CN116882273A - Electron beam injector macro-pulse optimization method and system based on NSGA-III algorithm - Google Patents
Electron beam injector macro-pulse optimization method and system based on NSGA-III algorithm Download PDFInfo
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Abstract
The invention discloses a macro-pulse optimization method and a macro-pulse optimization system for an electron beam injector based on an NSGA-III algorithm, which belong to the field of electron beam injectors, and comprise the steps of adopting a non-dominant sorting genetic algorithm with elite strategy, converging three parameters of stable energy, energy consistency and phase consistency of a macro-pulse beam cluster towards an optimal direction to serve as optimization targets, and optimizing to obtain a target parameter distribution result and corresponding injector initial system parameter setting; the fitness function in the non-dominant ordering genetic algorithm with elite strategy is a transient beam load effect and longitudinal particle motion calculation model; setting a group of initial parameters corresponding to each group of individuals in the optimization process; the initial parameter value interval is obtained by solving each parameter independently in advance to determine the optimal solution range; because of the interaction effect between the parameters, the resulting optimization result is not necessarily optimal for a single parameter, but satisfies the overall optimal effect.
Description
Technical Field
The invention belongs to the field of electron beam injectors, and particularly relates to an electron beam injector macro-pulse optimization method and system based on an NSGA-III algorithm.
Background
In recent years, the rapid development of high-quality electron beam injectors provides technical support for the development of large-scale scientific research devices such as free electron laser devices, diffraction limit storage rings, positive and negative electron collimators and the like, and the application of industrial accelerators such as photon therapy and high-energy X-ray sources. However, these facilities are large in large scale, complex in peripheral subsystems, and high in economic cost, and thus development of miniaturized and compact electron beam injectors is a trend. As a beam source, the injector determines the quality of the driving beam and even affects the performance of the whole plant, a typical case being a hci injector based on two Independently Tunable Cavities (ITCs) in combination with a traveling wave accelerator: the first cavity is used for inputting direct current beam, and the second cavity and the traveling wave accelerating tube are mainly used for accelerating beam. The energy and phase of the two chambers and acceleration tube can be independently adjusted to achieve both energy spread and self-compensation of lateral emittance within a limited beam line length, then limiting the overall injector to an acceptable range and at a lower cost. However, as the output beam passes through the standing wave cavity and accelerating tube in the injector, the cluster train will interact with the electromagnetic field established in the radio frequency structure, not only resulting in a reduction of energy, but also in an uneven distribution of the cluster train in macroscopic pulses. The former is mainly caused by steady state beam loading effects, while the latter is caused by transient beam loading effects, and the macro-pulse inconsistency caused by the beam loading ultimately affects the peak and average power of the overall injector device. Thus, it is very important to perform macroscopic pulse optimization for high power injectors.
For an established beam device, it is preferable to optimize beam performance. Compared with the design process which can be visually evaluated through electromagnetic calculation and beam simulation, the optimization can be limited by the defects of the existing test platform observation and adjustment method. Given the multiple parameters involved therein and the interactions that exist between these parameters, manual iterative calculations are typically required for optimization. For such multi-objective optimization, genetic Algorithm (GA) is a simple tool to seek optimal settings. Therefore, in order to reduce macro-pulse inconsistencies, beam optimization using multi-objective genetic algorithms is urgently needed.
Disclosure of Invention
Aiming at the defects and improvement requirements of the prior art, the invention provides an electron beam injector macro-pulse optimization method and system based on an NSGA-III algorithm, and aims to improve the output power of an injector to drive a high-power device. Compared with NSGA-II, NSGA-III can solve the problem of poor convergence and diversity of an algorithm, and avoid the algorithm from falling into local optimum.
In order to achieve the above object, the present invention provides a macro-pulse optimization method for an electron beam injector based on NSGA-III algorithm, comprising:
and a non-dominant sorting genetic algorithm with elite strategy based on reference points is adopted, and three parameters of stable energy, energy consistency and phase consistency of the macro-pulse beam cluster are converged towards the optimal direction to be used as optimization targets, so that the optimal beam quality under different parameter settings is obtained through optimization. The fitness function in the non-dominant sorting genetic algorithm with elite strategy based on the reference point is a calculation model for solving the transient beam load effect of the cavity based on the single particle motion theory; in the optimization process, each population of individuals corresponds to a macro pulse distribution, and the gene length of each population of individuals is determined by the variable points of different injection time and radio frequency phase; calculating the value of the required input parameter when calculating the fitness function of each population in each iteration, wherein the value is obtained by analyzing the influence of the input parameter on the beam quality in advance; the input parameters include radio frequency parameters and structural parameters. The radio frequency parameters comprise radio frequency injection time and radio frequency phase, and the structural parameters comprise time sequence and standing wave cavity coupling coefficient. The time sequence, the radio frequency injection time, the radio frequency phase, the standing wave cavity coupling coefficient and other factors are all input setting parameters, and the parameter range to be set is obtained according to the final optimization result. Taking into account the interplay between optimization objectives, it is not necessarily optimal for a single objective, but an overall optimal solution can be maintained.
Further, genetic operator operations to obtain a population of offspring include: the method comprises the steps of selecting based on reference point ordering, crossing by a single-point crossing method and mutation by a single-point mutation method.
Further, the energy consistency and phase consistency are:
wherein B is specific output energy or phase, B end For final end output energy or phase, rms is the root mean square value.
Further, the analysis expression of the transient beam load of the traveling wave cavity is as follows:
the analytical expression of the standing wave cavity transient beam load is as follows:
wherein ,P 0 for initial injection power, r is shunt impedance, l is cavity length, ω=2pi f, ε (t) is a step function, f=2856 mhz, q is quality factor, I g For beam generator current, < >>P g Is power, beta c R is the coupling coefficient between the waveguide and the cavity s For equivalent shunt impedance, I b For beam load current, t b For the beam injection time, i 0 Is the average beam current, τ is the decay constant, +.>To take into account the energy actually carried away by the beam.
Further, the input setting parameters are obtained by inverse solution according to the final optimization result. Because the final optimal solution is presented by the Pareto front, the input setting parameter is a small-range interval, and the specific value needs to be obtained according to the actual situation.
The invention also provides an electron beam injector macro-pulse optimization system based on NSGA-III algorithm, which comprises: a computer readable storage medium and a processor, the computer readable storage medium for storing executable instructions;
the processor is configured to read executable instructions stored in the computer readable storage medium and execute the above-mentioned macro-pulse optimization method of the electron beam injector based on the NSGA-III algorithm.
By the above technical scheme, compared with the prior art, the invention can obtain the following
The beneficial effects are that:
(1) The invention provides a macro-pulse optimization method of an electron beam injector based on a multi-target genetic algorithm NSGA-III, which is characterized in that when a macro-pulse beam optimization calculation model is established, on the basis of considering radio frequency injection time and radio frequency phase, the adjustable coupling coefficient of a standing wave cavity and radio frequency separation injection to be planned are added, so that macro-pulse width is more than 3.3 mu s, energy inconsistency is less than 0.3, phase inconsistency is less than 0.2, the limitation of the existing system is overcome, and the future upgrading plan of the injector is considered.
(2) Before beam cluster energy and macro pulse consistency are calculated, the transient beam load effect in the traveling wave tube and the standing wave cavity is subjected to numerical analysis to obtain an expression, so that the design operation process is convenient, the multi-objective genetic algorithm has the characteristics of good convergence, and the optimization target can be changed into other beam parameters, namely, the universality is high, and the multi-objective genetic algorithm is suitable for being applied to the design optimization of an injector.
(3) The invention provides a multi-target genetic algorithm NSGA-III-based macro pulse optimization method for an electron beam injector, which gets rid of the difficulty and the complexity of manual calculation and has the characteristics of high optimization speed, good consistency of Shu Liuhong pulses obtained by optimization and high stable energy of macro pulse clusters.
Drawings
Fig. 1 is a schematic flow chart of an electron beam injector macro-pulse optimization method based on NSGA-III algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a beam optimization test platform of a high-quality electron beam injector according to an embodiment of the present invention;
FIG. 3 shows the result of beam optimization when adjusting the RF injection time and RF phase according to the embodiment of the present invention;
FIG. 4 shows the result of beam optimization when the coupling coefficients of the standing wave cavity and the standing wave cavity are adjusted by adopting the radio frequency separation injection standing wave cavity and the accelerating tube according to the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not interfere with each other.
Currently, although multi-objective genetic algorithms are useful in the accelerator field, more of them are optimized for large accelerators, for example, optimized multi-objective genetic algorithms can be used to optimize magnetic field distribution, focusing systems and parameter selection in accelerators, improve beam transport efficiency and particle focusing performance, enable more efficient free electron laser generation and transport, more stable particle beam motion and higher radiance, etc. But the optimized design related to macro-pulse beam current of a compact type free electron laser terahertz source injector applied to the industrial field is few.
The consistency of the macro-pulsed beam is critical to the successful development of high power beam injectors, especially those intended to produce terahertz radiation with high peak and average powers. However, due to the transient beam loading effect that prevails with high gradient accelerators used in high quality electron beam injectors, the energy distribution extracted along the macroscopic pulse may become non-uniform. Furthermore, during the injector low energy phase, the phase distribution is also affected by the non-uniformity of the beam energy in the macroscopic pulse. Optimizing the macro-pulsed beam under limited tunable system settings is more important for established high quality electron beam injector facilities.
The invention provides an electron beam injector macro-pulse optimization method based on NSGA-III algorithm, which comprises the following steps:
and a non-dominant sorting genetic algorithm with elite strategy based on reference points is adopted, and three parameters of stable energy, energy consistency and phase consistency of the macro-pulse beam cluster are converged towards the optimal direction to be used as optimization targets, so that the optimal beam quality under different parameter settings is obtained through optimization. The fitness function in the non-dominant sorting genetic algorithm with elite strategy based on the reference point is a calculation model for solving the transient beam load effect of the cavity based on the single particle motion theory; in the optimization process, each population of individuals corresponds to a macro pulse distribution, and the gene length of each population of individuals is determined by the variable points of different injection time and radio frequency phase; calculating the value of the required input parameter when calculating the fitness function of each population in each iteration, wherein the value is obtained by analyzing the influence of the input parameter on the beam quality in advance; the input parameters include radio frequency parameters and structural parameters. The radio frequency parameters comprise radio frequency injection time and radio frequency phase, and the structural parameters comprise time sequence and standing wave cavity coupling coefficient. The time sequence, the radio frequency injection time, the radio frequency phase, the standing wave cavity coupling coefficient and other factors are all input setting parameters, and the parameter range to be set is obtained according to the final optimization result. Taking into account the interplay between optimization objectives, it is not necessarily optimal for a single objective, but an overall optimal solution can be maintained.
The invention provides the following embodiments based on the above analysis to solve the technical problems existing in the prior art of macro-pulse beam optimization design.
Example 1
An electron beam injector macro-pulse optimization method based on NSGA-III algorithm, wherein the optimization targets comprise stable energy, energy consistency and phase consistency of macro-pulse beam clusters of the injector, and the method comprises the following steps:
(1) And obtaining transient beam load effect expressions of the traveling wave cavity and the standing wave cavity through numerical analysis.
The high-quality electron beam injector mainly adopts pulse beam current in the beam adjusting stage, and the transient beam current load effect is serious because the pulse beam current is too short in time length, the electron gun structure mainly comprises a traveling wave tube and a standing wave cavity, and the analysis expression of the transient beam current load effect is discussed from the two structures.
In a beam load calculation model, an analytical expression of a transient beam load effect of the traveling wave tube is obtained by the formulas (1) - (3), wherein the formula (1) gives a radio frequency power loss equation of a unit length, alpha (z) is a structural attenuation coefficient, i (t) is a beam current, and E (z, t) is an axial electric field amplitude. The power loss consists of two parts: the power dissipated at the walls of the cavity and the power absorbed by the beam. The formula (2) gives the electric field and current expression in the case of beam injection, where t b Is the time of beam injection, i 0 Is the average beam current, E 0 Is the magnitude of E (z, t), ε (t) is a step function. Equation (3) gives an analytical expression of the final traveling wave cavity transient beam load, whereinP 0 For initial injection power, r is shunt impedance, l is cavity length, ω=2pi f, f=2856 mhz, q is quality factor, filling time: />As can be seen from equation (3), in addition to design parameters such as field strength magnitude, quality factor, shunt impedance, etc. affecting traveling wave tube bundle flow energy, injection time is another major contribution, and on-line adjustments can be made to the built facility.
The analytical expression of the transient beam load of the standing wave cavity is given based on the circuit formula (4),
wherein Ig For beam generator current, the power P is commonly used g Instead, beta c R is the coupling coefficient between the waveguide and the cavity s For equivalent shunt impedance, I b For beam load current, t b For the beam injection time, τ is the decay constant,to take into account the energy actually carried away by the beam. With traveling wave tubes, in addition to the inherent design parameters and initial beam parameters of the standing wave cavity, the injection time also has an effect on the output beam energy of the standing wave cavity.
(2) Numerical solution expression of beam optimization measurement and consistency
The high quality electron beam injector beam optimization test bed is shown in fig. 2, and the beam is injected into the standing wave cavity first and enters the accelerating tube with the subsequent length of 0.853 m. Two drift sections are installed upstream and downstream of the acceleration tube, the lengths of which are respectively designed to be 0.265m (drift section 1) and 0.8m (drift section 2). There are three observation points on the beam line, namely the end of the drift section 1, the outlet of the acceleration tube and the end of the drift section 2, to capture the energy and phase distribution of the macro-pulses. The radio frequency injection time of the whole system is controlled by a master clock.
For macro-pulses consisting of clusters, their consistency in the statistical distribution is described by the root mean square value (rms), denoted by the symbol σ (B):
wherein B is a specific output energy or phase, B end The energy or phase is output for the final end. Parameter consistency can be assessed by σ (B), the smaller σ (B), the better the consistency. The numerical solution is based on the following settings: (1) Each cluster within a macro-pulse is represented by a macro-particle; (2) The phases of all clusters are relative values of the relatively stable phases; (3) The phase slip of the cluster is also a relative value to a relatively stable value.
(3) NSGA-III uses a reference point-based selection mechanism instead, so the algorithm ensures solution diversity, and is particularly suitable for solving optimization problems with 3 and more targets, the execution flow of which is shown in fig. 1. The optimized result of the genetic algorithm is related to the independent variable parameter interval selection, and the radio frequency injection time is calculated to be 0.95t in advance f The left and right energy uniformity is optimal, but at 0.89t f The left and right phases have the worst consistency, and the optimal injection time will have a certain deviation due to the relation, so the radio frequency injection time interval takes [0.6t f ,1.3t f ]. According to beam dynamics, the particles can obtain maximum output energy when the phase is close to 90 °. However, due to the phase slip, the phase of the maximum energy of the particles will shift 90 DEG, so the RF phase interval takes [90 DEG, 140 DEG]。
Since the energy consistency and phase consistency optimization targets are minimum values, the stable energy optimization targets of the output macro pulse beam clusters are maximum values, in order to keep the optimization targets consistent, the minimum values are selected as objective functions in the algorithm, and the opposite numbers are adopted for processing under the condition that the maximum values are needed.
And after initializing the population, judging whether a first generation sub-population is generated, if not, generating the population after calculating the fitness function (namely the energy magnitude and the energy phase inconsistency degree of the output beam group), rapidly non-dominating and sequencing, and executing the genetic operator. Regarding the rapid non-dominant ranking, the number of layers of the non-dominant ranking is first made 1, all non-dominant individuals are placed therein, then the number of layers is increased by 1, all non-dominant individuals among the remaining individuals are placed therein, and so on until all individuals have the number of layers. And combining the generated child population and the parent population, calculating the fitness function of the combined population, rapidly performing non-dominant sorting to obtain a layering result, calculating the reference point distance of the individuals, filling the individuals with small non-dominant sequence numbers and small reference point distances into the new parent population until the initial population is large, and obtaining the individual set as the generated new generation child population. Regarding genetic operations, performing selection operations based on reference points; the single-point crossing method is adopted for crossing operation, the crossing probability is generally 0.5-1.0, and 0.8 is taken in the example; the mutation operation is performed by a single-point mutation method, and the mutation probability is generally 0 to 0.05, and 0.02 is taken in this example. If the population reproduction algebra does not reach the preset iteration times, continuing, and if the population reproduction algebra reaches the preset iteration times, outputting an adaptability value solution set with the minimum non-dominant sequence number, namely a Pareto front, and finally obtaining the result with the maximum output particle energy and the minimum energy phase inconsistency degree. With respect to the termination algebra, the calculation is terminated when the population reproduction algebra of this example is 30.
Fig. 3 is a diagram of beam optimization results when radio frequency injection time and radio frequency phase are adjusted, and it can be seen that the phase consistency and the energy consistency trend are opposite, the beam group stabilizing energy output by the traveling wave tube is concentrated at 13.5-14.5 MeV, the energy inconsistency is concentrated in 0.007-0.01, and the phase inconsistency is concentrated in 0.5-1.5. However, since the macro-pulse optimization is limited by the radio frequency characteristics of the standing wave cavity and the accelerating tube, which mainly depends on the adjustment of the single radio frequency injection time, the coupling coefficient (beta c ) And adding a radio frequency source to realize independent control of the standing wave cavity and the accelerating tube radio frequency injection.
FIG. 4 is a graph showing the results of beam optimization during RF separation injection into a standing wave cavity and an accelerating tube, and adjustment of RF phase and coupling coefficient of the standing wave cavity, and the coupling coefficient of the standing wave cavity is input into parameter intervals [2,12]The injection time of the standing wave cavity is 1.5 times later than that of the accelerating tube, and the rest parameters are unchanged. The stable energy of the beam group output by the traveling wave tube is concentrated at 13.5-14.5 MeV, the energy inconsistency is concentrated at 0.005-0.025, and the phase inconsistency is concentrated at 0.3-0.9. Compared with the result of fig. 3, the phase consistency is improved by about 40% while the result that the stable energy and the energy consistency of the output beam mass are better is maintained. At the moment, the initial parameter is reversely calculated and set as the injection time of the traveling wave tubeInter: 0.67t f ～0.73t f The method comprises the steps of carrying out a first treatment on the surface of the Standing wave cavity injection time: 1.07t f ～1.14t f The method comprises the steps of carrying out a first treatment on the surface of the Radio frequency phase: 115-118 degrees; standing wave cavity coupling coefficient: 8.6 to 9.2.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. An electron beam injector macro-pulse optimization method based on NSGA-III algorithm is characterized by comprising the following steps:
adopting a non-dominant sorting genetic algorithm with elite strategy and based on reference points, converging three beam parameters of stable energy, energy consistency and phase consistency of the macro pulse beam group to an optimal direction as an optimization target, and optimizing to obtain optimal beam quality;
the fitness function in the non-dominant sorting genetic algorithm with elite strategy based on the reference point is a calculation model for solving the transient beam load effect of the cavity based on the single particle motion theory; in the optimization process, each population of individuals corresponds to a macro pulse distribution, and the gene length of each population of individuals is determined by different injection time and radio frequency phase position available value points; calculating the value of the required input parameter when calculating the fitness function of each population in each iteration, wherein the value is obtained by analyzing the influence of the input parameter on the beam quality in advance; the input parameters include radio frequency parameters and structural parameters.
2. The optimization method of claim 1 wherein the genetic operator operations to obtain the population of offspring during the optimization process include: the method comprises the steps of selecting based on reference point ordering, crossing by a single-point crossing method and mutation by a single-point mutation method.
3. The optimization method of claim 1, wherein the radio frequency parameters include radio frequency injection time, radio frequency phase.
4. The optimization method of claim 1, wherein the structural parameters include timing, standing wave cavity coupling coefficient.
5. The optimization method according to claim 1, wherein the energy consistency and phase consistency are:
wherein B is specific output energy or phase, B end For final end output energy or phase, rms is the root mean square value.
6. The optimization method according to claim 1, characterized in that,
the analytical expression of the transient beam load of the traveling wave cavity is as follows:
the analytical expression of the standing wave cavity transient beam load is as follows:
wherein ,P 0 for initial injection power, r is shunt impedance, l is cavity length, ω=2pi f, ε (t) is a step function, f=2856 mhz, q is quality factor, I g For beam generator current, < >>P g Is power, beta c R is the coupling coefficient between the waveguide and the cavity s For equivalent shunt impedance, I b For beam load current, t b For the beam injection time, i 0 Is the average beam current, τ is the decay constant, +.>To take into account the energy actually carried away by the beam.
7. An NSGA-III algorithm-based macro-pulse optimization system for an electron beam implanter, comprising: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
the processor is configured to read executable instructions stored in the computer readable storage medium and execute the NSGA-III algorithm-based e-beam injector macro-pulse optimization method of any of claims 1 to 6.
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