A tightly coupled implementation method for 'road-field-particle' co-simulation

Abstract

This invention discloses a tightly coupled implementation method for 'path-field-particle' co-simulation, relating to the field of computer numerical simulation technology. When simulating charged particles and electromagnetic fields, this invention employs a time-biased finite-difference time-domain method (an algorithm with a noise filtering mechanism). This not only enables the simulation of many complex physical problems in pulsed power devices but also allows for accurate simulation of the electron emission process of the load diode in pulsed power devices. Furthermore, the tightly coupled 'path-field-particle' co-simulation algorithm overcomes the deficiency in traditional 'path-field' co-simulation methods where each iteration step requires a different communication protocol.

Description

Technical Field

[0001] This invention relates to the field of computer numerical simulation technology. Background Technology

[0002] Numerical simulation technology has significant application value in the design and optimization of pulsed power devices. Currently, there are three main methods for simulating the formation and transmission of electromagnetic pulses in pulsed power devices. One method is circuit simulation, which uses software such as PSPICE or self-developed circuit simulation programs. This method constructs an equivalent circuit of the entire device based on the impedance, capacitance, and inductance characteristics of different parts of the device. The advantage of this method is its low computational cost and ability to construct a complete circuit loop. Therefore, the pulsed power simulated by this method covers the entire process from the power source module to the energy transmission module and then to the load. However, the impedance of components such as diode loads in pulsed power devices is closely related to their applied voltage and diode configuration parameters. Changes in load impedance will affect the formation of pulsed electromagnetic waves in the device. Furthermore, for some three-dimensional angularly asymmetric structures, the influence of angular field non-uniformity on the pulse waveform must be considered during simulation. These factors can lead to significant deviations between the circuit simulation and actual conditions. The second method is particle simulation, primarily using particle simulation software such as CHIPIC, NEPTUNE, and UNIPIC. This method uses the finite-difference time-domain method to iteratively solve for the propagation and distribution of the electromagnetic field in the pulsed power device, and employs the Newton-Lorentz equations to solve for the motion of charged particles, accurately simulating the interaction between charged particles and the electromagnetic field. However, this method faces significant challenges in simulating devices such as capacitor energy storage devices. The third method is the 'field-circuit' co-simulation method, which can simulate pulsed power devices with partial cold cavities. This method connects the central finite-difference time-domain method with circuit simulation software (PSPICE) or a self-written circuit program through a special communication protocol built in each iteration step. Furthermore, when a diode is loaded in the pulsed power source, the diode's volt-ampere characteristic changes with the applied voltage; therefore, simulating the electron emission process of the diode loaded in the pulsed power device using the traditional 'field-circuit' co-simulation method will produce significant errors.

[0003] The reason for significant errors in simulating the electron emission process of a diode load in a pulsed power device using the traditional 'circuit-field' co-simulation method is that charged particles (such as electrons emitted by the diode) are introduced during the simulation. The traditional 'circuit-field' co-simulation method can only simulate devices containing circuits and electromagnetic fields, failing to consider the presence of charged particles. Furthermore, the traditional 'circuit-field' co-simulation method uses a central finite-difference time-domain (CDCT) algorithm combined with circuit simulation algorithms to simulate the device. When charged particles are present, their velocities are often relativistic, causing high-speed and non-statistically abrupt charge movement distributions, which in turn introduce unwanted high-frequency numerical noise components into the space current. The simulation must then consider how to eliminate these high-frequency numerical noise components. The CDCT method cannot filter out the high-frequency numerical noise generated by relativistically charged particles. These are the reasons why the traditional 'circuit-field' co-simulation method cannot accurately simulate the electron emission process of a diode load in a pulsed power device.

[0004] In summary, using only one of the circuit simulation method and particle simulation method, or the traditional 'circuit-field' co-simulation method, for the optimization simulation study of pulsed power devices has the following shortcomings:

[0005] (1) Circuit simulation methods can be used to simulate the circuit part, but these methods cannot simulate the impedance change of the diode and the three-dimensional electromagnetic field distribution.

[0006] (2) Particle simulation can be used to simulate vacuum parts such as diodes, but it lacks the ability to describe the circuit part. Many physical problems in pulsed power devices are relatively complex and cannot be explained simply by circuits or fields / particles.

[0007] (3) The traditional 'circuit-field' co-simulation method can only simulate devices containing circuits and electromagnetic fields. Therefore, using the traditional 'circuit-field' co-simulation method to simulate the electron emission process of the load diode of the pulse power device will produce a large error. Summary of the Invention

[0008] The technical problem to be solved by this invention is that, in view of the fact that circuit simulation or particle simulation methods alone cannot simulate and study many complex physical problems in pulse power devices, and that the traditional 'path-field' co-simulation method cannot accurately simulate the electron emission process of the load diode of the pulse power device, a tightly coupled 'path-field-particle' co-simulation method for pulse power devices that can accurately simulate both the pulse power device and the load diode is provided.

[0009] The technical solution adopted by this invention to solve the above-mentioned technical problems is a tightly coupled implementation method for 'path-field-particle' co-simulation, which includes the following steps:

[0010] Step 1: Divide the particle simulation region into a mesh and determine the total simulation time; set the time step for the particle simulation region and the circuit simulation region to work together.

[0011] Step 2: Transform each port of the part that needs to be simulated by the circuit program into a Nordon equivalent circuit, then call the circuit simulation program to calculate the voltage of each port of the circuit in step n, and finally calculate the electric field of the corresponding port in step n based on the field distribution function of the particle simulation module port as the excitation value in the particle simulation module.

[0012] The method for calculating the electric field is as follows:

[0013] A. The method for updating the velocity and position of charged particles in the difference space grid based on known electric and magnetic fields in particle simulation is as follows:

[0014] Based on Maxwell's equations:

[0015]

[0016]

[0017]

[0018]

[0019] in

[0020] D=ε0·E

[0021] B = μ0·H

[0022] in, Let be the Hamiltonian operator, D be the electric displacement vector, ρ be the space charge density, E be the electric field vector, B be the magnetic induction vector, H be the magnetic field vector, t be time, J be the current density vector, ε0 be the free space permittivity, and μ0 be the free space permeability. For partial differential operators in time; the solution for charged particles is based on the Lorentz relativistic equations:

[0023]

[0024] Where F is the force exerted on the charged particle in the electromagnetic field, and is in vector units; p is the vector representation of the charged particle's momentum. Let q be the time derivative of the vector of the charged particle's momentum, q be the charge of the charged particle, and v be the velocity vector of the charged particle in the grid. Its value is:

[0025]

[0026] Where x is the displacement vector of the charged particle. Let be the time derivative of the charged particle's displacement vector, m be the mass of the charged particle, and γ be the relativistic factor; the current density J of the charged particle is generated by the displacement of the charged particle, and its value is:

[0027] J = -ρv

[0028] Furthermore, the particle simulation process must adhere to the law of conservation of charge and satisfy the current continuity equation, the specific form of which is:

[0029]

[0030] According to the theory of relativity, the relativistic factor is:

[0031]

[0032] Where c is the speed of light in a vacuum; the difference form of the Lorentz relativistic equations for charged particles can be obtained:

[0033]

[0034]

[0035]

[0036] in

[0037]

[0038] In the formula, n is the number of spatial grids, Δt is the time step, and B n and E n These are the magnetic field vector and electric field vector on the nth grid, respectively, v n The velocity vector on the nth grid;

[0039] B. Calculate the electric field on the grid:

[0040] Suppose that the movement of a charged particle from grid (i,j) to (i+1,j) can be divided into two processes: within grid (i,j) and within grid (i+1,j). The calculations for these two processes need to be performed separately. We define the weights as follows:

[0041] Δw=w t+Δt -w t

[0042]

[0043] Where Δw is the grid weight ratio of charged particles per unit time step. w represents the average weighting of charged particles per unit time step. t This represents the weight ratio of charged particles on the grid at time t;

[0044] Using the basic method of weighting, the contribution value of charged particles is weighted onto the current at the grid edge, resulting in the current at the edge of the spatial grid as follows:

[0045]

[0046]

[0047]

[0048]

[0049] Among them, (I) x ) i,j Let q be the current in the x-direction on the edge of the spatial grid, i,j be the x and y coordinates of the points on the grid, and q be the current in the x-direction. α w represents the charge of a single charged particle α. x w represents the weighting ratio of charged particles in the x-direction. y The weight ratio of charged particles in the y-direction. The average weighting ratio of charged particles in the x-direction per unit time step. Let Δw be the average weighting ratio of charged particles in the y-direction per unit time step. x Let Δw be the grid weight ratio of charged particles in the x-direction per unit time step. y Let y be the grid weight ratio of the charged particle in the y direction per unit time step; finally, according to the methods in steps A and B, perform iterative calculations on all grids traversed by the charged particle to find the current on the edges of all spatial grids, and then find the electric field on the grid.

[0050] Step 3: Obtain the current density of charged particles in the grid at step n+1 / 2 using the Lorentz relativistic equations; use the time-biased finite-difference time-domain method to iteratively solve for the electric field strength at step n+1 based on the electric field at step n+1 / 2, the surface current density at step n+1 / 2, the electric field at step n, and the magnetic fields at steps n+3 / 2 and n+1 / 2 calculated from the corresponding ports in the circuit module.

[0051] Step 4: Calculate the magnetic field of step (n+1 / 2) based on the magnetic field of step (n-1 / 2) and the electric field of step (n) on the spatial grid;

[0052] The iterative formula for the time-biased finite-difference time-domain method is as follows:

[0053]

[0054]

[0055] Where α1, α2, and α3 satisfy the following relationship:

[0056]

[0057] In the formula, τ k For a decreasing sequence of low relaxation factors, k = 1, 2, 3, ..., K, E n+1,k In the superscript, k represents the subscript of the relaxation factor sequence. The first term in the superscript is the spatial grid iteration step, H is the magnetic field strength vector, ε is the permittivity, μ is the permeability, and α1, α2, and α3 are time-biased factors set according to the proportion of the influence value of the magnetic field at three times. Together with the decreasing low relaxation factor sequence, they achieve the purpose of filtering out noise. At this point, the simulation process of the particle simulation region is completed.

[0058] Step 5: Based on the magnetic field calculated from the particle simulation region, the total Norton current is determined using Ampere's law, and then the current is fed back to the circuit module program for calculation.

[0059] This invention employs a time-biased finite-difference time-domain method (an algorithm with a noise filtering mechanism) to simulate charged particles and electromagnetic fields. This not only enables the simulation of many complex physical problems in pulsed power devices but also allows for accurate simulation of the electron emission process of the load diode in pulsed power devices. Furthermore, it utilizes a tightly coupled 'path-field-particle' cooperative algorithm, overcoming the limitation of traditional 'path-field' cooperative simulation methods where each iteration step requires a different communication protocol. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of a resistor.

[0061] Figure 2 This is a circuit diagram containing resistors.

[0062] Figure 3 This is the equivalent circuit diagram for capacitor linearization.

[0063] Figure 4 This is a hybrid circuit diagram containing RLC.

[0064] Figure 5 The simulation results of the developed circuit module are shown in the figure.

[0065] Figure 6 The image shows the simulation results from the PSPICE software.

[0066] Figure 7 This is a schematic diagram of the mean field solution in the grid.

[0067] Figure 8 This is a schematic diagram of the motion of charged particles.

[0068] Figure 9 This is a flowchart of the method for implementing the present invention.

[0069] Figure 10 This is the circuit equivalent diagram combining circuit and particle simulation.

[0070] Figure 11 This is a diagram of the tightly coupled interaction mode for 'road-field-particle' co-simulation.

[0071] Figure 12 This is a schematic diagram of a ten-stage LTD and a tapered transition section pulse power device.

[0072] Figure 13 This is a comparison chart of simulation results and experimental results for the simulation method of this invention. Detailed Implementation

[0073] The present invention will now be described in detail with reference to the accompanying drawings.

[0074] This invention provides a tightly coupled implementation method for 'circuit-field-particle' co-simulation, which can accurately simulate pulsed power devices containing relativistically charged particles. To achieve tight coupling, a circuit simulation module is first developed, based on an improved nodal voltage analysis method and circuit analysis theory. This module mainly includes the linearization equivalence of source devices (such as voltage sources), linear components (such as resistors), and nonlinear components (such as inductors, capacitors, transmission lines, and switches).

[0075] (1) Linear devices

[0076] like Figure 1 The diagram shown is a schematic of a resistor. According to Ohm's law, the relationship between the voltage and current of the resistor can be written, which is its current-voltage characteristic curve (VAR).

[0077] u=R·i (1)

[0078] That is to say

[0079] i = G·u (2)

[0080] Where u is the voltage across the resistor, i is the current flowing through the resistor, R is the resistance, and G is the conductance (G = 1 / R). According to the above formula, the VAR curve of a resistor is a straight line passing through the origin. Figure 2 For a circuit diagram containing resistors, based on the improved node analysis method and circuit analysis theory, we can obtain:

[0081]

[0082] Write it in matrix form as

[0083]

[0084] Where R1 is the first resistor, R2 is the second resistor, v1 is the voltage at node 1, v2 is the voltage at node 2, i is the current flowing through the voltage source, V1 is the voltage of the voltage source, I1 is the current of the current source, and U1 is the voltage at the positive terminal of the voltage source.

[0085] (2) Nonlinear devices

[0086] For nonlinear devices (such as capacitors, inductors, transmission lines, switches, etc.), linearization must be performed first. Taking capacitors as an example, the linearization process consists of three steps:

[0087] Step 1: Based on circuit theory, construct the capacitor's current-voltage characteristic curve using numerical methods;

[0088] Step 2: Linearize the capacitor's current-voltage characteristic curve using the implicit Euler method;

[0089] Step 3: Write the volt-ampere characteristic curve of the capacitor linearized into an improved nodal voltage analysis matrix.

[0090] First, write the equation for the capacitor's volt-ampere characteristic:

[0091] V=Q / C , I=dQ / dt (5)

[0092] Where V is the voltage across the capacitor, Q is the charge on the capacitor, C is the capacitance, I is the current in the capacitor, t is time, and dQ / dt is the time derivative of the charge on the capacitor.

[0093] Then, based on the implicit Euler method, the difference formula for the capacitor voltage is written as follows:

[0094]

[0095] Where l is the number of iterations, V l V is the voltage across the capacitor at time step l. l+1 Here, h represents the voltage across the capacitor at time step l+1, and h is the time step size. The derivative of the voltage across the capacitor at time step l+1 is given. Substituting V = Q / C into the above equation, we obtain...

[0096]

[0097] Among them, Q l+1The charge on the capacitor at time step l+1. This is the time derivative of the charge on the capacitor at time step l+1. Substituting I = dQ / dt into the above equation, we can obtain the recursive relationship between the voltage and current on the capacitor.

[0098]

[0099] Where I l+1 Let be the current through the capacitor at time step l+1. Then, by a simple transformation, we can obtain the relationship between the current and voltage through the capacitor:

[0100]

[0101] You can Consider it as conductance G eq The above formula can be written as

[0102] I l+1 =(G eq )·V l+1 +(G eq )·V l (10)

[0103] The above formula can be expressed as follows: Figure 3 The circuit diagram shows that this achieves the linearization process of the nonlinear capacitor.

[0104] The above expression can be written in matrix form as follows:

[0105]

[0106] in This is the voltage across node 1 on the left side of the capacitor. I is the voltage across node 2 on the right side of the capacitor. eq =(G eq )·V l This represents the past voltage V. l The contribution to capacitor current is a key characteristic of energy storage components. The linearization process for other nonlinear components is similar and will not be elaborated upon here. After the circuit module is developed, it is constructed as follows: Figure 4 Circuits containing capacitors, inductors, current sources, and resistors were tested, and the simulation results were compared with those obtained using PSPICE, a common software in this field. Figure 5 The image shows the results of the circuit simulation program developed. Figure 6 The results are from simulations using PSPICE circuit simulation software. Figure 5 and Figure 6 As can be seen, the simulation results of the developed circuit module are consistent with the simulation results of PSPICE, which proves the effectiveness and accuracy of the developed circuit module.

[0107] Then, when relativistically charged particles are present in the simulation, certain high-frequency noise components are generated, which traditional central finite-difference time-domain (FDTD) methods cannot accurately simulate. This necessitates the use of a simulation algorithm with a filtering mechanism—the time-biased FDTD method. Particle simulation consists of the following steps:

[0108] Step 1: Grid the simulation area;

[0109] Step 2: Obtain the current density on the grid in the simulation region using the Lorentz relativistic equations;

[0110] The derivation process is based on Maxwell's equations:

[0111]

[0112]

[0113]

[0114]

[0115] in

[0116] D=ε0·E (16)

[0117] B=μ0·H (17)

[0118] In the formula, Let be the Hamiltonian operator, D be the electric displacement vector, ρ be the space charge density, B be the magnetic induction vector, H be the magnetic field strength vector, t be time, J be the current density vector, ε0 be the free space permittivity, and μ0 be the free space permeability. This is a partial differential operator in time. The solution for charged particles is based on the Lorentz relativistic equations:

[0119]

[0120] Where F is the force exerted on the charged particle in the electromagnetic field, and is in vector units; p is the vector representation of the charged particle's momentum. Let q be the time derivative of the vector of the charged particle's momentum, q be the charge of the charged particle, and v be the velocity vector of the charged particle in the grid. Its value is:

[0121]

[0122] Where x is the displacement vector of the charged particle. Let be the time derivative of the displacement vector of the charged particle, m be the mass of the charged particle, and γ be the relativistic factor; the current density of the charged particle is generated by the displacement of the charged particle, and its value is...

[0123] J=-ρv (20)

[0124] Furthermore, the particle simulation process must adhere to the law of conservation of charge and satisfy the current continuity equation, the specific form of which is:

[0125]

[0126] Neglecting relativistic effects in real-world physics problems can lead to significant numerical simulation errors; therefore, it is necessary to consider relativistic effects within the spatial grid. According to relativistic theory, the relativistic factor is:

[0127]

[0128] Where c is the speed of light in a vacuum. Substituting this into equations (18)-(21), we obtain the difference form of the Lorentz relativistic equations for charged particles:

[0129]

[0130]

[0131]

[0132] in

[0133]

[0134] In the formula, n is the number of spatial grids, Δt is the time step, and B n and E n These are the magnetic field vector and electric field vector on the nth grid, respectively, v n This is the velocity vector on the nth grid, and so on for other variables of the same type.

[0135] Therefore, we can deduce how to update the velocity and position of charged particles in a differential space grid based on known electric and magnetic fields in particle simulation. In the space grid, the force exerted by the field on the charged particle is closely related to the value of the electromagnetic field and the velocity of the charged particle. The charged particle's reaction to the field requires considering its contribution to the current density. Generally, all charged particles are emitted through the emission boundary. In the grid space, the initial velocity and distribution of charged particles are known. We can enter the iterative loop of the entire particle simulation based on the initial state of the charged particle distribution and then update the charged particle positions. Considering the general case, assuming that a charged particle moves into the space grid, we need to weight the electromagnetic field values ​​of each vertex of the cell where the charged particle is located to the particle's position. The field values ​​at the cell vertices, such as... Figure 7As shown, the electromagnetic field value at point S is the average of the electromagnetic field values ​​at its six vertices (up, down, left, right, front, and back). Then, under relativistic effects, the velocity and position of the charged particle are obtained according to the Lorentz difference equation for charged particles, and finally, the current density is calculated, forming a complete cyclic scheme that propels the charged particle's motion in the field.

[0136] Charged particles move under the influence of a field, causing changes in the current density within the grid space. These changes in current density are then added as known terms to the iterative calculation of the field in the next time step. Taking a two-dimensional case as an example, suppose a charged particle with charge q moves from one grid to another; for instance... Figure 8 The movement of the charged particle from grid (i,j) to (i+1,j) can be divided into two processes: within grid (i,j) and within grid (i+1,j). These two processes need to be calculated separately, and the weights are defined as follows:

[0137] Δw=w t+Δt -w t (27)

[0138]

[0139] Where Δw is the grid weight ratio of charged particles per unit time step. denoted as , where is the average weight ratio of charged particles per unit time step, and w is the weight ratio of charged particles on the grid.

[0140] Using the basic method of weighting, the contribution value of charged particles is weighted onto the current at the grid edge, resulting in the current at the edge of the spatial grid as follows:

[0141]

[0142]

[0143]

[0144]

[0145] Among them, (I) x ) i,j Let q be the current in the x-direction on the edge of the spatial grid, i,j be the x and y coordinates of the points on the grid, and q be the current in the x-direction. α w represents the charge of a single charged particle α. x w represents the weighting ratio of charged particles in the x-direction. y The weight ratio of charged particles in the y-direction. The average weighting ratio of charged particles in the x-direction per unit time step. Let Δw be the average weighting ratio of charged particles in the y-direction per unit time step. x Let Δw be the grid weight ratio of charged particles in the x-direction per unit time step. y Let be the grid weight ratio in the y-direction for charged particles per unit time step. Finally, perform iterative calculations on all grids traversed by the charged particle to determine the current on the edges of all spatial grids, and then calculate the current density on the grid.

[0146] Step 3: Using a time-biased finite-difference time-domain algorithm with a filtering mechanism, the electric field at step n+1 is iterated based on the electric field at step n+1, the surface current density at step n+1 / 2, the magnetic field at step n+3 / 2, and the magnetic field at step n+1 / 2 on the spatial grid. Finally, the magnetic field at step n+1 / 2 is calculated based on the magnetic field at step n-1 / 2 and the electric field at step n on the spatial grid.

[0147] The iterative formula for the time-biased finite-difference time-domain algorithm is:

[0148]

[0149]

[0150] To ensure the stability of the algorithm, α1, α2, and α3 satisfy the following relationship:

[0151]

[0152] In the formula, τ k (k = 1, 2, 3, ..., K) is a decreasing sequence of low relaxation factors, E n+1,k In the superscript 'k', k represents the subscript of the relaxation factor sequence. The first term in the superscript is the spatial grid iteration step, ε is the permittivity, μ is the permeability, and α1, α2, and α3 are time-biased factors set according to the weight of the magnetic field influence values ​​at three time points. These, together with the decreasing low relaxation factor sequence, achieve the purpose of filtering out noise. The simulation process of the particle simulation region is now complete.

[0153] Finally, there is the tightly coupled implementation process of 'road-field-particle' co-simulation. Figure 9 The flowchart shows the implementation method of this invention. This invention is implemented by tightly coupling the developed circuit module and the particle simulation module. The advantage of this method is that it can not only simulate and study many complex physical problems in pulse power devices, but also accurately simulate the electron emission process of the load diode of the pulse power device. It also overcomes the defect that each iteration step in the traditional 'path-field' co-simulation method requires a different communication protocol.

[0154] Figure 10This is the equivalent circuit diagram combining the circuit module and the particle simulation module. As mentioned earlier, relativistically charged particles are coupled to the electromagnetic field through the Lorentz equations of relativity, and the coupling between the circuit and the particle simulation module is as follows: Figure 10 The method shown consists of the following steps:

[0155] Step 1: Divide the particle simulation region into a grid, coordinate the simulation time of the circuit simulation module and the particle simulation module, and synchronize the simulation time of the two modules.

[0156] Figure 11 The diagram illustrates the computational theory of the fully coupled equation system for 'circuit-field-particle' co-simulation. It shows that the electric and magnetic fields calculated using the time-biased time-domain difference method act as a bridge between the circuit and the charged particles. At each time step in the co-simulation, the voltage or current at the connection node between the circuit and the particle simulation can serve as the excitation condition for the excitation source port of the electric or magnetic field in the particle simulation. The electromagnetic field determines the force experienced by the charged particles, which in turn determines the spatial charge density and current density distribution of the charged particles. The distribution of charged particles, in turn, affects the spatial electromagnetic field. Finally, the voltage or current is obtained by integrating the electric or magnetic field at the excitation source port of the particle simulation and fed back to the connection node of the circuit, thus realizing the 'circuit-field-particle' co-simulation.

[0157] Step 2: Perform 'path-field-particle' cooperative simulation on the corresponding device at the cooperative simulation time step.

[0158] Finally, the same device was simulated using the tightly coupled simulation method of 'road-field-particle' co-simulation implemented in this invention and the traditional 'road-field' co-simulation method, respectively, and the simulation results were compared with the experimental results. Figure 12 The diagram shows a pulsed power device containing a ten-stage LTD and a tapered transition section. The parameters for each LTD module are: capacitance: 100nF; inductance: 40nH; internal resistance: 0.1Ω; capacitor charging voltage: 150kV. A diode emitting charged particles is loaded at the right end of the device. The simulation results and experimental comparison of the tightly coupled simulation method of 'path-field-particle' co-simulation implemented in this invention are shown in the figure. Figure 13 The results show that the simulation results obtained using the tightly coupled simulation method of 'road-field-particle' co-simulation implemented in this invention agree well with the experimental results. This also proves the effectiveness and reliability of the method presented in this paper.

Claims

1. A tightly coupled implementation method for 'path-field-particle' co-simulation, comprising the following steps: Step 1: Divide the particle simulation region into a mesh and determine the total simulation time; set the time step for the particle simulation region and the circuit simulation region to work together. Step 2: Transform each port of the part that needs to be simulated by the circuit program into a Nordon equivalent circuit, then call the circuit simulation program to calculate the voltage of each port of the circuit in step n, and finally calculate the electric field of the corresponding port in step n based on the field distribution function of the particle simulation module port as the excitation value in the particle simulation module. The method for calculating the electric field is as follows: A. The method for updating the velocity and position of charged particles in the difference space grid based on known electric and magnetic fields in particle simulation is as follows: Based on Maxwell's equations: in D=ε0·E B = μ0·H in, Let be the Hamiltonian operator, D be the electric displacement vector, ρ be the space charge density, E be the electric field vector, B be the magnetic induction vector, H be the magnetic field vector, t be time, J be the current density vector, ε0 be the free space permittivity, and μ0 be the free space permeability. For partial differential operators in time; the solution for charged particles is based on the Lorentz relativistic equations: Where F is the force exerted on the charged particle in the electromagnetic field, and is in vector units; p is the vector representation of the charged particle's momentum. Let q be the time derivative of the vector of the charged particle's momentum, q be the charge of the charged particle, and v be the velocity vector of the charged particle in the grid. Its value is: Where x is the displacement vector of the charged particle. Let be the time derivative of the displacement vector of the charged particle, m be the mass of the charged particle, and γ be the relativistic factor; the current density J of the charged particle is generated by the displacement of the charged particle, and its value is: J = -ρv Furthermore, the particle simulation process must adhere to the law of conservation of charge and satisfy the current continuity equation, the specific form of which is: According to the theory of relativity, the relativistic factor is: Where c is the speed of light in a vacuum; the difference form of the Lorentz relativistic equations for charged particles can be obtained: in In the formula, n is the number of spatial grids, Δt is the time step, and B n and E n These are the magnetic field vector and electric field vector on the nth grid, respectively, v n The velocity vector on the nth grid; B. Calculate the electric field on the grid: Suppose that the movement of a charged particle from grid (i,j) to (i+1,j) can be divided into two processes: within grid (i,j) and within grid (i+1,j). The calculations for these two processes need to be performed separately. We define the weights as follows: Δw=w t+Δt -In t Where Δw is the grid weight ratio of charged particles per unit time step. w represents the average weighting of charged particles per unit time step. t This represents the weight ratio of charged particles on the grid at time t; Using the basic method of weighting, the contribution value of charged particles is weighted onto the current at the grid edge, resulting in the current at the edge of the spatial grid as follows: Among them, (I) x ) i,j Let q be the current in the x-direction on the edge of the spatial grid, i,j be the x and y coordinates of the points on the grid, and q be the current in the x-direction. α w represents the charge of a single charged particle α. x w represents the weighting ratio of charged particles in the x-direction. y The weight ratio of charged particles in the y-direction. The average weighting ratio of charged particles in the x-direction per unit time step. Let Δw be the average weighting ratio of charged particles in the y-direction per unit time step. x Let Δw be the grid weight ratio of charged particles in the x-direction per unit time step. y Let y be the grid weight ratio of the charged particle in the y direction per unit time step; finally, according to the methods in steps A and B, perform iterative calculations on all grids traversed by the charged particle to find the current on the edges of all spatial grids, and then find the electric field on the grid. Step 3: Obtain the current density of charged particles in the grid at step n+1 / 2 using the Lorentz relativistic equations; use the time-biased finite-difference time-domain method to iteratively solve for the electric field strength at step n+1 based on the electric field at step n+1 / 2, the surface current density at step n+1 / 2, the electric field at step n, and the magnetic fields at steps n+3 / 2 and n+1 / 2 calculated from the corresponding ports in the circuit module. Step 4: Calculate the magnetic field of step (n+1 / 2) based on the magnetic field of step (n-1 / 2) and the electric field of step (n) on the spatial grid; The iterative formula for the time-biased finite-difference time-domain method is as follows: Where α1, α2, and α3 satisfy the following relationship: In the formula, τ k For a decreasing sequence of low relaxation factors, k = 1, 2, 3, ..., K, E n+1,k In the superscript, k represents the subscript of the relaxation factor sequence. The first term in the superscript is the spatial grid iteration step, H is the magnetic field strength vector, ε is the permittivity, μ is the permeability, and α1, α2, and α3 are time-biased factors set according to the proportion of the influence value of the magnetic field at three times. Together with the decreasing low relaxation factor sequence, they achieve the purpose of filtering out noise. At this point, the simulation process of the particle simulation region is completed. Step 5: Based on the magnetic field calculated from the particle simulation region, the total Norton current is determined using Ampere's law, and then the current is fed back to the circuit module program for calculation.

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