Three-dimensional motion trail analysis method for high-energy electrons in tight focusing circular polarization laser field
By constructing a vector potential model and deriving the Lorentz equation, calculating the electron velocity component and performing numerical simulation, the problem of low prediction accuracy of high-energy electron three-dimensional motion trajectory in the tight-focused circular polarization laser field is solved, and the precise control of electron motion is achieved and efficient prediction.
Patent Information
- Application Number
- CN202411585435.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-08
- Publication Date
- 2025-02-18
AI Technical Summary
The prior art has low prediction accuracy of the three-dimensional motion trajectory of high-energy electrons in the tightly focused circular polarization laser field, and limited regulation methods, making it difficult to achieve accurate manipulation of electronic motion.
By constructing a vector potential model of femtosecond focused Gaussian laser pulse, the Lorentz equation describing the motion of electrons in the laser field is derived, the velocity component of the electron is calculated, and the three-dimensional motion trajectory of the electron is obtained through numerical simulation.
It significantly improves the accuracy of prediction of high-energy electronic motion trajectory, realizes precise control of electron motion in three-dimensional space, and supports the development of laser accelerators and high-energy physics experiments.
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Abstract
Description
Technical Field
[0001] The invention relates to a three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field, and in particular to a three-dimensional motion trajectory analysis method of high-energy electrons in a tightly focused circularly polarized laser field. Background Art
[0002] At present, the motion of high-energy electrons in tightly focused circularly polarized laser fields is mainly studied through experimental observations and theoretical simulations. When electrons are accelerated to near the speed of light in a strong laser field, their motion follows relativistic mechanics, which is called relativistic electron motion. By detecting relativistic electron motion, scientists can accurately understand the dynamic characteristics of high-speed electrons, such as trajectory, velocity, acceleration, energy, and their interaction with electromagnetic fields. This is of great significance to the development of new particle accelerators, the exploration of laser-matter interactions, and the advancement of high-energy physics research.
[0003] Although linearly polarized laser fields have been used to study electron motion, their electron trajectories are usually confined to a two-dimensional plane, making it difficult to fully describe and control electron motion in three-dimensional space. In order to further study the three-dimensional motion laws of electrons, tightly focused circularly polarized laser fields were proposed. This field has good symmetry and stable phase relationships, and can more effectively control the three-dimensional trajectory of electrons. However, existing technologies still face challenges in this field, such as low three-dimensional simulation accuracy and limited control methods.
[0004] Therefore, if the deficiencies in current technology can be further addressed, precise control of high-energy electron motion can be achieved. This will provide strong support for the development of laser accelerators, laser fusion research, and high-energy physics experiments, and promote the development of strong field physics. Summary of the invention
[0005] Technical problem to be solved by the present invention: The purpose of the present invention is to solve the deficiencies in the prior art and to provide a three-dimensional motion trajectory analysis method that can effectively predict the motion trajectory of electrons in a tightly focused circularly polarized laser field and improve the accuracy of motion trajectory prediction, as well as an electronic device that can call a computer program stored in a memory to execute the three-dimensional motion trajectory analysis method.
[0006] The technical solution of the present invention: A method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field of the present invention comprises the following steps:
[0007] S1. Determination of vector potential model: Based on the amplitude parameters, phase parameters, focal diameter, pulse width and laser pulse width of relativistic electrons, a vector potential model of femtosecond tightly focused Gaussian laser pulses is constructed to describe the electric field and magnetic field distribution of the laser pulse;
[0008] S2. Determine the equation of motion: Based on the vector potential model, derive the Lorentz equation describing the motion of charged particles in the electromagnetic field and the energy change of electrons in the laser field;
[0009] S3. determine the velocity components of the electron in the electromagnetic field, and further analyze the motion trajectory of the electron based on these velocity components;
[0010] S4. Trajectory simulation: Substitute the velocity components into the rectangular coordinate system to simulate the three-dimensional motion trajectory of the electron. Through numerical calculation, the motion path of the electron in the laser field is obtained.
[0011] Furthermore, in step S1, the amplitude parameter a0 is expressed as follows: The C0 value is 0.85×10 -9 , λ0 and I represent the length and wavelength of the laser, respectively;
[0012] The vector potential model of the femtosecond tightly focused Gaussian laser pulse is expressed as follows:
[0013]
[0014] Where a0 is the amplitude parameter, which characterizes the intensity of the laser pulse; is the phase parameter of the femtosecond tightly focused Gaussian laser pulse; C is the first intermediate parameter, C L is the second intermediate parameter; b0 is the focal diameter, L is the laser pulse width;
[0015] In the formula,
[0016] Where C0 is the chirp coefficient, is the initial phase of the laser pulse, which is related to the curvature of the tightly focused wavefront;
[0017] represents the z-coordinate radius of curvature where the wavefront intersects the beam axis, is the paleophase displacement related to R(z).
[0018] Furthermore, the components of the vector potential in the rectangular coordinate system are determined according to the vector potential model and are expressed as
[0019]
[0020] in a x 、a y 、a z Represent the components of the vector potential on the x, y, and z axes respectively;
[0021] The Lorentz equation is:
[0022] The energy equation is:
[0023] In the formula, is the normalized momentum, is the vector potential, is the speed, Y is the energy;
[0024] Velocity components of the differential equation:
[0025]
[0026] In the formula, u x ,u y ,u z are the electron velocity components of the x, y, and z axes respectively, a represents acceleration, It represents the acceleration increment, that is, taking the derivative of a in the x, y, and z directions respectively and then multiplying it by the unit vector in each direction respectively.
[0027] Furthermore, after obtaining the velocity component, the normalized radiation power per unit solid angle can be determined based on the velocity component and the radiation of the high-energy electron in a specific direction. Based on the distribution of the radiation power, the acceleration of the electron in the solid angle direction can be derived. By analyzing the changes in the radiation intensity and frequency of the electron in different directions, the trajectory of the electron can be further determined.
[0028] Furthermore, the radiation power per unit solid angle is:
[0029]
[0030] In the formula, the radiated power is normalized to e 2 W 2 / 4πc, given the delay time t of the electron; is the radiation direction of high energy electron emission, R0 is the distance from the origin to the observer; represents the position vector, Ω represents the solid angle, and P(t) represents the radiated power.
[0031] Furthermore, the electron position vector And the distance R0 from the origin to the observer is defined as follows:
[0032] Where R represents the distance between the electron in motion and the origin, This distance depends on the delay time of the electron and the distance from the origin to the observer.
[0033] Further, numerical simulation and verification: Use numerical simulation methods to verify the three-dimensional trajectory of electrons to ensure the accuracy and consistency of calculations
[0034] The present invention also discloses an electronic device, comprising: a processor and a memory, wherein the memory stores a computer program that can be called by the processor;
[0035] The processor executes the above-mentioned three-dimensional motion trajectory analysis method of high-energy electrons in a tightly focused circularly polarized laser field by calling the computer program stored in the memory.
[0036] The present invention also discloses a computer-readable storage medium, on which instructions are stored. When the instructions are executed on a computer, the computer executes the above-mentioned method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field. 。
[0037] The beneficial effects of the present invention compared with the prior art are as follows:
[0038] The present invention describes the relativistic oscillation of electrons and their full-space radiation by establishing a vector potential model of femtosecond tightly focused Gaussian laser pulses driven by the electromagnetic field generated by laser pulses. Based on this model, a method for determining the electron velocity component is proposed, which can effectively predict the motion trajectory of electrons. This method can obtain the emission spatial distribution of a single electron model and all the characteristics of its dynamics without relying on complex and high-cost experimental equipment, thereby significantly improving the accuracy of motion trajectory prediction.
[0039] 1. Construction and precise control of circularly polarized laser fields. This method relies on the generation and control of tightly focused circularly polarized laser fields. Circularly polarized light fields have unique symmetry and phase stability, which can provide a reliable control basis for the three-dimensional motion of electrons. By accurately setting and dynamically adjusting the intensity, frequency, focus point position and other parameters of the laser field, not only can the real-time correction of the electron motion trajectory be achieved, but it can also ensure that it meets expectations, thereby ensuring the precise control of the electron trajectory.
[0040] 2. Control and adaptability of electron motion in three-dimensional space. This method breaks through the limitation of traditional linear polarization laser field that restricts electron motion to a two-dimensional plane, and realizes precise motion control of high-energy electrons in three-dimensional space. By dynamically adjusting the phase and amplitude of the laser, it not only ensures the flexibility and controllability of the electron motion trajectory, but also meets different experimental needs and shows good adaptability, including diversified regulation of trajectory and motion mode under different experimental conditions.
[0041] 3. Simulation and calculation method of relativistic electron motion. In a high-energy laser field close to the speed of light, the relativistic motion effect of electrons is significant. Therefore, this method comprehensively considers the importance of relativistic mechanics in describing electron trajectories. Through a high-precision relativistic calculation model, the three-dimensional motion trajectory of electrons in a high-energy environment can be accurately simulated and verified to ensure that the calculation results are consistent with reality. This method provides important theoretical and technical support for the precise control of the motion trajectory of relativistic electrons. BRIEF DESCRIPTION OF THE DRAWINGS
[0042] Figure 1 is a three-dimensional motion trajectory diagram of the relativistic electron with amplitude parameter a0=3 in Example 1 of the present invention;
[0043] Figure 2 It is the three-dimensional motion trajectory of the relativistic electron with amplitude parameter a0=5 in Example 2 of the present invention. DETAILED DESCRIPTION
[0044] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. The embodiments are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention.
[0045] Example 1
[0046] Motion trajectory steps:
[0047] Determine the vector potential model: Use the amplitude parameter a0=3 of the relativistic electron to calculate the corresponding vector potential Including its components in the x, y, and z directions.
[0048] Build a phase parameter model: Use the phase parameter formula Get the phase φ of the laser pulse.
[0049] Compute the Lorentz force equation: Substitute the vector potential According to the Lorentz equation Determine the forces acting on the electron.
[0050] Solving for velocity components: via the energy equation and the Lorentz equation Solve for the velocity components u of the electron in the x, y, and z directions x ,u y ,u z .
[0051] Determine the radiation power: Calculate the radiation power P(t) of the electron in different directions and analyze its radiation intensity.
[0052] Derivation of three-dimensional motion trajectory: Combining the velocity component and the radiation power, the motion trajectory of the electron in three-dimensional space is derived, such as Figure 1shown.
[0053] Numerical simulation and verification: Use numerical simulation methods to verify the three-dimensional trajectory of electrons to ensure the accuracy and consistency of the calculations.
[0054] like Figure 1 As shown in the figure, in a circularly polarized laser field with a0=3, the three-dimensional motion trajectory of high-energy electrons exhibits complex spiral motion characteristics, and their trajectory is no longer limited to the two-dimensional plane, but undergoes significant acceleration and deceleration in three-dimensional space. Driven by the laser field, the electrons not only move along the spiral trajectory, but also drift in the direction of laser propagation.
[0055] Example 2
[0056] Motion trajectory steps:
[0057] Determine the vector potential model: Use the amplitude parameter a0=5 of the relativistic electron to calculate the corresponding vector potential Including its components in the x, y, and z directions.
[0058] Build a phase parameter model: Use the phase parameter formula Get the phase φ of the laser pulse.
[0059] Compute the Lorentz force equation: Substitute the vector potential According to the Lorentz equation Determine the forces acting on the electron.
[0060] Solving for velocity components: via the energy equation and the Lorentz equation Solve for the velocity components u of the electron in the x, y, and z directions x ,u y ,u z .
[0061] Determine the radiation power: Calculate the radiation power P(t) of the electron in different directions and analyze its radiation intensity.
[0062] Derivation of three-dimensional motion trajectory: Combining the velocity component and the radiation power, the motion trajectory of the electron in three-dimensional space is derived, such as Figure 2 shown.
[0063] Numerical simulation and verification: Use numerical simulation methods to verify the three-dimensional trajectory of electrons to ensure the accuracy and consistency of the calculations.
[0064] like Figure 2 As shown in the figure, when a0 = 5, the electron's motion trajectory changes from a regular symmetrical spiral structure to a complex three-dimensional spiral cone. The electron's deviation in the direction of laser propagation increases significantly, and the trajectory presents a more significant spiral amplitude and three-dimensional distribution.
[0065] Combination Figure 1 and Figure 2 It can be seen that with the increase of the amplitude parameter a0, the effect of the laser field on the electrons gradually evolves from a relatively simple drive to a significant nonlinear and relativistic effect drive, causing the electron motion trajectory to gradually change from a regular, symmetrical spiral motion to a more complex and dynamic three-dimensional spiral cone structure.
[0066] Compared with Example 1, the results of Example 2 demonstrate the dynamic adjustment capability of the electron trajectory in a high-intensity laser field, indicating the adaptability and stability of the method in dealing with different experimental requirements.
[0067] It can be seen from these two examples that as the amplitude parameter a0 increases, the effect of the laser field on the electron motion gradually evolves from simple linear drive to complex nonlinear relativistic effect drive. The electron trajectory in Example 1 is regular and symmetrical, indicating that under low amplitude parameter conditions, this method can accurately control the electron motion trajectory; while in Example 2, the electron motion presents a complex three-dimensional spiral cone structure, proving that under high amplitude parameter conditions, this method can also effectively adapt to and control more complex electron motion.
[0068] Example 3
[0069] An electronic device is used for simulating and analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field and performing data processing. The device can automatically perform the calculation and analysis process of the motion trajectory of high-energy electrons, and provide support for experimental research on the interaction between lasers and electrons. The electronic device includes a processor and a memory. The memory pre-stores a computer program for analyzing the three-dimensional motion trajectory of high-energy electrons, and the processor automatically executes a motion trajectory analysis method for electrons in a tightly focused circularly polarized laser field by calling the computer program.
[0070] Including functional modules of computer programs, the computer programs stored in the memory mainly include the following modules:
[0071] Laser field construction module: Generates a vector potential model of a tightly focused circularly polarized laser field based on the laser field parameters (such as amplitude parameter a0, frequency, focus point position, etc.) input by the user.
[0072] Motion equation solving module: Use the generated vector potential model to call the Lorentz equation and energy equation to calculate the velocity component u of the electron x ,u y ,u z .
[0073] 3D trajectory simulation module: simulates the 3D motion trajectory of electrons in the laser field according to the calculated velocity components. The program visualizes the motion trajectory under different amplitude parameter conditions, such as a0=3a_0=3a0=3 or a0=5a_0=5a0=5.
[0074] Trajectory data analysis module: Analyze the motion trajectory of electrons, record the shape, symmetry, offset and other characteristic data of the motion trajectory, and provide a reference for studying the influence of nonlinear and relativistic effects on electron motion.
[0075] Result storage and output module: stores the simulation results and analysis data of the electron motion trajectory in the memory, and generates graphics and reports for users to view.
[0076] Execution Process
[0077] When running a program on a device, the processor performs the following steps in sequence:
[0078] Input laser field parameters: The user inputs relevant parameters of the laser field through the device interface, such as amplitude parameter a0a_0a0, pulse width, focus point position, etc.
[0079] Calling modules for calculation: The processor calls the laser field construction module, the motion equation solving module and the three-dimensional trajectory simulation module in sequence to analyze the three-dimensional motion of electrons.
[0080] Output results: The device interface displays the three-dimensional trajectory of the electrons and provides numerical data (such as trajectory deviation, spiral amplitude, etc.) for user analysis. Users can also export the results as a report for further study.
[0081] For example, when the amplitude parameter of the laser field is set to a0 = 5, the processor automatically builds an intensity-enhanced laser field model. The motion equation solving module calculates the nonlinear spiral motion trajectory of electrons in three-dimensional space based on the model and presents a complex spiral cone structure in the trajectory simulation module.
[0082] The results show that under high-amplitude parameter conditions, the device can effectively capture the nonlinear and relativistic effects of electron motion. By using this device, experimenters can quickly analyze and predict the trajectory of electron motion under different laser parameters without manual calculations or complex numerical simulations, which improves research efficiency. The device can accurately control and display the three-dimensional motion trajectory of electrons and generate detailed analysis reports, which is helpful for studying the nonlinear characteristics and relativistic effects in the interaction between lasers and electrons. By using this device, experimenters can quickly analyze and predict the trajectory of electron motion under different laser parameters without manual calculations or complex numerical simulations, which improves research efficiency. The device can accurately control and display the three-dimensional motion trajectory of electrons and generate detailed analysis reports, which is helpful for studying the nonlinear characteristics and relativistic effects in the interaction between lasers and electrons.
[0083] Example 4
[0084] A computer-readable storage medium stores instructions for implementing a method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field. When these instructions are executed on a computer, the computer can perform simulation and analysis of the three-dimensional motion trajectory of high-energy electrons, thereby achieving precise motion trajectory control and data output.
[0085] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above specific embodiments. The above specific embodiments and the description in the specification are only for further illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of the present invention to be protected is defined by the claims and their equivalents.
Claims
1. A method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field, characterized in that: The steps include: S1. Determination of vector potential model: Based on the amplitude parameters, phase parameters, focal diameter, pulse width and laser pulse width of relativistic electrons, a vector potential model of femtosecond tightly focused Gaussian laser pulses is constructed to describe the electric field and magnetic field distribution of the laser pulse; S2. Determine the equation of motion: Based on the vector potential model, derive the Lorentz equation describing the motion of charged particles in the electromagnetic field and the energy change of electrons in the laser field; S3. determine the velocity components of the electron in the electromagnetic field, and further analyze the motion trajectory of the electron based on these velocity components; S4. Trajectory simulation: Substitute the velocity components into the rectangular coordinate system to simulate the three-dimensional motion trajectory of the electron. Through numerical calculation, the motion path of the electron in the laser field is obtained.
2. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 1, characterized in that: In step S1, the amplitude parameter a0 is expressed as follows: The C0 value is 0.85×10 -9 , λ0 and I represent the length and wavelength of the laser, respectively; The vector potential model of the femtosecond tightly focused Gaussian laser pulse is expressed as follows: Where a0 is the amplitude parameter, which characterizes the intensity of the laser pulse; is the phase parameter of the femtosecond tightly focused Gaussian laser pulse; C is the first intermediate parameter, C L is the second intermediate parameter; b0 is the focal diameter, L is the laser pulse width; In the formula, Where C0 is the chirp coefficient, is the initial phase of the laser pulse, which is related to the curvature of the tightly focused wavefront; represents the z-coordinate radius of curvature where the wavefront intersects the beam axis, is the paleophase displacement related to R(z).
3. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 2, characterized in that: According to the vector potential model, the components of the vector potential in the rectangular coordinate system are determined and expressed as in a x 、a y 、a z Represent the components of the vector potential on the x, y, and z axes respectively; The Lorentz equation is: The energy equation is: In the formula, is the normalized momentum, is the vector potential, is the speed, Y is the energy; Velocity components of the differential equation: In the formula, u x ,u y ,u z are the electron velocity components of the x, y, and z axes respectively, a represents acceleration, It represents the acceleration increment, that is, after taking the derivative of a in the x, y, and z directions respectively, it is multiplied by the unit vector in each direction respectively.
4. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 3, characterized in that: After obtaining the velocity component, the normalized radiation power per unit solid angle can be determined based on the velocity component and the radiation of the high-energy electrons in a specific direction.
5. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 4, characterized in that: Based on the distribution of radiation power, the acceleration of electrons in the solid angle direction can be deduced. By analyzing the changes in radiation intensity and frequency of electrons in different directions, the movement trajectory of electrons can be further determined.
6. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 5, characterized in that: The radiant power per unit solid angle is: In the formula, the radiated power is normalized to e 2 W 2 / 4πc, given the delay time t of the electron; is the radiation direction of high-energy electron emission, R0 is the distance from the origin to the observer; represents the position vector, Ω represents the solid angle, and P(t) represents the radiated power.
7. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 6, characterized in that: The electron's position vector And the distance R0 from the origin to the observer is defined as follows: Where R represents the distance between the electron in motion and the origin, This distance depends on the delay time of the electron and the distance from the origin to the observer.
8. The method for analyzing the three-dimensional motion trajectory of high-energy electrons in a tightly focused circularly polarized laser field according to claim 5, characterized in that: It also includes numerical simulation and verification: using numerical simulation methods to verify the three-dimensional trajectory of electrons to ensure the accuracy and consistency of the calculations.
9. An electronic device, characterized in that: include: A processor and a memory, wherein the memory stores a computer program that can be called by the processor; The processor executes the three-dimensional motion trajectory analysis method of high-energy electrons in a tightly focused circularly polarized laser field according to any one of claims 1 to 8 by calling the computer program stored in the memory.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, and when the instructions are executed on a computer, the computer executes the three-dimensional motion trajectory analysis method of high-energy electrons in a tightly focused circularly polarized laser field as described in any one of claims 1 to 8.