A numerical calculation method and system for long-distance transmission of a relativistic charged particle beam

Abstract

The present invention relates to a numerical calculation method for the long-distance transmission of relativistic charged particle beams, which solves the problems of inaccurate calculation methods of empirical formulas for the long-distance transmission of high-energy particle beams and great difficulty in numerical calculation in the current fields of space magnetic field measurement and accelerator system design. First, set the initial parameters of the particle beam in the laboratory reference frame, and obtain the positions and velocities of all particles after emitting a single pulse under these parameters. Then, according to the Lorentz transformation formula, transform the positions, velocities of all particles and the external electromagnetic field into an inertial reference frame with a certain intermediate velocity of particle motion. Next, perform numerical calculations in the new reference frame to obtain the positions and velocities of the particles in the final state. Finally, according to the Lorentz transformation formula, transform the positions and velocities of the particles in the final state in the new inertial reference frame back to the laboratory reference frame, and the state of the particle beam in the final state of the laboratory reference frame can be analyzed.

Description

Technical Field

[0001] The present invention belongs to the fields of space magnetic field measurement and accelerator system design, and relates to a calculation method for the motion trajectory of a charged particle beam during long-distance transmission under the action of an electromagnetic field and its own space charge, which can greatly reduce the influence of the retarded potential in the calculation of the space charge effect, achieve higher accuracy, and thus can better evaluate the space magnetic field or assist in the design of the accelerator system. Background Art

[0002] Launching a relativistic particle beam into space and tracking its changes during transmission can track the Earth's magnetic field lines and obtain some parameters required for astrophysical research. Due to the influence of the space charge effect on the particle beam, the beam divergence angle continuously increases, and the radial size of the beam spot will continuously increase during transmission. Therefore, in this process, it is necessary to more precisely determine to what extent the divergence of the particle beam is due to the spatial variation of the space magnetic field and to what extent it is the result of the action of the space charge effect of the particle beam itself, and high-precision numerical calculations of the long-distance transmission of relativistic particle beams are required.

[0003] In addition, when a particle beam freely transmits over a long distance in a large accelerator, it is necessary to simulate and calculate its beam trajectory to assist in the design of the beam control system.

[0004] The particle beam is affected by the space charge effect, that is, the electromagnetic field generated by the particle beam acts on itself in turn. The Coulomb repulsion between particles causes the beam to have a tendency to diverge, and at the same time, it is also affected by the radial pinch effect of the magnetic field formed by the beam, and the overall performance is outward divergence. However, the current research on this process mainly includes formula calculation and direct numerical calculation. The formula calculation method has a very low accuracy in long-distance transmission due to the assumption of uniform and infinite axial dimensions. The Particle In Cell (PIC) simulation method is a main tool for studying the motion of charged particles. For the long-distance transmission of charged particle beams, the physical laws involved are not complex, but when directly using PIC to calculate the particle motion trajectory of the particle beam, due to the extremely large spatial dimensions involved in this process, and because the particle distribution space is small and the required grid division is small, the degree of freedom of this model is extremely large, and the simulation time is long, making it almost impossible to calculate; and there is a relatively obvious retarded potential for high-energy particles, and there are also large errors when directly using the PIC method. In view of this, the present invention proposes a feasible numerical calculation method for the long-distance transmission of high-energy particles with high accuracy, which can better evaluate beam characteristics such as the trajectory, phase space distribution, and beam radius of the particle beam.

[0005] By conducting keyword searches in domestic and foreign literature and patent databases, no patents or literature on the numerical calculation of the long-distance transmission of high-energy particle beams based on reference frame transformation were found. Summary of the Invention

[0006] The object of the present invention is to overcome the problems existing in the prior art and propose a numerical calculation method for the long-distance transmission of relativistic charged particle beams. By converting the transmission process of the charged particle beam into a high-speed moving reference frame for PIC numerical calculation, the influence of the retarded potential in numerical calculation can be avoided, higher-precision results can be obtained, and at the same time, the simulation space and time can be greatly reduced, thus greatly reducing the calculation cost.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A numerical calculation method for the long-distance transmission of relativistic charged particle beams, comprising:

[0009] (1) Generating the initial positions and velocities of the particles in the particle beam;

[0010] (2) According to the Lorentz transformation formula, converting the initial positions, velocities of all particles, and the external electromagnetic field into the moving reference frame;

[0011] (3) Performing PIC numerical simulation calculation in the moving reference frame to obtain the particle positions and velocities at the required final state time;

[0012] (4) Again according to the Lorentz transformation formula, converting the particle positions and velocities calculated in the moving reference frame back to the laboratory reference frame, and then analyzing the state of the final-state particle beam in the laboratory reference frame based on this.

[0013] Further, the laboratory reference frame specifically refers to: an inertial reference frame with the coordinate origin fixed at a certain point in the laboratory, such as the exit of an electron beam accelerator;

[0014] Further, the generation of the initial positions and velocities of the particles in the particle beam is specifically as follows:

[0015] Setting the initial parameters of the charged particle beam in the laboratory reference frame, generating a single pulse of the particle beam according to the initial beam parameters of the charged particle beam in the laboratory reference frame, and obtaining the positions and velocities of all charged particles in the single pulse at a very short time after emission.

[0016] Further, the generation of the initial positions and velocities of the particles in the particle beam can also directly use the output of an accelerator or the previous beam optical element as the positions and velocities of all charged particles in a single pulse.

[0017] Further, the moving reference frame specifically refers to: an inertial reference frame moving relative to the laboratory reference frame at a uniform speed;

[0018] The moving reference frame is denoted as the S' frame, and the selection principle is to minimize the maximum value of the velocities of all particles after the reference frame transformation.

[0019] Further, the initial positions, velocities of all particles, and the external electromagnetic field are transformed into a moving reference frame. The specific transformation operations are as follows:

[0020] The special relativity space-time transformation formula from frame S to frame S' is:

[0021] x' = x, y' = y,

[0022] where (x, y, z, t) and (x', y', z', t') are the space-time coordinates of any particle in frame S and frame S' respectively; v is the relative velocity of frame S' with respect to frame S, and c is the speed of light.

[0023] Further, during the transformation, all particles at a certain moment in frame S are directly transformed into frame S' according to the special relativity space-time transformation formula. After the transformation, the particles in frame S' are not at the same moment. Then, each particle is inserted at different moments in frame S', and the particles inserted earlier are not affected by the latter before the subsequent particles are inserted.

[0024] Further, during the transformation, calculations are performed for a period of time in frame S, and then different moments are taken for different particles so that all particles are transformed into frame S' at the same moment.

[0025] Further, a numerical calculation system for long-distance transmission of relativistic charged particle beams includes:

[0026] Particle position and velocity generation module: Generates the initial positions and velocities of each particle in the particle beam current;

[0027] First reference frame transformation module: According to the Lorentz transformation formula, transforms the initial positions, velocities of all particles, and the external electromagnetic field into a moving reference frame;

[0028] PIC numerical simulation module: Performs PIC numerical simulation calculations in the moving reference frame to obtain the particle positions and velocities at the required final state moment;

[0029] Second reference frame transformation module: Again according to the Lorentz transformation formula, transforms the particle positions and velocities calculated in the moving reference frame back into the laboratory reference frame, and then analyzes the state of the final state particle beam current in the laboratory reference frame based on this.

[0030] The advantages of the present invention compared with the prior art are as follows:

[0031] The numerical calculation method for long-distance transmission of relativistic charged particle beams has not been reported in the visible literature at home and abroad, and has strong creativity, which is mainly manifested in the following aspects:

[0032] (1) Based on the complete equality of different inertial reference frames, the method of the present invention proposes a brand-new numerical calculation method for the long-distance transmission of relativistic charged particle beams;

[0033] (2) By changing the reference frame, the method of the present invention transforms high-energy particles into low-speed particles, and excellently eliminates the influence of the retarded potential in the PIC numerical calculation process;

[0034] (3) The method of the present invention has the characteristics of high calculation accuracy, wide application range, high numerical calculation efficiency, etc.

[0035] (4) The numerical calculation method for the long-distance transmission of relativistic particle beams proposed by the present invention can be applied to the calculation of beam characteristics for space magnetic field measurement and the design of accelerator systems. This method effectively improves the calculation accuracy and calculation efficiency, and has broad market prospects and application values in the fields of space magnetic field measurement, accelerator design, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic diagram of the conversion between two inertial reference frames;

[0037] Figure 2 is a flow chart of the numerical calculation method for the long-distance transmission of relativistic charged particle beams based on the reference frame conversion. DETAILED DESCRIPTION OF THE INVENTION

[0038] For the numerical calculation method for the long-distance transmission of relativistic charged particle beams designed by the present invention, according to the fact that different inertial reference frames are completely equal, and in all reference frames, the laws of physics have the same expression form, the long-distance transmission process of relativistic charged particle beams is converted into another high-speed inertial reference frame, then PIC numerical calculation is carried out, and finally the result analysis is carried out in the laboratory reference frame.

[0039] As Figure 2 shown, the specific steps of the present invention are as follows:

[0040] (1) Generate the initial positions and velocities of the particles in the particle beam.

[0041] Set the initial parameters of the charged particle beam in the laboratory reference frame, generate a single pulse of the particle beam according to the initial parameters of the charged particle beam in the laboratory reference frame, and obtain the positions and velocities of all charged particles in the single pulse at a very short moment after emission.

[0042] Alternatively, the output of an accelerator or the previous beam optics element can be directly used as the position and velocity vectors of all charged particles in the single pulse.

[0043] The laboratory reference frame specifically refers to an inertial reference frame with the coordinate origin fixed at a certain point in the laboratory (such as the exit of an electron beam accelerator).

[0044] (2) According to the Lorentz transformation formula, the initial positions, velocities and external electromagnetic fields of all particles are converted into the moving reference frame.

[0045] A new inertial reference frame is chosen, in which the velocities of all particles are kept as low as possible. Then, using the Lorentz transformation formula from special relativity, the positions, velocities, and external electromagnetic fields of all particles are converted to this new inertial reference frame. If the velocity or direction of the particle beam changes significantly during its motion, the trajectory must be split into multiple segments, each of which is numerically calculated using a different inertial frame, ensuring that the particle velocities within each segment remain consistently low in that reference frame.

[0046] The new inertial reference system is recorded as the motion reference system (S' system), which makes the maximum value of the velocity of all particles after the reference system conversion minimum (or close to the minimum), as shown in the following example: Figure 1 shown.

[0047] For example, if a particle beam (with a certain energy dispersion) is emitted in a laboratory reference frame (the S-frame) along a certain direction (let's call it the z-axis) and is not affected by external electromagnetic fields, then the velocity of the S'-frame is assumed to be along the z-axis, with the velocity being a certain intermediate value in the particle beam's velocity distribution. If the particle beam undergoes significant changes in velocity or direction during its motion, such as large-radius circular motion in a uniform magnetic field, the trajectory must be split into multiple segments, with a different S'-frame selected for each segment for numerical calculation.

[0048] The formula for the space-time transformation of special relativity from the S system to the S' system is:

[0049] x'=x,y'=y,

[0050] Among them, (x, y, z, t) and (x', y', z', t') are the space-time coordinates of any particle in the S system and the S' system respectively; v is the speed of the S' system relative to the S system, and c is the speed of light.

[0051] During conversion, method one: directly convert all particles in the S system at a certain moment into the S' system according to the space-time transformation formula of special relativity. After the conversion, the particles in the S' system are not at the same moment, so each particle is inserted into the S' system at different moments, and the particles inserted first are not affected by the latter before the subsequent particles are inserted.

[0052] When converting, method 2: perform calculations in the S system for a period of time, and then take different particles at different times so that all particles are converted to the S' system at the same time.

[0053] (3) Perform PIC numerical simulation calculations in the moving reference frame to obtain the particle positions and velocities at the required final state time. Using the multi-physics coupling and transient research method of electromagnetic field-particle interaction, when the number of particles is large, macro-particles (combining multiple particles into one particle) are used. After calculation, the particle positions and velocities at the required final state time are obtained. If a periodic pulsed particle beam is studied, the boundary conditions can be set as periodic, or iterative calculations can be performed.

[0054] (4) Again, according to the Lorentz transformation formula, convert the particle positions and velocities calculated in the moving reference frame back to the laboratory reference frame (the velocities and positions of different particles at different times in S’ can be extracted respectively according to the problem to be solved in the laboratory reference frame). Then the final state particle beam state can be analyzed in the laboratory reference frame.

[0055] By converting the physical process of long-distance transmission of a charged particle beam in the laboratory reference frame to another high-speed inertial reference frame, this method makes particles with nearly the speed of light become low-speed particles, almost eliminating the influence of the retarded potential in the PIC numerical calculation process. In addition, the physical process of long-distance and long-time particle beam transmission in the laboratory reference frame becomes a short-distance and short-time transmission process in the new reference frame, greatly reducing the spatial size and physical process time of the simulation calculation, significantly improving the calculation efficiency, and shortening the time required for calculation. In addition, this method has excellent versatility and can study the particle beam transmission process under different energies (including low-energy and high-energy particle beams), different energy dispersions, different particle beam emission conditions, different transmission distances, and different external electromagnetic fields.

[0056] The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A numerical calculation method for long-distance transmission of a relativistic charged particle beam, characterized in that Including: (1) Generating the initial positions and velocities of each particle in the particle beam; (2) According to the Lorentz transformation formula, transforming the initial positions, velocities of all particles, and the external electromagnetic field into the moving reference frame; (3) Conducting PIC numerical simulation calculations in the moving reference frame to obtain the particle positions and velocities at the required final state time; (4) Again, according to the Lorentz transformation formula, transforming the particle positions and velocities calculated in the moving reference frame back to the laboratory reference frame, and then analyzing the state of the final-state particle beam in the laboratory reference frame based on this; Transforming the initial positions, velocities of all particles, and the external electromagnetic field into the moving reference frame. The specific transformation operations are as follows: The special relativity space-time transformation formula from the S frame to the S' frame is: where, (x, y, z, t) and (x', y', z', t') are the space-time coordinates of any particle in the S frame and the S' frame respectively; v is the relative motion velocity of the S' frame with respect to the S frame, and c is the speed of light; During the transformation, directly transform all particles at a certain moment in the S frame to the S' frame according to the special relativity space-time transformation formula. After the transformation, the particles in the S' frame are not at the same moment. Then, insert each particle at different moments in the S' frame, and the particles inserted first are not affected by the latter before the subsequent particles are inserted; Or during the transformation, perform operations in the S frame for a period of time, and then take different moments for different particles so that all particles are transformed to the same moment in the S' frame.

2. The numerical calculation method for long-distance transmission of a relativistic charged particle beam according to claim 1, wherein: The specific laboratory reference frame refers to: an inertial reference frame with the coordinate origin fixed at a certain point in the laboratory.

3. A numerical calculation method for long-distance transmission of a relativistic charged particle beam according to claim 2, characterized in that: The generation of the initial positions and velocities of each particle in the particle beam is specifically: Setting the initial parameters of the charged particle beam in the laboratory reference frame, generating a single pulse of the particle beam according to the initial parameters of the charged particle beam in the laboratory reference frame, and obtaining the positions and velocities of all charged particles in the single pulse at a very short moment after emission.

4. A numerical calculation method for long-distance transmission of a relativistic charged particle beam according to claim 2, characterized in that: The generation of the initial positions and velocities of each particle in the particle beam directly uses the output of an accelerator or the previous beam optical element as the positions and velocities of all charged particles in the single pulse.

5. A numerical calculation method for long-distance transmission of a relativistic charged particle beam according to claim 3 or 4, characterized in that: The specific moving reference frame is: an inertial reference frame moving relative to the laboratory reference frame at a uniform speed; The moving reference frame is denoted as the S' frame, and the selection principle is to minimize the maximum value of the velocities of all particles after the reference frame transformation.

6. A numerical calculation system for long-distance transmission of a relativistic charged particle beam, characterized in that Including: Particle position and velocity generation module: Generating the initial positions and velocities of each particle in the particle beam; First reference frame transformation module: According to the Lorentz transformation formula, transforming the initial positions, velocities of all particles, and the external electromagnetic field into the moving reference frame; PIC numerical simulation module: Conducting PIC numerical simulation calculations in the moving reference frame to obtain the particle positions and velocities at the required final state time; Second reference frame transformation module: Again, according to the Lorentz transformation formula, transforming the particle positions and velocities calculated in the moving reference frame back to the laboratory reference frame, and then analyzing the state of the final-state particle beam in the laboratory reference frame based on this; The moving reference frame is denoted as the S' frame, and the selection principle is to minimize the maximum value of the magnitudes of the velocities of all particles after the reference frame transformation; Convert the initial positions, velocities of all particles, and the external electromagnetic field into the moving reference frame. The specific conversion operations are as follows: The special relativity space-time transformation formula from the S frame to the S' frame is: where (x, y, z, t) and (x', y', z', t') are the space-time coordinates of any particle in the S frame and the S' frame respectively; v is the relative velocity of the S' frame with respect to the S frame, and c is the speed of light; During the conversion, directly convert all particles at a certain moment in the S frame to the S' frame according to the special relativity space-time transformation formula. After the conversion, the particles in the S' frame are not at the same moment. Then insert each particle at different moments in the S' frame, and the particles inserted first are not affected by the latter before the subsequent particles are inserted; Or during the conversion, perform calculations for a period of time in the S frame, and then take different moments for different particles so that all particles are converted to the S' frame at the same moment.

7. A numerical calculation system for long-distance transmission of a relativistic charged particle beam according to claim 6, characterized in that: The initial positions and velocities of the individual particles that generate the particle beam are specifically: Set the initial parameters of the charged particle beam in the laboratory reference frame, generate a single pulse of the particle beam according to the initial parameters of the charged particle beam in the laboratory reference frame, and obtain the positions and velocities of all charged particles in the single pulse at a very short moment after emission; The moving reference frame is specifically: an inertial reference frame moving relative to the laboratory reference frame at a uniform speed.

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