A full electromagnetic particle-in-cell simulation method in an axisymmetric vacuum electron device

Abstract

The present application relates to a kind of full electromagnetic particle simulation method, to solve the problem of long time-consuming and high cost of computing resources of existing full electromagnetic particle simulation method, and provide a kind of full electromagnetic particle simulation method in axisymmetric vacuum electron device.The present application fuses the full electromagnetic particle method of time domain discontinuous finite element and finite difference hybrid, including the following steps:1) draw the three-dimensional structure diagram of the axisymmetric structure of vacuum electron device;2) the axisymmetric profile of electron device is divided into two identical sub-profiles, two-dimensional calculation space, and the two-dimensional calculation space is divided into calculation area A and calculation area B;3) the calculation area A is divided into non-structured triangular grid, and the calculation area B is divided into right-angle orthogonal structure grid;4) according to the iteration calculation of electric field, magnetic field in calculation area A and calculation area B and charged particle in calculation area B in time step;5) repeat step four;6) collate and analyze the data obtained.

Description

Technical Field

[0001] This invention relates to a fully electromagnetic particle simulation method, specifically to a fully electromagnetic particle simulation method for axisymmetric vacuum electronic devices that integrates time-domain discontinuous finite element method and finite difference hybrid method. Background Technology

[0002] The all-electromagnetic particle simulation method accurately describes the time-varying processes of electric and magnetic fields and the trajectories of charged particles by solving the coupling equations between charged particles and electric and magnetic fields. This method has been widely applied in the study of plasma-related physical phenomena and the design and structural optimization of vacuum electronic devices. Currently, this method is widely used in the research of high-power microwave devices such as relativistic backward wave tubes, gyrotrons, and magnetically insulated wire oscillators. These devices are all axisymmetric structures. When the devices operate in axisymmetric mode, the all-electromagnetic particle simulation method can obtain the distribution characteristics of the internal electromagnetic field of the device by simulating only the electromagnetic field distribution of the cross-section of the vacuum electronic device. This method can significantly reduce the computation time in the device design process.

[0003] In all-electromagnetic particle simulation methods, the finite-difference time-domain (FDTD) method is generally used to solve for the time-varying electromagnetic field. This method's computational cost is linearly related to the number of grid cells, and it offers advantages such as relatively simple implementation and ease of parallelization. The FDTD algorithm uses orthogonal rectangular meshes. Traditional structured meshes introduce step errors when dealing with complex boundaries. While conformal mesh-based FDTD methods can improve computational accuracy, the time step is related to the minimum mesh size. To maintain the method's stability, the time step needs to be significantly reduced. Furthermore, because conformal meshes approximate complex boundaries with hypotenuses, it is difficult to further improve computational accuracy using higher-order electromagnetic field numerical methods. Currently, several all-electromagnetic particle simulation software programs based on the FDTD method have been developed both domestically and internationally. Examples include CHIPIC software developed by the University of Electronic Science and Technology of China, UNIPIC software developed by Xi'an Jiaotong University and the Northwest Institute of Nuclear Technology, and international software such as MAGIC, KARAT, and CST.

[0004] Finite element method (FEM)-based numerical simulation of electromagnetic fields employs unstructured meshes, enabling accurate simulation of complex structures. However, FEM algorithms require solving large inverse matrices and linear equations. Since the resulting mass matrices are often full-rank matrices, the FEM method becomes computationally very time-consuming when there are numerous unknowns. The latest discontinuous time-domain FEM method introduces numerical flux by using weak integrals of Maxwell's equations within the mesh elements. After discretization, it obtains the propagation formula for the electromagnetic field within each element, where the solution depends only on neighboring elements. The discontinuous FEM algorithm retains the advantage of the FEM method—accurately describing complex structures using unstructured meshes—and can significantly improve the computational accuracy of the electromagnetic field by employing scalar higher-order basis functions. Both domestic and international research has been conducted on fully electromagnetic particle simulation methods based on discontinuous finite element method. Since fully electromagnetic particle algorithms often need to track hundreds of thousands or even millions of macro particles, and the charged particles are constantly moving under the influence of electromagnetic fields, at each time step, the program needs to traverse a large number of unstructured meshes, determine the mesh number where the charged particle is located, and calculate the local (reference) coordinates of the charged particle in the unstructured element. This calculation process is very time-consuming. Researchers at the Northwest Institute of Nuclear Technology, including Chen Zaigao, found that tracking the motion of charged particles within unstructured meshes is computationally expensive, making it difficult to use for rapid computation of vacuum electronic devices and optimization design of device structures. Duan Shaoqing et al. from East China Normal University proposed a hybrid DGTD / FDTD electromagnetic field algorithm in Cartesian coordinates (Duan Shaoqing. DGTD Loaded Incident Plane Wave and Two-Dimensional DGTD / FDTD Hybrid Algorithm [D], East China Normal University, 2022), which solved the scattering problem of a two-dimensional model under TM mode electromagnetic wave irradiation. This method mainly uses the FDTD method to set the electromagnetic wave radiation source and absorption boundary conditions, and uses first-order basis functions to describe the electromagnetic field within the unstructured mesh. However, the above methods still suffer from drawbacks such as long computation time and high computational resource consumption. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of long computation time and high computational resource consumption in existing full electromagnetic particle simulation methods, and to provide a full electromagnetic particle simulation method for axisymmetric vacuum electronic devices that integrates time-domain discontinuous finite element method and finite difference hybrid method.

[0006] To achieve the above objectives, the technical solution provided by this invention is:

[0007] A method for simulating fully electromagnetic particles in an axisymmetric vacuum electronic device, characterized by the following steps:

[0008] Step 1: Draw a 3D structural diagram of the axisymmetric vacuum electronic device;

[0009] Step 2: Divide the axisymmetric section into two identical sub-sections along the axis of symmetry of the above three-dimensional structure diagram. Set one of the sub-sections as the calculation section. Based on the calculation section, establish the two-dimensional calculation space of the three-dimensional structure diagram described in Step 1. Divide the two-dimensional calculation space into calculation region A and calculation region B, and generate input file F1.

[0010] Step 3: Divide computational domain A into an unstructured triangular mesh and computational domain B into a rectangular orthogonal structured mesh, generating mesh file F2; set the total computation time steps X0, X0≥10000, where X0 is an integer;

[0011] Step 4: Iterate the electric field, magnetic field and charged particles in calculation region A and calculation region B alternately according to the calculation time step until the calculation time step X = X0, and obtain the magnetic field, electric field and velocity and position data of charged particles.

[0012] Step 5: Based on the magnetic field, electric field, and velocity and position data of charged particles obtained in Step 4, calculate the operating frequency, electron beam current, electron beam energy conversion efficiency, and electromagnetic wave output power of the vacuum electronic device.

[0013] Furthermore, the computational region A mentioned in step two is the region in the two-dimensional computational space near the boundary of the vacuum electronic device.

[0014] Furthermore, the calculation region B mentioned in step two is the vacuum region where charged particles are located within the vacuum electronic device.

[0015] Furthermore, step four specifically involves:

[0016] Step 4.1: Start the main calculation program, read the input file F1 and mesh file F2 in the main calculation program, combine F1 and F2, set the initial conditions and boundary conditions for the calculation, and initialize the calculation time step X to 0;

[0017] Step 4.2: In computational domain A, advance the magnetic field using the time-domain discontinuous finite element method based on scalar higher-order basis functions, and then in computational domain B, calculate and update the magnetic field using the time-domain finite difference method; let X+1;

[0018] Step 4.3: In computational region A, the electric field is advanced using the time-domain discontinuous finite element method based on scalar higher-order basis functions. Then, the current generated by the electron beam motion in computational region B is used as the source term of the electric field equation, and the electric field is updated using the time-domain finite difference method; let X+1;

[0019] Step 4.4: Calculate and update the velocity and position of the charged particles in computational region B using the Newton-Lorentz force equations; let X+1;

[0020] Step 4.5: Determine if X is equal to X0. If yes, proceed to step 5; otherwise, return to step 4.2. Further, the grid size used in computational region A is 0.002m; the grid size used in computational region B is 0.001875m.

[0021] Furthermore, X is 40000.

[0022] Compared with the prior art, the beneficial effects of the present invention are:

[0023] 1. The full electromagnetic particle simulation method in axisymmetric vacuum electronic devices provided by this invention divides the computational region A into an unstructured triangular mesh and the computational region B into a right-angled orthogonal structured mesh during calculation. At the same time, it uses the time-domain discontinuous finite element method with scalar higher-order basis functions to calculate the influence of complex boundaries on the electromagnetic field. It can accurately describe complex boundaries and use higher-order scalar basis functions to approximate the electric and magnetic field distributions within the complex boundary region, which greatly improves the simulation accuracy.

[0024] 2. The full electromagnetic particle simulation method in axisymmetric vacuum electronic devices provided by this invention adopts the time-domain discontinuous finite element method with scalar high-order basis functions. It can achieve the same accuracy as traditional electromagnetic field calculation methods with fewer meshes, which greatly reduces the number of meshes in calculation regions A and B. At the same time, the hybrid method proposed in this invention overcomes the disadvantage of using very small mesh sizes to identify the fine structures inside vacuum electronic devices when simulating complex vacuum electronic devices, and greatly improves the calculation speed of electromagnetic fields inside vacuum electronic devices.

[0025] 3. The full electromagnetic particle simulation method in axisymmetric vacuum electronic devices provided by this invention divides the computational region B into a right-angled orthogonal structure grid. The orthogonal structure grid uses integer pairs to number the grid cells. The logical relationship between the grid cells is simple, which can quickly realize the positioning and retrieval of charged particles in the structure grid. At the same time, it can quickly interpolate the electromagnetic field value to the position of the charged particles, thereby improving the calculation speed of updating the velocity and position of charged particles in vacuum electronic devices. Attached Figure Description

[0026] Figure 1 This is a flowchart of an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the computational region of the high-voltage vacuum coaxial diode in an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of calculation region B in an embodiment of the present invention;

[0029] Figure 4This is a comparison chart of the current results calculated by the full electromagnetic particle simulation method in the axisymmetric vacuum electronic device provided by the present invention and the UNIPIC software in an embodiment of the present invention.

[0030] Figure 5 This is a comparison chart of the diode voltage results calculated by the full electromagnetic particle simulation method in the axisymmetric vacuum electronic device provided by this invention and the UNIPIC software in an embodiment of this invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0032] A method for simulating fully electromagnetic particles in axisymmetric vacuum electronic devices; see flowchart below. Figure 1 This includes the following steps:

[0033] Step 1: Prepare a high-voltage vacuum coaxial diode and use computer software to draw its three-dimensional structure diagram;

[0034] Step 2: Select the axisymmetric section of the above three-dimensional structure. Divide the axisymmetric section into two identical sub-sections along the axis of symmetry. Set one of these sub-sections as the calculation section. Divide the calculation region into two sub-regions along a straight line with radial coordinate position R5 = 0.04 and parallel to the horizontal coordinate axis. One is calculation region A, and the other is calculation region B. Calculation region B is the region where the electron beam is located. It is the rectangular region in the calculation region corresponding to all radial coordinates less than R5. All regions in the calculation region except calculation region B are set as calculation region A. See the calculation region section. Figure 2 and Figure 3 , Figure 2 The inner radius of the coaxial structure at the diode voltage wave injection port is R1=0.05m, the outer radius of the coaxial structure is R2=0.059m, the length of the inner conductor of the coaxial structure is L1=0.1m, the length of the outer conductor of the coaxial structure is L2=0.115m, the inner radius of the annular cathode surface is R3=0.024m, the outer radius is R4=0.027m, and the external guiding static magnetic induction intensity along the positive z-axis is B0=1.0T;

[0035] Step 3: Divide computational region A into an unstructured triangular mesh and computational region B into a right-angled orthogonal structured mesh. In this embodiment, the mesh size of computational region A is 0.002m and the mesh size of computational region B is 0.001875m; set the total computation time steps X0 = 40000.

[0036] Step 4: Iterate the electric field and magnetic field in computational region A and computational region B, and the charged particles in computational region B alternately;

[0037] Step 4.1: Start the main calculation program, read the input file F1 and mesh file F2 in the main calculation program, combine F1 and F2, set the initial conditions and boundary conditions for the calculation, and initialize the calculation time step X to 0;

[0038] Step 4.2: In computational domain A, advance the magnetic field using the time-domain discontinuous finite element method based on scalar higher-order basis functions, and then in computational domain B, calculate and update the magnetic field using the time-domain finite difference method; let X+1;

[0039] Step 4.3: In computational region A, the electric field is advanced using the time-domain discontinuous finite element method based on scalar higher-order basis functions. Then, the current generated by the electron beam motion in computational region B is used as the source term of the electric field equation, and the electric field is updated using the time-domain finite difference method; let X+1;

[0040] Step 4.4: Calculate and update the velocity and position of the charged particles in computational region B using the Newton-Lorentz force equations; let X+1;

[0041] Step 4.5: Determine if X is equal to X0. If yes, proceed to step 5; otherwise, return to step 4.2.

[0042] Step 5: Organize and analyze the data obtained in Step 4 to obtain the operating characteristic parameters of the vacuum electronic device, such as the operating frequency, electron beam current, electron beam energy conversion efficiency, and electromagnetic wave output power.

[0043] Figure 4 This is a comparison chart of the current results obtained by using the fully electromagnetic particle simulation method proposed in this invention and the UNIPIC software in this embodiment of the invention; Figure 5 This is a comparison chart showing the diode voltage results obtained using the proposed all-electromagnetic particle simulation method and UNIPIC software in this embodiment of the invention. From... Figure 4 and Figure 5 It can be seen that the voltage and current waveforms calculated using the hybrid method proposed in this invention agree well with the calculation results of the UNIPIC software, with a relative error of less than 0.1% for voltage and less than 2% for current. Furthermore, comparing the calculation results of the proposed all-electromagnetic particle simulation method with those of the all-electromagnetic particle simulation software based on the time-domain discontinuous finite element method shows that the calculation time of this invention is approximately 1 / 5 of that of the all-electromagnetic particle simulation software based on the time-domain discontinuous finite element method, significantly reducing the calculation time for vacuum electronic devices while maintaining calculation accuracy.

[0044] The fully electromagnetic particle simulation method for axisymmetric vacuum electronic devices provided in this embodiment, which integrates the time-domain discontinuous finite element method and the finite difference hybrid method, is mainly used for numerical simulation of axisymmetric vacuum electronic devices, including a series of axisymmetric structure vacuum electronic devices such as high-voltage vacuum coaxial diodes, relativistic backward wave tubes, magnetically insulated wire oscillators, and cyclotron oscillators. While improving the calculation accuracy of the fully electromagnetic particle simulation method, it overcomes the disadvantage of large computational resource consumption caused by using high-order calculation methods in the entire calculation domain. It can be used for the design and parameter optimization of vacuum electronic devices with high operating frequencies. This embodiment of the invention can also be partially applied to the simulation of plasma phenomena in multi-scale structures.

[0045] In summary, the full electromagnetic particle simulation method for axisymmetric vacuum electronic devices provided by the embodiments of the present invention can save a significant amount of computation time while ensuring computational accuracy.

Claims

1. A method for simulating fully electromagnetic particles in an axisymmetric vacuum electronic device, characterized in that, Includes the following steps: Step 1: Draw a 3D structural diagram of the axisymmetric vacuum electronic device; Step 2: Divide the axisymmetric section along the axis of symmetry of the above three-dimensional structure diagram into two identical sub-sections. Set one of the sub-sections as the calculation section. Based on this calculation section, establish the two-dimensional calculation space of the three-dimensional structure diagram described in Step 1, and divide the two-dimensional calculation space into calculation region A and calculation region B, generating input file F1. Calculation region A is the region in the two-dimensional calculation space near the boundary of the vacuum electronic device; calculation region B is the vacuum region where charged particles are located within the vacuum electronic device. Step 3: Divide computational domain A into an unstructured triangular mesh and computational domain B into a rectangular orthogonal structured mesh, generating mesh file F2; Set the total computation time steps to X0, where X0 ≥ 10000 and X0 is an integer; Step 4: Iterate the electric field, magnetic field and charged particles in calculation region A and calculation region B alternately according to the calculation time step until the calculation time step X = X0, and obtain the magnetic field, electric field and velocity and position data of charged particles. Step four is as follows: Step 4.1: Start the main calculation program, read the input file F1 and mesh file F2 in the main calculation program, combine F1 and F2, set the initial conditions and boundary conditions for the calculation, and initialize the calculation time step X to 0; Step 4.2: In computational domain A, advance the magnetic field using the time-domain discontinuous finite element method based on scalar higher-order basis functions, and then in computational domain B, calculate and update the magnetic field using the time-domain finite difference method; let X+1; Step 4.3: In computational region A, the electric field is advanced using the time-domain discontinuous finite element method based on scalar higher-order basis functions. Then, the current generated by the electron beam motion in computational region B is used as the source term of the electric field equation, and the electric field is updated using the time-domain finite difference method. Let X+1; Step 4.4: Calculate and update the velocity and position of the charged particles in computational region B using the Newton-Lorentz force equations; let X+1; Step 4.5: Determine if X is equal to X0. If yes, proceed to step 5; otherwise, return to step 4.

2. Step 5: Based on the magnetic field, electric field, and velocity and position data of charged particles obtained in Step 4, calculate the operating frequency, electron beam current, electron beam energy conversion efficiency, and electromagnetic wave output power of the vacuum electronic device.

2. The method for simulating all-electromagnetic particles in an axisymmetric vacuum electronic device according to claim 1, characterized in that: In step three, the computational region A is divided into a grid with a size of 0.002m; the computational region B is divided into a grid with a size of 0.001875m.

3. The method for simulating all-electromagnetic particles in an axisymmetric vacuum electronic device according to claim 2, characterized in that: In step three, X0 is 40000.

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