An electron beam injector macro-pulse optimization method and system based on NSGA-III algorithm

Abstract

The application discloses a kind of based on NSGA-III algorithm's electron beam injector macro pulse optimization method and system, belong to electron beam injector field, including using non-dominated sorting genetic algorithm with elite strategy, with the stable energy of macro pulse beam cluster, energy consistency and phase consistency Three parameters converge to optimal direction as optimization goal, optimization obtains target parameter distribution result and corresponding injector initial system parameter setting;Wherein, the fitness function in non-dominated sorting genetic algorithm with elite strategy is transient beam load effect and longitudinal particle motion calculation model;Various groups of individuals in the process of optimization correspond to a set of initial parameter setting;And initial parameter value interval is determined by solving each parameter separately in advance to obtain its optimal solution range;Because the interaction between each parameter influences, the optimization result finally obtained is not necessarily optimal for single parameter, but meets overall optimal effect.

Description

Technical Field

[0001] This invention belongs to the field of electron beam injectors, and more specifically, relates to a macro-pulse optimization method and system for electron beam injectors based on the NSGA-III algorithm. Background Technology

[0002] In recent years, the rapid development of high-quality electron beam injectors has provided technical support for the development of large-scale scientific research facilities such as free-electron laser devices, diffraction-limited storage rings, and electron-positron colliders, as well as for the application of industrial accelerators such as photon therapy and high-energy X-ray sources. However, these facilities are mostly large in scale, have complex peripheral subsystems, and are costly. Therefore, the development of miniaturized and compact electron beam injectors has become a trend. As a beam source, the injector determines the quality of the driving beam and even affects the performance of the entire facility. A typical example is a hot cathode electron injector based on two independent tunable cavities (ITCs) combined with a traveling-wave accelerating tube: the first cavity is used to input a DC beam, and the second cavity and the traveling-wave accelerating tube are mainly used to accelerate the beam. The energy and phase of the two cavities and the accelerating tube can be adjusted independently, thereby achieving self-compensation of energy diffusion and transverse emittance within a limited beamline length, thus limiting the entire injector to an acceptable range and at a low cost. However, when the output beam passes through the standing-wave cavity and accelerating tube in the injector, the bundle sequence will interact with the electromagnetic field established in the radio frequency structure, leading not only to energy reduction but also to non-uniform distribution of the bundle sequence in the macroscopic pulse. The former is mainly caused by steady-state beam loading effects, while the latter is caused by transient beam loading effects. Furthermore, the macro-pulse inconsistency caused by beam loading ultimately affects the peak and average power of the entire injector device. Therefore, macro-pulse optimization is crucial for high-power injectors.

[0003] For existing beam installations, optimizing beam performance is preferable. However, optimization can be limited by the observation and adjustment methods available on existing test platforms, compared to the design process which can be intuitively evaluated through electromagnetic calculations and beam simulations. Given the involvement of multiple parameters and their interactions, optimization typically requires repeated manual calculations. For such multi-objective optimization, genetic algorithms (GA) are a simple tool for finding optimal settings. Therefore, to reduce macropulse inconsistencies, it is urgent to utilize multi-objective genetic algorithms for beam optimization. Summary of the Invention

[0004] To address the shortcomings and improvement needs of existing technologies, this invention provides a macropulse optimization method and system for electron beam injectors based on the NSGA-III algorithm. Its purpose is to increase the output power of the injector to drive high-power devices. Compared to NSGA-II, NSGA-III solves the problems of poor convergence and diversity in the algorithm, avoiding the algorithm from getting trapped in local optima.

[0005] To achieve the above objectives, this invention provides a macropulse optimization method for electron beam injectors based on the NSGA-III algorithm, comprising: A reference-point-based non-dominated sorting genetic algorithm with an elitist strategy is employed to optimize the beam quality under different parameter settings, aiming to achieve convergence of the three parameters—stable energy, energy consistency, and phase consistency—of the macropulse bundle towards the optimal direction. The fitness function in this algorithm is a computational model based on single-particle motion theory to solve for the transient beam load effect in the cavity. During the optimization process, each population corresponds to a macropulse distribution, and the gene length of a single population individual is determined by the available values ​​of different injection times and radio frequency (RF) phases. In each iteration, the values ​​of the input parameters required for calculating the fitness function of each population are obtained through pre-analysis of the individual impact of each input parameter on beam quality. These input parameters include RF parameters and structural parameters. RF parameters include RF injection time and RF phase, while structural parameters include timing and VSWR coupling coefficient. Timing, RF injection time, RF phase, and VSWR coupling coefficient are all input setting parameters, and the appropriate parameter range is determined based on the final optimization results. The interaction between optimization objectives is taken into account. While it may not be optimal for a single objective, it can maintain the overall optimal solution.

[0006] Furthermore, the genetic operator operations for obtaining the offspring population include: selection operation based on reference point sorting, crossover operation using single-point crossover, and mutation operation using single-point mutation.

[0007] Furthermore, the energy consistency and phase consistency are as follows:

[0008] in, B For specific output energy or phase, B end The final output energy or phase is rms, which is the root mean square value.

[0009] Furthermore, the analytical expression for the transient beam load of the traveling wave cavity is:

[0010] The analytical expression for the transient beam load of the standing wave cavity is:

[0011] in, , The initial injected power, r For shunt impedance, l The length of the cavity. , It is a step function. , Q For quality factor, This is the beam generator current. , For power, The coupling coefficient between the waveguide and the cavity. For equivalent shunt impedance, For the load current, For the beam injection time, It is the average beam current. It is the attenuation constant. To take into account the energy actually carried away by the beam.

[0012] Furthermore, the input setting parameters are obtained by inverse solving based on the final optimization result. Since the final optimal solution is presented as a Pareto front, the input setting parameters are within a small range, and the specific values ​​need to be obtained based on the actual situation.

[0013] The present invention also provides an electron beam injector macropulse optimization system based on the NSGA-III algorithm, comprising: a computer-readable storage medium and a processor, wherein the computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the above-described electron beam injector macropulse optimization method based on the NSGA-III algorithm.

[0014] Compared with the prior art, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) This invention proposes a macro-pulse optimization method for electron beam injectors based on the multi-objective genetic algorithm NSGA-III. When establishing the macro-pulse beam optimization calculation model, in addition to considering the radio frequency injection time and radio frequency phase, the adjustable coupling coefficient of the standing wave cavity and the planned radio frequency separation injection are added to make the macro-pulse width greater than 3.3μs, the energy inconsistency less than 0.3, and the phase inconsistency less than 0.2, overcoming the limitations of the existing system, and considering the future upgrade plan for the injector.

[0015] (2) Before calculating the bundle energy and macropulse consistency, the transient beam load effect in the traveling wave tube and standing wave cavity is expressed by numerical analysis, which facilitates the design calculation process. This multi-objective genetic algorithm has the characteristics of good convergence and the optimization objective can be changed to other beam parameters, that is, high versatility, and is suitable for application in the design optimization of injectors.

[0016] (3) This invention proposes an electron beam injector macropulse optimization method based on the multi-objective genetic algorithm NSGA-III, which gets rid of the difficulty and tediousness of manual calculation, and has the characteristics of fast optimization speed, good consistency of the optimized beam macropulse, and high stable energy of the macropulse bundle. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the electron beam injector macropulse optimization method based on the NSGA-III algorithm provided in an embodiment of the present invention; Figure 2 A schematic diagram of a high-quality electron beam injector beam current optimization test platform provided in an embodiment of the present invention; Figure 3 The beam optimization results provided by the embodiments of the present invention when adjusting the radio frequency injection time and radio frequency phase; Figure 4 The beam optimization results provided in this embodiment of the invention are achieved by using radio frequency separation injection of the standing wave cavity and the accelerating tube, and by adjusting the radio frequency phase and the coupling coefficient of the standing wave cavity. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0019] Currently, while multi-objective genetic algorithms are used in the accelerator field, they are primarily applied to optimizing large-scale accelerators. For example, optimizing multi-objective genetic algorithms can be used to optimize magnetic field distribution, focusing systems, and parameter selection in accelerators, improving beam transmission efficiency and particle focusing performance. This can lead to more efficient free-electron laser generation and transmission, more stable particle beam motion, and higher radiance, among other things. However, there is very little application to the optimization design of macropulse beams for compact free-electron laser terahertz source injectors used in industrial applications.

[0020] The uniformity of macropulse beams is crucial for the successful development of high-power beam injectors, especially those aiming to produce terahertz radiation with high peak and average power. However, due to the pervasive transient beam loading effects in the high-gradient accelerators used in high-quality electron beam injectors, the energy distribution extracted along the macropulse can become inconsistent. Furthermore, inconsistencies in the energy distribution across the macropulse during the low-energy phase of the injector can also affect the phase distribution. Optimizing the macropulse beam within a limited tunable system setup is particularly important for existing high-quality electron beam injector facilities.

[0021] This invention provides a macropulse optimization method for electron beam injectors based on the NSGA-III algorithm, comprising: A reference-point-based non-dominated sorting genetic algorithm with an elitist strategy is employed to optimize the beam quality under different parameter settings, aiming to achieve convergence of the three parameters—stable energy, energy consistency, and phase consistency—of the macropulse bundle towards the optimal direction. The fitness function in this algorithm is a computational model based on single-particle motion theory to solve for the transient beam load effect in the cavity. During the optimization process, each population corresponds to a macropulse distribution, and the gene length of a single population individual is determined by the available values ​​of different injection times and radio frequency (RF) phases. In each iteration, the values ​​of the input parameters required for calculating the fitness function of each population are obtained through pre-analysis of the individual impact of each input parameter on beam quality. These input parameters include RF parameters and structural parameters. RF parameters include RF injection time and RF phase, while structural parameters include timing and VSWR coupling coefficient. Timing, RF injection time, RF phase, and VSWR coupling coefficient are all input setting parameters, and the appropriate parameter range is determined based on the final optimization results. The interaction between optimization objectives is taken into account. While it may not be optimal for a single objective, it can maintain the overall optimal solution.

[0022] Based on the above analysis, the present invention provides the following embodiments to solve the technical problems existing in the optimization design of macropulse beams.

[0023] Example 1 An optimization method for macropulse of an electron beam injector based on the NSGA-III algorithm is proposed. The optimization objectives include the stable energy, energy consistency, and phase consistency of the macropulse bundle of the injector. The method includes: (1) The transient beam load effect expressions of traveling wave cavity and standing wave cavity are obtained by numerical analysis.

[0024] High-quality electron beam injectors mainly use pulsed beams during the beam tuning stage. Due to the short duration of the pulsed beam, the transient beam load effect is quite severe. The electron gun structure mainly consists of traveling wave tubes and standing wave cavities. The following discussion will focus on these two structures and explore the analytical expression of the transient beam load effect.

[0025] In the calculation model of beam load, the analytical expression of the transient beam load effect of the traveling wave tube is obtained from equations (1)-(3). Equation (1) gives the RF power loss equation per unit length, where, It is the structural attenuation coefficient. It is beam current. It is the axial electric field amplitude. Power loss consists of two parts: the power dissipated on the cavity wall and the power absorbed by the beam. Equation (2) gives the expressions for the electric field and current under the beam injection condition, where It is the beam injection time. It is the average beam current. yes Amplitude, Let be the step function. Equation (3) gives the analytical expression for the final transient beam load of the traveling wave cavity, where , The initial injected power, r For shunt impedance, l The length of the cavity. , , Q For quality factors, fill time: As can be seen from equation (3), in addition to design parameters such as field strength amplitude, quality factor, and shunt impedance affecting the traveling wave tube beam energy, injection time is another major contributor, which can be adjusted online for existing facilities.

[0026] (1) (2) (3) The analytical expression for the transient beam load of the standing wave cavity is given by equation (4) based on the circuit. (4) in This refers to the beam generator current, typically with high power. Replacement The coupling coefficient between the waveguide and the cavity. For equivalent shunt impedance, For the load current, For the beam injection time, It is the attenuation constant. To account for the energy actually carried away by the beam, in parallel wave tubes, in addition to the inherent design parameters of the standing wave cavity and the initial beam parameters, the injection time also affects the output beam energy of the standing wave cavity.

[0027] (2) Numerical expression for beam optimization measurement and consistency High-quality electron beam injector beam optimization test bench, such as Figure 2As shown, the beam is first injected into the standing wave cavity and then into a subsequent accelerating tube with a length of 0.853m. Two drift sections are installed upstream and downstream of the accelerating tube, with lengths designed to be 0.265m (drift section 1) and 0.8m (drift section 2), respectively. Three observation points are located along the beam path: the end of drift section 1, the exit of the accelerating tube, and the end of drift section 2, to capture the energy and phase distribution of the macropulse. The RF injection time of the entire system is controlled by a master clock.

[0028] For macropulse composed of bundles, the root mean square value (rms) is used to describe its consistency in the statistical distribution, and the symbol is used to represent this consistency. express: (5) in B It refers to the specific output energy or phase. This provides the final output energy or phase. It can be achieved through... To assess parameter consistency, The smaller the value, the better the consistency. The numerical solution is based on the following settings: (1) each bundle within the macropulse is represented by a macroparticle; (2) the phase of all bundles is a relative value of the relatively stable phase; (3) the phase slip of the bundle is also a relative value of the relatively stable value.

[0029] (3) NSGA-III adopts a reference point-based selection mechanism, thus ensuring solution diversity and making it particularly suitable for solving optimization problems with three or more objectives. Its execution flow is as follows: Figure 1 As shown. The optimization result of the genetic algorithm is related to the selection of the independent variable parameter range. Preliminary calculations showed the radiofrequency injection time to be around 0.95 seconds. The left and right energy consistency is optimal, but at 0.89 The left-right phase consistency is the worst, and the optimal injection time will deviate to some extent due to this relationship. Therefore, the radiofrequency injection time range is taken as [0.6]. 1.3 According to beam dynamics, particles can obtain the maximum output energy when the phase is close to 90°. However, due to phase slip, the phase with the maximum particle energy will shift by 90°. Therefore, the radio frequency phase range is [90°, 140°].

[0030] Since the optimization objectives for energy consistency and phase consistency are to be minimized, and the optimization objective for the stable energy of the output macropulse bundle is to be maximized, in order to keep the optimization objectives consistent, the objective function in the algorithm selects the minimum value, while the opposite number is used to handle the case where the maximum value should be taken.

[0031] After initializing the population, it is determined whether a first-generation offspring population has been generated. If not, the population is generated after calculating the fitness function (i.e., the degree of inconsistency between the output bundle energy size and energy phase), performing fast non-dominated sorting, and executing the genetic operators. Regarding fast non-dominated sorting, first, the non-dominated sorting layer number is set to 1, and all non-dominated individuals are placed into it. Then, the layer number is incremented by 1, and all non-dominated individuals from the remaining individuals are placed into it, and so on, until all individuals have a layer number. Then, the generated offspring population is merged with the parent population. After calculating the fitness function of the merged population, fast non-dominated sorting is performed to obtain the stratification result. Then, the reference point distance of the individuals is calculated, and individuals with smaller non-dominated indices and smaller reference point distances are added to the new parent population until the initial population size is reached. This set of individuals is the generated new generation offspring population. Regarding genetic operations, selection is performed based on a reference point; crossover is performed using a single-point crossover method with a crossover probability typically between 0.5 and 1.0 (0.8 in this example); mutation is performed using a single-point mutation method with a mutation probability typically between 0 and 0.05 (0.02 in this example). If the population has not reached the preset number of generations, the process continues. If the preset number of iterations is reached, the solution set with the smallest non-dominated index, i.e., the Pareto front, is output. Ultimately, the result with the maximum output particle energy and the minimum energy-phase inconsistency is obtained. Regarding the termination generation, in this example, the calculation terminates when the population has reached 30 generations.

[0032] Figure 3 The beam optimization results for adjusting the RF injection time and RF phase show that phase consistency and energy consistency exhibit opposite trends. The stable energy of the traveling wave tube output beam is concentrated between 13.5 and 14.5 MeV, with energy inconsistency concentrated between 0.007 and 0.01, and phase inconsistency concentrated between 0.5 and 1.5. However, since macropulse optimization mainly relies on adjusting the single RF injection time, it is limited by the RF characteristics of the standing wave cavity and the accelerating tube. Therefore, the coupling coefficient of the standing wave cavity is considered (…). And add an RF source to achieve separate control of the RF injection of the standing wave cavity and the accelerating tube.

[0033] Figure 4 The image shows the beam optimization results when injecting the RF-separated standing wave cavity (SWR) and accelerating tube, and adjusting the RF phase and SWR coupling coefficient. The input parameter range for the SWR coupling coefficient is [2,12]. The injection time of the SWR lags behind the injection time of the accelerating tube by 1.5 times, while other parameters remain unchanged. The stable energy of the traveling wave tube output beam is concentrated between 13.5 and 14.5 MeV, the energy inconsistency is concentrated between 0.005 and 0.025, and the phase inconsistency is concentrated between 0.3 and 0.9. Figure 3 Compared to the previous results, the current method maintains better output bundle stability and energy consistency while improving phase consistency by approximately 40%. The initial parameters are then determined by setting the traveling wave tube injection time as the inverse initial parameters. ~ Standing wave cavity injection time: ~ ; Radio frequency phase: 115°~118°; Standing wave cavity coupling coefficient: 8.6~9.2.

[0034] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A macropulse optimization method for electron beam injectors based on the NSGA-III algorithm, characterized in that, Includes the following steps: A reference-point-based non-dominated sorting genetic algorithm with an elitist strategy is adopted to optimize the three beam parameters of macropulse bundle—stable energy, energy consistency, and phase consistency—to converge toward the optimal direction, thereby obtaining the best beam quality. The fitness function in the reference-point-based non-dominated sorting genetic algorithm with elite strategy is a computational model based on single-particle motion theory to solve the transient beam load effect of the cavity. The computational model includes solving the transient beam load of the traveling wave cavity and the transient beam load of the standing wave cavity. During the optimization process, each population corresponds to a macropulse distribution, and the gene length of a single population individual is determined by different injection times and radio frequency phase values. When calculating the fitness function of each population in each iteration, the values ​​of the input parameters required for calculation are obtained by pre-analyzing the influence of the input parameter on the beam quality. The input parameters include radio frequency parameters and structural parameters. The radio frequency parameters include radio frequency injection time and radio frequency phase, and the structural parameters include timing and standing wave cavity coupling coefficient.

2. The optimization method according to claim 1, characterized in that, The optimization process involves genetic operator operations on the offspring population, including: selection based on reference point sorting, crossover using single-point crossover, and mutation using single-point mutation.

3. The optimization method according to claim 1, characterized in that, The energy consistency and phase consistency are as follows: in, B For specific output energy or phase, B end The final output energy or phase is rms, which is the root mean square value.

4. The optimization method according to claim 1, characterized in that, The analytical expression for the transient beam load of the traveling wave cavity is: The analytical expression for the transient beam load of the standing wave cavity is: in, , The initial injected power, r For shunt impedance, l The length of the cavity. , It is a step function. , Q For quality factor, This is the beam generator current. , For power, The coupling coefficient between the waveguide and the cavity. For equivalent shunt impedance, For the load current, For the beam injection time, It is the average beam current. The attenuation constant is To take into account the energy actually carried away by the beam.

5. A macro-pulse optimization system for an electron beam injector based on the NSGA-III algorithm, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the electron beam injector macropulse optimization method based on the NSGA-III algorithm as described in any one of claims 1 to 4.

Images