A Method and System for Simulating the Motion of Charged Particles in a Magnetic Field

Abstract

The present application provides a method and system for simulating the motion of charged particles in a magnetic field. The method includes: substituting the magnetic vector potential of the electromagnetic field where the charged particles are located into the established dynamic equation, solving the dynamic equation to obtain the motion trajectory of the charged particles; the dynamic equation is the Hamiltonian equation after the Lorentz force is added with the special relativity correction. The advantages of the present application are as follows: a more comprehensive simulation method for the motion of charged particles in an electromagnetic field is constructed, a simulation model based on energy conservation is considered, the divergence behavior of the long-period prediction of the simulation system is improved, and the simulation of high-speed charged particles in the Earth's magnetic field with high precision over a long period is realized.

Description

Technical Field

[0001] This application belongs to the technical fields of computer technology and charged particle motion analysis technology, and specifically relates to a method and system for simulating the motion of charged particles in a magnetic field. Background Art

[0002] Simulating the motion of charged particles can help us understand the motion laws of charged particles in electromagnetic fields, including their motion behaviors in uniform magnetic fields, non-uniform magnetic fields, and electric fields; in the design of devices such as spectrometers, electron guns, and particle accelerators, accurately predicting the motion of ions or electrons in the field is crucial, and simulation can provide this prediction ability; through simulation, numerical integration and trajectory visualization can be efficiently achieved, which is very useful for studying the motion behaviors of particles in various complex electromagnetic fields.

[0003] Currently, analytical solutions for the motion of charged particles in only a few simple cases of electromagnetic fields can be obtained. For more general actual electromagnetic field environments, such as the Earth's magnetic field, the motion of charged particles needs to be solved through numerical simulation.

[0004] Existing simulation schemes directly solve the dynamic equations of Newtonian mechanics using a Runge-Kutta method solver. The advantage of traditional simulation methods is that they have an intuitive physical meaning and are convenient for program implementation, but the Runge-Kutta method for solving differential equations inevitably produces error accumulation, and this error accumulation will rapidly destroy the energy conservation of the system as the integration time increases. And the motion of charged particles in a magnetic field is a strictly energy-conserving system, and the destruction of energy conservation will cause serious distortion of the simulation results. Therefore, traditional schemes have significant problems in the long-term high-precision simulation of the motion of charged particles in a magnetic field. Summary of the Invention

[0005] The purpose of this application is to overcome the defect of error accumulation in the prior art.

[0006] To achieve the above purpose, this application proposes a method for simulating the motion of charged particles in a magnetic field, including:

[0007] Substitute the magnetic vector potential of the magnetic field where the charged particle is located into the established dynamic equation, solve the dynamic equation, and obtain the motion trajectory of the charged particle;

[0008] The dynamic equation is the Hamiltonian equation after the Lorentz force is added with the special relativity correction.

[0009] As an improvement of the above method, the dynamic equation is:

[0010]

[0011] where the subscript i = 1, 2, 3 represents the x, y, and z components of the vector respectively; x i represents the position of the charged particle; π i represents the components of the generalized momentum in each direction; H represents the Hamiltonian of the charged particle in the magnetic field; t represents time;

[0012] π i = γ0mv i + qA i

[0013] where γ0 represents the special relativity factor; m represents the rest mass of the charged particle; q represents the charge carried by the charged particle; v i represents the components of the charged particle velocity in each direction; A i represents the magnetic vector potential of the magnetic field in each direction;

[0014]

[0015] where c represents the speed of light.

[0016] As an improvement of the above method, the solving of the dynamic equation includes:

[0017] Discretizing the dynamic equation:

[0018]

[0019]

[0020] where n represents the number of iterations in the discrete equation; the subscripts i, j = 1, 2, 3 represent the x, y, and z components of the vector respectively.

[0021] As an improvement of the above method, when the magnetic field where the charged particle is located is the Earth's magnetic field, the magnetic vector potential is:

[0022]

[0023]

[0024] where, represents the magnetic vector potential of the Earth's magnetic field; represents the position of the charged particle in the geocentric rectangular coordinate system; a represents the average reference radius of the Earth; r represents the radial distance of the charged particle from the Earth's center; represents the spherical harmonic coefficient of the 1st order and 0th degree term; and represent the spherical harmonic coefficients of the 1st order and 1st degree terms.

[0025] As an improvement of the above method, when the magnetic field where the charged particle is located is a magnetic field with a uniform magnetic field in the z direction, the magnetic vector potential is:

[0026] A y = Bx

[0027] A x = A z = 0

[0028] where A x 、A y 、A z respectively represent the components of the magnetic vector potential in the x, y, and z directions; B represents the magnetic field strength; x represents the coordinate of the charged particle in the x direction in the coordinate system.

[0029] As an improvement of the above method, it further includes:

[0030] Representing the motion trajectory of the charged particle in the form of an x - y - z three - dimensional diagram of the motion trajectory of the charged particle in three - dimensional space, an image of the evolution of the velocity and position coordinates of the charged particle with time, and an image of the evolution of the energy of the charged particle with time.

[0031] This application also provides a simulation system for the motion of charged particles in a magnetic field, which is implemented based on the above method. The system includes:

[0032] A magnetic vector potential calculation module, used to calculate the magnetic vector potential of the magnetic field where the charged particle is located;

[0033] A motion trajectory calculation module, used to substitute the magnetic vector potential into the established dynamic equation, solve the dynamic equation, and obtain the motion trajectory of the charged particle.

[0034] As an improvement of the above system, it further includes:

[0035] A result display module, used to represent the motion trajectory of the charged particle in the form of an x - y - z three - dimensional diagram of the motion trajectory of the charged particle in three - dimensional space, an image of the evolution of the velocity and position coordinates of the charged particle with time, and an image of the evolution of the energy of the charged particle with time.

[0036] Compared with the prior art, the advantages of this application are:

[0037] 1. A more comprehensive simulation method for the motion of charged particles in a magnetic field is constructed. A simulation model based on energy conservation is considered, which improves the divergent behavior of the long - term prediction of the simulation system and realizes the simulation of high - speed charged particles in the Earth's magnetic field with high accuracy over a long period.

[0038] 2. A general simulation model for the motion of charged particles in a magnetic field is constructed, including a dynamic equation establishment module, a dynamic equation solution module, an Earth's magnetic field simulation module, and a display module.

[0039] 3. Establish a simulation system based on the Hamiltonian mechanics system with a wider applicability, which has the expandability to add an electric field force and gravitational coupling system, providing a basis for the subsequent development of a simulation system for charged particles in electric and gravitational fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The figure shows a flow chart of a method for simulating the motion of charged particles in a magnetic field;

[0041] Figure 2 The figure shows a flow chart of the Earth's magnetic field simulation module;

[0042] Figure 3 The figure shows the electron motion trajectory in the Earth's magnetic field;

[0043] Figure 4 The figure shows the motion trajectory of charged particles in a uniform magnetic field simulated by the method of this application;

[0044] Figure 5 The figure shows the difference in the x direction between the simulation result and the analytical result of the method of this application;

[0045] Figure 6 The figure shows the difference in the x direction between the simulation result and the analytical result of the prior art;

[0046] Figure 7 The figure shows the difference in the y direction between the simulation result and the analytical result of the method of this application;

[0047] Figure 8 The figure shows the difference in the y direction between the simulation result and the analytical result of the prior art;

[0048] Figure 9 The figure shows a schematic diagram of the change of the speed magnitude of the simulation result of the method of this application over time;

[0049] Figure 10 The figure shows a schematic diagram of the change of the speed magnitude of the simulation result of the prior art over time. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The technical solutions of this application will be described in detail below with reference to the accompanying drawings.

[0051] The object of the present invention is to establish a simulation model applicable to an energy conservation system under long-term conditions, optimize the simulation process, and construct a method and system for simulating the motion of charged particles in a magnetic field to ensure long-term stability.

[0052] For the problem of long-period and high-precision simulation of high-speed charged particles in a magnetic field, the method and system for simulating the motion of charged particles in a magnetic field proposed in this application consider the error problem of energy non-conservation caused by the inherent defects of traditional schemes. Through the processes of magnetic field simulation, establishing a dynamic equation, solving the dynamic equation, and result display, it is possible to achieve the simulation and visual display of the motion of charged particles while ensuring long period and high precision.

[0053] Embodiment 1

[0054] A method for simulating the motion of charged particles in a magnetic field includes: magnetic field simulation, establishing a dynamic equation, solving the dynamic equation, and result display.

[0055] In this embodiment, the Earth's magnetic field is described as a typical scenario of the magnetic field.

[0056] Step 1: Electromagnetic field simulation:

[0057] The Earth's magnetic field simulation has the following steps:

[0058] Step 1-1: Read magnetic field data through the IGRF model

[0059] This solution uses the International Geomagnetic Reference (IGRF) model to describe the Earth's magnetic field and gives the Earth's magnetic field data required for particle motion simulation. The IGRF model describes the Earth's magnetic field mainly generated by internal sources in the Earth's core. The magnetic field provided by IGRF is valid at and above the Earth's surface, and its main geomagnetic field can be described as the gradient function of a scalar potential represents the Nabla operator, and the scalar potential can be represented by the following spherical harmonic coefficients as:

[0060]

[0061] where, is the coordinate of the satellite in the geocentric spherical coordinate system, r is the radial distance from the Earth's center, are the co-latitude and longitude with respect to the Earth's center respectively. a is the average reference radius of the Earth, taken as 6371.2 km. is the Schmidt semi-normalized associated Legendre function of order n and degree m. The parameter N specifies the maximum order of the spherical harmonics, equal to 13. The spherical harmonic coefficients vary with time, with the unit of nT. IGRF provides this parameter at 5-year epoch intervals. The time dependence of these parameters is modeled as piecewise linear and is given by the following formula:

[0062]

[0063] where, and represents the epoch T before time t t of the spherical harmonic coefficients. The model epochs in IGRF-13 are provided at exact multiples of 5 years. and represents the linear approximation of the variation of the spherical harmonic coefficients within a 5-year interval, in units of nT / year, and the calculation formula is:

[0064]

[0065] Step 1-2: Determine the magnetic field order according to requirements

[0066] The specific parameters are given by the IGRF model and are updated every 5 years. For the Earth's magnetic field model, its low order and represents the low-order Earth's magnetic field model ( represents the spherical harmonic coefficient of the 1st order and 0th degree), corresponding to the magnetic dipole field, and its accuracy difference from the 13th order Earth's magnetic field model is about 6%. Therefore, when conducting Earth's magnetic field simulation, the low-order Earth's magnetic field model can be used. At this time, the Earth's magnetic field model is:

[0067]

[0068] where is the position of the particle in the geocentric rectangular coordinate system:

[0069]

[0070] where x, y, z are the coordinates of the geocentric rectangular coordinate system.

[0071] Step 1-3: Calculate the magnetic vector potential

[0072] Calculate the magnetic vector potential corresponding to the magnetic dipole field according to the definition method of the magnetic vector potential in the step of establishing the dynamic equation.

[0073] Equation (4) is the magnetic dipole field equation, which can give the magnetic vector potential corresponding to the magnetic dipole field:

[0074]

[0075] where

[0076] The above is the dipole moment expansion of the magnetic vector potential. If a higher-precision magnetic field is required, higher-order magnetic vector potential multipole terms can be added on the basis of the dipole moment.

[0077] Step 1-4: Output simulation data

[0078] Output the simulation results of this step to the step of establishing the kinetic equation as the input of the step of establishing the kinetic equation to establish an equation describing the motion of particles.

[0079] Step 2: Establish the kinetic equation:

[0080] Under the action of the Earth's magnetic field, many high-speed moving charged particles are trapped in the space hundreds of kilometers above the Earth's surface, forming a high-energy particle radiation belt around the Earth, which is called the Van Allen radiation belt. The motion of these high-energy particles is mainly controlled by the Earth's magnetic field. Especially for small-mass charged particles such as electrons, the magnitude of the magnetic force generated by the Earth's magnetic field is much higher than that of the gravity acting on the particle. In order to simulate the motion of these high-energy particles, this solution needs to establish a simulation system for the motion of high-speed moving charged particles in a magnetic field.

[0081] The establishment of the kinetic equation of charged particles has the following steps:

[0082] Step 2-1: Parameter setting

[0083] Step 2-1-1 Particle parameter setting

[0084] In Newtonian mechanics, a charged particle in an electromagnetic field is subjected to the Lorentz force:

[0085]

[0086] where is the momentum of the particle, q is the charge carried by the particle, is the electric field strength, is the velocity of the particle, is the magnetic induction intensity. If the position and velocity of the particle are used as the parameters to describe the state of the particle at a certain moment, the motion of a high-speed charged particle (considering the special relativity effect) in a non-time-varying magnetic field can be described as:

[0087]

[0088] As shown in the above formula, where is the position of the particle, is the velocity of the particle, q is the charge carried by the particle, is the function of the magnetic induction intensity in space with respect to position.

[0089] Step 2-1-2: Add special relativity correction

[0090] In the formula, m is the rest mass of the particle, and γ0 is the special relativity factor. Since the charged particles studied in this solution move at a very high speed, the special relativity effect needs to be considered. According to the special relativity, the mass of a high-speed moving particle will increase, and its mass m′ satisfies the following relationship:

[0091]

[0092] Where \(v\) is the velocity of the particle and \(c\) is the speed of light. From the above equation, it can be seen that the coefficient of the mass relative to the rest mass is a function of the square of the magnitude of the velocity. However, for a particle only under the action of the Lorentz force of the magnetic field, the direction of the force is always perpendicular to the velocity direction, and the force perpendicular to the velocity direction does not do work on the particle. The kinetic energy of the particle is conserved, the square of the magnitude of the velocity does not change with time, and this coefficient is a constant. Therefore, the special relativity factor \(\gamma_0\) in Equation (8) is also a constant.

[0093] Step 2-2: Establish the Hamiltonian equation of particle motion

[0094] Step 2-2-1: Define the magnetic vector potential

[0095] This solution first starts from ensuring the energy conservation of the system, selects a way of Hamiltonian mechanics, and establishes a new simulation system on the basis of establishing the Hamiltonian equation of the system.

[0096] The Lorentz force expressed by the electric field strength and magnetic induction intensity is used in Equation (7). This solution will introduce the potential functions of the electromagnetic field to describe the electric field and magnetic field. First, the magnetic vector potential is defined. Since the divergence of the magnetic field is 0:

[0097]

[0098] where represents the divergence operator.

[0099] Therefore, a vector field can be defined as the magnetic vector potential of the magnetic field:

[0100]

[0101] According to Faraday's law of electromagnetic induction, a scalar field \(\varphi\) is defined as the generalized electric field potential:

[0102]

[0103] Step 2-2-2: Express the Lorentz force using the electric field potential and magnetic vector potential

[0104] Substitute the electric field and magnetic field expressed by the electric field potential and magnetic vector potential into the Lorentz force expression to obtain

[0105]

[0106] The magnetic vector potential is a vector field. At each point in space, there is a corresponding magnetic field at each moment. Therefore, the magnetic vector potential is a function of position and time, and its total differential is:

[0107]

[0108] Substituting into Equation (13), we can obtain:

[0109]

[0110] Equation (15) is the Lorentz force equation expressed in terms of the potential function. This equation describes the force exerted on a charged particle in an electromagnetic field. The first term on the right side of the equation corresponds to the action of the magnetic field on the particle, and the second term represents the action of the electric field on the particle.

[0111] Step 2-2-3: Incorporate the special relativity correction to the Lorentz force

[0112] For a charged particle moving at high speed in a magnetic field, rewrite the momentum in a form with relativistic corrections and omit the term representing the action of the electric field on the right side of the equation. The equation then becomes:

[0113]

[0114] Step 2-2-4: Define the generalized momentum

[0115] The total differential part with respect to time in Equation (16) is not the momentum in Newtonian mechanics, but has a form similar to the momentum in Newtonian mechanics. Therefore, we define it as the generalized momentum

[0116] π i = γ0mv i + qA i (17)

[0117] where the subscripts i = 1, 2, 3 represent the x, y, and z components of the vector respectively. The generalized momentum is a function of the particle's velocity and position. Therefore, using the set of parameters of the particle's position and generalized momentum to describe the state of the system is equivalent to using the set of parameters of the particle's position and velocity to describe the state of the system. Corresponding to the Newtonian mechanics equation (8) regarding position and velocity, the Hamiltonian equation regarding position and generalized momentum can also equivalently describe the motion of a charged particle in a magnetic field.

[0118] Step 2-2-5: Define the system Hamiltonian

[0119] The magnetic field does no work on the charged particle. Therefore, the energy of a charged particle only under the action of the magnetic field is equal to its kinetic energy. According to special relativity, the Hamiltonian (i.e., energy) of a particle moving at high speed is:

[0120]

[0121] If using the generalized momentum It is expressed as:

[0122]

[0123] Step 2-2-6: Establish the Hamiltonian equation

[0124] In Hamiltonian mechanics, the evolution of the system state over time satisfies the Hamiltonian equation:

[0125]

[0126] where the subscript i = 1, 2, 3 represents the x, y, and z direction components of the vector respectively. For this simulation system, x in Equation (20) i is the position of the particle, and π i is the generalized momentum defined in Equation (17), and H is the Hamiltonian of the charged particle in the magnetic field defined in Equation (19).

[0127] For the given initial state x0, π0, solving the above Hamiltonian equation (20) can obtain the motion state of the particle.

[0128] Step 3: Solve the dynamic equation:

[0129] The Hamiltonian equation is a continuous differential equation. To build the simulation system, it needs to be discretized. The discretized Hamiltonian equation is:

[0130]

[0131] However, considering the divergence caused by Δπ i and Δx i tending to 0, it is necessary to transform the discretized Hamiltonian equation. Let n represent the number of iterations in the discrete equation. First, consider the first equation in Equation (21):

[0132]

[0133] where q represents the charge of the charged particle; m represents the mass of the charged particle; n represents the number of iterations in the discrete equation.

[0134] Similarly, for the second equation in Equation (21):

[0135]

[0136] where the subscripts i, j = 1, 2, 3 represent the x, y, and z direction components of the vector respectively.

[0137] Step 4: Result display:

[0138] Solving the kinetic equation can output the variations of particle velocity and position with time as simulation results. To visualize the simulation results for intuitive understanding. The current result display is mainly used to generate the following images:

[0139] A three-dimensional x-y-z graph representing the particle motion trajectory in three-dimensional space, an image of the evolution of particle velocity and position coordinates with time, and an image of the evolution of particle energy with time.

[0140] According to specific task requirements, personalized simulation result output can be achieved by changing the result display settings.

[0141] This embodiment constructs a simulation of charged particles in the Earth's magnetic field, taking the motion of electrons in the Earth's magnetic field as an example. The particle mass is 9.10956×10 -31 kg, the charge is -1.602176634×10 -19 C, and its velocity is assumed to be 0.86 times the speed of light. Figure 3 It is the motion trajectory of the electrons obtained from the simulation.

[0142] Embodiment 2

[0143] Embodiment 1 is a simulation for the case of the Earth's magnetic field. In this embodiment, for all systems that are only affected by the magnetic field or the forces other than the magnetic field can be ignored, the system provided in this application can be used for simulation, and only the magnetic vector potential module needs to be replaced with the required magnetic field. At the same time, the motion of charged particles in a uniform magnetic field has an analytical solution. Therefore, to verify the simulation accuracy of a simulation system, it can be judged by calculating the difference between the simulation results and the analytical results.

[0144] Taking the simulation of particle motion in a uniform magnetic field as an example, assume there is a uniform magnetic field in the z direction:

[0145]

[0146] Consider the definition of the magnetic vector potential:

[0147]

[0148] Since there is:

[0149]

[0150] Therefore, the magnetic vector potential can be set as:

[0151]

[0152] Taking Equation (27) as the replacement for the magnetic vector potential of the Earth's magnetic field can simulate the motion of charged particles in a uniform magnetic field.

[0153] Simulate a particle moving in a uniform magnetic field. Assume that the magnetic field strength of the system is 1, the initial velocity of the particle is 0.1 times the speed of light, the charge is 1, and the mass is 1. Use the simulation system of the present application and the traditional simulation system for simulation respectively. The results are as Figures 5 - 8 shown. The horizontal axis in the figure is time, and the vertical axis is the difference between the position coordinates of the simulation result and the analytical result. The difference between the simulation result of the present application and the analytical result in the x direction is as Figure 5 shown, and the difference between the simulation result of the prior art and the analytical result in the x direction is as Figure 6 shown. The difference between the simulation result of the present application and the analytical result in the y direction is as Figure 7 shown, and the difference between the simulation result of the prior art and the analytical result in the y direction is as Figure 8 shown. By comparison, it can be seen that compared with the prior art, the present application can improve the accuracy by about two orders of magnitude when the simulation duration is 200 s.

[0154] Energy conservation is an important reference factor for measuring whether a simulation system can reflect the real physical situation. The energy conservation of a charged particle moving in a magnetic field is reflected in that the magnitude of the particle's velocity does not change with time. Simulate a particle moving in a uniform magnetic field. Assume that the magnetic field strength of the system is 1, the initial velocity of the particle is 0.1 times the speed of light, the charge is 1, and the mass is 1. Use the simulation system of the present application and the traditional simulation system for simulation respectively. The results are as Figure 9 and Figure 10 shown. The horizontal axis in the figure is time, and the vertical axis is the magnitude of the velocity of the simulation result. Figure 9 shows the change of the magnitude of the velocity of the simulation result of the present application with time, Figure 10 shows the change of the magnitude of the velocity of the simulation result of the prior art with time. By comparison, it can be seen that in the case of simulating for 200 s, the present application performs better than the prior art in maintaining the velocity of the particle.

[0155] Embodiment 3

[0156] The present application also provides a simulation system for the motion of a charged particle in a magnetic field, which is implemented based on the above method. The system includes:

[0157] A magnetic vector potential calculation module for calculating the magnetic vector potential of the electromagnetic field where the charged particle is located;

[0158] A motion trajectory calculation module for substituting the magnetic vector potential into the established dynamic equation, solving the dynamic equation, and obtaining the motion trajectory of the charged particle;

[0159] A result display module for representing the motion trajectory of the charged particle in the form of a three-dimensional x-y-z graph of the motion trajectory of the charged particle in three-dimensional space, an image of the evolution of the charged particle's velocity and position coordinates with time, and an image of the evolution of the charged particle's energy with time.

[0160] The present application can also provide a computer device, including: at least one processor, a memory, at least one network interface, and a user interface. Each component in the device is coupled together through a bus system. It can be understood that the bus system is used to implement the connection and communication between these components. In addition to the data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0161] Among them, the user interface can include a display, a keyboard, or a pointing device. For example, a mouse, a trackball, a touchpad, or a touch screen, etc.

[0162] It can be understood that the memory in the disclosed embodiments of the present application can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. Among them, the non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory can be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchlink dynamic random access memory (SLDRAM), and direct rambus random access memory (DRRAM). The memories described herein are intended to include but not be limited to these and any other suitable types of memories.

[0163] In some embodiments, the memory stores the following elements, executable modules, or data structures, or subsets thereof, or extended sets thereof: an operating system and applications.

[0164] Among them, the operating system includes various system programs, such as the framework layer, the core library layer, the driver layer, etc., which are used to implement various basic services and handle hardware-based tasks. The application programs include various application programs, such as Media Player, Browser, etc., which are used to implement various application services. The program for implementing the method of the embodiments of the present disclosure may be included in the application programs.

[0165] In the above-mentioned embodiments, the program or instruction stored in the memory may also be called. Specifically, it may be the program or instruction stored in the application program. The processor is used for:

[0166] Executing the steps of the above method.

[0167] The above method may be applied to the processor or implemented by the processor. The processor may be an integrated circuit chip with signal processing capabilities. During the implementation process, each step of the above method may be completed by the integrated logic circuit in the hardware of the processor or the instruction in the form of software. The above-mentioned processor may be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed above. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. Combining the steps of the above-disclosed method may be directly embodied as being executed and completed by the hardware decoding processor, or executed and completed by the combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0168] It can be understood that these embodiments described in the present application can be implemented by hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in the present application, or a combination thereof.

[0169] For software implementation, the techniques of the present application can be implemented by executing the functional modules of the present application (such as procedures, functions, etc.). The software code can be stored in a memory and executed by a processor. The memory can be implemented within the processor or outside the processor.

[0170] The present application can also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, the various steps in the above method embodiments can be implemented.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present application does not depart from the spirit and scope of the technical solutions of the present application, and they should all be covered within the scope of the claims of the present application.

Claims

1. A method for simulating the motion of charged particles in a magnetic field, comprising: Magnetic field simulation, establishing dynamic equations, solving dynamic equations and displaying results; Specifically include: Through magnetic field simulation, the magnetic vector potential of the magnetic field where the charged particle is located is substituted into the established dynamic equation, and the dynamic equation is solved to obtain the motion trajectory of the charged particle; the motion trajectory of the charged particle is displayed in the form of an xyz three-dimensional graph of the motion trajectory of the charged particle in three-dimensional space, an image of the evolution of the velocity and position coordinates of the charged particle over time, and an image of the evolution of the energy of the charged particle over time; The magnetic field simulation process includes: reading magnetic field data through the International Geomagnetic Field Reference Model, determining the magnetic field order, and calculating the magnetic vector potential; The dynamic equation is the Hamiltonian equation modified by the special theory of relativity with the Lorentz force added: ； Among them, the subscript Respectively represent the x, y, and z components of the vector; represents the position of a charged particle; represents generalized momentum Components in each direction; represents the Hamiltonian of a charged particle in a magnetic field; t represents time; ； in, represents the special relativity factor; represents the rest mass of a charged particle; Indicates the charge carried by a charged particle; Represents the components of the velocity of charged particles in each direction; Magnetic vector potential representing magnetic field Components in each direction; ； Here, c represents the speed of light.

2. The method for simulating the motion of charged particles in a magnetic field according to claim 1, characterized in that: The solution of the kinetic equation comprises: Discretize the dynamic equation: ； ； Where n represents the number of iterations in the discrete equation; subscript Represent the x, y, and z direction components of the vector respectively.

3. The method for simulating the motion of charged particles in a magnetic field according to claim 1, characterized in that: When the magnetic field where the charged particle is located is the earth's magnetic field, the magnetic vector potential is: ； ； in, represents the magnetic vector potential of the Earth's magnetic field; It represents the position of a charged particle in a geocentric rectangular coordinate system; represents the average reference radius of the Earth; It represents the radial distance of the charged particle from the center of the earth; Represents the spherical harmonic coefficient of the 1st order 0th degree term; and Represents the spherical harmonic coefficient of the first-order first-degree term.

4. The method for simulating the motion of charged particles in a magnetic field according to claim 1, characterized in that: When the magnetic field where the charged particle is located is a magnetic field with a uniform magnetic field in the z direction, the magnetic vector potential is: ； in, , , They represent the components of the magnetic vector potential in the x, y, and z directions respectively; B represents the magnetic field intensity; x represents the coordinate of the charged particle in the x direction in the coordinate system.

5. A system for simulating the motion of charged particles in a magnetic field, implemented based on the method described in any one of claims 1 to 4, characterized in that: The system comprises: The module for calculating magnetic vector potential is used to calculate the magnetic vector potential of the magnetic field where the charged particles are located; A motion trajectory calculation module is used to substitute the magnetic vector potential into the established dynamic equation, solve the dynamic equation, and obtain the motion trajectory of the charged particle; and The result display module is used to represent the motion trajectory of the charged particle in the form of an xyz three-dimensional graph of the motion trajectory of the charged particle in three-dimensional space, an image of the evolution of the velocity and position coordinates of the charged particle over time, and an image of the evolution of the energy of the charged particle over time.

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