A method, apparatus and storage medium for measuring Doppler frequency shift using a low-energy ion beam

Abstract

This invention discloses a method, device, and storage medium for measuring the Doppler frequency shift of a low-energy ion beam, belonging to the field of ion beam energy analysis and precision spectral measurement technology. It solves for the electromagnetic field environment of the ion beam line system using finite element numerical simulation. The invention treats the overlapping region of the electron and atomic beams as an equivalent cylinder. By iteratively optimizing the equivalent axial spatial width of the overlapping region, an equivalent axial spatial width conforming to the actual kinetic energy distribution is obtained, thus yielding the final ion distribution space. Finally, the ion velocity distribution is obtained from the final ion distribution space, and the Doppler frequency shift of the ion beam is derived from the ion velocity distribution. This invention uses finite element numerical simulation to uniformly calculate the electromagnetic field distribution and trajectory of the ion beam, enabling the calculation of the ion velocity of each ion and the Doppler frequency shift measured in any directional spectrum.

Description

Technical Field

[0001] This invention belongs to the field of ion beam energy analysis and precision spectral measurement technology, specifically relating to a Doppler frequency shift measurement method, equipment and storage medium for low-energy ion beams. Background Technology

[0002] Ion beam spectroscopy is widely used in atomic and molecular physics, precision spectral measurement, measurement of fundamental physical constants, and nuclear physics. During the spectral measurement process, ions move at a certain speed under the influence of an electromagnetic field. Due to the Doppler effect, a Doppler frequency shift occurs, which directly affects the accuracy of the spectral measurement results.

[0003] Currently, the main methods for assessing Doppler shift are the electromagnetic field method and the laser-ion beam collinear method. The electromagnetic field method uses instruments such as deceleration field energy analyzers, which can only acquire the component of ion velocity in the instrument-defined direction (usually along the beam axis). This single-degree-of-freedom measurement means that it can only assess the first-order Doppler shift in that specific direction. These instruments include detectors such as Faraday cups and microchannel plate detectors, which require physical ion interception, resulting in significant beam loss. The laser-ion beam collinear method also only allows for single-degree-of-freedom measurement, and the alignment of the laser beam and ion beam is difficult, requiring measurement techniques such as optical frequency comb locking, heterodyne interferometers, or saturated absorption spectroscopy, resulting in extremely high system complexity and cost.

[0004] Numerical simulation-based methods naturally record the position coordinates and velocity vectors of each ion, allowing the velocity vectors to be projected into any direction to analyze the Doppler frequency shift in that direction. Numerical simulation is a zero-loss measurement method, which not only protects the precious beam but also allows for simultaneous parameter analysis across multiple virtual cross-sections. Furthermore, numerical simulation does not require real optical excitation and frequency references; it directly extracts ion velocity information through calculation, avoiding technical difficulties and simulating the Doppler frequency shift at any transition wavelength. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned problems in the prior art by providing a method, device, and storage medium for measuring Doppler frequency shift using a low-energy ion beam.

[0006] The above-mentioned objectives of the present invention are achieved by the following technical means: A method for measuring the Doppler frequency shift of a low-energy ion beam includes the following steps: Step 1: Establish a three-dimensional geometric model of the ion beam line system and establish a coordinate system, wherein the coordinate system is based on the ion beam flight direction. The positive axis direction, with the fluorescence acquisition direction as the reference direction. Positive axis direction The positive direction of the axis is determined by the right-hand rule.

[0007] Step 2: Import the three-dimensional geometric model of the ion beamline system into the finite element solver, and calculate the electromagnetic field distribution of the ion beamline system using the finite element solver.

[0008] Step 3: Based on the electromagnetic field distribution of the ion beam system, set the initial distribution space of the ions; sample the initial state of the ions using Monte Carlo sampling, and simulate and calculate the trajectory of the ion beam using a finite element solver.

[0009] Step 4: Obtain the actual energy of the ion beam through the deceleration field energy analyzer of the ion beam line system. Axial kinetic energy distribution.

[0010] The position of the deceleration field energy analyzer detecting ion velocities in the 3D geometric model is plotted perpendicular to... The first cross section along the axial direction is used to extract the ion velocity distribution frozen on the first cross section based on the ion beam's trajectory, and the simulation of the ion beam is obtained based on the ion velocity distribution on the first cross section. Axial kinetic energy distribution.

[0011] Judgment Simulation Shaft kinetic energy distribution and actual Check if the axial kinetic energy distribution is the same; if not, return to step 3, reset the initial ion distribution space, and repeat steps 3 and 4; until the simulation is complete. Shaft kinetic energy distribution and actual The axial kinetic energy distribution is the same, resulting in the final ion distribution space.

[0012] Step 5: Based on the final ion distribution space, calculate the ion trajectory using the simulation method from Step 3; plot the trajectory perpendicular to the spectral measurement area. The second cross section along the axial direction is used to extract the ion velocity distribution frozen on the second cross section; the Doppler frequency shift of the ion beam is calculated based on the ion velocity distribution.

[0013] As described above, simulating the trajectory of an ion beam using a finite element solver specifically includes the following steps: Step 3.1: Emit an electron beam, calculate the trajectory of the electron beam in the electromagnetic field based on the electromagnetic field distribution, and obtain the beam width of the electron beam based on the trajectory of the electron beam in the electromagnetic field.

[0014] Step 3.2: Set the initial ion distribution space. The initial ion distribution space is the overlapping region of the electron beam and the atomic beam. The overlapping region of the electron beam and the atomic beam is set to... The axis is an equivalent cylinder in the axial direction. The transverse diameter of the overlapping region of the electron beam and the atomic beam is set as the beam width of the electron beam in the ion generation region, and the initial value of the equivalent axial spatial width of the overlapping region of the electron beam and the atomic beam is set.

[0015] Step 3.3: Set the initial state of the ions. The initial state of the ions includes the ion release location, the initial velocity distribution of the ions, the ion mass, and the ion charge.

[0016] The ion release location is set by Monte Carlo sampling within the initial distribution space according to a uniform probability density; the initial ion velocity distribution is set by Monte Carlo sampling according to the Maxwell-Boltzmann velocity distribution corresponding to the source plasma temperature.

[0017] Step 3.4: Based on the electromagnetic field distribution, solve the Lorentz force equation of the ions in the electromagnetic field using a finite element solver to calculate the trajectory of the ion beam.

[0018] The reset of the initial distribution space of the ions is to reset the equivalent axial space width.

[0019] Simulation as described above Shaft kinetic energy distribution and the actual Whether the kinetic energy distribution of the shafts is the same can be determined by the following method: for simulation Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is fitted with Gaussian vectors. The difference between the means and the variance of the fitted Gaussian vectors is compared to see if they are within a preset range. If both the difference between the means and the variance of the fitted Gaussian vectors are within the preset range, the simulation is considered complete. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shafts is the same; if the difference between the means or the difference between the variances after Gaussian fitting is not within the preset range, then the simulation is judged to be flawed. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is not the same.

[0020] As described above, the Doppler frequency shift of the ion beam is calculated based on the ion velocity distribution using the following formula: ; In the formula, The spectral line shape of the ion fluorescence signal actually observed by the ion beamline system. The intrinsic spectral line shape of the ion. For the intrinsic spectral line shape Move the Doppler frequency shift on the frequency axis The resulting spectral line shape; Let be the ion velocity distribution function. For speed is Doppler frequency shift of ions within the range Let be a infinitesimal element representing velocity.

[0021] The Doppler frequency shift of the ion beam is and The center frequency difference.

[0022] The ion velocity distribution function is obtained by fitting the ion velocity distribution frozen on the second cross section using a Gaussian distribution. .

[0023] When the incident direction of the detection laser is First-order Doppler frequency shift in the positive axis direction and second-order Doppler frequency shift They are respectively: ; ; In the formula, ν is the intrinsic transition frequency of the ion. , as well as The ion velocity vectors are respectively in Axial direction, Axial direction and Components in the axial direction, It is the speed of light.

[0024] The Doppler frequency shift of the ion is: .

[0025] As described above, the ion beamline system includes a vacuum chamber and an ion source, an electrostatic lens assembly, a deceleration field energy analyzer, and a detection laser and fluorescence acquisition device located in the spectral measurement region, all disposed within the vacuum chamber. The ion source includes an electron gun, a magnetic field coil, a nuclear furnace, and extraction electrodes. The magnetic field coil includes a focusing coil and a deflection coil. The focusing coil is... The shaft is an axially energized solenoid, the focusing coil is positioned between the electron gun and the reactor, and the deflection coil includes... Axis Helmholtz coil and Axial Helmholtz coil; electrostatic lens assembly including sequentially along Multiple electrostatic lenses and drift tubes arranged in the axial direction and sharing a common central axis; the deceleration field energy analyzer includes three grids and a Faraday cup, with the three grids being the ground electrode, the deceleration electrode, and the secondary electron suppression electrode, respectively; the fluorescence acquisition device includes, in sequence, an optical lens group, a filter, and a photomultiplier tube.

[0026] The electron beam emitted by the electron gun passes through a energized solenoid, Axis Helmholtz coil and The beam flies above the nuclear reactor under the influence of the Helmholtz coil, collides with the atomic beam evaporated from the reactor, and ionizes to produce ions. The generated ions form an ion beam under the action of the extraction electrode. The ion beam is then focused by an electrostatic lens group, and then flies through a drift tube to the spectral measurement region. The fluorescence generated by the interaction between the laser and the ions passes through an optical lens group and a filter before being input into a photomultiplier tube. The photomultiplier tube collects the ion fluorescence signal. Finally, the ion beam continues to fly into the deceleration field energy analyzer installed on the vacuum cavity at the end of the flight.

[0027] The deceleration field energy analyzer detects the ion velocity at the location of the Faraday cup.

[0028] The electromagnetic field distribution described above is obtained through the following steps: Step 2.1: Set the material of the electron gun in the three-dimensional geometric model to oxygen-free copper, and set the lead-out electrodes, electrostatic lens group, grid, vacuum cavity and deceleration field energy analyzer to stainless steel. Set the relative permeability of the vacuum region within the vacuum chamber. and relative permittivity The relative permeability and relative permittivity are set according to the materials of the electron gun, lead-out electrode, electrostatic lens group, grid, vacuum cavity and deceleration field energy analyzer, respectively.

[0029] Step 2.2: Ground the vacuum chamber, set the number of turns and current of the magnetic field coil, and set the potential of the vacuum chamber, lead-out electrodes, electrostatic lens group, and grid in the deceleration field energy analyzer.

[0030] Step 2.3: Perform steady-state solution on the electromagnetic field to obtain the electromagnetic field distribution inside the ion beam line system. The electromagnetic field distribution includes the potential distribution, electrostatic field distribution and magnetic field distribution.

[0031] Step 2.3.1: Using the potentials of the lead-out electrodes, electrostatic lens group, grid in the deceleration field energy analyzer, and vacuum cavity as boundary conditions for the electrostatic field, calculate the potentials of the grid points on the spatial grid using a finite element solver to obtain the potential distribution, and further solve for the electrostatic field distribution.

[0032] Step 2.3.2: Given the current in the magnetic field coil, solve for the magnetic field distribution using a finite element solver.

[0033] A computer device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement step 5 of the Doppler frequency shift measurement method for a low-energy ion beam as described above.

[0034] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements step 5 of the Doppler frequency shift measurement method for a low-energy ion beam as described above.

[0035] A computer program product includes a computer program that, when executed by a processor, implements step 5 of a low-energy ion beam Doppler shift measurement method as described above.

[0036] Compared with the prior art, the present invention has the following advantages: (1) The present invention uses the finite element numerical simulation method to uniformly calculate the electromagnetic field distribution and motion trajectory of the ion beam. It can obtain the ion velocity of each ion and the Doppler frequency shift of the spectrum in any direction without additional hardware modification. This not only reduces the technical difficulty of system implementation and parameter debugging, but also reduces the investment and operating cost of experimental equipment. It is suitable for promotion and application in ion beam spectral measurement systems.

[0037] (2) In this invention, the overlapping region of the electron beam and the atomic beam is equivalent to a region with... The axis is a cylinder in the axial direction. By iteratively optimizing the equivalent axial space width of the overlapping region of the electron beam and the atomic beam, the equivalent axial space width that conforms to the actual kinetic energy distribution is obtained, thus obtaining the final ion distribution space. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the ion beamline system of the present invention; Figure 3 Simulated for the present invention The axial potential distribution and the trajectory of the ion beam (where the blue line represents the ion beam's trajectory). The potential distribution along the axis, with the red line representing the ion beam trajectory. The units for axial and radial positions are millimeters (mm), and the unit for potential is volts (V). Figure labels and corresponding component names: 1-Vacuum cavity; 2-Leading electrode; 3-First electrostatic lens; 4-Second electrostatic lens; 5-Third electrostatic lens; 6-Drift tube; 7-Electron beam; 8-Atomic beam; 9-Atomic furnace; 10-Ion beam. Detailed Implementation

[0039] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. The embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0040] Example 1: like Figure 1 As shown, a method for measuring the Doppler frequency shift of a low-energy ion beam includes the following steps: The ion beam system used in this embodiment for Doppler frequency shift measurement is as follows: Figure 2 As shown, the ion beamline system includes a vacuum chamber 1 and an ion source, an electrostatic lens group, a deceleration field energy analyzer, and a detection laser and fluorescence acquisition device located in the spectral measurement area, all disposed inside the vacuum chamber 1.

[0041] The ion source includes an electron gun, a magnetic field coil, a nuclear furnace 9, and an extraction electrode 2. The magnetic field coil includes a focusing coil and a deflection coil. The focusing coil uses a... The shaft is an axially energized solenoid, the focusing coil is positioned between the electron gun and the nuclear reactor 9, and the deflection coil includes... Axis Helmholtz coil and Axial Helmholtz coil, Axis Helmholtz coil and The central axes of the axial Helmholtz coils are respectively located at Axial direction and Axial direction, Axis Helmholtz coil and The axial Helmholtz coils are responsible for electron beam 7. Axial direction and Deflection in the axial direction.

[0042] The electrostatic lens group in this embodiment includes sequentially along... A first electrostatic lens 3, a second electrostatic lens 4, a third electrostatic lens 5, and a drift tube 6 are arranged in the axial direction and share a common central axis.

[0043] The deceleration field energy analyzer includes three grids and a Faraday cup. The three grids are ground, deceleration, and secondary electron suppression. The deceleration field energy analyzer applies a variable voltage to the deceleration electrode to analyze the energy of electrons or ions. The Faraday cup is located at the position where the deceleration field energy analyzer detects the ion velocity.

[0044] In this embodiment, the ion beam 10, the detection laser, and the fluorescence acquisition device are located in three orthogonal directions. The fluorescence acquisition device includes, in sequence, an optical lens group, a filter, and a photomultiplier tube.

[0045] The specific process of ion generation is as follows: the electron beam 7 emitted by the electron gun passes through an energized solenoid, Axis Helmholtz coil and The beam flies above the atomic furnace 9 under the action of the Helmholtz coil, collides with the atomic beam 8 evaporated from the atomic furnace 9, and ionizes to produce ions. The generated ions form an ion beam 10 under the action of the extraction electrode 2. The ion beam 10 is then focused by the electrostatic lens group, and then flies to the spectral measurement area through the drift tube 6. The fluorescence generated by the interaction between the detection laser and the ions passes through the optical lens group and the filter in sequence and is input into the photomultiplier tube. The photomultiplier tube collects the ion fluorescence signal. Finally, the ion beam 10 continues to fly and enters the deceleration field energy analyzer installed on the vacuum cavity 1 at the end of the flight.

[0046] In this embodiment, the drift tube 6 is a cylinder with a length of 125mm, an inner diameter of 13mm, and an outer diameter of 21mm. It is coaxial with the three single lenses and is 6mm away from the adjacent lenses. The deceleration field energy analyzer can be a finished product from Kimball Physics. In this embodiment, the distance between the deceleration field energy analyzer and the drift tube 6 is 140mm.

[0047] Step 1: Establish a three-dimensional geometric model of the ion beamline system and create a coordinate system and a spatial grid. The grid shape is tetrahedral.

[0048] In this embodiment, the ion generation location is defined as the origin of the coordinate system, and the flight direction of the ion beam 10 is defined as... The positive axis direction is defined as the fluorescence acquisition direction of the fluorescence acquisition device. Positive axis direction The positive direction of the axis is determined by the right-hand rule (i.e., satisfying the following conditions). ,in, for Axial direction vector, for Axial direction vector, for Axial direction vector, (For cross product), in this embodiment, the incident direction of the detection laser is along... Positive direction of the axis.

[0049] Step 2: Import the 3D geometric model of the ion beam system into the finite element solver, set the materials and corresponding material properties of the components in the 3D geometric model of the ion beam system; set the electrode potential and magnetic field coil current, and calculate the electromagnetic field distribution of the ion beam system through the finite element solver to provide the electromagnetic field environment for calculating the trajectory of the ion beam 10. This specifically includes the following steps: Step 2.1: Set the materials of the components in the three-dimensional geometric model: Set the material of the electron gun to oxygen-free copper, and set the lead-out electrode 2, electrostatic lens group, grid, vacuum cavity 1 and deceleration field energy analyzer to stainless steel. Material properties include relative permeability and relative permittivity, which determine the relative permeability of the vacuum region within the vacuum cavity. and relative permittivity The relative permeability and relative permittivity are set according to the materials of the electron gun, lead-out electrode 2, electrostatic lens group, grid, vacuum cavity 1 and deceleration field energy analyzer, respectively.

[0050] Step 2.2: Ground the vacuum chamber 1, set the number of turns and current of the magnetic field coil, and set the potential of the vacuum chamber 1, lead-out electrode 2, electrostatic lens group and grid.

[0051] Step 2.3: Perform steady-state solution for the electromagnetic field to obtain the electromagnetic field distribution inside the ion beam system. The electromagnetic field distribution includes the potential distribution, electrostatic field distribution, and magnetic field distribution. The electromagnetic field distribution serves as the background field for subsequent ion trajectory calculations. The potential distribution along the axis is as follows Figure 3 As shown, specifically: Step 2.3.1: The electrostatic field generated by lead-out electrode 2, electrostatic lens group, grid, and vacuum cavity 1 obeys Maxwell's equations: ,electric field constitutive relation ,in It is the electric displacement vector. Free charge density, For the Nabla operator, Represents vector field divergence, Dot product; For electric potential, and The vacuum permittivity and the relative permittivity of the material are respectively used. The potentials of the lead-out electrode 2, the electrostatic lens group, the grid and the vacuum cavity 1 in step 2.2 are used as the boundary conditions of the electrostatic field. At this time, the electrostatic field has a unique solution. The potential of the grid points on the spatial grid is calculated by the finite element solver to obtain the potential distribution, and the electrostatic field distribution is further solved.

[0052] Step 2.3.2: The magnetic field generated by the magnetic field coil also obeys Maxwell's equations: magnetic induction intensity constitutive relation ,in The magnetic field strength, For free current density, Represents the curl of a vector field. Cross product; The magnetic vector potential, and These are the vacuum permeability and the relative permeability of the material, respectively. Given the current in the magnetic field coil, the magnetic field distribution inside the ion beam line system is solved using a finite element solver.

[0053] Step 3: Based on the experimental or pre-simulated ion generation information and the electromagnetic field distribution of the ion beam system, set the initial ion distribution space; by sampling the initial state of the ions using Monte Carlo simulation, calculate the trajectory of the ion beam 10 using a finite element solver. This specifically includes the following steps: Information about ion generation includes the initial spatial distribution of ions and the initial state of ions.

[0054] Step 3.1: Emit electron beam 7 from electron gun, calculate the trajectory of electron beam 7 in electromagnetic field based on electromagnetic field distribution, and obtain the beam width of electron beam 7 based on the trajectory of electron beam 7 in electromagnetic field.

[0055] Step 3.2: Assuming that ions are generated by electrons colliding with and ionizing atoms, determine the initial distribution space of ions in the ion generation region (the ion generation region refers to the region where electrons collide with and ionize atoms to generate ions). The initial distribution space is determined by the overlapping region of electron beam 7 and atomic beam 8.

[0056] In this embodiment, the overlapping region of electron beam 7 and atomic beam 8 is considered as the overlapping region of two mutually perpendicular cylinders. Since the focusing diameter of electron beam 7 is much smaller than that of atomic beam 8, the overlapping region of electron beam 7 and atomic beam 8 is further considered as a region with... The axis is an equivalent cylinder in the axial direction, and can pass through the transverse (perpendicular to) of the equivalent cylinder. (Axis is transverse) Diameter and equivalent axis (ion beam 10 flight direction, parallel to) The volume of the overlapping region of electron beam 7 and atomic beam 8 is calculated using the axial direction spatial width, where the lateral diameter is set as the beam width of electron beam 7 in the ion generation region.

[0057] The beam width of electron beam 7 in the ion generation region can be measured experimentally: by experimentally measuring the bombardment position and beam width of electron beam 7, the lateral diameter of the initial distribution space can be determined; specifically, this can be achieved by placing a beam perpendicular to the electron beam 7 in the overlapping region of the electron beam 7 and the atomic beam 8. The electron beam 7 bombardment of the axial metal target will produce ablation marks on the metal target, and the transverse diameter is determined by the ablation location and area. Alternatively, the trajectory of electron beam 7 can be simulated to determine the location and extent of the ionization region that collides with atomic beam 8, thereby determining the lateral diameter of the initial distribution space.

[0058] The actual atomic beam 8 collides with the electron beam 7, ionizing and producing ions at any point in space. Ion generation rate per unit volume and per unit time It is determined by the following formula: (1); In the formula, The local number density of atomic beam 8; The local current density of electron beam 7 ( (Amperes per square meter) It is the fundamental charge; For electron energy The reaction cross section of the electron collision ionization of the atom.

[0059] As can be seen from formula (1), ions will be generated in the overlapping region of electron beam 7 and atomic beam 8. That is, the volume of the initial distribution space and the volume of the overlapping region of electron beam 7 and atomic beam 8 are equal. However, the ion generation rate at different positions in this region is different, which is reflected in the initial value setting of the simulation. That is, the ion density at different positions in the initial distribution space is different. However, since this density distribution is difficult to determine and the width of atomic beam 8 is difficult to determine, this embodiment defines an equivalent axial space width and sets the ions in the initial distribution space to be uniformly distributed. By setting the initial value of the equivalent axial space width, and then optimizing the equivalent axial space width through the loop of steps 3 and 4, the equivalent axial space width is finally determined, and the overlapping region of electron beam 7 and atomic beam 8 is finally obtained, thereby obtaining the initial distribution space of ions, that is, the ion distribution space.

[0060] Step 3.3: Set the initial state of the ions. The initial state of the ions includes the ion release location, the initial velocity distribution of the ions (usually the thermal distribution), the ion mass, and the ion charge. The ion release location is set by Monte Carlo sampling with uniform probability density within the initial distribution space; the initial ion velocity is set by Monte Carlo sampling based on the Maxwell-Boltzmann velocity distribution corresponding to the source plasma temperature.

[0061] Step 3.4: Based on the electromagnetic field distribution, solve the Lorentz force equation of the ions in the electromagnetic field using a finite element method (FEM) to calculate the trajectory of the ion beam 10 and the variation of ion velocity with time and space. The trajectory of the ion beam 10 is as follows: Figure 3 As shown.

[0062] Step 4: Obtain the actual energy of ion beam 10 through the deceleration field energy analyzer of the ion beam line system. Axial kinetic energy distribution; the location of the ion velocity probe in the deceleration field energy analyzer in the three-dimensional geometric model is plotted perpendicular to the axis. The first cross section along the axial direction is used to extract the ion velocity distribution frozen on the first cross section based on the motion trajectory of the ion beam 10, and the simulation of the ion beam 10 is obtained based on the ion velocity distribution on the first cross section. Axial kinetic energy distribution.

[0063] Judgment Simulation Shaft kinetic energy distribution and actual Check if the axial kinetic energy distribution is the same; if not, return to step 3, reset the initial ion distribution space, and repeat steps 3 and 4; until the simulation is complete. Shaft kinetic energy distribution and actual The axial kinetic energy distribution is the same, resulting in the final ion distribution space.

[0064] This embodiment simulates... Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is fitted with Gaussian vectors. The difference between the means and the variance of the fitted Gaussian vectors is compared to see if they are within a preset range. If both the difference between the means and the variance of the fitted Gaussian vectors are within the preset range, the simulation is considered complete. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shafts is the same; if the difference between the means or the difference between the variances after Gaussian fitting is not within the preset range, then the simulation is judged to be flawed. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is not the same.

[0065] Step 5: Based on the final ion distribution space, calculate the ion trajectory using the simulation method from Step 3; plot the trajectory perpendicular to the spectral measurement area. The second cross section along the axial direction is used to extract the ion velocity distribution frozen on the second cross section; the Doppler frequency shift of the ion beam 10 is calculated based on the ion velocity distribution; the specific process includes the following: A schematic diagram of the interaction between a laser and ions, showing the transition frequencies of ions after a Doppler shift. for: (2); Among them, the ratio It is the ion rate with the speed of light The ratio, , For ion velocity vectors, , , as well as The ion velocity vectors are respectively in Axial direction, Axial direction and Components in the axial direction, The magnitude of the ion velocity vector; To detect the angle between the laser wave vector (the vector direction of the laser) and the ion velocity vector, ,in, for and The inner product (dot product); To detect the laser wave vector, and thus calculate the Doppler frequency shift of each ion in any directional spectral measurement, To detect laser wave vector The model; Lorentz factor, .

[0066] This is the intrinsic transition frequency of the ion, that is, the transition frequency of the ion in the stationary coordinate system. In the stationary coordinate system, the stationary coordinate system is a follower coordinate system "attached" to the ion (moving with the ion). In the stationary coordinate system of the ion, the ion is stationary. The Doppler shift is the transition frequency of the ion after the Doppler shift, which is the transition frequency of the ion in the laboratory coordinate system. The laboratory coordinate system is a reference system in which the external observer is stationary, that is, a coordinate system attached to the observer. In the laboratory coordinate system, all the components of the ion beam system are stationary, while the ions are moving. When the ions are irradiated with a probe laser, the Doppler effect will occur, and the transition frequency of the ions will undergo a Doppler shift.

[0067] For low-energy ion beam 10 Therefore, the Doppler frequency shift contrast value Taylor expansion yields: (3); in, represent higher-order infinitesimals, Let $\mathbf{a}$ be the Peano remainder in the Taylor expansion.

[0068] Ignoring higher-order terms ,in, For first-order Doppler frequency shift, This is a second-order Doppler frequency shift.

[0069] Because the probe laser is less than 10 times the width of the ion beam, not all ions interact with the laser, and the location and extent of the interaction depend on the laser's incident position and width. The laser's incident position and width are determined on a practical device to screen out ions that can interact.

[0070] When the incident direction of the detection laser is The positive direction of the axis, i.e., the probe laser wave vector is At that time, the first-order Doppler frequency shift for: (4).

[0071] Second-order Doppler frequency shift ( When the laser incident direction is (Approximately 0 in the positive direction of the axis) is: (5).

[0072] Based on the extracted ion velocity, the first-order Doppler shift and second-order Doppler shift of a single ion can be calculated according to formulas (4) and (5), respectively.

[0073] Since ion beam 10 has a certain kinetic energy distribution, the Doppler frequency shift of ion beam 10 should be the sum of the contributions of each ion: (6); in, The spectral line shape of the ion fluorescence signal actually observed by the ion beamline system. This represents the intrinsic spectral line shape of the ion in a stationary coordinate system. This is an inherent property of ions. For the intrinsic spectral line shape The Doppler frequency shift was moved on the frequency axis. The resulting spectral line shape; The ion velocity distribution function is obtained by fitting the ion velocity distribution frozen on the cross section of the spectral measurement region using a Gaussian distribution. ), For speed is Doppler frequency shift of ions within the range As a infinitesimal element of velocity, the Doppler frequency shift of the ion beam 10 should be... and The center frequency difference.

[0074] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement step 5 in the above method embodiments.

[0075] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements step 5 in the above method embodiments.

[0076] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements step 5 in the above method embodiments.

[0077] It should be noted that the embodiments described in this invention are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains can make various modifications or additions to the described embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for measuring the Doppler frequency shift of a low-energy ion beam, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional geometric model of the ion beam line system and establish a coordinate system, wherein the coordinate system is based on the flight direction of the ion beam (10). The positive axis direction, with the fluorescence acquisition direction as the reference direction. Positive axis direction The positive direction of the axis is determined by the right-hand rule; Step 2: Import the three-dimensional geometric model of the ion beam line system into the finite element solver, and calculate the electromagnetic field distribution of the ion beam line system using the finite element solver. Step 3: Based on the electromagnetic field distribution of the ion beam system, set the initial distribution space of the ions; sample the initial state of the ions using Monte Carlo sampling, and simulate and calculate the motion trajectory of the ion beam (10) using a finite element solver. Step 4: Obtain the actual energy of the ion beam (10) through the deceleration field energy analyzer of the ion beam line system. Shaft kinetic energy distribution; The position of the deceleration field energy analyzer detecting ion velocities in the 3D geometric model is plotted perpendicular to... The first cross section along the axial direction is used to extract the ion velocity distribution frozen on the first cross section based on the motion trajectory of the ion beam (10), and the simulation of the ion beam (10) is obtained based on the ion velocity distribution on the first cross section. Shaft kinetic energy distribution; Judgment Simulation Shaft kinetic energy distribution and actual Check if the axial kinetic energy distribution is the same; if not, return to step 3, reset the initial ion distribution space, and repeat steps 3 and 4; until the simulation is complete. Shaft kinetic energy distribution and actual The axial kinetic energy distribution is the same, resulting in the final ion distribution space; Step 5: Based on the final ion distribution space, calculate the ion trajectory using the simulation method from Step 3; plot the trajectory perpendicular to the spectral measurement area. The second section along the axial direction is used to extract the ion velocity distribution frozen on the second section; the Doppler shift of the ion beam (10) is calculated based on the ion velocity distribution.

2. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 1, characterized in that, The simulation calculation of the motion trajectory of the ion beam (10) using a finite element solver specifically includes the following steps: Step 3.1: Emit an electron beam (7), calculate the trajectory of the electron beam (7) in the electromagnetic field based on the electromagnetic field distribution, and obtain the beam width of the electron beam (7) based on the trajectory of the electron beam (7) in the electromagnetic field; Step 3.2: Set the initial ion distribution space. The initial ion distribution space is the overlapping region of the electron beam (7) and the atomic beam (8). The overlapping region of the electron beam (7) and the atomic beam (8) is set to... The axis is an equivalent cylinder in the axial direction. The transverse diameter of the overlapping region of the electron beam (7) and the atomic beam (8) is set as the beam width of the electron beam (7) in the ion generation region, and the initial value of the equivalent axial space width of the overlapping region of the electron beam (7) and the atomic beam (8) is set. Step 3.3: Set the initial state of the ions, which includes the ion release location, the initial velocity distribution of the ions, the ion mass, and the ion charge. The ion release location is set by Monte Carlo sampling within the initial distribution space according to a uniform probability density; the initial ion velocity distribution is set by Monte Carlo sampling according to the Maxwell-Boltzmann velocity distribution corresponding to the source plasma temperature. Step 3.4: Based on the electromagnetic field distribution, solve the Lorentz force equation of the ion in the electromagnetic field using a finite element solver, and calculate the trajectory of the ion beam (10). The reset of the initial distribution space of the ions is to reset the equivalent axial space width.

3. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 2, characterized in that, The simulation Shaft kinetic energy distribution and the actual Whether the kinetic energy distribution of the shafts is the same can be determined by the following method: for simulation Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is fitted with Gaussian vectors. The difference between the means and the variance of the fitted Gaussian vectors is compared to see if they are within a preset range. If both the difference between the means and the variance of the fitted Gaussian vectors are within the preset range, the simulation is considered complete. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shafts is the same; if the difference between the means or the difference between the variances after Gaussian fitting is not within the preset range, then the simulation is judged to be flawed. Shaft kinetic energy distribution and actual The kinetic energy distribution of the shaft is not the same.

4. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 3, characterized in that, The Doppler frequency shift of the ion beam (10) calculated based on the ion velocity distribution is based on the following formula: ； In the formula, The spectral line shape of the ion fluorescence signal actually observed by the ion beamline system. The intrinsic spectral line shape of the ion. For the intrinsic spectral line shape Move the Doppler frequency shift on the frequency axis The resulting spectral line shape; Let be the ion velocity distribution function. For speed is Doppler frequency shift of ions within the range For infinitesimal elements of velocity; The Doppler frequency shift of the ion beam (10) is and The center frequency difference; The ion velocity distribution function is obtained by fitting the ion velocity distribution frozen on the second cross section using a Gaussian distribution. .

5. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 4, characterized in that, When the incident direction of the detection laser is First-order Doppler frequency shift in the positive axis direction and second-order Doppler frequency shift They are respectively: ； ； In the formula, is the intrinsic transition frequency of the ion. , as well as The ion velocity vectors are respectively in Axial direction, Axial direction and Components in the axial direction, The speed of light; The Doppler frequency shift of the ion is: .

6. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 5, characterized in that, The ion beamline system includes a vacuum chamber (1) and an ion source, an electrostatic lens group, a deceleration field energy analyzer, and a detection laser and fluorescence acquisition device located in the spectral measurement area, all disposed inside the vacuum chamber (1). The ion source includes an electron gun, a magnetic field coil, an atomic furnace (9), and an extraction electrode (2). The magnetic field coil includes a focusing coil and a deflection coil. The focusing coil is a... The shaft is an axially energized solenoid, the focusing coil is positioned between the electron gun and the nuclear reactor (9), and the deflection coil includes... Axis Helmholtz coil and Axial Helmholtz coil; electrostatic lens assembly including sequentially along Multiple electrostatic lenses and drift tubes (6) are arranged in the axial direction and share a common central axis; the deceleration field energy analyzer includes three grids and a Faraday cup, the three grids being the ground electrode, the deceleration electrode and the secondary electron suppression electrode, respectively; the fluorescence acquisition device includes an optical lens group, a filter and a photomultiplier tube in sequence; The electron beam (7) emitted by the electron gun is in the energized solenoid, Axis Helmholtz coil and The beam flies to the top of the atomic furnace (9) under the action of the Helmholtz coil and collides with the atomic beam (8) evaporated from the atomic furnace (9) to generate ions. The generated ions form an ion beam (10) under the action of the extraction electrode (2). The ion beam (10) is then focused by the electrostatic lens group and then flies to the spectral measurement area through the drift tube (6). The fluorescence generated by the interaction between the laser and the ions passes through the optical lens group and the filter in sequence and is input into the photomultiplier tube. The ion fluorescence signal is collected by the photomultiplier tube. Finally, the ion beam (10) continues to fly into the deceleration field energy analyzer installed on the vacuum cavity (1) at the end of the flight. The deceleration field energy analyzer detects the ion velocity at the location of the Faraday cup.

7. The Doppler frequency shift measurement method for a low-energy ion beam according to claim 6, characterized in that, The electromagnetic field distribution is obtained through the following steps: Step 2.1: Set the material of the electron gun in the three-dimensional geometric model to oxygen-free copper, and set the lead-out electrode (2), electrostatic lens group, grid, vacuum cavity (1) and deceleration field energy analyzer to stainless steel. Set the relative magnetic permeability of the vacuum region within the vacuum chamber. and relative permittivity The relative permeability and relative permittivity are set according to the materials of the electron gun, the lead-out electrode (2), the electrostatic lens group, the grid, the vacuum cavity (1) and the deceleration field energy analyzer, respectively. Step 2.2: Ground the vacuum chamber (1), set the number of turns and current of the magnetic field coil, and set the potential of the vacuum chamber (1), lead-out electrode (2), electrostatic lens group and grid in the deceleration field energy analyzer; Step 2.3: Perform steady-state solution on the electromagnetic field to obtain the electromagnetic field distribution inside the ion beam line system. The electromagnetic field distribution includes the potential distribution, electrostatic field distribution, and magnetic field distribution. Step 2.3.1: Using the potential of the lead-out electrode (2), the electrostatic lens group, the grid in the deceleration field energy analyzer and the vacuum cavity (1) as the boundary conditions of the electrostatic field, calculate the potential of the grid points on the spatial grid through the finite element solver to obtain the potential distribution, and further solve the electrostatic field distribution. Step 2.3.2: Given the current in the magnetic field coil, solve for the magnetic field distribution using a finite element solver.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements step 5 of the Doppler frequency shift measurement method for a low-energy ion beam as described in claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements step 5 of the Doppler frequency shift measurement method for a low-energy ion beam as described in claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements step 5 of the Doppler frequency shift measurement method for a low-energy ion beam as described in claims 1-7.

Images