Simulation method for space charge effect of charged particle beam with large energy dispersion and large divergence angle

Abstract

The invention relates to a large-energy-dispersion large-divergence-angle charged particle beam space charge effect simulation method which is used for simulation calculation of beam transmission in large-energy-dispersion or large-divergence-angle or nonlinear transmission. Firstly, the initial state of each charged particle in a charged particle beam and external electromagnetic field information are obtained; secondly, dividing the particles into different sets, respectively converting the different sets into different inertial systems, calculating a generated electric field, and performing conversion and superposition to obtain a space charge field of an original coordinate system; then, calculating the position and speed of each particle in the next time step according to the external electromagnetic field and the space charge field; and finally, repeating the field calculation and particle movement until the calculation beam moves to the required moment or position. According to the method, the calculation accuracy in the beam transmission simulation process is improved.

Description

A Simulation Method for Space Charge Effect of High-Energy, Large-Divergence-Angle Charged Particle Beams Technical Field

[0001] This invention relates to a simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam in a non-linear propagation scenario, belonging to the field of electromagnetic simulation of charged particle beams. Background Technology

[0002] Particle accelerators can be used in high-energy physics, radiation sterilization, cancer treatment, and other applications. In order to better achieve the target function, high-precision simulation calculations are required when designing beam transmission component systems for these applications.

[0003] The spatial distribution and motion of charges in a charged particle beam alter the electromagnetic field in space, which in turn affects the distribution and motion of particles. The space charge effect is a general term for this complex physical process, in which the field excited by the beam is called the space charge field.

[0004] Current beam simulation software typically employs the method of solving the Poisson equation by neglecting the retardation potential of all charged particles in a single inertial frame to calculate the space charge field of the beam. This method is suitable for low energy dissipation, low divergence angle, and straight-line propagation. However, when simulating beams, especially high-current beams, with high energy dissipation, large divergence angle, or non-linear propagation, the calculation method deviates significantly from the actual physical process, making it difficult to meet the needs of practical applications. Summary of the Invention

[0005] The purpose of this invention is to improve the calculation accuracy in the above-mentioned beam transmission simulation process. This invention proposes a simulation method for the space charge effect of charged particle beams with large energy dispersion and large divergence angle in non-linear transmission scenarios.

[0006] The present invention adopts the following technical solution:

[0007] A simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam includes:

[0008] (1) Obtain the initial state and external electromagnetic field information of each charged particle in the charged particle beam, wherein the initial state includes position and velocity;

[0009] (2) Calculate the space charge field generated by the beam based on the position and velocity of the charged particles;

[0010] (3) Calculate the position and velocity of the charged particle at the next time step based on the external electromagnetic field and the space charge field generated by the beam;

[0011] (4) Repeat steps (2) and (3) until the beam moves to the desired time or position.

[0012] Furthermore, step (2) calculates the space charge field generated by the beam based on the position and velocity of the charged particles, specifically through a decomposition method:

[0013] (2.1) Divide the charged particles in the charged particle beam in the laboratory inertial frame S into multiple sets;

[0014] (2.2) By using the Lorentz transformation, the charged particles in a certain set A are transferred to a certain moving inertial frame S′, and the electromagnetic field generated by the charged particles in set A is calculated in the moving inertial frame S′; the charged particles in multiple sets are transferred to different inertial frames respectively, and the electromagnetic field generated is calculated respectively.

[0015] (2.3) The electromagnetic fields generated by charged particles in set A are obtained by the Lorentz transformation of the field to obtain the electromagnetic fields generated by charged particles in set A in the laboratory inertial frame; the electromagnetic fields generated by charged particles in the remaining sets are all transformed in the same way to obtain the electromagnetic fields generated by charged particles in all sets.

[0016] (2.4) By vector superimposing the electromagnetic fields generated by all the charged particles in the set, the electromagnetic field generated by the entire charged particle beam in the laboratory inertial frame is obtained.

[0017] Furthermore, the principle for dividing the charged particles in the charged particle beam into multiple sets is as follows:

[0018] The velocity vectors of charged particles within a single set are close;

[0019] The principle for selecting a moving inertial frame of reference is to minimize the maximum velocity of the particle ensemble within that frame.

[0020] Furthermore, the electromagnetic field generated by a charged particle in a moving inertial frame S′ is approximated as follows: the electric potential is obtained by solving the Poisson equation using the finite element method or by calculating the Green's function using FFT, and then the electromagnetic field is obtained from the electric potential.

[0021] Furthermore, the specific method for setting the spatial boundary in the moving inertial frame S′ for finite element calculation is as follows:

[0022] When the coordinate space of the charged particle beam in the S system is less than a certain set threshold A, the boundary of the finite element calculation space in the S′ system needs to cover the beam distribution space in the S system transformed to the beam distribution space in the S′ system.

[0023] When the space of charged particle beams in the S system is greater than the set threshold A, the boundary of the finite element calculation space in the S′ system only covers the coordinate space of the adjacent beam collection in the S system transformed to the coordinate space in the S′ system. The electromagnetic field outside the simulation calculation area will be approximated as the electromagnetic field generated by a single charge.

[0024] Furthermore, if the charged particle beam is a discontinuous steady-state beam, and the changes in beam morphology, size, and relative velocity distribution are small (i.e., the change ratio is less than the set threshold), step (2) is calculated as follows:

[0025] Based on the change ratio of the beam size distribution and the electromagnetic field obtained by the previous decomposition method, the electromagnetic field is calculated according to the approximate formula; when the change ratio of the beam size and relative velocity distribution is large, that is, when the change ratio is greater than the set threshold, step (2) needs to be recalculated according to the decomposition method.

[0026] Furthermore, the calculation of the electromagnetic field based on the approximate formula specifically involves:

[0027] For rod-shaped beams, specifically:

[0028]

[0029] in E represents the ratio of beam radius, beam length, and energy at the previous moment to the approximate calculated moment, respectively. r E z These are the electric field intensities in the radial and axial directions, respectively;

[0030] The approximate formula for the beam is not the same for different morphologies and needs to be obtained by fitting data.

[0031] Furthermore, when the number of charged particles in the charged particle beam is large, macroparticles are used to replace real particles for numerical simulation calculations. Macroparticles refer to multiple charged particles combined into one charged particle.

[0032] Furthermore, if the charged particle beam is a continuous steady-state beam, the calculation is performed as follows:

[0033] (a) Obtain the initial state and external electromagnetic field information of each charged particle on a cross section of a charged particle beam, wherein the initial state includes position and velocity;

[0034] (b) Starting from the initial state of the particle, the position and velocity of the charged particle at the next time step are calculated based on the external electromagnetic field and the space charge field generated by the beam calculated in (c). This process is repeated until the beam moves to the required time or position.

[0035] (c) Based on the beam current, charge particles are uniformly placed on the particle trajectory over time. Their velocity is the velocity of the particle at this position calculated in step (b). Then, the space charge field generated by the beam is calculated based on the position and velocity of all charge particles.

[0036] (d) Repeat steps (b) and (c) until the particle trajectory and the space charge field converge.

[0037] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0038] 1. The present invention has wide applicability and can be used to simulate beam transmission in scenarios with large differences in particle velocity distribution, such as large energy dissipation, large divergence angle, or non-linear transmission. It is applicable to both unsteady and steady beams.

[0039] 2. Compared to current beam simulation software that uses a single inertial frame to solve the Poisson equation for all charged particles in a single inertial frame to calculate the space charge field, the present invention solves the space charge field by converting different particles to different inertial frames, which can effectively solve the influence of the retardation potential and achieve high calculation accuracy.

[0040] 3. The present invention has strong practicality and can be effectively applied to the design of various applications of particle accelerators. Better calculation accuracy can speed up the efficiency of the commissioning process. Attached Figure Description

[0041] Figure 1 is a flowchart of the method for dedispersion of charged particle beams in an interfering magnetic field environment based on electrode plates;

[0042] Figure 2 is a schematic diagram showing the relationship between the laboratory inertial frame S and a certain moving inertial frame S′;

[0043] Figure 3 shows the velocity of the S′ system relative to the S system as u = 2.985 × 10⁻⁶. 8 A schematic diagram showing the range of particle velocities in the S-frame corresponding to a relativistic factor γ ≤ 1.1 at m / s;

[0044] Figure 4 is a schematic diagram of a beam segmentation method for beams with electron energy spread between 1 and 8 MeV and unidirectional divergence angle in the range of -0.1 to 0.1 rad. Detailed Implementation

[0045] As shown in Figure 1, this invention proposes a simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam in a non-linear propagation scenario. The specific steps are as follows:

[0046] Step 1. Obtain the initial state of each charged particle in the charged particle beam and the information of the external electromagnetic field, including magnetic induction intensity, through testing or simulation calculations. and electric field strength

[0047] The initial state includes the initial position (x) i ,y i ,z i ) and initial velocity (v xi ,vyi ,v zi )

[0048] In particular, when the number of charged particles in the charged particle beam is large, macroparticles are used as a substitute, which refers to merging multiple charged particles into one charged particle.

[0049] Step 2. Calculate the electromagnetic field generated by the beam based on the position and velocity of the charged particles. Specifically, the calculation is performed using the decomposition method as follows:

[0050] (2.1) The particles in the laboratory inertial frame S are arranged according to their velocities (v... xi ,v yi ,v zi The particles are divided into multiple sets, and a suitable inertial frame S′ is obtained for each set (the relationship between the S′ frame and the S frame is shown in Figure 2). Since it is difficult to convert all particles to the same inertial frame when the divergence angle or energy dispersion is large, or when the beam is not propagated in a straight line, the velocity of all particles in the inertial frame is relatively small. Therefore, it is necessary to divide the particles into different sets.

[0051] The principle for dividing particles into multiple sets is that the velocity vectors of particles within a single set are close; the closeness refers to the distribution of particles in a continuous region, such as being homeomorphic to a sphere.

[0052] The selection principle for the inertial frame S′ is: the maximum velocity of the particle ensemble in the inertial frame S′ should be as small as possible. "As small as possible" can be achieved by setting a certain threshold; if the velocity is less than this threshold, it is considered to meet the requirement of being as small as possible.

[0053] This is because if the velocities of each particle in the moving inertial frame S′ are relatively small, the field generated by the particle collection in that frame can be approximated as an electrostatic field (without a magnetic field). Therefore, solving the d'Alembert equation can be simplified to solving the Poisson equation.

[0054] For example, consider a stationary inertial frame S′ relative to a 5 MeV electron moving along the z-axis. That is, S′ moves along the z-axis relative to the laboratory inertial frame S with a velocity of u = 2.985 × 10⁻⁶. 8 m / s, if the relativistic factor is required that all particles in the set are in the S′ system. (The electric field distortion and magnetic field generated by uniformly moving charges are positively correlated with γ), then the particle velocity within this range is within the range of the curve shown in Figure 3, where v r Indicates the particle in the S system Therefore, a lattice of motion velocity values ​​can be selected based on computing resources and accuracy requirements, and the particle set can be divided based on the lattice.

[0055] When the beam size is large, it is also possible to further divide it appropriately according to the position, which can reduce the computational space of the model and make the time difference after the transformation to the S′ system during the Lorentz transformation smaller.

[0056] The following example illustrates a two-dimensional beam distribution (with a third-dimensional velocity of 0), as shown in Figure 4. For a beam with electron energy spread between 1 and 8 MeV and a unidirectional divergence angle between -0.1 and 0.1 rad, the division shown in Figure 4 is used. The intervals separated by blue lines represent particle ensembles, and the red dots represent the adapted inertial frames within those intervals. Under this division, the maximum relativistic factor of each particle ensemble under its adapted inertial frame does not exceed 1.1. For a three-dimensional distribution, a three-dimensional region division is required.

[0057] (2.2) Through the Lorentz transformation, the particles in a certain set are transferred to their suitable inertial frame S′. Since particles that are simultaneous in frame S are no longer simultaneous in frame S′, when the acceleration and time difference are small, each particle is regarded as moving at a uniform speed and treated as being at the same moment in frame S′. The electric field generated by these particles in S′ is calculated by solving the Poisson equation using the finite element method or by calculating the Green's function using FFT to obtain the electric potential, and then obtaining the electric field by calculating the gradient of the electric potential.

[0058] The method for setting the spatial boundary of finite element calculations in the moving inertial frame S′ is as follows: when the coordinate space distribution of charged particle beams in the S frame is small (less than a certain set threshold A), the finite element calculation space boundary under the S′ frame needs to cover the beam distribution space in the S frame transformed to the beam distribution space under the S′ frame; when the spatial distribution of charged particle beams in the S frame is large (greater than the set threshold A), the finite element calculation space boundary under the S′ frame can only cover the coordinate space of the adjacent beam collection in the S frame (the space centered on the centroid of the beam collection and with the threshold A as its size) transformed to the coordinate space under the S′ frame. Electromagnetic fields at a greater distance (beyond the simulation calculation area) can be approximated as electromagnetic fields generated by a single macrocharge.

[0059] (2.3) The electric field calculated in the S′ system is transformed by the Lorentz transformation of the field to obtain the electromagnetic field generated by the particles in the laboratory inertial frame S. The electric field that is concurrent in the S′ system is not concurrent at different positions in the S system. By considering the electric field in the S′ system as invariant with time for a short period of time, the electromagnetic field that is concurrent in the S system can be obtained.

[0060] (2.4) Perform the above steps (2.2) and (2.3) on the particles of each set respectively, and then perform vector superposition of the electromagnetic fields generated by the particles of all sets in the S system to obtain the electromagnetic field generated by the entire charged particle beam in the laboratory inertial frame.

[0061] Step 3: Vector superposition of the external electromagnetic field and the electromagnetic field generated by the calculated beam, and calculate the position and velocity of each macroparticle in the next time step according to special relativistic dynamics.

[0062] Step 4: Repeat steps 2 and 3 until the beam has moved to the desired time or position.

[0063] Furthermore, if the charged particle beam is a discontinuous steady-state beam, and the changes in beam morphology, size, and relative velocity distribution are small (i.e., the change ratio is less than the set threshold), step (2) is calculated as follows: based on the change ratio of beam size distribution and the electromagnetic field obtained by the previous decomposition method, the electromagnetic field is calculated according to the approximate formula; when the changes in beam size and relative velocity distribution are large (i.e., the change ratio is greater than the set threshold), step (2) needs to be recalculated according to the decomposition method.

[0064] The calculation of the electromagnetic field based on the approximate formula is as follows:

[0065] For rod-shaped beams, specifically:

[0066]

[0067]

[0068] in E represents the ratio of beam radius, beam length, and energy at the previous moment to the approximate calculated moment, respectively. r E z These represent the electric field strengths in the radial and axial directions, respectively.

[0069] If the charged particle beam is a continuous steady-state beam, then the calculation is performed according to the steady-state solution method, specifically:

[0070] (a) Obtain the initial state and external electromagnetic field information of each charged particle on a cross section of a charged particle beam, wherein the initial state includes position and velocity;

[0071] (b) Starting from the initial state of the particle, calculate the position and velocity of the charged particle at the next time step based on the external electromagnetic field and the space charge field generated by the beam calculated in step (c) (set to 0 for the first calculation), and repeat this process until the beam moves to the required time or position.

[0072] (c) Based on the beam current, charge particles are uniformly placed on the particle trajectory over time. Their velocity is the velocity of the particle at this position calculated in step (b). Then, the space charge field generated by the beam is calculated based on the position and velocity of all charge particles (the calculation method is the same as in step 2).

[0073] (d) Repeat steps (b) and (c) until both the particle trajectory and the space charge field converge. (That is, the difference between the final position of the particle in a certain calculation result and the previous calculation result is less than a certain threshold, and the difference between the space charge field generated by the beam and the result obtained in the previous calculation is less than a certain threshold).

[0074] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A simulation method for the space charge effect of a high-energy, large-divergence-angle charged particle beam, characterized in that: include: (1) Obtain the initial state and external electromagnetic field information of each charged particle in the charged particle beam, wherein the initial state includes position and velocity; (2) Calculate the space charge field generated by the beam based on the position and velocity of the charged particles; (3) Calculate the position and velocity of the charged particles at the next time step based on the external electromagnetic field and the space charge field generated by the beam; (4) Repeat steps (2) and (3) until the beam moves to the required time or position.

2. The simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam according to claim 1, characterized in that: Step (2) calculates the space charge field generated by the beam based on the position and velocity of the charged particles. Specifically, it is calculated by decomposition: (2.1) Divide the charged particles of the charged particle beam in the laboratory inertial frame S into multiple sets; (2.2) Transform the charged particles in a certain set A into a certain moving inertial frame S′ through Lorentz transformation, and calculate the electromagnetic field generated by the charged particles in set A in the moving inertial frame S′; the charged particles in multiple sets are transformed into different inertial frames respectively, and the generated electromagnetic fields are calculated respectively; (2.3) Transform the electromagnetic field generated by the charged particles in set A into the electromagnetic field generated by the charged particles in set A in the laboratory inertial frame through the Lorentz transformation of the field; the electromagnetic fields generated by the charged particles in the remaining sets are transformed in the same way to obtain the electromagnetic fields generated by the charged particles in all sets; (2.4) Vector superposition of the electromagnetic fields generated by the charged particles in all sets is used to obtain the electromagnetic field generated by the entire charged particle beam in the laboratory inertial frame.

3. The simulation method for the space charge effect of a high-energy, large-divergence-angle charged particle beam according to claim 2, characterized in that: The principle for dividing charged particles in a charged particle beam into multiple sets is that the velocity vectors of charged particles within a single set are close; the principle for selecting a motion inertial frame is that the maximum velocity of the particle set in that inertial frame is as small as possible.

4. The simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam according to claim 2, characterized in that: The electromagnetic field generated by a charged particle in a moving inertial frame S′ is approximated as follows: the electric potential is obtained by solving the Poisson equation using the finite element method or by calculating the Green's function using FFT, and then the electromagnetic field is obtained from the electric potential.

5. The simulation method for the space charge effect of a high-energy, large-divergence-angle charged particle beam according to claim 4, characterized in that: The specific method for setting the spatial boundary of finite element calculations in the moving inertial frame S′ is as follows: when the coordinate space of the charged particle beam in the S frame is less than a certain set threshold A, the finite element calculation space boundary under the S′ frame needs to cover the beam distribution space in the S frame transformed to the beam distribution space under the S′ frame; when the charged particle beam space in the S frame is greater than the set threshold A, the finite element calculation space boundary under the S′ frame only covers the coordinate space of the adjacent beam collection in the S frame transformed to the coordinate space under the S′ frame, and the electromagnetic field outside the simulation calculation area is approximated as the electromagnetic field generated by a single charge.

6. The simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam according to claim 2, characterized in that: If the charged particle beam is a discontinuous steady-state beam, and the changes in beam morphology, size, and relative velocity distribution are small (i.e., the change ratio is less than the set threshold), step (2) is calculated as follows: based on the change ratio of beam size distribution and the electromagnetic field obtained by the previous decomposition method, the electromagnetic field is calculated according to the approximate formula; when the changes in beam size and relative velocity distribution are large (i.e., the change ratio is greater than the set threshold), step (2) needs to be recalculated according to the decomposition method.

7. The simulation method for the space charge effect of a high-energy, large-divergence-angle charged particle beam according to claim 6, characterized in that: The calculation of the electromagnetic field based on the approximate formula is specifically as follows: For a rod-shaped beam, specifically: in E represents the ratio of beam radius, beam length, and energy at the previous moment to the approximate calculated moment, respectively. r E z These represent the electric field intensities in the radial and axial directions, respectively. The approximate formulas for the beam current are not the same for different morphologies and need to be obtained by fitting data.

8. The simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam according to claim 1, characterized in that: When the number of charged particles in a charged particle beam is large, macroparticles are used to replace real particles for numerical simulation calculations. Macroparticles refer to multiple charged particles that are combined into one charged particle.

9. The simulation method for the space charge effect of a high-energy, high-divergence-angle charged particle beam according to claim 2, characterized in that: If the charged particle beam is a continuous steady-state beam, the calculation is performed as follows: (a) Obtain the initial state and external electromagnetic field information of each charged particle on a beam spot cross section of the charged particle beam, wherein the initial state includes position and velocity; (b) Starting from the initial state of the particles, calculate the position and velocity of the charged particles at the next time step based on the external electromagnetic field and the space charge field generated by the beam calculated in (c), and repeat this process until the beam moves to the required time or position; (c) According to the beam current intensity, uniformly place charged particles on the particle trajectory over time, and their velocity is the velocity of the particle at this position calculated in step (b). Then, calculate the space charge field generated by the beam based on the position and velocity of all charged particles; (d) Repeat steps (b) and (c) until the particle trajectory and the space charge field converge.

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