A method and device for designing a double focusing mass spectrometer based on electromagnetic field transmission matrix

Abstract

The application discloses a double-focusing mass spectrometer design method and device based on an electromagnetic field transmission matrix, comprising the following steps: S1, constructing a characteristic sampling particle set based on a multi-dimensional initial phase space coordinate at an incident section of a double-focusing magnetic mass spectrometer; S2, establishing a three-dimensional finite element electromagnetic field model of a first-stage electromagnetic analysis component, and acquiring coordinate data of particles when the particles reach an intermediate slit; and S3, establishing a three-dimensional finite element electromagnetic field model of a second-stage electromagnetic analysis component, and acquiring coordinate data of the particles when the particles reach an outlet slit. The application realizes high-precision combination of a three-dimensional finite element electromagnetic field and algebraic transmission matrix optics; the characteristic sampling particle set covers key sampling points of a five-dimensional phase space, and converts black-box particle tracking into explicit algebraic parameters, so that the design process has clear physical directivity. A two-stage closed-loop optimization strategy realizes component decoupling design, and avoids blindness of global multi-variable optimization; and finally, the robustness of a design result is verified through large-sample particle tracking.

Description

Technical Field

[0001] This application belongs to the field of charged particle beam transmission system design technology, and more specifically, relates to a design method and device for a dual-focusing mass spectrometer based on an electromagnetic field transmission matrix. Background Technology

[0002] A dual-focusing mass spectrometer is an analytical instrument that achieves energy and directional focusing through the combined action of an electrostatic analyzer and a magnetic analyzer. It is primarily used for elemental analysis and high-resolution mass spectrometry detection in nuclear energy and nuclear science, and isotope geology. Its design is based on the complete energy and directional dual-focusing theory of ion beams proposed by J. Mattauch and REHerzog in 1934. A key feature of the Nier-Johnson ion beam path structure is its ability to eliminate second-order angular aberrations, improving sensitivity without sacrificing resolution. Therefore, it is widely used in high-performance instruments such as dual-focusing mass spectrometers and multi-receiver mass spectrometers using thermal ionization or inductively coupled plasma sources, playing a crucial role in nuclear physics, isotope geochronology, and environmental tracing.

[0003] Although the theoretical optical design methods for dual-focusing magnetic mass spectrometers are quite mature, a fundamental problem remains in practical design: a discrepancy exists between ion optical calculations and actual engineering models. Traditional designs often calculate ion optical parameters based on ideal electromagnetic field models—that is, assuming abrupt changes in the electromagnetic field at the boundaries, negligible or simplified edge fields, and ideally homogeneous electromagnetic fields. However, in real physical devices, these simplified assumptions lead to significant differences in the mapping between optical calculation results and three-dimensional finite element simulation results. To achieve high resolution (e.g., resolutions exceeding 1000), second-order and higher-order geometric aberrations introduced by the edge fields of the analytical magnets and the nonlinear electric field of the electrostatic analyzer (ESA) must be suppressed.

[0004] In the design process of dual-focusing mass spectrometers, the existing design methods mainly fall into three categories: ① Incorporating edge field and aberration correction functions into ion optics theory. Since the 1970s, researchers have developed second-order and higher-order aberration theories that incorporate edge fields, but analytical calculations are complex and difficult to optimize in a closed loop; moreover, idealized assumptions cannot reflect the actual nonlinear electromagnetic field distribution, resulting in large deviations between calculation results and reality, making it difficult to guide engineering design. ② Multi-particle tracking design method based on finite element simulation of electromagnetic fields. This method is more realistic than optical calculations, but it suffers from the problem of balancing efficiency and accuracy: it requires a large number of particles, is computationally time-consuming, and cannot obtain the coefficients of each order of transmission matrix, which is not conducive to targeted optimization. ③ Using multi-pole lenses to correct higher-order aberrations in actual devices. Researchers have attempted to introduce hexapole, octapole, and other multi-pole lenses to correct aberrations, but these themselves introduce new aberrations, still requiring complex calculations and repeated simulations, resulting in low design efficiency.

[0005] Based on the above methods for designing high-resolution mass spectrometers, existing ion optics design systems have two problems that need to be addressed: (1) The disconnect between ideal matrix optics and real physical fields. Traditional first-order and higher-order transfer matrix theories (such as those based on one-dimensional analytical deflection models) cannot accurately describe the edge field distribution, magnetic field distortion caused by magnetic saturation, and electric field distortion at the edge of the electrode plate in real three-dimensional electromagnetic fields. Geometric structures designed based on analytical formulas often exhibit aberrations that exceed the limits after being introduced into actual finite element physical fields.

[0006] (2) The "black box blind tuning" problem of large-sample particle tracking. In order to compensate for the difference between theory and simulation, full particle tracking (e.g., importing tens of thousands of random particles) is often used to blindly optimize the beam spot size at the overall exit. This method completely mixes the first-order dispersion, first-order focusing, and second-order principal aberrations in the final beam spot size, and it is impossible to quantify and resolve the specific individual aberration coefficients. This leads to a lack of clear physical direction in parameter adjustment, the optimization process is prone to getting trapped in local optima, the computational cost is high, and it is difficult to achieve global convergence.

[0007] Existing technology (patent document CN114883173A) discloses a design method for a surface thermal ionization mass spectrometer; this scheme optimizes the structural parameters of the ion optical system through three-dimensional modeling and particle tracking simulation. However, the all-particle tracking method used in this scheme requires the import of tens of thousands of random particles for beam spot size optimization, completely mixing first-order dispersion, first-order focusing, and second-order aberrations into the final beam spot size. It is impossible to quantify and identify individual aberration coefficients, resulting in a lack of clear physical direction for parameter adjustment. The optimization process is computationally expensive and difficult to achieve global convergence.

[0008] Furthermore, traditional analytical ion optics methods calculate the transfer matrix based on the assumption of an ideal uniform field, neglecting edge field effects such as magnetic field distortion caused by the magnet end face and electric field distortion at the electrode plate edge. This leads to significant deviations between the design results and the actual physical field. Therefore, a highly efficient closed-loop design method is needed that can achieve clear algebraic parameter orientation while preserving the complete edge field effects of the three-dimensional finite element electromagnetic field. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this application aims to provide a design method for a dual-focusing mass spectrometer based on an electromagnetic field transfer matrix, thereby solving the following technical problems in existing technologies: ideal matrix optical calculations are difficult to adapt to the edge field effects of complex electromagnetic components, resulting in significant deviations between the design results and the actual physical field; the three-dimensional electromagnetic field-based full particle tracking method requires the import of tens of thousands of random particles, completely mixing first-order dispersion, first-order focusing, and second-order aberrations in the final beam spot size, making it impossible to quantify and identify individual aberration coefficients, resulting in a lack of clear physical direction for parameter adjustment, high computational cost in the optimization process, and difficulty in achieving global convergence.

[0010] To achieve the above objectives, this application adopts the following technical solution: This application provides a design method for a dual-focusing magnetic mass spectrometer based on a three-dimensional electromagnetic field transfer matrix, including the following steps: Step S1: At the incident section of the dual-focusing magnetic mass spectrometer, a set of characteristic sampling particles is constructed based on multidimensional initial phase space coordinates. The multidimensional initial phase space coordinates include the position coordinates, divergence angle, and energy deviation of the particles. The coordinate combination of the set of characteristic sampling particles covers the central reference orbit, horizontal position boundary, vertical position boundary, horizontal divergence angle boundary, vertical divergence angle boundary, energy deviation boundary, and first-order and second-order cross-product terms. Step S2 involves establishing a three-dimensional finite element electromagnetic field model containing the complete edge field for the first-level electromagnetic analysis component; importing the feature sampling particle set into the model; and obtaining the coordinate data of the particles when they reach the middle slit through a particle tracking algorithm. Based on the Taylor expansion model, the first-order transfer matrix coefficients and second-order aberration coefficients are obtained by inverse solving of coordinate data, and the above coefficients at the middle slit are used as explicit quantification indicators. By iteratively adjusting the geometric parameters, the first-level closed-loop optimization is completed until the absolute value of the first-order transfer matrix coefficients is lower than the first preset threshold and the absolute value of the second-order aberration coefficients is lower than the second preset threshold. Step S3: For the second-level electromagnetic analysis component, establish a three-dimensional finite element electromagnetic field model containing the complete edge field; using the output particles optimized in step S2 as the input source, calculate the particle trajectory to the exit slit through the particle tracking algorithm, and obtain the coordinate data when the particle reaches the exit slit. The total system transmission matrix coefficients are obtained by inverse solving of coordinate data based on the Taylor expansion model, and the total system energy dispersion coefficient, total system focusing coefficient and preset cross-coupling aberration coefficient at the exit slit are extracted as explicit quantitative indicators for the second-level closed-loop optimization. Under the constraint of dual focusing of the whole system, the geometric parameters of the second-level electromagnetic analysis component are iteratively adjusted until the sum of the preset cross-coupling aberration coefficients is less than the third preset threshold, thus completing the second-level closed-loop optimization. Step S4: After the closed-loop iterations in steps S2 and S3 have converged, a large sample beam containing random discrete particles in the entire space is imported for high statistical particle tracking to verify whether the beam transmission characteristics at the exit slit meet the preset performance indicators.

[0011] Through the above technical solution, this application achieves a high-precision combination of three-dimensional finite element electromagnetic field and algebraic transfer matrix optics. The feature sampling particle set covers key sampling points in the five-dimensional phase space. After obtaining coordinate data through particle tracking, the transfer matrix coefficients are solved inversely, transforming black-box particle tracking into explicit algebraic parameters, giving the design process clear physical directionality. A two-stage closed-loop optimization strategy achieves decoupled component design: the first-stage closed loop eliminates local aberrations at the intermediate slit by adjusting the geometric parameters of the first-stage electromagnetic analysis component; the second-stage closed loop achieves coordinated compensation of aberrations across the entire system by adjusting the geometric parameters of the second-stage electromagnetic analysis component, avoiding the blindness of global multivariable optimization. Finally, the robustness of the design results is verified through large-sample particle tracking.

[0012] Furthermore, the multidimensional initial phase space coordinates are five-dimensional initial phase space coordinates, including x, x', y, y', and δ, where x and y represent the position coordinates of the particle in the horizontal and vertical directions, respectively; x' and y' represent the divergence angles of the particle in the horizontal and vertical directions, respectively; and δ represents the relative energy deviation of the particle. This five-dimensional coordinate system fully describes the spatial position, direction of motion, and energy state of the particle at the incident section.

[0013] Preferably, the feature sampling particle set consists of 25 feature particles. This number is sufficient to support the accurate inverse solution of the coefficients of the first and second order matrices in the Taylor expansion model, while keeping the computational load within a reasonable range, significantly reducing computational costs compared to the tens of thousands of particles required by traditional methods.

[0014] Specifically, the 25 characteristic particles include: one central reference particle with coordinates (0, 0, 0, 0, 0); four horizontal position boundary particles and four vertical position boundary particles; two energy deviation boundary particles; and 14 first-order and second-order cross-product term particles, the coordinates of which are combinations of the products of two or more coordinates in the five-dimensional coordinate system. This specific particle distribution design ensures sufficient sampling of all key regions in the five-dimensional phase space, providing the necessary data foundation for the accurate extraction of the transfer matrix coefficients.

[0015] Furthermore, in the five-dimensional initial phase space coordinates, the values ​​of x and y range from [-x...]. max x max ] and [-y max y max The range of values ​​for x' and y' is [-θ]. max θmax The range of δ is [-Δp / p]. max Δp / p max These value ranges are determined based on the beam characteristics of the actual ion source to ensure that the characteristic particle set can cover the phase space distribution of the actual beam.

[0016] Furthermore, in step S2, the first preset threshold is the first-order horizontal focusing aberration coefficient R. 12 The second preset threshold is the second-order principal aberration coefficient T. 122 R 12 This reflects the focusing properties of particles in the horizontal direction, T 122 This reflects the second-order nonlinear aberration within the dispersive surface. By using these two coefficients as explicit quantification indicators for the first-level closed-loop optimization, the local aberrations introduced by the first-level electromagnetic analysis component can be precisely controlled.

[0017] Preferably, in step S2, the first-stage electromagnetic analysis component is a magnetic analyzer, and adjusting the geometric parameters of the first-stage electromagnetic analysis component includes changing the radius of curvature of the cut cylindrical surface at the edge of the magnet pole face of the magnetic analyzer. The geometry of the edge of the magnet pole face directly affects the distribution of the edge magnetic field, thereby affecting the particle trajectory and the transfer matrix coefficients. By adjusting the radius of curvature of the cut cylindrical surface, R can be effectively controlled. 12 and T 122 The value.

[0018] Specifically, in step S2, the first preset threshold is 0.001, and the second preset threshold is 0.2. These thresholds are determined based on the resolution requirements of the mass spectrometer to ensure that aberrations at the intermediate slit are sufficiently suppressed, providing good initial conditions for subsequent second-stage closed-loop optimization.

[0019] Furthermore, the dual-focusing constraint of the entire system in step S3 is: the total system focusing coefficient is equal to 0 and the total system energy dispersion coefficient matches the preset energy dispersion design value. The dual-focusing constraint is a necessary condition for a dual-focusing mass spectrometer to achieve high resolution, requiring the system to achieve energy focusing while focusing in space, so that particles of the same mass but with different energies can converge to the same detection position.

[0020] Preferably, in step S3, the second-stage electromagnetic analysis component is a ring electrostatic analyzer, and adjusting the geometric parameters of the second-stage electromagnetic analysis component includes adjusting the ring factor and plate voltage of the ring electrostatic analyzer. The ring factor of the ring electrostatic analyzer affects its energy dispersion characteristics, and the plate voltage affects its focusing characteristics in the vertical direction. By synergistically adjusting these two parameters, the residual cross-coupling aberrations of the entire system can be compensated while satisfying the dual-focusing constraint.

[0021] Furthermore, the process of inversely solving the transmission matrix coefficients based on the Taylor expansion model in steps S2 and S3 is as follows: Based on the Taylor expansion relationship between the particle coordinates at the exit slit and the particle coordinates at the entrance section, where the Taylor expansion relationship is a linear combination of the first-order, second-order, and higher-order terms of the particle coordinates at the exit slit equal to those at the entrance section, a system of linear equations is constructed using the coordinate data of the feature sampled particle set. This system is then solved using the least squares method or matrix inversion to obtain the first-order transmission matrix coefficients and the second-order aberration coefficients. This Taylor expansion-based matrix coefficient extraction method is a classic theoretical method in ion optics. This application combines it with three-dimensional finite element electromagnetic field simulation, achieving a precise connection between theory and actual physical fields.

[0022] Preferably, the number of random discrete particles in step S4 can be 30,000. This number provides sufficient statistical samples to comprehensively verify the performance of the design results across the entire phase space, ensuring that the final mass resolution robustly meets the design specifications.

[0023] Furthermore, the charged particle beam transmission system includes a first-stage electromagnetic analysis unit and a second-stage electromagnetic analysis unit connected in sequence. The intermediate slit is located between the first-stage and second-stage electromagnetic analysis units, and the exit slit is located at the exit of the second-stage electromagnetic analysis unit. This two-stage cascaded system structure is a typical configuration of a dual-focusing mass spectrometer. The first-stage electromagnetic analysis unit achieves preliminary mass or energy separation, while the second-stage electromagnetic analysis unit achieves further focusing and aberration compensation. The two work together to achieve the final high-resolution isotope analysis.

[0024] Compared with the prior art, this application has the following beneficial effects: (1) By constructing a sampled particle set consisting of 25 characteristic particles and solving the transfer matrix coefficients from the three-dimensional finite element electromagnetic field based on the Taylor expansion model, the transformation from black-box particle tracking to explicit algebraic parameters is realized, giving the design process a clear matrix parameter orientation. Compared with the traditional full particle tracking method, which requires the import of tens of thousands of random particles and cannot quantify and identify individual aberration coefficients, this application reduces the number of tracking particles to 25, greatly reducing the calculation time of a single iteration, significantly reducing the consumption of computational resources, shortening the design cycle, and improving efficiency. At the same time, by extracting explicit matrix parameters as optimization indicators, the blindness of parameter adjustment is avoided, enabling the optimization process to quickly converge to the global optimum.

[0025] (2) It provides an engineering paradigm for aberration determination and control. Through multi-level matrix extraction of the intermediate slit and the exit slit, the complex global multivariate optimization is reconstructed into a logically progressive target aberration elimination: the first-level closed loop eliminates the first-order focusing aberration R at the intermediate slit by adjusting the geometric parameters of the first-level electromagnetic analysis component (such as the radius of curvature of the magnet end face).12 and the second principal aberration T 122 The second-stage closed loop compensates for the residual Y-axis cross-coupling aberration of the entire system by adjusting the geometric parameters of the second-stage electromagnetic analysis components (such as the toroidal factor and plate voltage of the toroidal electrostatic analyzer). This hierarchical decoupling optimization strategy avoids mutual coupling between the parameters of each component, ensuring that each optimization stage has a clear physical objective and adjustment means, significantly improving the controllability and repeatability of the design.

[0026] (3) It retains the complete edge field effect of the three-dimensional finite element electromagnetic field, realizing a high-precision combination of theoretical ion optics and actual physical field. Traditional analytical ion optics methods are based on the assumption of an ideal uniform field, neglecting the magnetic field distortion caused by the magnet end face and the electric field distortion at the edge of the electrode plate, resulting in a significant deviation between the design results and the actual physical field. This application fully considers the influence of edge field effect on particle trajectory by performing particle tracking and extracting the transfer matrix coefficients in the three-dimensional finite element electromagnetic field model. The final measured mass resolution is significantly lower than the simulation prediction, and the accuracy is effectively improved compared with the traditional analytical method, proving the accuracy and reliability of the method in this application.

[0027] (4) The method of this application has broad applicability and scalability. Although a dual-focusing magnetic mass spectrometer is used as an example for illustration, the core method (characteristic particle set construction, transmission matrix coefficient extraction, and hierarchical closed-loop optimization) is applicable to any charged particle beam transmission system containing multi-level electromagnetic analysis components, such as synchrotron beam transmission lines, electron microscope lens systems, ion implanters, and proton therapy beam transmission systems. The design method of this application can be used as long as the system requires optimization of transmission characteristics. Furthermore, the characteristic particle set construction method, matrix coefficient extraction algorithm, electromagnetic component selection, and optimization algorithm can all be flexibly adjusted according to specific application scenarios, demonstrating the universality and scalability of this application. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the principle structure of the dual-focusing magnetic mass spectrometer provided in this application.

[0029] Figure 2 A flowchart illustrating the design method of a dual-focusing magnetic mass spectrometer based on a transfer matrix provided in this application.

[0030] Figure 3 A schematic diagram showing the relationship between the transmission matrix parameters obtained from the computational characteristic particle trajectory provided in this application and the beam size. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0032] This application provides a design method and apparatus for a dual-focusing mass spectrometer based on a three-dimensional electromagnetic field transfer matrix. By constructing a feature-sampled particle set based on five-dimensional phase space coordinates, particle tracking is performed in a three-dimensional finite element electromagnetic field, and the transfer matrix coefficients are solved inversely, realizing the transformation from black-box particle tracking to explicit algebraic parameters. This method employs a two-stage closed-loop optimization strategy, resolving the contradiction that traditional ion optical calculations are difficult to adapt to complex edge fields, while full particle tracking is inefficient.

[0033] Figure 1 The principle structure of the dual-focusing magnetic mass spectrometer provided in this application is shown. For ease of explanation, only the parts relevant to this application are shown. The details are described below with reference to the accompanying drawings: The dual-focusing magnetic mass spectrometer specifically includes the following components: An ion source is used to generate ions from the sample being tested and to accelerate them to form an ion beam.

[0034] A magnetic analyzer, which can be a dipolar electromagnet, is used to perform momentum analysis based on the mass-to-charge ratio (m / z) of ions, thereby separating ions of different masses according to their orbits.

[0035] The central slit, located between the magnetic analyzer and the electrostatic analyzer, allows a suitable portion of the ion beam to pass through, further suppressing stray ions.

[0036] An electrostatic analyzer (ESA) is used to perform energy analysis based on the kinetic energy of ions, eliminating the impact of energy dispersion on resolution and achieving energy focusing.

[0037] The exit slit, located after the electrostatic analyzer, is used to define the width of the ion beam that ultimately reaches the detector, thus determining the mass resolution.

[0038] The detector is used to receive ions passing through the exit slit and generate a measurable electrical signal. It typically consists of a filter lens, a Faraday cup, and a microchannel plate signal receiver (SEM).

[0039] also, Figure 1 The deflection radius (R) of the magnetic analyzer is also indicated. magnet ), electrostatic analyzer deflection radius (R) ESA And drift segment lengths L2 and L3 and ESA entry angle θ ESA These geometric parameters collectively determine the instrument's focusing characteristics and overall size.

[0040] The dual-focusing magnetic mass spectrometer provided in this application is a reverse Nier-Johnson dual-focusing configuration. Through the coordinated operation of the magnetic analyzer and the electrostatic analyzer, it simultaneously achieves directional focusing and energy focusing, thereby obtaining high mass spectral resolution.

[0041] Figure 2 The following is a complete implementation process using a reverse Nier-Johnson configuration dual-focusing magnetic mass spectrometer as an example: Step 1: Design of Multidimensional Phase Space Reference Sampling Particle Set: At the ion source emitter (at the entrance slit), a sampled particle set consisting of 25 characteristic particles is constructed based on the five-dimensional initial phase space coordinates (x, x', y, y', δ). The spatial coordinate combination of these 25 characteristic particles covers the central reference orbit, horizontal / vertical position boundaries, horizontal / vertical divergence angle boundaries, energy deviation boundaries, and key first- and second-order cross-product terms, which serve as the benchmark for subsequently extracting Taylor expansion coefficients in the continuous physics field.

[0042] Step 2: Independent simulation of the magnetic analyzer and extraction of intermediate slit matrix coefficients (first-stage closed loop): A high-precision three-dimensional electromagnetic field model of the analytical magnet, containing a complete edge magnetic field, was established using finite element method (FEM) software. The 25 characteristic particles described in the previous step were imported into the three-dimensional electromagnetic field, and the precise trajectory coordinates of the characteristic particles up to the middle slit were calculated using a particle tracking algorithm. Based on the Taylor expansion model, the independent first-order transfer matrix coefficients R of the magnetic analyzer in the real three-dimensional field were obtained using the 25 sets of particle coordinates. ij and second-order aberration coefficient T ijk .

[0043] The extracted first-order horizontal focusing aberration coefficient R at the middle slit is... 12 and the second principal aberration coefficient T within the dispersion plane 122 As an explicit quantitative metric for closed-loop optimization, this is achieved by changing the geometry of the magnet's pole edge (e.g., the radius of curvature R of the cut cylindrical surface). edge ), perform local iterations until R at the intermediate slit section. 12 Approaching 0 and T 122 Reduced to below the target threshold. This step eliminates, as much as possible, the nonlinear in-plane aberrations introduced by the magnet at the intermediate slit.

[0044] Step 3: Spatial decoupling of the electrostatic analyzer (ESA) and coordinated aberration compensation across the entire system (second-level closed loop): After the magnet's geometric parameters converge, keeping its physical field unchanged, a three-dimensional finite element electrostatic field model of the downstream toroidal electrostatic analyzer (Toroidal ESA) is established. Using a beam of 25 characteristic particles with realistic physical field features, output after the first-stage optimization, as the input source, particle tracking continues in the actual three-dimensional non-uniform electric field of the ESA for the downstream half-range, up to the exit slit section. The overall transfer matrix coefficients are then algebraically solved again. At this point, the focus is on extracting the overall system's energy dispersion coefficient R. 16total Total horizontal focus coefficient R 12total And the second-order cross-coupled aberration coefficients of the non-dispersive surface (Y direction) not eliminated by the magnet (emphasis on T). 133total T 134total T 144total ).

[0045] Then, the calculated dispersion coefficient and aberration coupling coefficient at the exit slit section are used to perform ESA-based collaborative compensation to eliminate aberrations not eliminated by the upstream magnet. This is achieved using a system-wide dual-focusing constraint (R... 12total =0 and R 16total Based on the premise of matching, and taking the residual Y-axis cross aberration (T) as the benchmark, 133total T 134total T 144total With the goal of minimizing the aberrations, the ring factor and plate voltage of the ESA are adjusted through closed-loop iteration, and the non-uniform axial focusing force of the ESA is used to perfectly offset the spatial cross aberrations accumulated throughout the process.

[0046] Step 4: Large-sample statistical validation: After both closed-loop iterations converged, the final geometric layout and key geometric shapes of the electromagnetic components were locked. A large-sample beam containing 30,000 random discrete particles was imported for high-statistic particle tracking. The transverse and longitudinal phase space graphs and high-quality scanning peaks at the final exit slit were plotted to verify whether the actual quality resolution robustly met the design specifications.

[0047] Compared with the prior art, the design method provided in this application has the following advantages: (1) A high-precision closed-loop design of finite element three-dimensional physical field and algebraic transfer matrix optics that is closer to the real situation has been realized. It not only retains the absolute reality of the three-dimensional field containing complete edge field effects, but also gives the design process clear matrix parameter orientation.

[0048] (2) It provides an engineering paradigm for aberration determination and control. Through multi-level matrix extraction of the intermediate slit and the exit slit, the complex global multivariate is reconstructed into a logically progressive target aberration elimination, as well as the corresponding component design optimization (magnet end face adjustment). 122 →ESA cyclic factor adjusts Y-direction cross term).

[0049] (3) Improved design efficiency. The feature sampling matrix significantly reduces the number of tracking particles in the high-dimensional electromagnetic field (25 particles), which greatly shortens the convergence period of the mass spectrometer design.

[0050] Figure 3 The diagram demonstrates the relationship between the transmission matrix parameters calculated from characteristic particles obtained through multi-particle tracking simulation and the beam size at the endpoint, as well as the influence of the end radius of the magnet-dug slot on the transmission matrix parameters.

[0051] The comparison between the real field transfer matrix guidance method and the traditional all-particle tracking method in this application is detailed in Table 1 below, showing the differences in "interpretability", "decoupling optimization feasibility", and "design efficiency": Table 1:

[0052] To further illustrate the design method and apparatus for a dual-focusing magnetic mass spectrometer based on an electromagnetic field transfer matrix provided in this application, detailed embodiments are given below: Example 1 This embodiment provides a two-stage closed-loop design method for a reverse Nier-Johnson double-focusing magnetic mass spectrometer based on 25 characteristic particles, as well as the resulting magnetic mass spectrometer device.

[0053] The overall structure of this dual-focusing magnetic mass spectrometer includes, in sequence, an ion source, an entrance slit, a sector magnetic analyzer, an intermediate slit, a ring electrostatic analyzer, an exit slit, and a detector. The design goal is to achieve a mass resolution M / ΔM greater than 15000, Dm = 210 mm, and a dual-focusing constraint R0. 12total It equals 0.

[0054] Step S1: At the entrance slit, construct a sampling particle set consisting of 25 characteristic particles based on the five-dimensional initial phase space coordinates (x, x', y, y', δ).

[0055] Where x and y represent the position coordinates of the particle in the horizontal and vertical directions, respectively, x' and y' represent the divergence angles of the particle in the horizontal and vertical directions, respectively, and δ represents the relative energy deviation of the particle.

[0056] The 25 characteristic particles include (see Table 2 for details): Table 2:

[0057] Step S2: Establish a three-dimensional finite element electromagnetic field model of the sector magnetic analyzer and perform the first-level closed-loop optimization.

[0058] A three-dimensional electromagnetic field model of the sector magnetic analyzer was established using finite element method (FEM) software. This model includes the complete edge magnetic field effect. The magnetic field strength B was set to 0.78T, and the deflection angle was set to 60 degrees.

[0059] The 25 feature particles constructed in step S1 are imported into the three-dimensional electromagnetic field model. The particle tracking method is used to calculate the trajectory of the feature particles in the three-dimensional electromagnetic field up to the middle slit section. The particle trajectory is solved by the motion equations dx / dt = v and dv / dt = (q / m)(E+v×B), where q is the particle charge, m is the particle mass, E is the electric field strength, B is the magnetic field strength, and v is the particle velocity.

[0060] Record the coordinate data (x) of 25 characteristic particles when they reach the middle slit section. mid , x' mid y mid y' mid ).

[0061] A system of linear equations was constructed using the coordinate data of 25 characteristic particles. The equations were solved using the least squares method, and the inverse solution yielded the first-order transfer matrix coefficients R of the magnetic analyzer in a real three-dimensional field. ij and second-order aberration coefficient T ijk Extract the first-order horizontal focusing aberration coefficient R at the cross-section of the intermediate slit. 12 and the second principal aberration coefficient T in the dispersion plane 122 As an explicit quantitative indicator for the first-level closed-loop optimization.

[0062] Initially, R 12 With T 122 The values ​​all exceeded the target threshold by more than twice. This was achieved by changing the radius of curvature R of the cut cylindrical surface at the edge of the magnet's pole face. edge Perform local iterative optimization.

[0063] Perform a parameter scan: R edge The tracking time was increased from 150mm to 250mm, with a step size of 10mm. After each adjustment, the tracking of 25 feature particles was repeated and R was extracted. 12 and T 122 The value of .

[0064] After 5 iterations, R edge Convergence occurs when the absolute value |R| is satisfied. 12 | Less than 0.001 and absolute value|T 122 |Convergence criterion less than 0.1.

[0065] Through the first-level closed-loop optimization described above, the nonlinear in-plane aberrations introduced by the magnetic analyzer were locally eliminated at the middle slit.

[0066] Step S3: Establish a three-dimensional finite element electromagnetic field model of the ring electrostatic analyzer and perform the second-level closed-loop optimization.

[0067] Keeping the geometric parameters of the magnetic analyzer constant, a three-dimensional finite element electrostatic field model of the toroidal electrostatic analyzer is established. The ESA deflection angle is 90 degrees, and the inner and outer plates are set with arc-shaped cross sections to form a toroidal factor that generates a focusing effect in the Y direction.

[0068] The 25 characteristic particles output from the middle slit section after the first-stage optimization are used as the input source, and particle tracking continues in the three-dimensional non-uniform electric field of the ESA until the exit slit section. The trajectory of the particles in the electrostatic field is solved by the same equation of motion, but at this time the magnetic field B is 0 and the electric field E is not 0.

[0069] The coordinate data of 25 characteristic particles when they reach the exit slit section are recorded, and the transfer matrix coefficients of the whole system are obtained again by using the Taylor expansion model inverse solution.

[0070] Extract the total system energy dispersion coefficient R at the exit slit section. 16total Total horizontal focus coefficient R 12total and the Y-axis second-order cross-coupling aberration coefficient T 133total T 134total T 144total As an explicit quantitative indicator for the second-level closed-loop optimization.

[0071] In the initial design, D m The value is less than the design target, R 12total A value greater than 0.001 does not satisfy the dual-focusing constraint; T 133total T 134total T 144total The Y-axis aberration exceeds the standard.

[0072] With the whole system dual-focusing constraint R 12total Approaching 0 and D m Based on a baseline of 210mm, the sum of the absolute values ​​of the residual Y-direction cross aberrations |T 133total |+|T 134total |+|T 144total |With a target value of less than 5, the toroidal factor k and plate voltage of the ESA are adjusted through closed-loop iteration.

[0073] The cyclic factor k is defined as k equal to (r out Reduce r in Divide by R ESA。 The initial value of k is 0.091, r out With r in R is the radius of the arc surfaces of the inner and outer plates on both sides of the central channel in the ESA section. ESA It is the radius of the ESA.

[0074] Perform a two-dimensional parameter scan: k increases from 0 to 0.4 in a step of 0.005. After each adjustment, track 25 feature particles again and extract the matrix coefficients.

[0075] After 8 iterations, k converges, at which point D... m The value is 212mm, R 12total The value is 0.0006, T 133total The value is 2.23, T 134total The value is 0.02, T 144total The value is 1.41, which satisfies all convergence criteria.

[0076] Through the above-mentioned second-level closed-loop optimization, the non-uniform axial focusing force of ESA is used to compensate for the residual Y-direction cross aberration of the entire system, while satisfying the dual-focusing constraint.

[0077] Step S4: Import a large sample beam for verification.

[0078] After both closed-loop iterations converge, the final geometric layout and key geometric parameters of the electromagnetic components are locked.

[0079] A large-sample beam containing 30,000 random discrete particles was imported for high-statistic particle tracking. The initial coordinates of these random particles were uniformly distributed in the five-dimensional phase space, covering the beam characteristics of the actual ion source.

[0080] Plot the horizontal and vertical phase space graphs and high-quality scanning peaks at the exit slit to verify the final quality resolution.

[0081] The verification results show that the final measured quality resolution M / ΔM reaches 16200, robustly achieving the design target of M / ΔM greater than 15000.

[0082] By employing the aforementioned two-stage closed-loop design method, a high-precision combination of three-dimensional physical fields and algebraic transfer matrix optics is achieved. Compared to the traditional all-particle tracking method, which requires 50,000 particles and approximately 48 hours of computation, this method preserves the complete edge field effect and requires only 25 particles. This allows for improved accuracy in calculations while reducing iteration time and accelerating the design cycle.

[0083] Obviously, matrix coefficient extraction algorithms are not limited to directly solving linear equation systems. Least square fitting, singular value decomposition, or regularization methods, such as Tikhonov regularization, can also be used to improve numerical stability and noise resistance.

[0084] It is understood that the first-stage electromagnetic analysis component is not limited to a sector magnetic analyzer, but can also be a quadrupole magnet, a hexapole magnet, or a multipole magnetic lens; the second-stage electromagnetic analysis component is not limited to a ring electrostatic analyzer, but can also be a cylindrical electrostatic analyzer, a spherical electrostatic analyzer, or a multipole electrostatic lens. The method of this application is applicable to any charged particle beam transmission system that includes multiple stages of electromagnetic analysis components.

[0085] Clearly, iterative algorithms for closed-loop optimization are not limited to parameter scanning. Gradient descent, Newton's method, genetic algorithms, particle swarm optimization, or simulated annealing can also be used to accelerate convergence or avoid local optima.

[0086] Understandably, the number of particles for large-sample verification is not limited to 30,000, and can be adjusted within the range of 10,000 to 100,000 depending on computational resources and accuracy requirements. The particle distribution is not limited to a uniform random distribution, but can also use a Gaussian distribution, a truncated Gaussian distribution, or a distribution function obtained from actual ion source measurements.

[0087] Obviously, the method of this application is not limited to dual-focusing mass spectrometers, but is also applicable to other charged particle beam transport systems, such as synchrotron beam transport lines, electron microscope lens systems, ion implanters, proton therapy beam transport systems, etc. As long as the system contains multi-stage electromagnetic analysis components and requires optimization of transport characteristics, the characteristic particle set and hierarchical closed-loop optimization method of this application can be used.

[0088] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A design method for a dual-focusing magnetic mass spectrometer based on a three-dimensional electromagnetic field transport matrix, characterized in that, Includes the following steps: S1 constructs a set of characteristic sampling particles based on multidimensional initial phase space coordinates at the incident section of the dual-focusing magnetic mass spectrometer; The multidimensional initial phase space coordinates include the particle's position coordinates, divergence angle, and energy deviation. The coordinate combination of the feature sampled particle set covers the central reference orbit, horizontal position boundary, vertical position boundary, horizontal divergence angle boundary, vertical divergence angle boundary, energy deviation boundary, and first-order and second-order cross-product terms. S2 establishes a three-dimensional finite element electromagnetic field model containing the complete edge field for the first-level electromagnetic analysis component; the feature sampling particle set is imported into the model, and the coordinate data of the particles when they reach the middle slit is obtained through the particle tracking algorithm; Based on the Taylor expansion model, the first-order transfer matrix coefficients and second-order aberration coefficients are obtained by inverse solving of coordinate data, and the above coefficients at the middle slit are used as explicit quantification indicators. By iteratively adjusting the geometric parameters until the absolute value of the first-order transfer matrix coefficients is lower than the first preset threshold and the absolute value of the second-order aberration coefficients is lower than the second preset threshold, the first-level closed-loop optimization is completed. S3 establishes a three-dimensional finite element electromagnetic field model containing a complete edge field for the second-level electromagnetic analysis component; using the output particles optimized in step S2 as the input source, the particle trajectory to the exit slit is calculated through a particle tracking algorithm to obtain the coordinate data when the particle reaches the exit slit. The total system transmission matrix coefficients are obtained by inverse solving of coordinate data based on the Taylor expansion model, and the total system energy dispersion coefficient, total system focusing coefficient and preset cross-coupling aberration coefficient at the exit slit are extracted as explicit quantitative indicators for the second-level closed-loop optimization. Under the constraint of dual focusing of the whole system, the geometric parameters of the second-level electromagnetic analysis component are iteratively adjusted until the sum of the preset cross-coupling aberration coefficients is less than the third preset threshold, thus completing the second-level closed-loop optimization.

2. The design method as described in claim 1, characterized in that, The following steps are included after step S3: After the closed-loop iterations converge, S4 imports a large sample beam containing random discrete particles across the entire space for high-statistic particle tracking to verify whether the beam transmission characteristics at the exit slit meet the preset performance indicators. The design method shortens the design cycle by a preset percentage compared to traditional methods, and the final measured performance indicators deviate from the simulation prediction by less than a preset threshold.

3. The design method as described in claim 1, characterized in that, The feature sampling particle set consists of 25 feature particles.

4. The design method as described in claim 3, characterized in that, The 25 characteristic particles include: 1 central reference particle with coordinates (0, 0, 0, 0, 0); 4 horizontal position boundary particles and 4 vertical position boundary particles; 2 energy deviation boundary particles; and 14 first-order and second-order cross-product term particles, wherein the coordinates of the cross-product term particles are the product combination of two or more coordinates in the five-dimensional coordinate system.

5. The design method as described in claim 1, characterized in that, In step S2, the first preset threshold is the first-order horizontal focusing aberration coefficient R. 12 The second preset threshold is the second-order principal aberration coefficient T. 122 ; The first-stage electromagnetic analysis component is a magnetic analyzer, and adjusting the geometric parameters of the first-stage electromagnetic analysis component includes changing the radius of curvature of the cut cylindrical surface at the edge of the magnet pole face of the magnetic analyzer.

6. The design method as described in claim 1, characterized in that, In step S3, the whole system dual focusing constraint is: the total system focusing coefficient is equal to 0 and the total system energy dispersion coefficient matches the preset energy dispersion design value; The second-stage electromagnetic analysis component is a ring electrostatic analyzer, and adjusting the geometric parameters of the second-stage electromagnetic analysis component includes adjusting the ring factor and plate voltage of the ring electrostatic analyzer.

7. The design method as described in claim 1, characterized in that, The process of inversely solving the transfer matrix coefficients based on the Taylor expansion model in steps S2 and S3 is as follows: According to the Taylor expansion relationship between the particle coordinates at the exit slit and the particle coordinates at the inlet section, the Taylor expansion relationship is a linear combination of the first-order, second-order, and higher-order terms of the particle coordinates at the exit slit being equal to the particle coordinates at the inlet section. A linear system of equations is constructed using the coordinate data of the feature sampled particle set and solved by the least squares method or matrix inversion to obtain the first-order transfer matrix coefficients and the second-order aberration coefficients.

8. A dual-focusing magnetic mass spectrometer device obtained based on the design method according to any one of claims 1-7, characterized in that, include: The first-stage electromagnetic analysis unit and the second-stage electromagnetic analysis unit are connected in sequence, with an intermediate slit between the first-stage electromagnetic analysis unit and the second-stage electromagnetic analysis unit, and an outlet slit at the outlet of the second-stage electromagnetic analysis unit. The intermediate slit is used to select a suitable portion of the ion beam to pass through, further suppressing stray ions; The exit slit is used to define the width of the ion beam.

9. The dual-focusing magnetic mass spectrometer apparatus as described in claim 8, characterized in that, The first-stage electromagnetic analysis component is a magnetic analyzer, and the second-stage electromagnetic analysis component is an electrostatic analyzer.

10. The dual-focusing magnetic mass spectrometer apparatus as described in claim 8, characterized in that, It also includes a detector for receiving ions passing through the exit slit and generating a measurable electrical signal.

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