number of layers increases, the concentration of plasma in each layer also increases continuously. As the plasma concentration changes continuously, the equivalent dielectric constant also changes continuously.

[0026] In the second aspect, a simulation system for the propagation characteristics of an antenna array generating OAM vortex waves is disclosed, including:

[0027] A verification module, configured to: perform simulation on a single antenna using the FDTD (Finite-Difference Time-Domain) method to verify the credibility of modeling and simulating the antenna in Matlab using the FDTD algorithm;

[0028] The first antenna array simulation module is configured to: on the premise of meeting the credibility, design the first antenna array, and perform modeling and simulation on using the first antenna array to generate OAM waves, including: adding the ionosphere to the antenna array, adding the electron motion speed and plasma change concentration parameters on the basis of analyzing the ionosphere using the Drude model, and observing the different characteristics of the OAM wave propagating in the air and in the ionosphere.

[0029] The above one or more technical solutions have the following beneficial effects:

[0030] The technical solution of the present invention can solve the problem of observing the law after the array antenna formed by Yagi antennas is transmitted to the ionosphere under the large-scale propagation environment of the ionosphere through simulation. Compared with the existing technologies, the advantages are mainly reflected in:

[0031] With the increase of the computational domain size in existing electromagnetic simulation software, the computational complexity of electromagnetic solution increases sharply, and it is difficult to simulate the effect of the OAM wave transmitted to the ionosphere. The method of the technical solution of the present invention uses the finite-difference time-domain (FDTD) method, realizes the simulation of electrically large-sized problems through an optimized algorithm, can simulate the law after the electromagnetic wave is transmitted to the ionosphere, and has credibility.

[0032] In the existing technologies that observe the law of the OAM wave transmitted to the ionosphere through numerical simulation, the OAM wave is generated using an ideal point source or line source. The method of the technical solution of the present invention defines different materials in Matlab to simulate Yagi antennas, and generates the OAM wave by arranging the Yagi antennas into an array antenna, which is more flexible and credible compared with using an ideal point source.

[0033] At the same time, other common types or specifically designed array antennas can also be simulated. If different antenna types are used in the technical solution of the present invention, it does not affect the working principle and simulation process. Therefore, using the Yagi antenna as the wave source in the embodiments of the present invention does not constitute an improper limitation of the present invention.

[0034] The advantages of the additional aspects of the present invention will be partially given in the following description, partially will become obvious from the following description, or will be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.

[0036] Figure 1 Schematic diagram of a cuboid defined for modeling;

[0037] Figure 2 Schematic diagram of a sphere defined for modeling;

[0038] Figure 3 Schematic diagram of medium parameters;

[0039] Figure 4 3D diagram of Yagi antenna for modeling and simulation, where SC 1 is a voltage source;

[0040] Figure 5 (Left) Far-field pattern of Yagi antenna simulated in Matlab;

[0041] Figure 5 (Right) Far-field pattern of Yagi antenna simulated in other electromagnetic simulation software;

[0042] Figure 6 3D diagram of 4×4 Yagi antenna array for simulation modeling, where SC N is the voltage source of each antenna;

[0043] Figure 7 Comparison of simulation results of 4×4 antenna array in Matlab and in CST. The left is the simulation result in Matlab, and the right is the simulation result in CST;

[0044] Figure 8 Simulation result of 4×4 antenna array in Matlab;

[0045] Figure 9 3D diagram of propagation of 4×4 Yagi antenna array for simulation modeling in plasma;

[0046] Figure 10 xy-direction pattern under the condition of center frequency of 14.2 MHz. The left figure is the propagation result in plasma, and the right figure is the propagation result without plasma;

[0047] Figure 11 xz-direction pattern under the condition of center frequency of 14.2 MHz. The left figure is the propagation result in plasma, and the right figure is the propagation result without plasma;

[0048] Figure 12 yz-direction pattern under the condition of center frequency of 14.2 MHz. The left figure is the propagation result in plasma, and the right figure is the propagation result without plasma;

[0049] Figure 13 xy-direction pattern under the condition of center frequency of 14.5 MHz. The left figure is the propagation result in plasma, and the right figure is the propagation result without plasma;

[0050] Figure 14The xz-direction pattern under the condition that the central frequency is 14.5 MHz, where the left figure is the propagation result in the plasma and the right figure is the propagation result without plasma;

[0051] Figure 15 The yz-direction pattern under the condition that the central frequency is 14.5 MHz, where the left figure is the propagation result in the plasma and the right figure is the propagation result without plasma;

[0052] Figure 16 The simulation schematic diagram of the 4*4 Yagi antenna array in CST without plasma;

[0053] Figure 17 The comparison of the simulation results of the OAM wave generated by the 4*4 antenna array without plasma in Matlab and the simulation results in CST. The left is the simulation result in CST and the right is the schematic diagram of the simulation result in Matlab;

[0054] Figure 18 The schematic diagram of the FDTD simulation process flow. Detailed implementation mode

[0055] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0056] It should be noted that the terms used herein are only for describing specific implementation modes and are not intended to limit the exemplary implementation modes according to the present invention.

[0057] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0058] Embodiment 1

[0059] This embodiment discloses a simulation method for the propagation characteristics of the OAM vortex wave generated by an antenna array, including:

[0060] Simulating a single antenna using the FDTD (finite-difference time-domain) method to verify the credibility of using the FDTD algorithm to model and simulate the antenna in Matlab;

[0061] On the premise of meeting the credibility, design the first antenna array and conduct modeling and simulation on using the first antenna array to generate the OAM wave, including: adding an ionosphere to the antenna array, adding the electron motion speed and plasma change concentration parameters on the basis of analyzing the ionosphere using the Drude model, and conducting simulation analysis to observe the different characteristics of the OAM wave propagating in the air and in the ionosphere.

[0062] This embodiment specifically includes the following steps:

[0063] Step 1: First, model the antenna in Matlab software;

[0064] Update formula of FDTD (taking the equation in the Ex direction as an example);

[0065]

[0066] These formulas are based on the stepped grid composed of Yee cells in Cartesian coordinates. Material parameters related to field components such as linear media, anisotropic media, non-dispersive media, etc. are defined. The object represented in the FDTD space is reflected by the size of the constructed grid. To make programming simple and convenient and to simplify the program debugging process, a modular method is used to write the program.

[0067] First, name a program named fdtd_solve as the Matlab main program for running FDTD calculations. In the module for defining the parameters of the problem space, set the basic parameters of the problem space through the subroutine define_problem_space_parameters, define the geometry through the subroutine define_geometry, define the sources and lumped elements through the subroutine define_sources_and_lumped_elements, and the subroutine

[0068] define_output_parameters to define the output parameters. In the module for initializing the problem space and parameters, initialize the FDTD material grid through the subroutine initialize_fdtd_material_grid, display the problem space through the subroutine display_problem_space, and display the material mesh through the subroutine display_material_mesh.

[0069] After that, it is judged whether to run the simulation. If the simulation flag is true, the parameters related to the FDTD simulation are initialized. The FDTD parameters and arrays are initialized by the subroutine initialize_fdtd_parameters_and_arrays, the sources and lumped elements are initialized by the subroutine initialize_sources_and_lumped_elements, the updating coefficients are initialized by the subroutine initialize_updating_coefficients, the boundary conditions are initialized by the subroutine initialize_boundary_condition, the output parameters are initialized by the subroutine initialize_output_parameters, the far-field arrays are initialized by the subroutine initialize_farfield_arrays, and the display parameters are initialized by the subroutine initialize_display_parameters.

[0070] Subsequently, it enters the FDTD time marching loop. The FDTD time marching is executed and calculations are performed through the subroutine run_fdtd_time_marching_loop. Finally, the subroutine post_process_and_display_results performs post-processing and displays the simulation results. Each subroutine is named after its function. The FDTD simulation process is as shown in the following flowchart.

[0071] Some modeling parameters in the problem space of FDTD, including how to model, boundary types, and material types, are defined in the subroutine define_geometry. To make the structure simpler and more convenient, three-dimensional objects of different types are directly placed in the problem space. Examples of a prism and a sphere will be given below. More complex shapes can be constructed using two simple objects. A cuboid with one face parallel to the coordinate axes can be represented by two corner points: one is the vertex with smaller x, y,

[0072] z coordinate values; the other is the vertex with larger x, y, z coordinate values, as Figure 1 shown.

[0073] The specific definition is as follows: A structure array named brick is defined in the subroutine define_geometry to contain its position coordinates: min_x, min_y, min_z, max_x, max_y, max_z. Each element in the brick array is an index of the cuboid target, represented by brick(i). Another class of the parameter brick(i) is material_type, which is related to the type of the medium.

[0074] A sphere can be defined by the coordinates of its center and its radius, as Figure 2 shown below:

[0075] The specific definition is as follows: In the subroutine define_geometry, the structure array spheres is used to define the sphere, and the class variables center_x, center_y, center_z, and radius are used to give the information in the corresponding Cartesian coordinates. Similar to the case of the cuboid, material_type gives the medium type of the sphere. In addition, the program also makes a default setting for the priority. For example, there are definitions of two concentric spheres. Sphere 1 has a radius of 20 mm and the medium material is an ideal electric conductor, while sphere 2 has a radius of 15 mm and the medium material is air. If they are created in the order that sphere 1 is created first and sphere 2 is created later, since the medium material of the second sphere is air, the combination of the two will produce a hollow spherical shell with a wall thickness of 5 mm. As the program runs, these arrays will be called by some subroutines.

[0076] In addition, lumped elements are defined in define_sources_and_lumped_elements. Similar to the previous definition of the cuboid, these elements can be defined as elements on the grid edges and are distributed in a certain volume in the FDTD space. The elements on any grid edge can be given by the coordinates of two points in the Cartesian coordinates, that is, the low coordinate point and the high coordinate point. That is to say, the method of defining the position of the lumped parameter device is the same as that of defining the position of a cuboid. In the subroutine define_sources_and_lumped_elements, the respective characteristics of the lumped elements are stored and initialized as empty arrays. Similar to the position definition of the cuboid, the position and size of these devices are represented by the parameters min_x, min_y, min_z, max_x, max_y, max_z. In addition to the definition of the position parameters, some additional parameters are needed to specify the characteristics of these devices. In FDTD, the lumped elements are simulated by updating the respective electric field quantities of each device through the inherent voltage-current relationship of each device. For voltage sources, current sources, and diodes, 6-direction parameters are required to be defined in the FDTD stepped grid: xn, xp, yn, yp, zn, zp. Here, p represents the positive direction and n represents the negative direction. The other parameters required are magnitude, resistance, inductance, and capacitance, which represent the parameter values of the lumped elements.

[0077] The advantages of the above modeling method are mainly as follows:

[0078] Clear structure and easy to maintain: By allocating different functions to independent subroutines, the code structure becomes more concise and clear. Each module is responsible for a specific function, making the program logic easier to understand and manage, and it will not affect other parts during subsequent maintenance and modification. Easy to debug and verify: The modular design allows for step-by-step debugging and verification. The input and output of each module can be checked separately, helping to quickly locate and solve problems. The debugging process is more efficient, especially when dealing with complex simulations, which can reduce the debugging time and cost. Improve code reusability: By designing general modules, the same code can be reused in different simulation tasks. This reduces the workload of repeated development and ensures the consistency and reliability of functions in different projects. Strong flexibility and good adaptability: Modularity makes the functions and parameter settings of each subroutine relatively independent. Users can easily adjust and optimize the parameters of a certain module without affecting the entire simulation framework. Through simple modifications, it can easily adapt to different simulation requirements, such as changing the geometric structure, adjusting the source type, changing the material properties, etc.

[0079] Step 2: Use the finite-difference time-domain (FDTD) method to perform simulation calculations on the antenna;

[0080] The FDTD simulation process is as shown in the flowchart Figure 18 as follows.

[0081] Essentially, it first defines the basic parameters of the problem space. For example, the subroutine

[0082] define_problem_space_parameters defines the grid size of the problem space. After that, by adding boundary conditions to the defined geometric structure, the size of the entire solution space can be obtained. In addition, the source and lumped parameters are also defined. After defining the problem space, the total number of grids in each direction can be obtained based on the previously defined basic parameters. Then, in the subroutine initialize_fdtd_material_grid, the entire problem space is divided into individual solution grids. In these grids, according to the different materials defined previously, the coefficients in the FDTD equation formula for each grid point will be different. Then, in the subroutine run_fdtd_time_marching_loop, the entire FDTD problem space is solved. In each time step, the magnetic field components Hx, Hy, Hz and the electric field components Ex, Ey, Ez in this time step are updated based on the magnetic field components Hx, Hy, Hz and the electric field components Ex, Ey, Ez obtained in the previous time step:

[0083] In the subroutine run_fdtd_time_marching_loop, as the time steps are iterated, the magnetic and electric fields are updated through the subroutines update_magnetic_fields and update_electric_fields. The CPML boundary conditions are applied through the subroutines update_magnetic_field_CPML_ABC and update_electric_field_CPML_ABC to absorb the boundary fluctuations, ensuring the numerical stability of wave propagation. The magnetic field, current, electric field, and voltage data at key positions are captured through subroutines such as capture_sampled_electric_fields for analysis. At the same time, the dynamic behaviors of voltage sources, current sources, and components such as inductors and diodes in the circuit are simulated in the subroutines update_voltage_sources and update_current_sources. Finally, the subroutine calculate_JandM calculates the electromagnetic-related parameters and the subroutine display_sampled_parameters displays the sampling results in real time, thus realizing the comprehensive simulation and monitoring of the entire electromagnetic system.

[0084] Taking the equation of the FDTD algorithm in the Ex direction as an example:

[0085]

[0086] The first term reflects the contribution of the electric field at the current time step to the electric field at the next time step and is a continuation of the previous time step; the second term represents the update of the electric field caused by the change in the magnetic field Hz and is derived from the curl term in Maxwell's equations; the third term represents the update of the electric field caused by the change in the magnetic field Hy and is also derived from the curl term; the fourth term represents the influence of the current density on the electric field.

[0087] The update coefficient C exe represents the decay or growth coefficient of the change in the electric field over time and depends on the permittivity ε z and the conductivity The update coefficient C exhz represents the influence coefficient of the change in the magnetic field Hz on the electric field and depends on the permittivity and the spatial step Δx. The update coefficient C exhy represents the influence coefficient of the change in the magnetic field Hy on the electric field and depends on the permittivity and the spatial step Δy. The update coefficient C exj represents the influence coefficient of the current density on the change in the electric field.

[0088] The distribution of material parameters (permittivity, permeability, conductivity, and permeability) is over the entire FDTD grid and is related to the field quantities, so their notations are the same as those of the field quantities. Attached Figure 3 The notations of permittivity and permeability are given. The conductivity is distributed over the entire grid, the same as the permittivity. Similarly, the notation of permeability is also the same as that of permeability. For the discretely sampled field components.

[0089] This formula is a numerical discretization implementation based on Maxwell's equations, where the electric field is determined by the change of the surrounding magnetic field, the current density, and its own dielectric properties. These coefficients C control characteristics such as the propagation speed of the field, the attenuation rate, and the wave reflection behavior, and play a key role in FDTD. This formula is specifically defined in the subroutine update_electric_fields, and the coefficients in the formula are defined in initialize_updating_coefficients. The equations in other directions are similar.

[0090] Since each parameter is defined, any parameter can be analyzed in the subsequent post-processing, but the most notable ones are still the magnetic field components Hx, Hy, Hz and the electric field components Ex, Ey, Ez. The obtained result is the electromagnetic field components of each grid after the solution space is partitioned at this time step. Taking Ex as an example, Ex is a three-dimensional array of nx*ny*nz, where nx, ny, and nz are the number of grids in the x, y, and z directions respectively. If we focus on the input and output of the simulation calculation at each time step, then the coefficients in the FDTD formula are calculated through the previously defined parameters, and the electromagnetic field data at this step is updated by using the magnetic field component and electric field component data of the previous step at each step. It stops when the number of time steps reaches the set number, and the electromagnetic field data of the last time step is stored in the magnetic field components Hx, Hy, Hz and the electric field components Ex, Ey, Ez.

[0091] In addition, a near-field to far-field transformation is also set up in the program. In many applications, such as antennas and radar cross-sections, it is necessary to know the radiation field and scattering field far from the antenna and scatterer. Directly calculating the far field in FDTD calculations will lead to an overly large calculation area, which is not practical in applications. Instead, by applying the near-field to far-field transformation technique, the far field can be calculated from the near-field FDTD data. Generally speaking, the near-field to far-field transformation is divided into two steps. First, an imaginary surface is selected to enclose the antenna, and the electric field E and magnetic field H inside the calculation area are used to determine the current density J and magnetic current density M on the surface. According to the equivalence theorem, the radiation field generated by these equivalent currents and magnetic currents is equivalent to the radiation field of the antenna. Second, through the equivalent current density J and equivalent magnetic current density M, the vector potentials A and F are used to calculate the radiation field generated by the equivalent current J and equivalent magnetic current M. During this process, the far-field condition is applied when deriving the analytical formula. Compared with direct FDTD calculations, the direct calculation method requires the extension of a large number of grids several wavelengths away from the radiator to satisfy the far-field condition, while only a few grids are required to calculate the equivalent currents and magnetic currents. Therefore, applying the near-field to far-field conversion technique can greatly improve the calculation efficiency.

[0092] Of course, the field components at any time step in the solution space can also be obtained and then post-processed according to different needs.

[0093] Step 3: Use the Drude model to simulate and analyze the ionosphere.

[0094] The Drude model is a classical electromagnetic model used to describe the behavior of electrons in conductors. It is the basis of the electron gas model and is particularly suitable for understanding the conductivity, optical response of conductors such as metals, and the interaction between electromagnetic waves and matter. By considering the motion of free electrons under the action of an external electric field and magnetic field, this model provides an intuitive understanding of phenomena such as conductivity, optical absorption, and electron collisions.

[0095] In the Drude model, the plasma is similar to a material with the following relative permittivity

[0096]

[0097] where: ε is the permittivity of the material itself; ω p is the plasma resonance frequency; ν c is the plasma collision frequency.

[0098] Based on the Drude model, the changes in electron motion and electron concentration density are added. For the description of the particle state, the continuity equation and momentum equation in the hydrodynamic equations are used to describe the changes in the number density and velocity of the particles respectively, as follows:

[0099]

[0100] where N α represents the number density of particle species α; v α represents the velocity field of particle species α; m α is the particle mass; v α is the particle velocity field; q α is the particle charge; E is the electric field; B 0 is the magnetic field; T α is the temperature, representing the thermodynamic property of the particle; k B is the Boltzmann constant.

[0101] This set of equations describes the behavior of a population of charged particles (such as a plasma) in an electromagnetic field: the continuity equation expresses the conservation of particles and describes how the particle density changes over time. The momentum conservation equation illustrates the forces acting on the motion of the particles, including the combined effects of electromagnetic forces, momentum interaction forces, and thermal pressure.

[0102] Since the mass of ions is much larger than that of electrons, their characteristic frequencies are often much smaller than the radio wave frequency. Therefore, the motion of ions is generally ignored, and only the interaction between cold plasma and radio waves in the isotropic case, as well as the changes in electron velocity and number density, are considered. The change in collision frequency due to electron motion is ignored. Thus, the above equation can be simplified to obtain formulas for describing electron velocity and number density:

[0103]

[0104] where v a is the collision frequency with other particles, v e is the collision frequency of electrons, m e is the mass of the electron, and q is the electric charge of the electron.

[0105] Next, using the central difference approximation, the changes in electron velocity and number density are advanced in time. First, consider the change in electron velocity. In the Yee cell, the velocity component v of the electron is consistent with the component E of the electric field, and the update of velocity and electric field is staggered by half a time step to avoid large instabilities. The simplified momentum equation is differenced using the leapfrog scheme:

[0106]

[0107] Define the electron number density in the plasma medium to be in a uniformly stratified form in the horizontal direction. The change in electron number density is considered to be expressed as the sum of the background value and the small perturbation in the time domain using first-order linearization, as follows:

[0108] Ne(t) = N 0 + ΔNe(t)

[0109] where N 0 —— background value of number density;

[0110] ΔNe(t)——perturbation of number density, which is a function of the spatial lattice position, and their lattice positions are consistent with the angular component of the electric field.

[0111] Therefore, it is only necessary to update the perturbation of the number density in each loop. After simplifying the difference, the time-domain recurrence formula for the electron number density ΔNe(t) is as follows:

[0112]

[0113] Considering the influence of electron motion and the change of electron number density on the propagation form of the vortex electromagnetic wave, the distribution of the electron number density increases linearly with the increase of height, that is, the following formula:

[0114]

[0115] In addition, the calculation relationship between the eigenfrequency of the plasma and the electron number density is as follows:

[0116]

[0117] These formulas are the theoretical sources of adding the electron number density and electron velocity on the basis of the Drude model.

[0118] By summarizing the current research situation and simulation situation, the main laws of the OAM wave propagating in the plasma are as follows:

[0119] (1) When the vortex electromagnetic wave propagates in vacuum, it can maintain a good vortex shape and propagate along the radiation direction of the antenna. The central cavity gradually increases with the increase of height, which is consistent with the theoretical analysis.

[0120] (2) In the plasma medium, the propagation of the vortex electromagnetic wave still satisfies the linear theory, and the shape of the vortex can still be maintained very well; the vortex electromagnetic wave reflects at the cut-off frequency, and its simulation results of the linear interaction with the plasma show that the plasma will also present a vortex state. In the presence of plasma, the shape of the vortex wave will become more divergent. At the same time, when the vortex electromagnetic wave propagates in the plasma above the cut-off frequency, distortion will occur, and the distortion phenomenon is more obvious with the increase of height, and the field strength attenuation is greater.

[0121] In order to transmit the electromagnetic wave to the ionosphere, an electromagnetic wave with a frequency of 15 MHz and a wavelength of 20 m is used.

[0122] The details of some steps of Example 1 are as follows:

[0123] In steps one and two:

[0124] 1-1): First, a single Yagi antenna was simulated and modeled in Matlab. See the appendix Figure 4 as shown. The simulation results of the radiation pattern are as Figure 5 (left), which are close to the results obtained in commercial software ( Figure 5 right). This proves that the method of simulation and modeling in Matlab is feasible and reliable.

[0125] 1-2): The generation of OAM waves by a 4×4 Yagi antenna array was simulated. As shown in Figure 6 and 7 :

[0126] Specific implementation method:

[0127] First, the Yagi antenna was modeled in the subroutine define_geometry. Taking one of the Yagi antennas as an example, it was modeled by defining the sizes of its two vertices. A total of seven bricks were defined to form a Yagi antenna. Similarly, the other 15 Yagi antennas were defined, and an antenna array of 4×4 was formed with a distance of 20 m (i.e., one wavelength length) between antennas. Then, the field source was also defined. A voltage source with a frequency of 15 MHz, a sine wave waveform, and located at the center of the second cuboid from bottom to top was defined. The feeding positions of the other Yagi antennas were similar, all at the center of the second cuboid from bottom to top. However, it should be noted that the initial phases of the feeding sources of each Yagi antenna are different. Here, a very classic phase setting for implementing OAM waves was used. Assuming that the center point of the 4×4 antenna array is the origin, and the distances from any antenna to the origin are x(n) and y(n), then the initial phase of antenna n is arctan{y(n) / x(n)}. The initial phases of the 4×4 antenna array are shown in Table 1 below (all units are degrees):

[0128] Table 1

[0129]

[0130]

[0131] Thus, the generation of OAM waves by a 4×4 antenna array was realized, and the generated OAM wave is the OAM mode l = 1.

[0132] At the same time, the 4×4 Yagi antenna array was also simulated in the commercial software CST and the results were compared. As shown in Figure 8 : It can be seen that the left and right figures are basically the same, indicating that it is feasible to simulate OAM waves using the FDTD algorithm in Matlab.

[0133] In step 3, the simulation of the transmission of the OAM wave generated by the Yagi antenna based on FDTD in the ionosphere is as follows:

[0134] In this step, a 4×4 antenna array composed of 16 Yagi antennas is used to generate the OAM wave. The transmission of the OAM wave in air and in a plasma with a gradually changing height at a height of 250 m is simulated, and some results are obtained. There are obvious differences between the radiation patterns of the OAM wave in air and in the plasma. The plasma is divided into 50 layers with a layer thickness of 5 m. As the number of layers increases, the concentration of the plasma in each layer also increases. As the plasma concentration changes continuously, the equivalent permittivity also changes continuously. On the basis of the Drude model, the changes in electron motion and electron concentration density are added to simulate the transmission process of the OAM wave in the ionosphere. In addition, the grid used in the model is as follows: dx = 0.6; dy = 0.3; dz = 0.6.

[0135] The 3D model diagram is as shown in Figure 9 which. The 4×4 antenna array for generating the OAM wave is at the bottom, and above the antenna array is a plasma region with a total of 50 layers.

[0136] The results are as follows. The left side is with plasma, and the right side is without plasma:

[0137] Figure 10 、 11 、12 are the xy-plane radiation pattern, xz-plane radiation pattern, and yz-plane radiation pattern at 14.2 MHz respectively. The left figure shows the propagation result in the plasma, and the right figure shows the propagation result without plasma. Figure 13 、 14 、15 are the xy-plane radiation pattern, xz-plane radiation pattern, and yz-plane radiation pattern at 14.5 MHz respectively. Similarly, the left figure shows the propagation result in the plasma, and the right figure shows the propagation result without plasma.

[0138] In addition, CST is also used to simulate the case without plasma. The simulation model is as shown in Figure 16 which. The radiation pattern of CST at 14.4 MHz is compared with the result obtained in Matlab as shown in Figure 17 which. Among them, Figure 17 (left) is the result in CST, Figure 17 (right) is the result in Matlab. Generally, they are quite similar. There may be some differences due to grid division and code function limitations.

[0139] It can be seen from the difference in the propagation of the vortex wave with and without plasma that in the presence of plasma, the shape of the vortex wave becomes more divergent, but generally it still retains the shape of a vortex wave.

[0140] The finite-difference time-domain (FDTD) algorithm is used to solve the propagation law of the OAM electromagnetic wave generated by the antenna array in the plasma, so as to verify the following conclusion: the method proposed in this patent can observe the propagation of the OAM vortex electromagnetic wave in a more realistic plasma structure model.

[0141] The algorithm of the technical solution of this embodiment constructs a more realistic plasma structure model. Referring to the Drude model part, specifically, on the basis of the Drude model, parameters such as the change in plasma concentration and the electron motion speed, which are difficult to simulate in other commercial electromagnetic simulation software, are added to study the propagation law of the OAM electromagnetic wave generated by the array in the plasma structure, and its propagation characteristics are more accurate.

[0142] The reason why the technical solution of this embodiment uses the FDTD algorithm instead of commercial electromagnetic simulation software is as follows:

[0143] 1) Traditional commercial simulation software can simulate the electromagnetic wave generated by the antenna array in air, but it cannot construct a plasma structure model of the ionosphere, or the constructed ionosphere plasma model is a too simple static model and cannot obtain more realistic propagation characteristics.

[0144] 2) For existing electromagnetic simulation software, as the size of the computational domain increases, the computational complexity of electromagnetic solution also increases sharply, and it is very difficult to simulate the effect of the OAM wave transmitting to the ionosphere. This method uses the finite-difference time-domain (FDTD) method, which can simulate the law after the electromagnetic wave transmits to the ionosphere and has credibility.

[0145] Compared with other references, the advantage of the FDTD algorithm used in the technical solution of this embodiment lies in:

[0146] In the current papers that observe the law of OAM wave transmitting to the ionosphere through numerical simulation, ideal point sources or line sources are all used to generate the OAM wave. In this method, different materials are defined in Matlab to simulate a Yagi antenna, and the Yagi antennas are arranged into an array antenna to generate the OAM wave, which is more flexible and credible compared with using ideal point sources.

[0147] Embodiment 2

[0148] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the above method are implemented.

[0149] Example 3

[0150] The purpose of this embodiment is to provide a computer-readable storage medium.

[0151] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it executes the steps of the above method.

[0152] Example 4

[0153] The purpose of this embodiment is to provide a simulation system for the propagation characteristics of an antenna array to generate OAM vortex waves, including:

[0154] A verification module, configured to: perform simulation on a single antenna using the finite-difference time-domain (FDTD) method to verify the credibility of using the FDTD algorithm to model and simulate the antenna in Matlab;

[0155] The first antenna array simulation module, configured to: on the premise of meeting the credibility, design the first antenna array, and perform modeling and simulation on using the first antenna array to generate OAM waves, including: adding an ionosphere to the antenna array, adding parameters of electron motion velocity and plasma change concentration on the basis of analyzing the ionosphere using the Drude model, and observing the different characteristics of OAM waves propagating in air and in the ionosphere.

[0156] Example 5

[0157] The purpose of this embodiment is to provide a computer program product containing instructions, which when running on a computer, enables the computer to execute the methods and functions involved in any one of the above embodiments.

[0158] The steps involved in the devices of the above embodiments correspond to those of Method Embodiment 1, and for the specific implementation manners, reference may be made to the relevant description part of Embodiment 1. The term "computer-readable storage medium" should be understood to include a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0159] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module to implement. The present invention is not limited to any specific combination of hardware and software.

[0160] Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A method for simulating the propagation characteristics of OAM vortex waves generated by an antenna array, characterized in that: include: The FDTD finite-difference time-domain method is used to simulate a single antenna to verify the credibility of the antenna modeling and simulation in Matlab using the FDTD algorithm; On the premise of meeting the credibility, the first antenna array is designed, and the modeling and simulation of using the first antenna array to generate OAM waves are carried out, including: adding the ionosphere to the antenna array, adding the electron movement speed and plasma concentration change parameters on the basis of using the Durood model to analyze the ionosphere, observing the different characteristics of OAM waves propagating in the air and in the ionosphere, and obtaining the propagation law of OAM waves in plasma.

2. The method for simulating the propagation characteristics of OAM vortex waves generated by an antenna array as claimed in claim 1, characterized in that: The simulation is performed using the FDTD finite-difference time-domain method, including: Define the basic parameters of the problem space, including mesh size and geometry; Initialize the basic parameters of the problem space; Determine whether to run the simulation. If not, output the 3D model of the problem space. If the simulation is run, output the simulation results. If the simulation is run, initialize the relevant parameters of the FDTD simulation, enter the simulation, and start to update the magnetic field of this time step through the electric field of the previous time step, and update the electric field of this time step through the magnetic field of the previous time step. Determine whether the time step has reached the preset value. If so, output the 3D model of the problem space. If the simulation is run, output the simulation results. If not, start again to update the magnetic field of this time step through the electric field of the previous time step until the time step reaches the preset value.

3. The method for simulating the propagation characteristics of OAM vortex waves generated by an antenna array as claimed in claim 1, characterized in that: Modeling and simulating the generation of OAM waves using the first antenna array includes: Assume that the center point of the first antenna array is the origin; The distance from any antenna to the origin is x(n), y(n), then the initial phase of antenna n is arctan{y(n) / x(n)}, thereby obtaining the initial phase of the first antenna array; generating an OAM wave by a first antenna array; Observe the differences in the propagation patterns of OAM waves in plasma and air.

4. The method for simulating the propagation characteristics of OAM vortex waves generated by an antenna array as claimed in claim 1, characterized in that: Adding the ionosphere to the antenna array, the simulation process of the Yagi antenna generating OAM waves and transmitting them in the ionosphere based on FDTD is as follows: The first antenna array is used to generate OAM waves, and the transmission of OAM waves in the air at a set height and in a plasma that gradually changes with the height is simulated. There is a clear difference between the directional patterns of the waves in the air and in the plasma. The plasma is divided into multiple layers. As the number of layers increases, the concentration of plasma in each layer also increases continuously. In addition, the electron movement speed and plasma concentration change parameters are added. As the plasma concentration continues to change, the equivalent dielectric constant also changes continuously.

5. A simulation system for the propagation characteristics of OAM vortex waves generated by an antenna array, characterized in that: include: The verification module is configured to: simulate a single antenna using the FDTD finite difference time domain method to verify the credibility of the antenna modeling simulation in Matlab using the FDTD algorithm; The first antenna array simulation module is configured to: design the first antenna array under the premise of meeting the credibility, and model and simulate the use of the first antenna array to generate OAM waves, including: adding an ionosphere to the antenna array, adding electron movement speed and plasma concentration change parameters based on the analysis of the ionosphere using the Durood model, observing the different characteristics of OAM waves propagating in the air and in the ionosphere, and obtaining the propagation law of OAM waves in plasma.

6. The simulation system for the propagation characteristics of OAM vortex waves generated by an antenna array as claimed in claim 5, characterized in that: The simulation is performed using the FDTD finite-difference time-domain method, including: Define the basic parameters of the problem space, including mesh size and geometry; Initialize the basic parameters of the problem space; Determine whether to run the simulation. If not, output the 3D model of the problem space. If the simulation is run, output the simulation results. If the simulation is run, initialize the relevant parameters of the FDTD simulation, enter the simulation, and start to update the magnetic field of this time step through the electric field of the previous time step, and update the electric field of this time step through the magnetic field of the previous time step. Determine whether the time step has reached the preset value. If so, output the 3D model of the problem space. If the simulation is run, output the simulation results. If not, start again to update the magnetic field of this time step through the electric field of the previous time step until the time step reaches the preset value.

7. The simulation system for the propagation characteristics of OAM vortex waves generated by an antenna array as claimed in claim 5, characterized in that: Modeling and simulating the generation of OAM waves using the first antenna array includes: Assume that the center point of the first antenna array is the origin; The distance from any antenna to the origin is x(n), y(n), then the initial phase of antenna n is arctan{y(n) / x(n)}, thereby obtaining the initial phase of the first antenna array; generating an OAM wave by a first antenna array; Observe the differences in the propagation patterns of OAM waves in plasma and air.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method described in any one of claims 1 to 4 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 4 are performed.

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