Relativistic klystron design method and system based on multi-objective optimization

Abstract

The invention provides a relativistic klystron design method and system based on multi-objective optimization, and the method comprises the steps: obtaining simulation design parameters and optimization objectives of a relativistic klystron inputted by a user; according to the simulation design parameters, klystron large signal simulation software KlyH based on a one-dimensional disk model and developed independently is adopted to carry out analog simulation on a relativistic klystron, and a hybrid multi-objective optimization algorithm is adopted to optimize an optimization objective; through fusion of a hybrid multi-objective optimization algorithm and klystron large-signal simulation software KlyH based on a one-dimensional disk model, design schemes of different relativistic klystron can be efficiently explored in a multi-dimensional parameter space, multiple key indexes such as efficiency, interaction length and power can be optimized at the same time, the global search capability is also remarkably improved, and the method is suitable for large-signal simulation of klystron. High-quality design meeting complex requirements is rapidly generated, and the reliability and engineering realizability of relativistic klystron design are improved to a great extent.

Description

Technical Field

[0001] The present invention relates to the technical field of relativistic klystron design, and particularly relates to a design method and system of a relativistic klystron based on multi-objective optimization. Background Art

[0002] The relativistic klystron amplifier (RKA) has the advantages of high peak power, high efficiency, high gain, and stable output microwave frequency and phase, and is of great significance for promoting the practical application of high-power microwave systems. The RKA is an electro-vacuum O-type microwave device that uses beam-wave interaction to achieve radio frequency (RF) amplification, and has broad application prospects in technical fields such as particle accelerators, pulsed radars, and power synthesis. In the process of the RKA moving towards practical application, the number of RKAs required is often large. If the efficiency of a single RKA can be improved, the total power consumption will decrease exponentially, and the value is quite significant. In the simulation and optimization process of the klystron, one-dimensional simulation has many remarkable advantages. Usually, one-dimensional simulation has a high calculation efficiency, especially in the large-scale parameter scanning and preliminary design stages. And one-dimensional simulation has the advantage of simplifying the model. Users can quickly define parameters when setting up the simulation without having to deal with complex geometric structures. It is very meaningful to conduct in-depth research and improvement on the one-dimensional large-signal calculation program.

[0003] With the significant improvement in the requirements for bandwidth performance, multi-objective optimization, and design flexibility in modern klystron applications, the limitations of traditional simulation methods have gradually emerged. For example, some one-dimensional simulation software uses fixed parameters and single-objective optimization methods, resulting in an overly long design cycle and difficulty in quickly approaching the target in terms of efficiency and accuracy.

[0004] Therefore, the existing technology still needs to be further developed. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above technical deficiencies and provide a design method and system of a relativistic klystron based on multi-objective optimization to solve the problems existing in the existing technology.

[0006] To achieve the above technical purpose, according to the first aspect of the present invention, the present invention provides a design method of a relativistic klystron based on multi-objective optimization, including: S100. Obtain the simulation design parameters and optimization objectives of the relativistic klystron input by the user; S200. According to the simulation design parameters, use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to simulate the relativistic klystron, and use the hybrid multi-objective optimization algorithm to optimize the optimization objectives to obtain an optimized relativistic klystron.

[0007] Specifically, the simulation design parameters include: The microwave parameters, calculation parameters, electron beam parameters, and resonator modulation parameters of a relativistic klystron.

[0008] Specifically, the hybrid multi-objective optimization algorithm includes a first-stage coarse search and a second-stage fine optimization.

[0009] Specifically, the method of using the hybrid multi-objective optimization algorithm to optimize the optimization objective includes: S210. Determine the optimization parameters; S220. Conduct the first-stage coarse search, and use the non-dominated sorting genetic algorithm to generate multiple design schemes for the optimization parameters of the relativistic klystron; S230. Conduct the second-stage fine optimization, finely optimize the multiple design schemes for the optimization parameters of the relativistic klystron generated in the first-stage coarse search, then generate multiple design schemes for the optimization parameters of the relativistic klystron, and select the optimal scheme from the multiple design schemes.

[0010] Specifically, S220 includes: Use the non-dominated sorting genetic algorithm to generate multiple design schemes for the optimization parameters of the relativistic klystron, and screen the Pareto optimal solution set of the non-dominated sorting genetic algorithm according to the physical characteristics of the relativistic klystron; The optimization parameters meet the requirements of the preset physical constraint mechanism.

[0011] Specifically, the method of conducting the first-stage coarse search and using the non-dominated sorting genetic algorithm to generate multiple design schemes for the optimization parameters of the relativistic klystron specifically includes: Use the non-dominated sorting genetic algorithm to generate multiple design schemes for the optimization parameters of the relativistic klystron, use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to calculate the objective function values of the optimization objectives obtained from multiple design schemes for the optimization parameters of the relativistic klystron in sequence, take the multiple design schemes for the optimization parameters of the relativistic klystron as the initial population, then conduct non-dominated sorting on the initial population, divide it into different ranks, and calculate the crowding distance to measure the diversity between individuals, and then enter the optimization iteration loop. The specific process of the optimization iteration loop is as follows: Generate an offspring population through selection, crossover, and mutation operations, merge the parent population and the offspring population and then conduct non-dominated sorting again, and select the first preset number of individuals according to the rank and crowding degree to form a new generation population. Determine whether the number of iterations reaches the preset number of iterations or converges. If so, output the Pareto solution set. Otherwise, repeat the optimization iteration loop process again until the preset number of iterations or convergence is reached.

[0012] Specifically, S230 includes: Perform the second - stage fine optimization. Use the design schemes of the optimized parameters of multiple relativistic klystrons generated in the first - stage rough search as part of the initial particles of the multi - objective particle swarm optimization algorithm with the optimal solution, then generate the design schemes of the optimized parameters of multiple relativistic klystrons, and select the optimal scheme from multiple design schemes.

[0013] Specifically, the preset physical constraint mechanism includes: Apply a physical constraint range to the optimized parameters.

[0014] Specifically, the optimization objectives include at least two of the following parameters: The parameters include the length of the electron beam drift tube section of the relativistic klystron, output efficiency, and bandwidth.

[0015] According to the second aspect of the present invention, a relativistic klystron design system based on multi - objective optimization is provided, including: An acquisition module: used to acquire the simulation design parameters and optimization objectives of the relativistic klystron input by the user; An optimization module: used to simulate and analyze the relativistic klystron using the klystron large - signal simulation software KlyH based on the one - dimensional disk model according to the simulation design parameters, and optimize the optimization objectives using a hybrid multi - objective optimization algorithm to obtain an optimized relativistic klystron.

[0016] Beneficial effects: The present invention provides a relativistic klystron design method based on multi - objective optimization. The klystron large - signal simulation software KlyH based on the one - dimensional disk model is used to simulate and analyze the relativistic klystron, and a hybrid multi - objective optimization algorithm is used to optimize the optimization objectives. Through the integration of the hybrid multi - objective optimization algorithm and the klystron large - signal simulation software KlyH based on the one - dimensional disk model, it is possible to efficiently explore different design schemes of relativistic klystrons in a multi - dimensional parameter space. It can not only optimize multiple key indicators such as efficiency, interaction length, and power simultaneously, but also significantly improve the global search ability, quickly generate high - quality designs that meet complex requirements. The multi - objective optimization method of this application is particularly suitable for the analysis of a large number of coupled variables and non - linear effects involved in high - efficiency and compact RKA designs, thereby breaking through the bottlenecks in terms of efficiency, bandwidth, and engineering practicality of traditional methods, and greatly improving the reliability and engineering feasibility of the relativistic klystron design in the present invention. Description of the Drawings

[0017] Figure 1 is the flowchart of the relativistic klystron design method based on multi - objective optimization provided in the specific embodiment of the present invention; Figure 2 is the schematic diagram of the composition of the relativistic klystron design system based on multi - objective optimization provided in the specific embodiment of the present invention; Figure 3 It is the workflow diagram of the klystron large-signal simulation software KlyH based on the one-dimensional disk model provided in the specific embodiment of the present invention; Figure 4 It is the flowchart of the implementation of the hybrid multi-objective optimization algorithm provided in the specific embodiment of the present invention; Figure 5 It is the solution set diagram after hybrid optimization provided in the specific embodiment of the present invention; Figure 6 It is the result of optimizing the efficiency and interaction length by using the NSGA-II algorithm and the OMOPSO algorithm respectively provided in the specific embodiment of the present invention; Figure 7 The schematic diagram of the computational efficiency comparison between the NSGA-II algorithm and the OMOPSO algorithm provided in the specific embodiment of the present invention. Specific Embodiment

[0018] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention. Based on the embodiments in this application, other similar embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of this application. In addition, the directional terms mentioned in the following embodiments, such as "upper", "lower", "left", "right", etc., are only with reference to the directions of the accompanying drawings. Therefore, the directional terms used are for illustration rather than to limit the present invention.

[0019] The present invention will be further described below in conjunction with the accompanying drawings and preferred embodiments.

[0020] Please refer to Figure 1 , this embodiment provides a design method for a relativistic klystron based on multi-objective optimization, including: S100. Obtain the simulation design parameters and optimization objectives of the relativistic klystron input by the user; S200. According to the simulation design parameters, use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to simulate and simulate the relativistic klystron, and use the hybrid multi-objective optimization algorithm to optimize the optimization objectives to obtain an optimized relativistic klystron.

[0021] It should be noted here that the klystron large-signal simulation software KlyH based on the one-dimensional disk model is an independently controllable relativistic klystron simulation software designed by the present invention. It is used to realize the one-dimensional large-signal simulation of the relativistic klystron, can efficiently simulate the working process of the relativistic klystron, and can efficiently perform calculation tasks such as large-signal simulation, bandwidth analysis and efficiency evaluation. Through highly optimized numerical calculation methods, the KlyH software greatly improves the simulation speed, supports the rapid scanning of large-scale parameter spaces and multi-objective optimization calculations, can accurately simulate the behavior of the relativistic klystron under different working conditions, and generates accurate simulation results, ensuring the scientificity and accuracy of design decisions, and greatly meeting the requirements of efficient and high-precision simulation.

[0022] Furthermore, the klystron large-signal simulation software KlyH based on the one-dimensional disk model has a numerical program based on the one-dimensional disk model developed in Fortran language as its core, which can simulate the modulation process of the electron beam in the cavity and calculate key performance parameters such as electron beam efficiency, interaction length, and gain. Compared with traditional analytical methods, this numerical simulation program can more accurately describe the electron-microwave interaction, especially suitable for the nonlinear analysis of relativistic klystrons. This method can perform simulation calculations based on input parameters such as electron beam parameters, cavity geometry parameters, input microwave power, and resonator modulation parameters, and provide high-precision performance output values, providing a reliable physical basis for optimization.

[0023] During the optimization process, the KlyH software serves as the core for calculating the objective function, providing simulation feedback for the optimization parameter design schemes of different relativistic klystrons. Compared with traditional empirical design methods, this method quantifies the relationships between parameters such as efficiency, gain, and interaction length through numerical calculations, avoiding the high-cost problem of over-reliance on three-dimensional simulations and experiments.

[0024] The core algorithms of KlyH one-dimensional simulation include the following parts: (1) One-dimensional electron disk model: For a solid electron beam, the following assumptions are made: It is considered to be composed of many layers of electrons, each layer is an infinitely thin electron disk, the behavior of each electron on the disk is the same, there is no transverse motion, and the disk does not deform during the motion, just like a rigid body. It is assumed that the disk is transparent, that is, other disks are allowed to pass through. When two disks are infinitely close, the force between them is zero, the focusing magnetic field is infinitely large, and the electron beam works in a space-charge-limited state; (2) Position and velocity model of electron disks: Calculated according to kinematic theory through relativistic equations of motion; (3) Resonator gap impedance model: Calculate the gap impedances of the input cavity, output cavity, and intermediate cavity according to the equivalent circuit; (4) Induced current and gap voltage model: By performing Fourier expansion on the induced current, the induced current components of each harmonic can be obtained, which are used to calculate the induced current. Then, based on parameters such as the gap impedance and the induced current, the gap voltage is calculated. (5) Output power and efficiency calculation model: Based on data such as the high-frequency voltage, current, and external quality factor of the output cavity, parameters such as the output power and efficiency of the relativistic klystron are calculated.

[0025] Specifically, the simulation design parameters include: The microwave parameters, calculation parameters, electron beam parameters, and resonator modulation parameters of the relativistic klystron.

[0026] It should be further noted that in the design method of the multi-objective optimized relativistic klystron in this embodiment, the microwave parameters of the relativistic klystron include the input microwave power and the input microwave frequency; the calculation parameters include the number of disks, the number of times each high-frequency cycle pushes the disk, the maximum number of iterations, and the initial value of the total number of times of pushing the disk; the electron beam parameters include the beam voltage, beam current, beam radius, and drift tube radius; the resonator modulation parameters include the resonant frequency of the resonator, the axial position of the resonator, the characteristic impedance of the resonator, the gap width, and the harmonic number. When using the klystron large-signal simulation software KlyH based on the one-dimensional disk model for simulation, the gap voltage and induced current of the resonator are calculated one by one through a loop, and it is judged whether the gap voltage converges. The output cavity is the resonator in the relativistic klystron that finally extracts energy, and its convergence state directly determines the performance index. The convergence result can ensure that the simulation result reflects the steady-state physical process and avoids transient errors. If the gap voltage converges and it is the output cavity, the output efficiency and output data are calculated.

[0027] In some specific embodiments, the optimization objectives include at least two of the following parameters: The parameters include the length of the electron beam drift tube section, output efficiency, bandwidth, etc. of the relativistic klystron.

[0028] It can be understood that in the simulation of the relativistic klystron, improving the efficiency usually requires a longer interaction length, that is, the length of the electron beam drift tube section, while shortening the interaction length often reduces the output efficiency. Therefore, the optimized design of the relativistic klystron needs to balance high efficiency and a compact structure. Therefore, the performance optimization objectives are high efficiency and low tube length. The optimization of the present invention is based on specific relativistic klystron examples to ensure that the optimization results meet physical constraints and engineering feasibility.

[0029] Further, the process of converting the simulation design parameters input by the user into a klystron simulation example is as follows: (1) Read the microwave parameters, calculation parameters, electron beam parameters, and resonator modulation parameters input by the user. (2)Construct the initialization model data of the relativistic klystron according to these parameters; (3)Set the initial parameters of the electron beam, including beam voltage, beam current, beam radius, drift tube radius, etc.; (4)Set the initial parameters of the input microwave, including input microwave power 、 Input microwave frequency, etc.; (5)Set the calculation parameters, including the number of disks, the number of times to push the disks per high-frequency period, the maximum number of iterations, the initial value of the total number of times to push the disks, etc.; (6)Set the modulation parameters of each resonant cavity, including the characteristic impedance R / Q of the resonant cavity, resonant frequency, the axial position of the resonant cavity, the external quality factor of the resonant cavity, etc.; (7)Transfer the constructed model to the core algorithm program of KlyH one-dimensional simulation for calculation.

[0030] After the core algorithm program of KlyH one-dimensional simulation is calculated, it will return the simulation results of the relativistic klystron, including parameters such as output power, efficiency, gain, bandwidth, etc.

[0031] Specifically, the hybrid multi-objective optimization algorithm includes a first-stage rough search and a second-stage fine optimization. The method of using the hybrid multi-objective optimization algorithm to optimize the optimization objective includes: S210. Determine the optimization parameters, and the optimization parameters include but are not limited to the resonant frequency of the resonant cavity, the length of the drift tube between cavities, the external quality factors of the input and output cavities, etc.; S220. Conduct the first-stage rough search, and use the non-dominated sorting genetic algorithm to quickly generate multiple design schemes of the optimization parameters of the relativistic klystron; Specifically, the S220 includes: Use the non-dominated sorting genetic algorithm to generate multiple design schemes of the optimization parameters of the relativistic klystron, and screen the Pareto optimal solution set of the non-dominated sorting genetic algorithm according to the physical characteristics of the relativistic klystron; Specifically, the method of conducting the first-stage rough search and using the non-dominated sorting genetic algorithm to generate multiple design schemes of the optimization parameters of the relativistic klystron specifically includes: Use the non-dominated sorting genetic algorithm to generate multiple design schemes of the optimization parameters of the relativistic klystron. Use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to calculate the objective function values of the optimization objectives obtained by multiple design schemes of the optimization parameters of the relativistic klystron in turn. Take multiple design schemes of the optimization parameters of the relativistic klystron as the initial population, and then conduct non-dominated sorting on the initial population, divide it into different levels, and calculate the crowding distance to measure the diversity between individuals. Then enter the optimization iteration loop. The specific process of the optimization iteration loop is as follows: Generate the offspring population through selection, crossover, and mutation operations. After merging the parent population and the offspring population, perform non-dominated sorting again, and select the first preset number of individuals according to the rank and crowding degree to form a new generation population. Determine whether the number of iterations reaches the preset number of iterations or converges. If so, output the Pareto solution set; otherwise, repeat the optimization iteration loop process again until the preset number of iterations or convergence is reached.

[0032] Furthermore, the first preset number in this embodiment can be selected by the user according to actual needs. For example, the first N individuals can be selected to form a new generation population. The preset number of iterations can also be set according to the user's settings. For example, the preset number of iterations can be set to 100 times.

[0033] The optimization parameters meet the requirements of the preset physical constraint mechanism.

[0034] Specifically, the preset physical constraint mechanism includes: imposing a physical constraint range on the optimization parameters.

[0035] It should be further noted that for the physical constraints of the relativistic klystron in this embodiment, the optimization examples and the selection of optimization parameters are both through physical simulation and effectiveness analysis. Since the design of the relativistic klystron is restricted by many factors, variables cannot be adjusted randomly during the optimization process, but must be optimized within the range that can be realized in engineering. To ensure the feasibility of the optimization results, a boundary constraint mechanism, that is, a preset physical constraint mechanism, is introduced in this method to ensure that the solution of the optimization parameters does not violate physical laws. Due to the mutual coupling of the physical characteristics such as the electron beam characteristics, resonator parameters, and input microwave power of the relativistic klystron, the range of the parameters to be optimized cannot be given randomly, but the key design variables need to be adjusted within a reasonable range.

[0036] See Figure 4 , in some specific embodiments, the specific steps of the first-stage coarse search are as follows: Step 1: Input stage; Determine the basic parameters (simulation design parameters) of the relativistic klystron instance to be optimized, determine the basic parameters of the non-dominated sorting genetic algorithm, and determine that the range of the optimization parameters is within the physically allowed range; Step 2: Initialize the population; Generate an initial population using the NSGA-II algorithm, and these individuals represent different schemes for the design of the relativistic klystron; Step 3: Calculate the objective function value; Evaluate each individual, and use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to calculate the objective function values of key indicators such as its output efficiency and interaction length.

[0037] Step 4: Fast non-dominated sorting and crowding degree calculation; a. Divide the population into different ranks through non - dominated sorting to determine which individuals are the current optimal solutions; b. Calculate the crowding degree of each individual to maintain the diversity of the population.

[0038] Step 5: Selection, crossover, and mutation; a. Adopt the elitist selection strategy to retain excellent individuals.

[0039] b. Perform crossover and mutation operations to generate a new offspring population.

[0040] Step 6: Output the Pareto solution set; After multiple iterations, a preliminary Pareto optimal solution set is obtained. These solutions cover the design space of the relativistic klystron and provide multiple output efficiency - tube length trade - off schemes.

[0041] It can be understood that in this embodiment, the large - signal simulation software KlyH of the klystron based on the one - dimensional disk model is used to calculate the objective function, avoiding physically infeasible solutions that may occur in pure mathematical optimization. By combining the actual working principle of the relativistic klystron, the optimization results can meet the effectiveness of the electron beam - microwave interaction and the rationality of the cavity resonance frequency and cavity position. This method not only improves the applicability of the optimization algorithm but also enhances the reliability and engineering feasibility of the relativistic klystron design.

[0042] S230. Conduct the second - stage fine optimization. Fine - optimize the design schemes of the optimization parameters of multiple relativistic klystrons generated in the first - stage rough search, then generate multiple design schemes of the optimization parameters of the relativistic klystron, and select the optimal scheme from multiple design schemes.

[0043] Specifically, S230 includes: Conduct the second - stage fine optimization. Use the design schemes of the optimization parameters of multiple relativistic klystrons generated in the first - stage rough search as part of the initial particles of the multi - objective particle swarm algorithm for the optimal solution, then generate multiple design schemes of the optimization parameters of the relativistic klystron, and select the optimal scheme from multiple design schemes.

[0044] It can be understood that the above - mentioned design schemes of the optimization parameters all meet the requirements of the preset physical constraint mechanism.

[0045] Specifically, the method specifically includes: Use the optimal solution multi-objective particle swarm algorithm to generate design schemes for the optimization parameters of multiple relativistic klystrons. Initialize their positions and velocities, and use the klystron large-signal simulation software KlyH based on the one-dimensional disk model to calculate the objective function values of the optimization objectives obtained from the design schemes of the optimization parameters of multiple relativistic klystrons in turn. At the same time, the individual optimal solution of each particle is initialized to its current position, and the global optimal solution is initialized to the optimal particle in the population. The velocity of each particle is adjusted according to the individual and global optimal solutions, and the position is updated accordingly. If the new position of the particle is better than its individual optimal solution, the individual optimal solution is updated. Then, the particles are mutated with a certain probability to increase diversity and avoid falling into local optima. The updated particles need to recalculate the objective function values. Then, through non-dominated sorting, all non-dominated particles in the population are identified and added to the non-dominated set. If the new position of the particle is better than its current individual optimal solution, the individual optimal solution is updated, and the non-dominated particles are stored in the external set to maintain the diversity of the solution set. Then, according to the particles in the external set, the global optimal solution is updated until the preset number of iterations or convergence is reached, and the Pareto solution set is output.

[0046] It can be understood that for the optimization problem of high-efficiency compact klystrons, those skilled in the art can find that the non-dominated sorting genetic algorithm (NSGA-II) has a low time cost and a relatively dispersed optimal solution set, which is suitable for global fast search. At the same time, the optimal solution multi-objective particle swarm algorithm (OMOPSO) has a high time cost and a relatively concentrated optimal solution set, which is suitable for local optimal search. Therefore, a hybrid multi-objective optimization algorithm (including NSGA-II and OMOPSO) is used to optimize the optimization objectives, as Figure 6 and Figure 7 shown. Figure 6 are the results of optimizing the output efficiency and interaction length using the NSGA-II algorithm and the OMOPSO algorithm respectively. It can also be seen from this that the optimal solution set obtained by the NSGA-II algorithm is relatively dispersed, but the general efficiency is lower than that of the OMOPSO algorithm. The optimal solution set obtained by the OMOPSO algorithm is relatively concentrated, but the total interaction length obtained is shorter. Figure 7The horizontal coordinate (population size) represents the size of the population during the algorithm's operation, ranging from 0 to 1000 individuals. The vertical coordinate (computational efficiency) represents the computational time cost of the algorithm under different population sizes, with the unit being minutes. It can be seen from the figure that in the case of 5 generations and 10 generations of the OMOPSO algorithm, as the population size increases, the computational time increases significantly. For example, when there are 1000 individuals, the computational time of OMOPSO_10 generations is close to 200 minutes. Therefore, the time cost of the OMOPSO algorithm is relatively high, especially when the population size is large. In the case of 5 generations and 10 generations of the NSGA-II algorithm, the computational time is significantly lower than that of the OMOPSO algorithm. Even at the maximum population size (1000 individuals), the computational time of NSGA-II_10 generations is only about 30 minutes. Therefore, the time cost of the NSGA-II algorithm is low and does not change much with the population size.

[0047] Furthermore, according to Figure 6 and Figure 7 , the multi-objective optimization strategy that combines the NSGA-II algorithm and the OMOPSO algorithm can give full play to their respective advantages and achieve efficient global and local optimization. Figure 5 is the optimization result obtained by optimizing the total interaction length and output efficiency using the hybrid multi-objective optimization algorithm that combines the NSGA-II algorithm and the OMOPSO algorithm. Its optimization effect is significantly better than Figure 6 the effects when only the NSGA-II algorithm or only the OMOPSO algorithm is used alone in . The output efficiency is increased by nearly 10%, and at the same time, the interaction length is shortened. Therefore, the combination of the above two algorithms can give full play to their respective advantages and enable the present application to achieve a balance in the optimization between high efficiency and a compact structure.

[0048] It should be further noted that the multi-objective particle swarm optimization algorithm (MOPSO) was proposed by Carlos Artemio Coello Coello in 2002. This algorithm is an extension based on the particle swarm optimization algorithm and aims to solve multi-objective optimization problems. The optimal multi-objective particle swarm algorithm (OMOPSO algorithm) in the present invention is proposed based on MOPSO. The OMOPSO algorithm constructs a non-dominated solution set based on the Pareto dominance relationship, uses an external set to save the currently found non-dominated solution set, proposes the concept of strong ε-dominance based on ε-dominance, and uses it to update the external set to enable the algorithm to maintain good distribution. By improving the selection methods of the global best and individual best in the MOPSO algorithm, at the same time adopting a new particle update strategy to accelerate the convergence of the solution set, adding an adaptive mutation operator to avoid falling into local non-dominated optimal solutions, and proposing a method for constructing a non-dominated set based on quicksort to accelerate the running efficiency of the algorithm. The main framework of the OMOPSO algorithm is as follows: (1) Initialization Randomly generate a population containing N particles, where each particle represents a solution. Initialize its position and velocity, calculate the objective function value of each particle, and initialize the individual best solution of each particle to its current position, and initialize the global best solution to the best particle in the population; (2) Iterative process (iteration reaches the preset maximum number of generations or the solution converges) The velocity of each particle is adjusted according to the individual and global best solutions, and the position is updated accordingly. If the new position of the particle is better than its individual best solution, update the individual best solution, and then mutate the particle with a certain probability to increase diversity and avoid falling into local optima. The updated particle needs to recalculate the objective function value; then, through non-dominated sorting, identify all non-dominated particles in the population and add them to the non-dominated set. If the new position of the particle is better than its current individual best solution, update the individual best solution; store the non-dominated particles in the external set to maintain the diversity of the solution set, and then update the global best solution according to the particles in the external set.

[0049] See Figure 4 , in some specific embodiments, the specific steps of the second-stage fine optimization are as follows: Step 1: Pareto solution screening and transformation; Convert the Pareto optimal solution set generated by the first-stage rough search into particles in the particle swarm optimization algorithm.

[0050] Step 2: Initialize the particle swarm: Use the screened Pareto solutions as part of the initial particles to initialize the particle swarm.

[0051] Step 3: Particle update and local search; a. The OMOPSO algorithm uses the information exchange and learning mechanism between particles to update the position and velocity of particles; b. Conduct local refinement search in the search space to further improve the quality and accuracy of the solution.

[0052] Step 4: Output Pareto solutions; After local optimization, obtain the final Pareto optimal solution set, and these solutions have higher convergence and accuracy.

[0053] Step 5: Output stage; Import the final Pareto solution set into the KlyH simulation software for verification and visualization analysis to ensure the feasibility and performance of the design scheme.

[0054] It is understandable that in the solution proposed in this embodiment, which combines the KlyH and multi-objective optimization hybrid algorithm, since the NSGA-II algorithm performs excellently in terms of computational output efficiency and global search, while the OMOPSO algorithm performs excellently in local search, a multi-objective optimization method that combines the NSGA-II algorithm and the OMOPSO algorithm is adopted. First, the NSGA-II algorithm is used in the first-stage rough search to construct a preliminary Pareto solution set within the range of optimized parameters of the given klystron instance. The goal of the first stage is to cover as much as possible the design space of the relativistic klystron, ensure the diversity of the optimization scheme, and provide multiple efficiency-length compromise schemes for subsequent optimization. Then, based on the Pareto optimal solution set generated by the NSGA-II algorithm, the OMOPSO algorithm is used in the second-stage fine optimization to further improve the quality of the solution. As an improved version of the particle swarm optimization algorithm, the OMOPSO algorithm can use the Pareto solutions of the NSGA-II algorithm as guiding particles to further refine the design scheme in the search space, improve the convergence and accuracy of the optimized solution, and at the same time strictly satisfy the physical constraint conditions of the klystron. This method can not only achieve a balance between high efficiency and a compact structure, but also ensure that the optimization results meet the actual engineering applications. Compared with a single optimization method, it can more efficiently find a design scheme for a relativistic klystron that takes into account both high efficiency and a compact structure, further enhancing the feasibility and stability of the relativistic klystron design of the present invention.

[0055] See Figures 3 - 5 , the working principle of the present invention will be described below through specific examples: 1. According to the idea of the present invention, design and implement the principle of a relativistic klystron simulation framework based on KlyH numerical simulation. Figure 3 is the working principle diagram of the klystron large-signal simulation software KlyH based on a one-dimensional disk model. The specific process is as follows: First, input simulation design parameters such as DC electron beam parameters, resonator high-frequency parameters, total number of resonators, injected microwave power and frequency, number of disks, maximum number of iterations, etc., and initialize the resonator gap voltage and induced current. Then, use the electron load conductance and resonator gap impedance calculation models to provide a basis for the calculation of the gap voltage. During the calculation process, the gap voltage and induced current of each resonator are solved one by one through a loop, and it is judged whether the gap voltage converges. If it does not converge, continue to iterate until the convergence condition is met. Specifically, it includes: (1) Start and input data, where the input data includes: DC electron beam parameters, resonator high-frequency parameters, total number of resonators Ncav, injected microwave power and frequency, number of disks, maximum number of iterations itermax, and the initial value of the total number of times to push the disks. (2) Initialization: Assign initial values to the gap voltages and induced currents of each resonant cavity, and initialize the loop variables \(i = 1\) and \(j = 0\). Here, \(i\) is used to traverse the resonant cavities, and \(j\) is used to control the number of iterations. (3) Calculate the electron load conductance and the gap impedances of each resonant cavity to prepare for the subsequent calculation of the gap voltages. (4) Calculate the gap voltages and induced currents of the resonant cavities one by one in a loop. Determine whether the gap voltages converge. If they do not converge, drive the disk to recalculate the induced currents and gap voltages until the gap voltages converge: (5) Determine whether the current cavity is the output cavity. If it is, calculate the efficiency and output data; otherwise, return to step (4). Finally, if the calculation reaches the output cavity, solve for the electron beam output efficiency and other output parameters; otherwise, return and continue the iterative calculation.

[0056] 2. Hybrid multi-objective optimization method based on NSGA-II algorithm and OMOPSO algorithm. The specific process is as Figure 4 shown; In this example, taking the optimization of a 6-cavity single-beam relativistic klystron as an example, the steps to determine the instance parameters of the relativistic klystron are as follows. The simulation design parameters include calculation parameters: the number of disks is 64, the disk is driven 32 times per high-frequency cycle, the maximum number of iterations is 200, and the initial value of the total number of disk drives is 1000; electron beam parameters: beam voltage \(V_0 = 450\ kV\), beam current \(I_0 = 105\ A\), beam radius \(R_b = 2.1\ mm\), drift tube radius \(R_t = 3.5\ mm\); microwave parameters: input microwave power \(P_0 = 100\ W\), input microwave frequency \(f_0 = 10\ GHz\); the modulation parameters of each resonant cavity are shown in Table 1, where \(f\) is the resonant frequency of the resonant cavity, \(z\) is the relative position of the resonant cavity along the axis with respect to the input cavity, \(Q\) ext is the external quality factor of the resonant cavity. To meet the requirements of engineering design, the value of \(Q\) ext of the bunching cavity is taken as 950000, \(R / Q\) is the characteristic impedance of the resonant cavity. Using the klystron large-signal simulation software KlyH based on the one-dimensional disk model, the output efficiency of the relativistic klystron in this example is 55.2%, and the total interaction length (the length of the electron beam drift tube section) is 43.57 cm.

[0057] Table 1 Modulation parameters of each resonant cavity before optimization Determine that the optimization objectives of this example are the electron beam drift tube section length and output efficiency of the relativistic klystron, and the optimization parameters are the resonant frequency (\(f\)) of the cavity, the drift tube length (\(l\)) between the cavities, and the external quality factors (\(Q\) ext ) of the input and output cavities; The number of seeds of the NSGA-II algorithm is determined to be 1000, the maximum number of iterations is 10, the mutation rate is 0.07, and the crossover rate is 0.9; the number of seeds of the OMOPSO algorithm is determined to be 1000, the maximum number of iterations is 10, and the mutation rate is 0.07. Use the NSGA-II algorithm for multi-objective optimization. Its general process is to randomly generate multiple relativistic klystron schemes according to the input data, calculate the objective function values using the klystron large-signal simulation software KlyH based on the one-dimensional disk model, and then start non-dominated sorting and crowding degree calculation. Through selection, crossover, and mutation, perform non-dominated sorting and crowding degree calculation on the new population until the iteration number is reached or convergence occurs, and then output the Pareto solution set. The design schemes in the Pareto solution set are used as part of the initial particle swarm of the OMOPSO algorithm to ensure that the initial solution set has good quality for further optimization. After the OMOPSO algorithm optimization is completed, the finally obtained optimal design scheme is output, including parameters such as high efficiency and low tube length, and a Pareto front graph is drawn. Figure 5 It is the solution set graph after hybrid optimization, and the selected optimal design scheme. Table 2 is the modulation parameter table of each resonant cavity after optimization. Perform KLY5 simulation, and its efficiency is increased by 26.6%, and the total interaction length is 41.6 cm, which is reduced by 19.7 mm compared with before optimization. Thus, it can be seen that the multi-objective optimization method of the present invention provides an intuitive basis for engineering decision-making.

[0058] Table 2 Modulation parameters of each resonant cavity after optimization 3. The optimization strategy combining optimization variable selection and physical constraints is as follows: In this example, for the physical constraints of the relativistic klystron, physical analysis is carried out when selecting examples and optimization parameters. Finally, key parameters such as the resonant frequency of the resonant cavity, the drift tube length between cavities, and the external quality factor of the input and output cavities are selected as optimization parameters. Due to the limitations of factors such as the velocity modulation and bunching of the electron beam, the application of microwave resonant cavities, and the structure design and manufacturing process, variables cannot be adjusted randomly during the optimization process, but must be optimized within the range that can be realized in engineering. To ensure the feasibility of the optimization results, a boundary constraint mechanism is introduced in the optimization process of this application, that is, a definite floating range is set for each optimization parameter to ensure that the optimization solution does not violate physical laws. This method not only improves the applicability of the optimization algorithm, avoids physically infeasible solutions that may occur in pure mathematical optimization, ensures that the final design scheme can effectively guide 3D simulation and practical applications, and improves the reliability and engineering realizability of relativistic klystron design.

[0059] It should be noted here that this embodiment provides a design method for a relativistic klystron based on multi-objective optimization. The large-signal simulation software KlyH for klystrons based on a one-dimensional disk model is used to simulate and analyze the relativistic klystron, and a hybrid multi-objective optimization algorithm is used to optimize the optimization objectives. Through the integration of the hybrid multi-objective optimization algorithm and the large-signal simulation software KlyH for klystrons based on a one-dimensional disk model, different design schemes of relativistic klystrons can be efficiently explored in a multi-dimensional parameter space. It can not only optimize multiple key indicators such as efficiency, interaction length, and power simultaneously, but also significantly improve the global search ability, quickly generate high-quality designs that meet complex requirements. The multi-objective optimization method of this application is particularly suitable for the analysis of a large number of coupled variables and nonlinear effects involved in efficient and compact RKA designs, thus breaking through the bottlenecks of traditional methods in terms of efficiency, bandwidth, and engineering practicability, and greatly improving the reliability and engineering feasibility of the relativistic klystron design in the present invention.

[0060] Please refer to Figure 2 , this embodiment provides a design system for a relativistic klystron based on multi-objective optimization. The system includes: An acquisition module 100: used to acquire the simulation design parameters and optimization objectives of the relativistic klystron input by the user; An optimization module 200: used to simulate and analyze the relativistic klystron according to the simulation design parameters by using the large-signal simulation software KlyH for klystrons based on a one-dimensional disk model, and optimize the optimization objectives by using a hybrid multi-objective optimization algorithm to obtain an optimized relativistic klystron.

[0061] It should be noted here that this embodiment provides a design system for a relativistic klystron based on multi-objective optimization. The large-signal simulation software KlyH for klystrons based on a one-dimensional disk model is used to simulate and analyze the relativistic klystron, and a hybrid multi-objective optimization algorithm is used to optimize the optimization objectives. Through the integration of the hybrid multi-objective optimization algorithm and the large-signal simulation software KlyH for klystrons based on a one-dimensional disk model, different design schemes of relativistic klystrons can be efficiently explored in a multi-dimensional parameter space. It can not only optimize multiple key indicators such as efficiency, interaction length, and power simultaneously, but also significantly improve the global search ability, quickly generate high-quality designs that meet complex requirements. The multi-objective optimization method of this application is particularly suitable for the analysis of a large number of coupled variables and nonlinear effects involved in efficient and compact RKA designs, thus breaking through the bottlenecks of traditional methods in terms of efficiency, bandwidth, and engineering practicability, and greatly improving the reliability and engineering feasibility of the relativistic klystron design in the present invention.

[0062] It should be noted that the terms "first", "second", etc. in the description, claims and the above-mentioned drawings of this application are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0063] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification as long as such a combination does not exist in contradiction.

[0064] The specific embodiments of the present invention described above do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and deformations made according to the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A relativistic klystron design method based on multi-objective optimization, characterized in that: include: S100, obtaining simulation design parameters and optimization targets of a relativistic klystron input by a user; S200, according to the simulation design parameters, using a klystron large signal simulation software KlyH based on a one-dimensional disk model to simulate the relativistic klystron, and using a hybrid multi-objective optimization algorithm to optimize the optimization target to obtain an optimized relativistic klystron.

2. The relativistic klystron design method based on multi-objective optimization according to claim 1, characterized in that: The simulation design parameters include: Microwave parameters, calculation parameters, electron beam parameters, and resonant cavity modulation parameters of the relativistic klystron.

3. The relativistic klystron design method based on multi-objective optimization according to claim 1, characterized in that: The hybrid multi-objective optimization algorithm includes a first-stage coarse search and a second-stage fine optimization.

4. The relativistic klystron design method based on multi-objective optimization according to claim 3, characterized in that: The method of optimizing the optimization target by using a hybrid multi-objective optimization algorithm comprises: S210, determining optimization parameters; S220, performing a first-stage rough search, using a non-dominated sorting genetic algorithm to generate a plurality of design schemes for optimizing parameters of relativistic klystrons; S230, performing a second stage of fine optimization, finely optimizing the design schemes of the optimization parameters of the multiple relativistic klystrons generated by the rough search in the first stage, then generating multiple design schemes of the optimization parameters of the relativistic klystrons, and selecting the best scheme from the multiple design schemes.

5. The relativistic klystron design method based on multi-objective optimization according to claim 4, characterized in that: The S220 includes: The non-dominated sorting genetic algorithm is used to generate multiple design schemes for optimizing parameters of relativistic klystrons, and the Pareto optimal solution set of the non-dominated sorting genetic algorithm is selected according to the physical characteristics of the relativistic klystron. The optimization parameters meet the requirements of the preset physical constraint mechanism.

6. The relativistic klystron design method based on multi-objective optimization according to claim 5, characterized in that: The method of performing the first-stage rough search and using a non-dominated sorting genetic algorithm to generate a plurality of design schemes for optimizing parameters of relativistic klystrons specifically includes: A non-dominated sorting genetic algorithm is used to generate multiple design schemes for the optimization parameters of relativistic klystrons. The klystron large signal simulation software KlyH based on a one-dimensional disk model is used to sequentially calculate the objective function values ​​of the optimization targets obtained by the design schemes for the optimization parameters of multiple relativistic klystrons. The design schemes for the optimization parameters of multiple relativistic klystrons are used as the initial population, and then the initial population is non-dominatedly sorted and divided into different levels. The crowding distance is calculated to measure the diversity between individuals, and then the optimization iteration cycle is entered. The specific process of the optimization iteration cycle is as follows: The offspring population is generated through selection, crossover and mutation operations. The parent population and the offspring population are merged and then non-dominated sorting is performed again. The first preset number of individuals are selected according to the level and crowding degree to form a new generation population. It is judged whether the number of iterations reaches the preset number of iterations or whether it converges. If so, the Pareto solution set is output. Otherwise, the optimization iterative cycle process is repeated again until the preset number of iterations is reached or convergence occurs.

7. The relativistic klystron design method based on multi-objective optimization according to claim 5, characterized in that: The S230 includes: The second stage of fine optimization is carried out, and the design schemes of the optimization parameters of multiple relativistic klystrons generated by the rough search in the first stage are used as some initial particles of the optimal solution multi-objective particle swarm algorithm. Then, multiple design schemes of the optimization parameters of relativistic klystrons are generated, and the optimal scheme is selected from multiple design schemes.

8. The relativistic klystron design method based on multi-objective optimization according to claim 6, characterized in that: The preset physical constraint mechanism includes: Imposing physical constraints on optimization parameters.

9. The relativistic klystron design method based on multi-objective optimization according to claim 1, characterized in that: The optimization objective includes at least two of the following parameters: The parameters include the electron beam drift tube interval length, output efficiency and bandwidth of the relativistic klystron.

10. A relativistic klystron design system based on multi-objective optimization, characterized in that: include: Acquisition module: used to obtain the simulation design parameters and optimization targets of the relativistic klystron input by the user; Optimization module: used to simulate the relativistic klystron according to the simulation design parameters, using the klystron large signal simulation software KlyH based on the one-dimensional disk model, and optimize the optimization target using a hybrid multi-objective optimization algorithm to obtain an optimized relativistic klystron.

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