Charged particle tracking calculation method
By directly calculating the field of charged particles at each time step and superimposing it with the external field, the motion trajectory of the particle cluster is generated iteratively. This solves the problem that existing technologies cannot calculate variable acceleration motion and complex external field superposition, and achieves accurate particle trajectory calculation and resource saving.
Patent Information
- Application Number
- CN202511879980.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-12
- Publication Date
- 2026-05-01
AI Technical Summary
Existing technologies cannot effectively calculate the long-distance transport trajectory of charged particles under the superposition of variable acceleration motion and complex external fields, especially under the conditions of circular orbit and complex external fields, the calculation accuracy is insufficient.
Based on the properties of the particles themselves, the field at each time step is directly calculated and superimposed with the external field. The motion trajectory of the particle cluster is generated iteratively, including calculating the common interaction field of each particle in the particle cluster, superimposing the external fields, solving the position and momentum of the particles under the total field, and using the Poincaré transform and the equation of motion to perform specific field calculations.
It achieves accurate trajectory calculation under variable acceleration motion and complex external field conditions, avoids the limitations of macroscopic field calculation, saves computing resources, and has clear logic that is easy to understand and correct.
Smart Images
Figure CN121958712A_ABST
Abstract
Description
A method for calculating charged particle tracking Technical Field
[0001] This invention relates to the field of long-distance transmission simulation technology for charged particles, and in particular to a method for tracking and calculating charged particles. Background Technology
[0002] The long-distance transport trajectory of charged particle clumps is a key research direction in accelerator physics. Traditional calculation methods mostly serve simple linear acceleration processes. In this case, a low-energy approximation in a moving frame can be used to transform high-energy particles into a moving frame. Thus, although there is relative motion between each particle in the entire clump, the momentum is not very high, and it can be calculated using classical electromagnetic theory. However, this calculation method has obvious defects: it cannot deal with variable acceleration motion, such as the motion of charged particle clumps in a circular orbit, and it cannot calculate the transport situation under complex external field superposition. Summary of the Invention
[0003] The technical problem solved by this invention is to overcome the limitations of existing methods in adapting to variable acceleration motion and superimposed complex external fields, and to provide a charged particle tracking calculation method. Starting from the characteristics of the particle itself, the field of the particle at each time step in the motion process is directly calculated and added to the external field to obtain the total electric field and the total magnetic field. Substituting these into the motion equation, the position and momentum at the end of the time step are obtained, thereby continuously iterating to generate the motion trajectory of the particle cluster.
[0004] The technical solution of the present invention is as follows: In a first aspect, a method for calculating charged particle tracking is provided, comprising: S1, calculating the common interaction field of all particles in the particle cluster except for the particle to be calculated on particle A based on the position and momentum of each particle in the particle cluster at the current time step; S2, superimposing the external electric field and external magnetic field onto the common interaction field to obtain the total electric field and total magnetic field of particle A; if the external electric field and external magnetic field exist, they are superimposed; if they do not exist, they are not superimposed, and the common interaction field is directly used as the total electric field and total magnetic field of particle A; S3, solving for the position and momentum of particle A in the current time step under the total electric field and total magnetic field; S4, traversing the particle cluster, changing the particle to be calculated, and repeating steps S1 to S3 to obtain the position and momentum of each particle in the particle cluster at the current time step; S5, using the position and momentum of each particle at the current time step obtained in step S4 as the initial state for the calculation of the next time step, returning to step S1, and continuously iterating to generate the motion trajectory of the particle cluster.
[0005] Furthermore, step S1, based on the position and momentum of each particle in the current particle cluster, calculates the common interaction field of all other particles in the particle cluster, excluding the particle i to be calculated, on particle i. Specifically, this includes: S11, determining a particle A to be calculated and the particle cluster coordinate system. S12. Select a particle B other than the particle A to be calculated; based on the position and momentum of particle B, establish a stationary frame relative to particle B. The relative B-particle stationary system Below, the momentum of particle B is 0; S13, calculate the momenta in the system of rest relative to particle B. In the process, the electric field of particle B is transformed back to the particle cluster coordinate system using the Poincaré transformation. The coordinate system of particle B in the particle cluster is obtained. The electric and magnetic fields in the particle cluster; S14, return to step S12, select a new particle B, and repeat steps S12~S13 until all other particles are obtained in the particle cluster coordinate system. The electric and magnetic fields in the sample are summed to obtain the common interaction field of all particles other than particle A on particle A.
[0006] Further, step S3, solving for the position and momentum of particle A within a preset time step under the total electric and magnetic fields, specifically includes: S31, establishing a new coordinate system: taking the position of particle A as the origin of the new coordinate system, taking the direction of the total magnetic field as the Z-axis of the new coordinate system, decomposing the momentum of particle A into two components parallel to and perpendicular to the Z-axis, taking the direction of the component perpendicular to the Z-axis as the X-axis of the new coordinate system, and then using the cross product to determine the Y-axis of the new coordinate system; S32, under the new coordinate system, assuming that the total energy of the particle is constant, solving the equation of motion of particle A to obtain the position and momentum of particle A; and then transforming the position and momentum back into the particle cluster coordinate system. That is, the position and momentum of particle A within a preset time step are obtained.
[0007] Secondly, a charged particle tracking calculation system is provided, comprising: a first module for calculating the common interaction field of all particles in the particle cluster, excluding the particle to be calculated, on particle A based on the position and momentum of each particle in the particle cluster at the current time step; a second module for superimposing an external electric field and an external magnetic field onto the common interaction field to obtain the total electric field and total magnetic field of particle A; if the external electric field and external magnetic field exist, they are superimposed; if they do not exist, they are not superimposed, and the common interaction field is directly used as the total electric field and total magnetic field of particle A; a third module for solving the position and momentum of particle A within a preset time step under the total electric field and total magnetic field; a fourth module for traversing the particle cluster, changing the particle to be calculated, and repeatedly calling the first to third modules to obtain the position and momentum of each particle in the particle cluster at the current time step; and a fifth module for inputting the position and momentum of each particle at the current time step obtained by the fourth module into the first module as the initial state for the calculation of the next time step, continuously iterating the calculation to generate the motion trajectory of the particle cluster.
[0008] Furthermore, the first module includes: a first unit, used to determine a coordinate system of a particle A to be calculated and a particle cluster. The second unit is used to select a particle B other than the particle A to be calculated; based on the position and momentum of particle B, a stationary frame relative to particle B is established. The relative B-particle stationary system Below, the momentum of particle B is 0; the third unit is used to calculate the momentum of particle B in a stationary system. In the process, the electric field of particle B is transformed back to the particle cluster coordinate system using the Poincaré transformation. The coordinate system of particle B in the particle cluster is obtained. The electric and magnetic fields; the fourth unit is used to return to the second unit, reselect a particle B, and repeat the second to third units until all other particles are in the particle cluster coordinate system. The electric and magnetic fields in the sample are summed to obtain the common interaction field of all particles other than particle A on particle A.
[0009] Furthermore, the third module includes: a fifth unit for establishing a new coordinate system: taking the position of particle A as the origin of the new coordinate system, taking the direction of the total magnetic field as the Z-axis of the new coordinate system, decomposing the momentum of particle A into two components parallel to and perpendicular to the Z-axis, taking the direction of the component perpendicular to the Z-axis as the X-axis of the new coordinate system, and then using the cross product to determine the Y-axis of the new coordinate system; a sixth unit for solving the equation of motion of particle A under the assumption of constant total energy of the particle in the new coordinate system to obtain the position and momentum of particle A; and then transforming the position and momentum back into the particle cluster coordinate system. That is, the position and momentum of particle A within a preset time step are obtained.
[0010] The present invention also relates to a computer program product that, when executed by a processor, implements the steps of the method as described above.
[0011] This invention also relates to the application of the charged particle tracking calculation method described above for trajectory calculation in the case of particle clusters undergoing variable acceleration.
[0012] The advantages of this invention compared to existing technologies are as follows: Compared to traditional methods for tracking charged particles based on the overall macroscopic characteristics of particle clusters, this invention starts from the particle itself, using specific single-particle motion equations as the primary calculation method, combined with interaction field calculation methods, to perform specific field calculations. This overcomes the limitations of macroscopic field calculations, enabling variable acceleration field calculations and providing approximate solutions with guaranteed accuracy. The external field addition method is very convenient, and the calculation logic is clear, concise, and easy to understand, thus facilitating correction and improvement. Since the calculations are performed from the specific particle itself, there is no need for mesh generation or boundary conditions, significantly saving computational resources. For the accuracy required during propagation, only the time step needs to be considered. Attached Figure Description
[0013] Figure 1 is a schematic diagram of the method flow of the present invention; Figure 2 is an electron array diagram generated in an embodiment of the present invention; Figure 3 is the calculation result of the electron array motion trajectory without an external field in an embodiment of the present invention; Figure 4 is the motion trajectory of the ZOX planar electron array without an external field in an embodiment of the present invention; Figure 5 is the motion trajectory of the ZOY planar electron array without an external field in an embodiment of the present invention; Figure 6 is the motion trajectory of the XOY planar electron array without an external field in an embodiment of the present invention; Figure 7 is the calculation result of the electron array motion trajectory with an external field in an embodiment of the present invention; Figure 8 is the motion trajectory of the ZOX planar electron array with an external field in an embodiment of the present invention; Figure 9 is the motion trajectory of the ZOY planar electron array with an external field in an embodiment of the present invention; Figure 10 is the motion trajectory of the XOY planar electron array with an external field in an embodiment of the present invention. Detailed Implementation
[0014] To better understand the technical solution of the present invention, the specific embodiments of the present invention are described below.
[0015] As shown in Figure 1, the charged particle tracking calculation method proposed in this invention specifically includes the following steps: S1. Based on the position and momentum of each particle in the particle cluster at the current time step, calculate the common action field of all other particles in the particle cluster except for the particle A to be calculated on particle A.
[0016] First, select a specific particle A from the particle cluster as the particle to be calculated, and determine its coordinates and momentum. Then select another particle B besides this particle, based on particle B's coordinates and momentum. Establish a new coordinate system In this coordinate system Below, the momentum of particle B is 0, which is called the stationary frame relative to particle B. This stationary frame is compared to the original frame of the particle cluster. There exists a Poincaré transformation. The electric field of the B particle in the stationary frame is calculated, and then the obtained electric field of the B particle in the stationary B frame is transformed back to the particle cluster coordinate system using the Poincaré transformation. The electric and magnetic fields of particle B in the particle cluster coordinate system are obtained; the specific calculation formulas and processes are as follows:
[0017] In the formula, It is the unit vector representing the direction of motion of particle B; It is particle B in the reference frame Momentum in Is particle A in the reference frame? Position vector in; It is particle B in the reference frame Position vector in; In the frame of reference The position vector from particle A to particle B; In the frame of reference middle The vector component parallel to the direction of motion of particle B; It is a frame of reference middle The vector component perpendicular to the direction of motion of particle B; It is a frame of reference middle Vectors after Lorentz transformation; It is the relativistic factor derived from the momentum of particle B; It is a frame of reference The electric field generated by particle B; It is the charge of particle B; It is the dielectric constant of a substance; It is a frame of reference electric field in; It is a frame of reference Magnetic field in; It is a frame of reference The velocity of particle B; It is the speed of light in a vacuum.
[0018] Next, different B particles are selected, and the electric and magnetic fields of all other particles on A are calculated and summed to obtain the common interaction field of all other particles in the particle cluster on A.
[0019] S2. Superimpose the external electric field and external magnetic field into a common field to obtain the total electric field and total magnetic field of particle A.
[0020] It should be noted that in this step, if the external electric field and external magnetic field exist, they are superimposed; if they do not exist, they are not superimposed, and the combined field is directly used as the total electric field and total magnetic field of particle A.
[0021] S3. Under the total electric field and total magnetic field, solve for the position and momentum of particle A in the current time step.
[0022] First, a new coordinate system is established, with the direction of the total magnetic field set as the Z-direction of the new coordinate system. The coordinates of particle A are selected as the origin of the new coordinate system. The velocity of particle A is decomposed using Schmidt orthogonalization, resulting in components parallel to and perpendicular to the Z-direction of the new coordinate system. The direction of the perpendicular component is set as the X-direction of the new coordinate system, and the Y-direction is determined using the cross product. Specifically:
[0023]
[0024]
[0025] In the formula, The total magnetic field representing the space in which the particle resides; It is the unit vector in the z-direction of the coordinate system; It is the momentum of particle A; It is the unit vector in the x-direction of the coordinate system; It is the unit vector in the y-direction of the coordinate system.
[0026] The specific process for solving the equations of motion in the new coordinate system is as follows: A constant approximation is applied to the total energy of the particles, ensuring that the following equation can be used as the basis for the next step of the solution.
[0027] The coordinates and momentum of particle A are obtained by solving the non-homogeneous differential equations of the equations of motion. Then, the coordinates and velocities are transformed back to the original coordinate system using an inverse transformation, as follows:
[0028] In the formula, , and These are coefficients set during the calculation process to make the expression more concise; It is the momentum of particle A in the x-direction at time 0; It is the charge of particle A; It is the magnetic field of the space where particle A is located; It is the y-component of the electric field in the space where particle A is located; It is the relativistic factor derived from the momentum of particle A; It is the rest mass of particle A; It is the component of the initial momentum of particle A in the y-direction at time 0; It is the x-component of the electric field in the space where particle A is located; It is the projection of the momentum of particle A in the x-direction at time t; It refers to the time taken during the solution process; It is the projection of the momentum of particle A in the z-direction at time t; It is the z-component of the electric field in the space where particle A is located; It is the component of the initial momentum of particle A in the z-direction at time 0; It is the projection of the position vector of particle A at time t onto the x-direction; It is the x-component of the initial position vector of particle A at time 0; It is the projection of the position vector of particle A at time t onto the y-direction; It is the y-component of the initial position vector of particle A at time 0; It is the projection of the position vector of particle A at time t onto the z-direction; It is the z-component of the initial position vector of particle A at time 0.
[0029] S4. Traverse the particle cluster, replace the particle to be calculated, and repeat steps S1~S3 to obtain the position and momentum of each particle in the particle cluster at the current time step.
[0030] S5. Using the position and momentum of each particle at the current time step obtained in step S4 as the initial state for the next time step calculation, return to step S1 and continuously iterate to calculate and generate the motion trajectory of the particle cluster.
[0031] Below is a specific simulation example of the method of the present invention: The method of the present invention is written into a simulation program, an electron array is generated as input, and the motion trajectory of the particle cluster is generated using the simulation program. Specifically, as shown in Figure 2, the generated electron array is characterized by being a cuboid, arranged in a 4×4×8 array, with electrons spaced 1×10 in all three directions. -4 m, in which 8 electrons are arranged in the Z direction of motion, and 4 electrons each in the X and Y directions. The initial energy of each particle is set to 10.511 MeV, the initial velocity direction is +Z, and the velocity in the other two directions is 0, without any external field.
[0032] In the absence of an external field superposition, the resulting trajectories are shown in Figures 3-6. It can be clearly seen that during the propagation process, the particles diverge due to the repulsion of like charges in the electric field. Furthermore, in the direction of motion, the particles in front experience a force in the same direction as their velocity, while the electrons behind experience a force in the opposite direction to their velocity, thus also resulting in divergence in the direction of motion.
[0033] The resulting motion trajectories under the superposition of external fields are shown in Figures 7-10. In this embodiment, the initial particle distribution remains unchanged, and a force of 1×10⁻⁶ is applied in the +Z direction. -6With the magnetic field T and other parameters unchanged, the calculation results are somewhat different. The most obvious difference is on the plane perpendicular to the propagation direction (XOY plane). The particle distribution changes from the original straight outward radial rectangular lattice to a lattice with a certain curvature, which is the result of the external magnetic field.
[0034] The simulation examples above demonstrate that the method of the present invention can correctly calculate particle trajectories.
[0035] It is understood that this invention has been described through embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of this invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific circumstances without departing from the spirit and scope of this invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are protected by this invention.
[0036] The contents not described in detail in this specification are common knowledge to those skilled in the art.
Claims
1. A method for calculating charged particle tracking, characterized in that, include: S1. Based on the position and momentum of each particle in the particle cluster at the current time step, calculate the common interaction field of all particles in the particle cluster, except for the particle A to be calculated, on particle A. S2. Superimpose the external electric field and external magnetic field onto the common interaction field to obtain the total electric field and total magnetic field of particle A. If the external electric field and external magnetic field exist, they are superimposed; otherwise, they are not superimposed, and the common interaction field is directly used as the total electric field and total magnetic field of particle A. S3. Under the total electric field and total magnetic field, solve for the position and momentum of particle A in the current time step. S4. Traverse the particle cluster, replace the particle to be calculated, and repeat steps S1 to S3 to obtain the position and momentum of each particle in the particle cluster at the current time step. S5. Use the position and momentum of each particle at the current time step obtained in step S4 as the initial state for the next time step calculation, return to step S1, and continuously iterate to generate the motion trajectory of the particle cluster.
2. The charged particle tracking calculation method according to claim 1, characterized in that: Step S1, based on the position and momentum of each particle in the current particle cluster, calculates the common interaction field of all other particles in the particle cluster, excluding the particle i to be calculated, on particle i. Specifically, this includes: S11, determining a particle A to be calculated and the particle cluster coordinate system. S12. Select a particle B other than the particle A to be calculated; based on the position and momentum of particle B, establish a stationary frame relative to particle B. The relative B-particle stationary system Below, the momentum of particle B is 0; S13, calculate the momenta in the system of rest relative to particle B. In the process, the electric field of particle B is transformed back to the particle cluster coordinate system using the Poincaré transformation. The coordinate system of particle B in the particle cluster is obtained. The electric and magnetic fields in the particle cluster; S14, return to step S12, select a new particle B, and repeat steps S12~S13 until all other particles are obtained in the particle cluster coordinate system. The electric and magnetic fields in the sample are summed to obtain the common interaction field of all particles other than particle A on particle A.
3. The charged particle tracking calculation method according to claim 1, characterized in that: Step S3, under the total electric field and total magnetic field, solves for the position and momentum of particle A within a preset time step, specifically including: S31, establishing a new coordinate system: taking the position of particle A as the origin of the new coordinate system, taking the direction of the total magnetic field as the Z-axis of the new coordinate system, decomposing the momentum of particle A into two components parallel to the Z-axis and perpendicular to the Z-axis, taking the direction of the component perpendicular to the Z-axis as the X-axis of the new coordinate system, and then using the cross product to determine the Y-axis of the new coordinate system; S32, under the new coordinate system, assuming that the total energy of the particle is constant, solving the equation of motion of particle A to obtain the position and momentum of particle A; then transforming the position and momentum back into the particle cluster coordinate system. That is, the position and momentum of particle A within a preset time step are obtained.
4. A charged particle tracking calculation system, characterized in that, include: The first module is used to calculate the common interaction field of all particles in the particle cluster, excluding the particle to be calculated, on particle A, based on the position and momentum of each particle in the particle cluster at the current time step. The second module is used to superimpose the external electric field and external magnetic field onto the common interaction field to obtain the total electric field and total magnetic field of particle A. If the external electric field and external magnetic field exist, they are superimposed; otherwise, they are not superimposed, and the common interaction field is directly used as the total electric field and total magnetic field of particle A. The third module is used to solve for the position and momentum of particle A within a preset time step under the total electric field and total magnetic field. The fourth module is used to traverse the particle cluster, change the particle to be calculated, and repeatedly call the first to third modules to obtain the position and momentum of each particle in the particle cluster at the current time step. The fifth module is used to input the position and momentum of each particle at the current time step obtained by the fourth module into the first module as the initial state for the calculation of the next time step, and continuously iterate to generate the motion trajectory of the particle cluster.
5. The charged particle tracking calculation system according to claim 4, characterized in that: The first module includes: a first unit, used to determine a particle A to be calculated and a particle cluster coordinate system. The second unit is used to select a particle B other than the particle A to be calculated; based on the position and momentum of particle B, a stationary frame relative to particle B is established. The relative B-particle stationary system Below, the momentum of particle B is 0; the third unit is used to calculate the momentum of particle B in a stationary system. In the process, the electric field of particle B is transformed back to the particle cluster coordinate system using the Poincaré transformation. The coordinate system of particle B in the particle cluster is obtained. The electric and magnetic fields; the fourth unit is used to return to the second unit, reselect a particle B, and repeat the second to third units until all other particles are in the particle cluster coordinate system. The electric and magnetic fields in the sample are summed to obtain the common interaction field of all particles other than particle A on particle A.
6. The charged particle tracking calculation system according to claim 4, characterized in that: The third module includes: a fifth unit for establishing a new coordinate system: using the position of particle A as the origin of the new coordinate system, the direction of the total magnetic field as the Z-axis of the new coordinate system, decomposing the momentum of particle A into two components parallel to and perpendicular to the Z-axis, using the direction of the component perpendicular to the Z-axis as the X-axis of the new coordinate system, and then using a cross product to determine the Y-axis of the new coordinate system; a sixth unit for solving the equation of motion of particle A under the assumption of constant total particle energy in the new coordinate system to obtain the position and momentum of particle A; and then transforming the position and momentum back into the particle cluster coordinate system. That is, the position and momentum of particle A within a preset time step are obtained.
7. A computer program product, characterized in that: When the computer program product is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 3.
8. The application of the charged particle tracking calculation method as described in any one of claims 1 to 3 for trajectory calculation in the case of particle clusters undergoing variable acceleration.