Lightning stroke pulsed magnetic field environment simulation method

By constructing a parameterizable Helmholtz coil model in CST software and employing a hexahedral TLM mesh and PBA algorithm, the problems of poor flexibility in adjusting Helmholtz coil parameters and inconvenience in adjusting waveform parameters are solved, thereby improving the accuracy and simulation efficiency of lightning pulse magnetic field simulation.

CN121959979APending Publication Date: 2026-05-01XIAN AIRBORNE ELECTROMAGNETIC TECH
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
XIAN AIRBORNE ELECTROMAGNETIC TECH
Filing Date
2026-04-03
Publication Date
2026-05-01

AI Technical Summary

Technical Problem

Existing methods for simulating the magnetic field of lightning pulses suffer from poor flexibility in adjusting the parameters of the Helmholtz coil and inconvenience in adjusting the parameters of the double exponential waveform, resulting in low simulation accuracy and long simulation calculation time.

Method used

A parameterizable Helmholtz coil model was constructed in the CST simulation software. The mesh was generated using a hexahedral TLM grid and the PBA algorithm. A double-exponential lightning pulse current was applied, and the simulation calculation was performed using the TLM algorithm to obtain the magnetic field distribution cloud map and the magnetic field strength at the point.

Benefits of technology

It enables rapid optimization of Helmholtz coil parameters, improves the accuracy and efficiency of magnetic field simulation, and is adaptable to various lightning pulse magnetic field simulation scenarios.

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Abstract

The invention discloses a lightning stroke pulsed magnetic field environment simulation method. The method comprises the steps of constructing a Helmholtz coil simulation model capable of being adjusted in a parameterization mode in CST simulation software, setting material parameters of the model, arranging a magnetic field probe in the model, constructing a background air domain based on the size of the model, and configuring an omni-directional open boundary; configuring a discrete current excitation port for the model, and loading a double-index lightning pulse current as a simulation excitation source; then, a hexahedral TLM grid is adopted to subdivide the model to form a hexahedral grid; finally, based on a transient time domain solver, simulation calculation is completed through a TLM algorithm, a magnetic field distribution cloud picture and point magnetic field intensity are obtained, and a coil simulation model meeting requirements is output after analysis and verification. The problem of low simulation accuracy caused by poor parameter adjustment flexibility of a Helmholtz coil and inconvenience in adjustment of lightning pulse double-index waveform parameters during existing lightning pulse magnetic field simulation is solved.
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Description

Simulation method of lightning pulse magnetic field environment Technical Field

[0001] This invention belongs to the field of magnetic field simulation technology, specifically relating to a method for simulating the magnetic field environment of a lightning pulse. Background Technology

[0002] Lightning is a common natural discharge phenomenon that poses a significant threat to the flight safety of aircraft. When lightning strikes an aircraft, it generates an alternating electromagnetic field on its exterior. This electromagnetic field induces voltage and current in the aircraft's internal cabling system through resistive coupling, electric field coupling, and magnetic field coupling. It can even penetrate the aircraft's interior through apertures to form an alternating magnetic field, thereby generating transient electrical signals in the internal circuits. These transient induced electrical signals can easily cause malfunctions or even physical damage to airborne electronic and electrical equipment, such as circuit breaker tripping and computer failures. Therefore, during the aircraft design phase, it is essential to simulate the electromagnetic effects of lightning pulse magnetic fields to predict the electromagnetic impact on the aircraft and provide a basis for the design of lightning electromagnetic protection for aircraft.

[0003] To reduce the impact of external interference magnetic fields, such as lightning pulse magnetic fields, on aircraft, existing external interference magnetic field control methods are mainly divided into two categories: passive shielding and active control. Passive shielding mainly achieves anti-interference by constructing magnetic shielding rooms. However, a complete performance parameter measurement and evaluation system for magnetic shielding devices has not yet been established, and the construction and maintenance conditions of magnetic shielding rooms are stringent and costly, making widespread application difficult. Therefore, active magnetic field control methods have been developed. This method uses a magnetic field generator to produce a compensating magnetic field that is equal in magnitude and opposite in direction to the ambient magnetic field to counteract the external interference magnetic field. As the core of the active control system, the uniformity and controllability of the magnetic field generated by the magnetic field generator directly determine the control effect of the external interference magnetic field.

[0004] Currently, magnetic field generating devices mainly include two types: permanent magnets and energized coils. The magnetic field generated by permanent magnets has inherent non-uniformity, and the magnetic field strength is difficult to control precisely, making it unsuitable for the fabrication of precision experimental instruments. Among energized coils, the magnetic field generated by solenoids has poor uniformity in the radial direction, while Helmholtz coils can generate a large-scale, controllable uniform magnetic field in the space between two coils, which is suitable for the fabrication of large-size magnetic field generating devices. They are often used for the elimination and compensation of environmental magnetic fields and the construction of stable magnetic field environments, making them the preferred coil type for lightning pulse magnetic field simulation.

[0005] However, the design of Helmholtz coils requires multi-objective optimization: coil design involves multiple parameters such as magnetic field strength, resonant frequency, current flow, number of turns, and size. These parameters are mutually restrictive and contradictory. Existing design methods only consider single parameter requirements and can only obtain parameter configurations under single objectives such as optimal resonant frequency or optimal field uniformity, without achieving comprehensive optimization design of multiple parameters.

[0006] Furthermore, traditional lightning pulse magnetic field simulation methods suffer from numerous practical application problems, becoming key constraints on the accuracy and efficiency of magnetic field simulation: First, the flexibility in adjusting parameters such as the number of turns of the Helmholtz coil is poor, making it difficult to quickly optimize magnetic field uniformity and adapt to different simulation requirements; Second, when performing simulations, full-detail modeling is required, resulting in a large number of meshes and excessively long simulation calculation times; Third, the double exponential function waveform parameters of lightning pulses are inconvenient to adjust, easily affecting the accuracy of magnetic field simulation. Summary of the Invention

[0007] The purpose of this invention is to provide a method for simulating the magnetic field environment of lightning pulses, which solves the problem of low simulation accuracy caused by the poor flexibility of adjusting the parameters of the Helmholtz coil and the inconvenience of adjusting the parameters of the double exponential waveform of the lightning pulse in existing lightning pulse magnetic field simulations.

[0008] The technical solution adopted in this invention is a simulation method for lightning pulse magnetic field environment, which includes constructing a parameterizable Helmholtz coil simulation model in CST simulation software, setting the material parameters of the model and placing magnetic field probes in the model, constructing a background air domain based on the model size and configuring an omnidirectional open boundary; then configuring discrete current excitation ports for the model and loading a double exponential lightning pulse current as the simulation excitation source; subsequently, using a hexahedral TLM mesh to partition the model into a hexahedral mesh; finally, based on a transient time-domain solver, using the TLM algorithm to complete the simulation calculation, obtaining the magnetic field distribution cloud map and the magnetic field strength at the point, and outputting a coil simulation model that meets the requirements after analysis and verification.

[0009] The technical solution of the present invention is further characterized by including the following steps:

[0010] S1. Construct a parameterizable Helmholtz coil simulation model in CST simulation software; S2. Set the material parameters of the Helmholtz coil simulation model, construct a background air domain according to the size of the Helmholtz coil simulation model, and set the omnidirectional physical boundary of the background air domain as an open boundary; S3. Configure a discrete current excitation port for the Helmholtz coil simulation model, and load a double-exponential lightning pulse current waveform as the simulation excitation source to the discrete current excitation port; S4. Deploy magnetic field probes within the Helmholtz coil simulation model to collect transient magnetic field strength values ​​at corresponding points; 5. For the simulation model set in steps S1 to S4, perform mesh generation using a hexahedral TLM mesh type, and optimize the mesh using the PBA algorithm; S6. Based on the transient time-domain solver of CST software, use the TLM transmission line matrix algorithm to perform simulation calculations on the mesh-optimized simulation model, obtain the magnetic field distribution cloud map of the simulation space, and the magnetic field strength values ​​at the corresponding points of each magnetic field probe; S7. Analyze the magnetic field strength in the simulation space based on the magnetic field distribution cloud map, and determine whether the magnetic field environment is satisfied based on the magnetic field strength values, and output the Helmholtz coil simulation model.

[0011] Step S1 involves constructing a parameterizable Helmholtz coil simulation model, specifically including: S11, constructing a pair of parallel, coaxial, and electrically connected circular coils in CST software, with the same number of turns and radius for both coils, and the number of turns and radius being parameterizable variables; S12, setting the axial distance between the two circular coils as the radius of the circular coil, and the axial distance being a parameterizable variable.

[0012] In step S2, the material parameters of the Helmholtz coil simulation model are set to copper; and the extension distances in the X, Y, and Z directions of the background air domain are all set to 1000 mm, and the background material is set to air.

[0013] Step S3 is as follows: S31. In the simulation settings of CST software, configure discrete ports for the Helmholtz coil simulation model and set the port type to current source; S32. Based on the three key parameters of lightning pulse current peak value, rise time, and half-wave width, select the double exponential waveform type in the excitation signal library of CST software, configure the corresponding waveform parameters, and generate a double exponential lightning pulse current waveform that matches the target lightning characteristics; S33. Load the configured double exponential lightning pulse current waveform onto the discrete current excitation port as the input excitation of the Helmholtz coil simulation model.

[0014] In step S4, multiple magnetic field probes are placed on the central axis of the Helmholtz coil simulation model. The coordinates of the probes are (0, 0, 0), (0, 0, 150), (0, 0, -150), (0, 0, 300), and (0, 0, -300).

[0015] In step S5, the hexahedral TLM mesh type is used for mesh generation. Specifically, based on the three-dimensional geometric model constructed in step S1, the basic mesh size is set as the initial threshold, and then adaptive meshing is performed according to the local features of the geometric model to generate a hexahedral mesh. Then, the mesh is optimized by the PBA algorithm. Specifically, "hybrid" mesh cells that are traversed by two or more different materials are identified, the precise position and orientation of the ideal geometric boundary inside the cell are calculated, and the electromagnetic property parameters inside the mesh cell are reconfigured to complete the optimization of the mesh.

[0016] The adaptive meshing is specifically implemented by continuously subdividing the wire region of the coil, the cross-sectional boundary, and the parts with drastic curvature changes until the preset minimum mesh size is reached; while in air regions far away from the coil, where the magnetic field changes gently, or in uniform background regions, the mesh cells are merged and enlarged to reduce the total number of cells.

[0017] In step S7, the analysis of the magnetic field strength in the simulation space specifically involves analyzing whether the magnetic field distribution cloud map shows a uniform distribution. If the distribution is uneven, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the magnetic field distribution is uniform.

[0018] In step S7, the criterion for determining whether the magnetic field environment is satisfied based on the magnetic field strength value is to compare the magnetic field strength value with the empty field check value. If the error range between the two values ​​does not exceed 2%, the simulation result is output; otherwise, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the two values ​​are within the 2% error range. The calculation expression for the empty field check value is shown in the following formula: In the formula, N is the number of turns in the Helmholtz coil; R is the radius of the coil; d is the distance between the two coils; and I is the input current value.

[0019] The beneficial effects of this invention are: by constructing a parameterizable Helmholtz coil model and utilizing the parameterized scanning function, the core parameters such as the number of coil turns, size, and spacing can be flexibly adjusted, enabling rapid optimization of magnetic field uniformity to match different simulation requirements; at the same time, it provides theoretical guidance and simulation support for the multi-objective optimization design of Helmholtz coils, effectively reducing the design cost and manufacturing cycle of the coil.

[0020] Furthermore, this invention uses a hexahedral TLM mesh type to mesh the constructed model, and uses the PBA algorithm to optimize the mesh meshing, which can take into account both the rationality of the global mesh and the refinement of the mesh in the local electromagnetic field concentration area, effectively reducing the number of meshes and shortening the simulation time.

[0021] This invention also solves the problem of inconvenient adjustment of pulse waveform parameters in traditional methods by substituting key parameters of the lightning current double exponential waveform into CST software to construct the excitation waveform, thereby improving the accuracy of lightning pulse magnetic field simulation. At the same time, the lightning excitation source waveform can be parameterized, and by adjusting key parameters, it can match the requirements of different magnetic field change rates and amplitudes, thus adapting to various lightning pulse magnetic field simulation scenarios. Attached Figure Description

[0022] Figure 1 is a flowchart of the lightning pulse magnetic field environment simulation method of the present invention; Figure 2 is the Helmholtz coil model constructed in the lightning pulse magnetic field environment simulation method of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] Example 1: The lightning pulse magnetic field environment simulation method of the present invention includes constructing a parameterizable Helmholtz coil simulation model in CST simulation software, setting the material parameters of the model and placing magnetic field probes within the model, constructing a background air domain based on the model size and configuring an omnidirectional open boundary; then configuring discrete current excitation ports for the model and loading a double-exponential lightning pulse current as the simulation excitation source; subsequently, using a hexahedral TLM mesh to partition the model into a hexahedral mesh; finally, based on a transient time-domain solver, using the TLM algorithm to complete the simulation calculation, obtaining the magnetic field distribution cloud map and the magnetic field strength at the point, and outputting a coil simulation model that meets the requirements after analysis and verification.

[0025] As shown in Figure 1, the specific steps include: S1, constructing a parameterizable Helmholtz coil simulation model in CST simulation software; S2, setting the material parameters of the Helmholtz coil simulation model, specifically, setting the material parameter to copper; and setting the extension distance of the background air domain in the X, Y, and Z directions to 1000mm, and the background material to air; constructing the background air domain according to the dimensions of the Helmholtz coil simulation model, and setting the omnidirectional physical boundary of the background air domain to an open boundary; S3, configuring a discrete current excitation port for the Helmholtz coil simulation model, and loading a double-exponential lightning pulse current waveform as the simulation excitation source to the discrete current excitation port; S4, in the Helmholtz... S5. Magnetic field probes are deployed within the Helmholtz coil simulation model to collect transient magnetic field strength values ​​at corresponding points. S6. The simulation model set up in steps S1 to S4 is meshed using a hexahedral TLM mesh type, and the mesh is optimized using the PBA algorithm. S7. Based on the transient time-domain solver of CST software, the TLM transmission line matrix algorithm is used to perform simulation calculations on the mesh-optimized simulation model, obtaining the magnetic field distribution cloud map of the simulation space and the magnetic field strength values ​​at corresponding points of each magnetic field probe. S8. The magnetic field strength in the simulation space is analyzed based on the magnetic field distribution cloud map, and the magnetic field strength values ​​are combined to determine whether the magnetic field environment is satisfied, outputting the Helmholtz coil simulation model.

[0026] Example 2. Based on Example 1 above, this example constructs a parameterizable Helmholtz coil simulation model in step S1, specifically including: S11, constructing a pair of parallel, coaxial, and electrically connected circular coils in CST software. The number of turns and radius of the two circular coils are the same, and the number of turns and radius of the coils are set as parameterizable variables; S12, setting the axial distance between the two circular coils as the radius of the circular coils, and the axial distance is a parameterizable variable.

[0027] Example 3: Based on Example 2 above, step S3 of this example is as follows: S31: In the simulation settings of CST software, configure discrete ports for the Helmholtz coil simulation model and set the port type to current source; S32: Based on the three key parameters of lightning pulse current peak value, rise time, and half-wave width, select the double exponential waveform type in the excitation signal library of CST software, configure the corresponding waveform parameters, and generate a double exponential lightning pulse current waveform that matches the target lightning characteristics; S33: Load the configured double exponential lightning pulse current waveform onto the discrete current excitation port as the input excitation of the Helmholtz coil simulation model.

[0028] Example 4: The lightning pulse magnetic field environment simulation method proposed in this example, as shown in Figure 1, specifically includes the following steps: S1: As shown in Figure 2, a parameterizable Helmholtz coil simulation model is constructed in CST simulation software; S2: The material parameters of the Helmholtz coil simulation model are set, specifically, the material parameter is set to copper; and the extension distances of the X, Y, and Z directions of the background air domain are all set to 1000mm, and the background material is set to air; the background air domain is constructed according to the size of the Helmholtz coil simulation model, and the omnidirectional physical boundary of the background air domain is set to an open boundary; S3: A discrete current excitation port is configured for the Helmholtz coil simulation model, and a double-exponential lightning pulse current waveform is loaded onto the discrete current excitation port as the simulation excitation source; S4: Multiple magnetic field probes are arranged on the central axis of the Helmholtz coil simulation model to collect the transient magnetic field strength values ​​at corresponding points; the specific probe coordinates are (0, 0, 0), (0, 0, 150), (0, 0, -150), (0, 0, 300), (0, 0, -300).

[0029] S5. For the simulation model set in steps S1 to S4, perform mesh generation using a hexahedral TLM mesh type, and optimize the mesh using the PBA algorithm; S6. Based on the transient time-domain solver of CST software, perform simulation calculations on the mesh-optimized simulation model using the TLM transmission line matrix algorithm to obtain the magnetic field distribution cloud map of the simulation space and the magnetic field strength values ​​at the corresponding points of each magnetic field probe; S7. Analyze the magnetic field strength in the simulation space based on the magnetic field distribution cloud map, and determine whether the magnetic field environment is satisfied based on the magnetic field strength values. If it is not satisfied, return to step S1; if it is satisfied, output the Helmholtz coil simulation model.

[0030] When selecting the specific magnetic field strength value, the magnetic field strength value is obtained using a probe with coordinates (0, 0, 0).

[0031] Example 5: Based on Example 4 above, in step S5 of this example, the meshing process using the hexahedral TLM mesh type is based on the octree data structure to recursively partition the solution space.

[0032] Specifically, based on the three-dimensional geometric model constructed in step S1, a basic mesh size is set as an initial threshold, and then the entire solution domain is traversed, and adaptive subdivision is performed according to the local features of the geometric model. Specifically, in the conductor region of the coil, the cross-sectional boundary, and the parts with drastic curvature changes, the octree structure will be continuously subdivided until the preset minimum mesh size is reached to ensure the accuracy of capturing the geometric contour. In the air region or uniform background region far away from the coil and with a gentle change in magnetic field, the mesh cells are merged and enlarged, and a larger size is used to reduce the total number of cells.

[0033] The final result is a non-uniform, well-conformal hexahedral mesh system that completely fills the computational space while achieving a discretized representation of the complex geometry of the Helmholtz coil. The resulting data provides a spatial indexing framework for subsequent electromagnetic property assignment and optimization.

[0034] Since the generated hexahedral mesh will cause the curved conductor boundary to have a "sawtooth" problem due to the step approximation, this invention introduces the Perfect Boundary Approximation (PBA) algorithm to optimize the mesh.

[0035] Specifically, the algorithm first identifies "hybrid" mesh cells traversed by two or more different materials (such as copper wire and air). For these cells, the PBA algorithm abandons the traditional whole-cell averaging method and instead calculates the precise location and orientation of the ideal geometric boundary (i.e., the actual curved surface of the conductor) within the cell. Based on this boundary location, the algorithm reconfigures the electromagnetic property parameters within the mesh cell: assigning the conductor region the conductivity and permeability of copper, and the air region the properties of air.

[0036] By using this technique of accurately subdividing and locating material properties within a single grid cell, the PBA algorithm enables the originally stepped discrete grid to closely approximate the original smooth curved surface geometry at the electromagnetic performance level. This significantly improves the simulation fidelity of coil wire surfaces and thin-layer structures without increasing the number of grid cells.

[0037] After the above partitioning and optimization processes, the final output mesh data is not simply a collection of geometric elements, but an enhanced mesh dataset that includes topological connectivity and physical properties. This dataset mainly includes: Mesh topology: recording the spatial indices, node coordinates, and adjacency relationships between all hexahedral elements, forming a discretized spatial architecture for iterative computation using the TLM algorithm.

[0038] Material distribution matrix: At the level of each grid cell or sub-region, the material type (such as copper, air) is clearly identified and associated with the corresponding electromagnetic property parameters (conductivity σ, permeability μ, dielectric constant ε).

[0039] PBA Correction Label: For boundary elements optimized by the PBA algorithm, record the material distribution weights and corrected equivalent electromagnetic parameters inside them to ensure that the propagation behavior of electromagnetic waves at the interface of the medium conforms to the laws of physics during the subsequent time-domain solution process.

[0040] Example 6 Based on Example 5 above, in step S7 of this embodiment, the analysis of the magnetic field strength in the simulation space specifically involves analyzing whether the magnetic field distribution cloud map shows a uniform distribution. If the distribution is uneven, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the magnetic field distribution is uniform. The magnetic field strength value is selected from the magnetic field strength value obtained by the probe with coordinates (0, 0, 0). The magnetic field strength value is compared with the empty field check value. If the error range between the two values ​​does not exceed 2%, the simulation result is output. Otherwise, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the two values ​​are within the 2% error range. The calculation expression of the empty field check value is shown in the following formula (1): (1); where N is the number of turns of the Helmholtz coil; R is the radius of the coil; d is the distance between the two coils; and I is the input current value.

[0041] Example 7: The lightning pulse magnetic field environment simulation method proposed in this example includes the following steps: Step 1: Construct a Helmholtz coil simulation model in CST simulation software. In the constructed model, the coil diameter D is 2m, the radius R is 1m, each coil N has 3 turns, and the distance d between two coils is 2m; Step 2: Configure a discrete current excitation port for the Helmholtz coil simulation model, and load a double exponential lightning pulse current waveform as the simulation excitation source to the discrete current excitation port. In this example, the peak current injected is 834.8A; Step 3: Place a magnetic field probe at the coordinate (0, 0, 0) position in the simulation model to collect the transient magnetic field strength value at the corresponding point; Step 4: For the simulation model constructed above, use a hexahedron... Step 5: The simulation model is meshed using the TLM mesh type, and the mesh is optimized using the PBA algorithm. Step 6: Based on the transient time-domain solver of CST software, the TLM transmission line matrix algorithm is used to perform simulation calculations on the mesh-optimized simulation model to obtain the transient magnetic field strength values ​​at the corresponding acquisition points. The obtained transient magnetic field strength value is 902.5 A / m. Step 7: The magnetic field strength in the simulation space is analyzed according to the magnetic field distribution cloud map, and the magnetic field strength value is combined to determine whether the magnetic field environment meets the requirements. When a peak current of 834.8 A is injected, the empty field check value is 885.4 A / m. The empty field check value is compared with the transient magnetic field strength value. The empty field check value is used as the benchmark. If it meets the error range specification, the simulation results are output.

[0042] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0043] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for simulating the magnetic field environment of a lightning pulse, characterized in that, This includes building a parameterizable Helmholtz coil simulation model in CST simulation software, setting the material parameters of the model and placing magnetic field probes inside the model, constructing a background air domain based on the model size and configuring an omnidirectional open boundary; Next, configure discrete current excitation ports for the model and load a double exponential lightning pulse current as the simulation excitation source; Subsequently, a hexahedral TLM mesh was used to subdivide the model into a hexahedral mesh; finally, based on the transient time-domain solver, the TLM algorithm was used to complete the simulation calculation, obtain the magnetic field distribution cloud map and the magnetic field strength at the point, and output a coil simulation model that meets the requirements after analysis and verification.

2. The method for simulating the magnetic field environment of a lightning pulse according to claim 1, characterized in that, Includes the following steps: S1. Construct a parameterizable Helmholtz coil simulation model in CST simulation software; S2. Set the material parameters of the Helmholtz coil simulation model, construct a background air domain according to the size of the Helmholtz coil simulation model, and set the omnidirectional physical boundary of the background air domain as an open boundary; S3. Configure a discrete current excitation port for the Helmholtz coil simulation model, and load a double-exponential lightning pulse current waveform as the simulation excitation source to the discrete current excitation port; S4. Deploy magnetic field probes in the Helmholtz coil simulation model to collect transient magnetic field strength values ​​at corresponding points; S5. For the simulation model set in steps S1 to S4, perform meshing using a hexahedral TLM mesh type, and optimize the mesh using the PBA algorithm; S6. Based on the transient time-domain solver of CST software, perform simulation calculations on the mesh-optimized simulation model using the TLM transmission line matrix algorithm to obtain the magnetic field distribution cloud map of the simulation space, as well as the magnetic field strength values ​​at corresponding points of each magnetic field probe; S7 analyzes the magnetic field strength in the simulation space based on the magnetic field distribution cloud map, and determines whether the magnetic field environment is satisfied by combining the magnetic field strength value, and outputs the Helmholtz coil simulation model.

3. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, The step S1, which involves constructing a parameterizable Helmholtz coil simulation model, specifically includes: S11, constructing a pair of parallel, coaxial, and electrically connected circular coils in CST software, wherein the number of turns and radius of the two circular coils are the same, and the number of turns and radius of the coils are set as parameterizable variables; S12, setting the axial distance between the two circular coils as the radius of the circular coils, and the axial distance is a parameterizable variable.

4. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, In step S2, the material parameters of the Helmholtz coil simulation model are set to copper; and the extension distances in the X, Y, and Z directions of the background air domain are all set to 1000mm, and the background material is set to air.

5. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, The specific process of step S3 is as follows: S31, in the simulation settings of CST software, configure discrete ports for the Helmholtz coil simulation model and set the port type to current source; S32, based on the three key parameters of lightning pulse current peak value, rise time, and half-wave width, select the double exponential waveform type in the excitation signal library of CST software, configure the corresponding waveform parameters, and generate a double exponential lightning pulse current waveform that matches the target lightning characteristics; S33, load the configured double exponential lightning pulse current waveform onto the discrete current excitation port as the input excitation of the Helmholtz coil simulation model.

6. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, In step S4, multiple magnetic field probes are placed on the central axis of the Helmholtz coil simulation model. The coordinates of the probes are (0, 0, 0), (0, 0, 150), (0, 0, -150), (0, 0, 300), and (0, 0, -300).

7. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, In step S5, the meshing using the hexahedral TLM mesh type is specifically based on the three-dimensional geometric model constructed in step S1. The basic mesh size is set as the initial threshold, and then adaptive meshing is performed according to the local features of the geometric model to generate a hexahedral mesh. Then, the meshing is optimized using the PBA algorithm. Specifically, "hybrid" mesh cells that are traversed by two or more different materials are identified, the precise position and orientation of the ideal geometric boundary inside the cell are calculated, and the electromagnetic property parameters within the mesh cell are reconfigured to complete the mesh optimization.

8. The method for simulating the magnetic field environment of a lightning pulse according to claim 7, characterized in that, The adaptive subdivision specifically involves continuously subdividing the coil in the conductor region, cross-sectional boundary, and areas with drastic curvature changes until a preset minimum grid size is reached; while in air regions far from the coil, in areas with gentle magnetic field changes, or in uniform background regions, the grid cells are merged and enlarged to reduce the total number of cells.

9. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, In step S7, analyzing the magnetic field strength in the simulation space specifically involves analyzing whether the magnetic field distribution cloud map shows a uniform distribution. If the distribution is uneven, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the magnetic field distribution is uniform.

10. The method for simulating the magnetic field environment of a lightning pulse according to claim 2, characterized in that, In step S7, the criterion for determining whether the magnetic field environment is satisfied based on the magnetic field strength value is to compare the magnetic field strength value with the empty field check value. If the error range between the two values ​​does not exceed 2%, the simulation result is output; otherwise, the parameterizable variables in the Helmholtz coil simulation model are adjusted until the two values ​​are within the 2% error range. The calculation expression for the empty field check value is shown in the following formula: In the formula, N is the number of turns in the Helmholtz coil; R is the radius of the coil; d is the distance between the two coils; and I is the input current value.

Citation Information

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