Refraction approximate ray tracing method for electric field calculation in metal cavity

Abstract

The invention belongs to the technical field of electromagnetic wave propagation, and particularly discloses a refraction approximation ray tracing method for calculating an electric field in a metal cavity, refraction approximation is carried out based on a mirror image method, and due to the fact that the mirror image method has the advantage of being high in accuracy in calculation of a regular geometric area, in a simplified model of a plasma large science device, the calculation accuracy is high. Under the condition that it is guaranteed that too large calculation amount is not generated, the area capable of being calculated is larger than that of a common electromagnetic calculation method, and the method is enough to be suitable for a calculation space in a metal cavity in a conventional experiment environment. The method can be applied to radio wave propagation calculation in the plasma under the condition that the radio wave frequency is greater than the plasma frequency. Errors generated by a receiving ball algorithm used by a forward ray tracing algorithm are avoided, redundant rays are filtered at the beginning of calculation, and discussion of receiving ball ray deduplication is avoided.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic wave propagation technology, specifically to a refraction approximation ray tracing method for calculating the electric field within a metal cavity. Background Technology

[0002] Studying the propagation of electromagnetic waves in plasma is of great significance, especially in addressing the "blackout" effect caused by the plasma sheath of hypersonic vehicles and the difficulties in target detection. Due to the high cost of plasma experiments under high temperature and pressure, a combination of computational electromagnetics numerical simulation and ground-based plasma experiments is often used to study the interaction between electromagnetic waves and the plasma sheath. However, this combination is often insufficient, and electromagnetic simulation rarely provides guidance for plasma experimental design and measurement. The reason for this is the lack of a method that can effectively simulate the experimental environment, typically the propagation of electromagnetic waves within a metallic vacuum cavity.

[0003] Commonly used electromagnetic computation methods, such as the Finite-Difference Time-Domain (FDTD), the Method of Moments (MOM), and Physical Optics (PO), are effective for calculating electromagnetic wave propagation and target scattering in small computational domains. However, when the computational domain is too large (relative to wavelength), the computational load becomes extremely high after meshing. For example, with FDTD, assuming convergence conditions are met, calculating the electric field inside a 5m cube with a 10GHz electromagnetic wave requires a total of 1 billion meshes, necessitating enormous computational resources and a very long computation time.

[0004] In high-frequency and large computational regions, none of the above methods are applicable. Another SBR algorithm often has significant advantages for electromagnetic wave propagation calculations in lossless media with large computational regions. However, in the experimental environment, there is a large area of ​​plasma inside the metal cavity. In the plasma region, the required number of meshes is still huge, and the calculation is still slow.

[0005] Therefore, how to calculate the electric field distribution inside a large metal cavity containing lossy media, avoid the unacceptable computational load caused by the large number of grids due to the increase in radio wave frequency, and thus improve the speed of electromagnetic simulation has always been a challenge in fully combining electromagnetic numerical simulation with ground plasma experiments. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned problems by providing a refraction-approximate ray tracing method for calculating the electric field within a metal cavity, used to calculate the propagation of electromagnetic waves within a metal cavity.

[0007] The technical solution adopted in this invention is as follows: A refractive approximate ray tracing method for calculating the electric field within a metallic cavity, the method comprising: Establish a target model, which is a metal cavity model of the electric field to be solved, and determine the number of ray reflections to be considered in the metal cavity according to the required accuracy of the electric field to be calculated. Target model region division: The target model is divided into surface elements; The antenna design includes setting the locations of the transmitting and receiving antennas, as well as the type of antenna source. Mirror point solution: Solve for the mirror points of the antenna transmission point with respect to each surface element; Valid ray identification involves connecting the antenna receiving point with each mirror point to determine the valid ray. Electric field tracing involves tracing the electric field of a determined effective ray and merging the electric field tracing results of each effective ray to obtain the electric field distribution of the desired solution.

[0008] Furthermore, the metal cavity model is a cylindrical cavity model, and a plasma jet model is established, with the number of ray reflections set to m.

[0009] Furthermore, in the surface element division, the circular arc surface within the metal cavity is approximated by dividing the planar surface elements.

[0010] Furthermore, the antenna source is a dipole antenna.

[0011] Furthermore, the solution for the mirror point is specifically as follows: Find the mirror image points of the antenna transmitting point with respect to each surface element, called the first-order mirror points T1, and there are n first-order mirror points in total. Then find the mirror images of the n first-order mirror points with respect to each surface element, called the second-order mirror points T2, and so on, until the m-order mirror points are found, for a total of n (n-1). m-1 m mirror points.

[0012] Furthermore, the specific determination of the effective radiation is as follows: Connect m mirror points T respectively m For each image point, determine whether the line connecting the antenna receiving point intersects with the corresponding surface element of each image point. If there is no intersection, the image point is invalid; if there is an intersection, the intersection point O is invalid. m This is the reflection point when the ray undergoes its m-th reflection; record this ray as... l Then connect the intersection points O respectively. m With m-1 times mirror point T m-1 Determine whether the connecting line intersects with the corresponding surface element of each mirror point. If there is an intersection, then the intersection point O is determined. m-1 This is the reflection point when the ray undergoes its (m-1)th reflection; and so on, until the first reflection point O1 of the ray is found.l This is considered an effective ray, and the effective ray is recorded. l The path.

[0013] Furthermore, the effectiveness of the radiation was verified: When the ray l When the rays pass through a metallic target, the radiation... l Invalid ray; When the ray l When effective, determine the radiation. l Whether it passes through the plasma medium region, if so, determines the final effective ray.

[0014] Furthermore, radiation l The process for determining the plasma medium region is as follows: Calculate the radiation... l The effective ray is determined by whether the distance between the ray equation and the nearest point of the plasma region's center is less than the radius of the plasma jet. l Whether it passes through a plasma region.

[0015] ray l The specific process for identifying metallic targets involves: calculating radiation... l The effective ray is determined by whether the distance between the ray equation and the center of the circumcircle of the metallic target is less than the radius of the target's circumcircle. l Whether it passes through the interior of a metallic target.

[0016] Furthermore, the electric field tracking is specifically achieved through the following formula: (1) In the formula, E The electric field intensity vector, E 0 represents the amplitude vector of the electric field intensity. r For position vectors, ω Angular frequency, t Let i be time, i be the imaginary unit, and i be a vector. k I The direction of electromagnetic wave amplitude attenuation, vector k R This represents the direction of electromagnetic wave phase propagation.

[0017] Furthermore, the electric field distribution is specifically as follows: based on the sum of vectors after tracing the electric field of each effective ray, the electric field distribution diagram of the cross section inside the metal cavity is drawn; (2).

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. The method of the present invention can calculate higher frequencies, avoiding the problem of excessive computational complexity caused by high electromagnetic wave frequencies. Furthermore, when the electromagnetic wave frequency is appropriately increased, it will help improve the accuracy of the simplified image method calculation.

[0019] 2. The method of the present invention is based on the refraction approximation of the mirror method. Since the mirror method itself has the advantage of high accuracy in the calculation of relatively regular geometric regions, in the simplified model of large-scale plasma scientific facilities, the area that can be calculated is larger than that of the usual electromagnetic calculation method such as FDTD, while ensuring that the amount of calculation is not too large, which is sufficient to be applicable to the calculation space in the metal cavity under conventional experimental conditions.

[0020] 3. By applying a refraction approximation to the image method, it can be applied to the calculation of electromagnetic wave propagation in plasmas where the electromagnetic wave frequency is higher than the plasma frequency. This avoids the errors caused by the receiver sphere algorithm used in the forward ray tracing algorithm, filtering out redundant rays at the beginning of the calculation and avoiding discussions on ray deduplication by the receiver sphere.

[0021] 4. Conventional electromagnetic simulation software such as HFSS can also be used to simulate the electric field of targets inside metal cavities. However, when using methods such as the Method of Moments (MOM) or the Finite-Difference Time-Domain (FDTD), the computational load is extremely high at high frequencies due to limitations imposed by the radio wave frequency band. Even when using the forward SBR algorithm in the software, the computational domain is too large, requiring a large number of tracking rays, resulting in slow computation and hindering parallel computing. In contrast, the method of this invention is a point-to-point algorithm, where the electric field calculations at each point are independent, making parallel computing very convenient and significantly reducing computation time. Attached Figure Description

[0022] Figure 1 This is a flowchart of a refraction approximation ray tracing method for calculating the electric field inside a metal cavity according to the present invention. Figure 2 This is a modeling diagram for calculating the incident frequency of 3GHz in an embodiment of the present invention; Figure 3 This is a comparison chart of the cross-sectional electric field calculated at an incident frequency of 3 GHz and the HFSS calculation results in an embodiment of the present invention; Figure 4 This is a schematic diagram of spherical target modeling when calculating the one-dimensional range image scattering result of a spherical target in an embodiment of the present invention; Figure 5 This is a comparison chart of the calculated one-dimensional range image scattering results of a spherical target and the experimental measurement results in an embodiment of the present invention. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings.

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0025] Example This embodiment provides a refraction-approximate ray tracing method for calculating the electric field within a metal cavity, specifically including: 1. Establish the target geometric model and determine the number of reflections: Modeling is done in simulation software; a model is created in the simulation software based on the target's external dimensions.

[0026] In this embodiment, a cylindrical cavity model is established in the simulation software HFSS. The cylinder has a diameter of 7m and a height of 3m. The origin of the coordinate system is located at the center of the cylinder. The plasma jet radius is 0.2m and the length is 1m. Figure 2 As shown; Determine the number of reflections to be considered: Based on the required accuracy of the electric field to be calculated, the number of electromagnetic wave reflections to be considered within the metal cavity is determined to be m. In this example, the number of electromagnetic wave reflections is considered to be 3. 2. Subdividing surface elements: Based on the required accuracy and considering the computing performance of the computer, the curved surface is approximated by dividing the plane elements. In order to verify the correctness of the method in this embodiment, a regular 50 prism is used to approximate the arc surface on the side of the device, which is sufficient to meet the requirements. Let the total number of dividing elements be n. Save the meshing results. In this example, the meshed surface elements are saved as txt files, and the equation of each meshed surface element in the spatial rectangular coordinate system is recorded. 3. Set the locations of the transmitting and receiving points, as well as the antenna type: The transmitting antenna is set to (0,0,1.5), and the antenna is a dipole antenna. 100×100=10000 points are sampled on the calculation section inside the metal cavity as receiving antenna positions. The electric field distribution at each position is calculated. The calculations at each point do not interfere with each other and can be performed in parallel. 4. Solve for each mirror point: First-order mirror point: Solve for the mirror point of the antenna transmitting point with respect to each surface element, and call it the first-order mirror point T1. There are n first-order mirror points in total. In this embodiment, there are 52 first-order mirror points. Calculate each mirror point sequentially: then solve for the mirror points of each first mirror point with respect to each surface element, and call them the second mirror points T2. Solve sequentially until m mirror points are obtained, for a total of n (n-1) mirror points. m-1There are m mirror points; in this example, there are a total of 52×51 = 2652 quadratic mirror points and a total of 52×51×51 = 135252 cubic mirror points.

[0027] 5. Solve for the effective ray: Connect m mirror points T respectively m For each mirror point, determine whether the line connecting the receiving antenna location point intersects with the corresponding surface element. If there is no intersection, the mirror point is invalid; otherwise, the intersection point is O. m This is the reflection point when the ray undergoes its m-th reflection, and the ray is recorded as [missing information]. l Next, connect the intersection points O respectively. m With m-1 times mirror point T m-1 Determine whether the connecting line intersects with the surface element corresponding to each mirror point. If there is no intersection, the mirror point is an invalid mirror point. l Invalid; if there is an intersection, then the intersection point O is invalid. m-1 This is the reflection point where the ray undergoes its (m-1)th reflection; and so on, until the point O1 where the ray undergoes its first reflection is found. l This constitutes an effective ray; the ray is recorded. l The path; 6. For effective radiation l Further testing is required: The effective ray is determined by calculating whether the distance between the ray equation containing the ray and the nearest point to the center of the plasma region is less than the radius of the plasma jet. l Did it pass through a plasma region? Calculate whether the distance between the ray equation and the center of the circumcircle of the metallic target is less than the radius of the target's circumcircle to determine the effective ray. l Whether the radiation passes through the interior of a metallic target; if it does, then the radiation... l It needs to be removed.

[0028] 7. For effective radiation l Perform electric field tracking: All identified effective rays are traced sequentially, and the field strength is determined by the following formula: (1) In the formula, E The electric field intensity vector, E 0 represents the amplitude vector of the electric field intensity. r For position vectors, ω Angular frequency, t Let i be time, i be the imaginary unit, and i be a vector. k I The direction of electromagnetic wave amplitude attenuation, vector k RThe direction of electromagnetic wave phase propagation; when the ray does not pass through the interior of the plasma. k I and k R The direction remains unchanged, only changing due to reflection at the reflection point; when the ray passes through the interior of the plasma, k R The direction remains unchanged. k I The direction can be determined using the complex Snell's law; 8. Combine the results of each valid ray: By calculating the sum of the field strengths propagating from the antenna transmitter to the antenna receiver, the electric field strength at the receiver point can be obtained. Based on the calculation results of each field strength receiver point, a field strength cross-sectional electric field distribution diagram can be drawn.

[0029] This example uses the sum of vectors obtained after each effective ray tracing to plot the electric field distribution across the cross-section of the metal cavity, such as... Figure 3 As shown.

[0030] The experimental results of the method in this embodiment can be further illustrated by the following calculation experiments: Experimental conditions: The target model is a cylindrical metal cavity with a diameter of 7m and a height of 3m. The coordinate system is located at the center of the cylinder. The target within the metal cavity consists of a cylindrically distributed plasma jet. The metal cavity model is as follows: Figure 2 As shown: The electric field distribution inside the computing device is calculated using an antenna located near the wall of a metal cavity with a dipole antenna as the antenna source. The electric field distribution of the cross-section inside the metal cavity is calculated using this method, and the one-dimensional range image of the target scattering can be obtained from the electric field calculation results, thereby verifying the effectiveness of the refraction approximation method of the present invention.

[0031] Experimental content and results analysis: Experiment 1: Calculate the cross-sectional electric field at an incident frequency of 3 GHz to verify the effectiveness of the refraction approximation method of this invention.

[0032] The specific steps are as follows: The first step is to create a cylindrical cavity model, such as... Figure 2 As shown, its inner wall diameter is 7m and its height is 3m. The origin of the metal cavity coordinate system is determined, a plasma jet model is established, and its electron number density is set to a uniform 10. 17 m -3 Given the distribution and collision frequency of 5 GHz, the required number of ray reflections is determined to be 3. The second step is to partition the model: For a simple cylindrical model, manual partitioning can be used to divide the outer metal wall of the cylinder into regular 50 prisms, and solve for the coefficients of the plane equations of each partitioned surface element in the spatial coordinate system. The third step is to set the transmitting antenna position to (0,0,1.5), and the antenna is a dipole antenna. 10,000 points are sampled on the cross-section of the metal cavity as the receiving antenna positions. The electric field distribution at each position is calculated. The calculations at each point do not interfere with each other and can be performed in parallel. The electric field distribution diagram of the cross-section of the device is then plotted. The fourth step is to compare the results.

[0033] The calculated electric field distribution across the cross-section inside the metal cavity is compared with the electric field calculated by the simulation software HFSS under the same conditions. Figure 5 As shown.

[0034] Since the calculation conditions in the simulation software HFSS are the same as those in this experiment, the correctness of the method of this invention is proven as long as the calculation results of the method of this invention match the calculation results of the HFSS software.

[0035] Depend on Figure 5 As can be seen, the experimental and simulation software calculations show good agreement on the target RCS, confirming the correctness of the present invention.

[0036] Furthermore, by utilizing the algorithm of this invention for parallel computation, the calculation of the cross-sectional electric field distribution with 10,000 sampling points can be completed in as little as ten minutes. In contrast, calculation using the SBR+ solver in HFSS would take approximately four hours, demonstrating the computational speed of the method of this invention.

[0037] Experiment 2: The scattering results of the one-dimensional range image of a spherical target were calculated using the present invention and compared with the one-dimensional range image of a spherical plasma-encased target measured under a real experimental setup to verify the correctness of the method of the present invention. Taking a spherical target as an example, a metal sphere with a radius of 200mm is set as the target, surrounded by plasma. The plasma target modeling method is as follows: Figure 4 As shown, the plasma outside the sphere is divided into five layers, each 5 cm in size. From the edge near the wall to the edge away, the electron density is N1 = 4.1 × 10⁻⁶. 17 m -3 N2 = 3.5 × 10 17 m -3 N3 = 2.5 × 10 17 m -3 N4 = 1 × 10 17 m -3 N5 = 8 × 10 16 m -3Each layer is 5cm thick, and the collision frequency of each plasma layer is 10GHz.

[0038] Frequency sweep calculations were performed in the 10GHz-13GHz range, with 201 frequency points scanned. The antenna was 3m away from the target. The one-dimensional range image of the spherical target could be obtained by using the calculation results of the scattered electric field at different frequencies.

[0039] The one-dimensional range image of the spherical target was calculated using the method of this invention, and compared with the one-dimensional range image measurement results under the same conditions in a real experimental setup. Figure 5 As shown: from Figure 5 As can be seen, the simulated data of the one-dimensional range image of the metal sphere inside the metal cavity agrees well with the measured data. The image of the metal sphere is shown at a distance of 3m from the antenna, and the amplitude of the images is close, indicating that the imaging results are accurate. However, it can also be seen that the calculated one-dimensional range image results show significant fluctuations in both the measured and simulated results. This is because, in the sealed metal cavity environment, electromagnetic waves undergo multiple scatterings within the device, which is consistent with the scattering characteristics of radio waves inside a metal cavity. Comparison with experimental measurement results verifies the correctness of the method of this invention.

[0040] This article uses specific embodiments to illustrate the principles and implementation methods of the present invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A refraction-approximate ray tracing method for calculating the electric field within a metallic cavity, characterized in that, The method includes: Establish a target model, which is a metal cavity model of the electric field to be solved, and determine the number of ray reflections to be considered in the metal cavity according to the required accuracy of the electric field to be calculated. Target model region division: The target model is divided into surface elements; The antenna design includes setting the locations of the transmitting and receiving antennas, as well as the type of antenna source. Mirror point solution: Solve for the mirror points of the antenna transmission point with respect to each surface element; Valid ray identification involves connecting the antenna receiving point with each mirror point to determine the valid ray. Electric field tracing involves tracing the electric field of a determined effective ray and merging the electric field tracing results of each effective ray to obtain the electric field distribution of the desired solution.

2. A refraction-approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, The metal cavity model is a cylindrical cavity model, and a plasma jet model is established, with the number of ray reflections set to m.

3. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, In the surface element division, the circular arc surface inside the metal cavity is approximated by dividing the planar surface elements.

4. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, The antenna source is a dipole antenna.

5. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, The specific steps for solving the mirror point are as follows: Find the mirror image points of the antenna transmitting point with respect to each surface element, called the first-order mirror points T1, and there are n first-order mirror points in total. Then find the mirror images of the n first-order mirror points with respect to each surface element, called the second-order mirror points T2, and so on, until the m-order mirror points are found, for a total of n (n-1). m-1 m mirror points.

6. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, The specific details of the valid radiation identification are as follows: Connect m mirror points T respectively m For each image point, determine whether the line connecting the antenna receiving point intersects with the corresponding surface element of each image point. If there is no intersection, the image point is invalid; if there is an intersection, the intersection point O is invalid. m This is the reflection point when the ray undergoes its m-th reflection; record this ray as... l Then connect the intersection points O respectively. m With m-1 times mirror point T m-1 Determine whether the connecting line intersects with the corresponding surface element of each mirror point. If there is an intersection, then the intersection point O is determined. m-1 This is the reflection point when the ray undergoes its (m-1)th reflection; and so on, until the first reflection point O1 of the ray is found, then the ray... l This is considered an effective ray, and the effective ray is recorded. l The path.

7. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 6, characterized in that, Verification of effective radiation: When the ray l When the rays pass through a metallic target, the radiation... l Invalid ray; When the ray l When effective, determine the radiation. l Whether it passes through the plasma medium region, if so, determines the final effective ray.

8. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 7, characterized in that, ray l The process for determining the plasma medium region is as follows: Calculate the radiation... l The effective ray is determined by whether the distance between the ray equation and the nearest point of the plasma region's center is less than the radius of the plasma jet. l Did it pass through a plasma region? ray l The specific process for identifying metallic targets involves: calculating radiation... l The distance between the ray equation and the center of the circumcircle of the metal target is less than the radius of the circumcircle of the target, which is used to determine whether the effective ray l passes through the interior of the metal target.

9. A refractional approximate ray tracing method for calculating the electric field within a metal cavity according to claim 1, characterized in that, The electric field tracking is specifically achieved through the following formula: （1） In the formula, E The electric field intensity vector, E 0 represents the amplitude vector of the electric field intensity. r For position vectors, ω Angular frequency, t Let i be time, i be the imaginary unit, and i be a vector. k I The direction of electromagnetic wave amplitude attenuation, vector k R This represents the direction of electromagnetic wave phase propagation.

10. A refractive approximate ray tracing method for calculating the electric field within a metal cavity according to claim 9, characterized in that, The electric field distribution is specifically as follows: based on the sum of vectors after tracing the electric field of each effective ray, the electric field distribution diagram of the cross section inside the metal cavity is drawn. （2）。

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