基于粒子群优化算法的电子储存环磁聚焦结构设计与优化
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摘要
对于同步辐射光源,电子储存环磁聚焦结构(lattice)设计与优化中的参数直接决定着其主要性能。电子储存环lattice设计与优化工作可分为线性lattice设计与非线性lattice优化两部分。对于同步辐射光源,线性lattice设计的主要目标是获得尽量低的电子束流自然发射度与满意的线性光学函数,以主要提高同步辐射亮度；非线性lattice优化的主要目标是获得足够大的动力学孔径与可以接受的动量孔径,以提高束流注入效率以及增加束流寿命。本论文将快速搜索全局最优解的粒子群优化算法应用于电子储存环lattice设计与优化,并提出一些相关方法。
首先应用全局扫描法得到了合肥光源改造储存环线性lattice解与参数数据库,从而方便了lattice研究,并筛选出了几个具有较好线性参数与非线性表现的lattice候选解。接着应用粒子群优化算法同样研究了合肥光源改造储存环线性lattice。先通过与全局扫描法的对比,表明了粒子群优化算法可以用于高效率地搜索线性lattice的全局最优信息；之后应用粒子群优化算法研究了多变量情况下的合肥光源改造储存环超周期结构lattice,结果表明其lattice灵活性有限。然后将粒子群优化算法应用于非线性lattice优化。在优化动力学孔径时,为了比较不同动力学孔径的优劣,提出了一种动力孔径量化判据；根据动力学孔径跟踪计算中的变化特点,提出了多圈与少圈策略来降低计算量；为了更容易地搜索到质量较好的动力学孔径,提出可以在优化时设置一个专门用于粒子跟踪的孔径,并对其尺寸选择做了说明。还提出了一种动量孔径量化判据,并同时优化了动力学孔径与动量孔径。以合肥光源改造储存环和上海光源储存环为例进行了非线性lattice优化,优化结果表明应用粒子群优化算法以及所提出的策略与方法可以较快地搜索到非线性表现较好的lattice解。
指出了在线性lattice设计时直接应用智能优化算法的不足之处,这主要是由于在线性lattice设计中一般很难给出优化问题的完备的约束条件与目标函数的集合。接着提出了定位方法来加以解决。定位方法通过应用多目标智能优化算法来快速得到满足约束条件的所有lattice解域,从而为储存环lattice设计与优化提供多样性的lattice解。解释说明了逐步补偿色品方法存在不足之处的原因,并指出可以通过引入智能优化算法来加以解决,由此提出用于非线性lattice优化的色品六极铁对优化方法。色品六极铁对优化方法克服掉了逐步补偿色品方法的不足之处,因此优化效果好于逐步补偿色品方法。还指出了六极铁补偿色品公式可以把智能优化算法优化色品六极铁对相关的量和优化色品六极铁强度两种方法联系起来,并进一步说明了这两种基于智能优化算法的数值优化方法的等价性。
For a synchrotron radiation light source, its main performance is directly determined by the parameters in electron storage ring lattice design and optimization. The work of the electron storage ring lattice design and optimization can be divided into two parts:linear lattice design and nonlinear lattice optimization. For synchrotron radiation light sources, the main objectives in the linear lattice design are to obtain electron beam natural emittance as low as possible and satisfactory linear optics functions mainly for increasing synchrotron radiation brightness. The main objectives in the nonlinear lattice optimization are to obtain large enough dynamic aperture (DA) and acceptable momentum aperture for increasing beam injection efficiency and beam lifetime. In this dissertation, the particle swarm optimization (PSO) algorithm, widely used for quickly searching for global optimal solutions, is applied to the electron storage ring lattice design and optimization, and some related methods are proposed.
First, the global scan method is applied to study the storage ring of the upgraded Hefei Light Source (HLS) named HLS-II, and the database of its linear lattice solutions and parameters is obtained, which is helpful for lattice study. Several candidate lattice solutions are selected from the database, which have both better linear parameters and better nonlinear performance. Then the PSO algorithm is applied to study the linear lattice of the HLS-Ⅱ storage ring. The comparison of the results obtained by the PSO algorithm and the global scan method, respectively, shows that the PSO algorithm can be used for searching for global optimal information highly efficiently for linear lattice design. The PSO algorithm is naturally applied to study the case of the superperiod lattice for the HLS-Ⅱ storage ring, in which there are more variables, and the results show that the flexibility of the HLS-Ⅱ storage ring lattice is limited. Then the PSO algorithm is also applied to nonlinear lattice optimization. To optimize the DA, a quantitative criterion of DA is proposed for the comparison of different DAs. Based on the characteristic of the change of DA in particle tracing, a strategy named more turns and less turns is proposed for reducing the amount of computation. To more easily search for DAs of better quality, a method is proposed of setting up one aperture specially used for particle tracking in nonlinear lattice optimization, and the determination of the dimensions of the aperture is demonstrated. In addition, a quantitative criterion of momentum aperture is proposed, and the PSO algorithm is applied to simultaneously optimize DA and momentum aperture. As examples of application, the nonlinear lattices of the storage rings of HLS-II and Shanghai Synchrotron Radiation Facility are optimized, and the optimization results show that some lattice solutions with better nonlinear performance can be found more quickly using the PSO algorithm combined with the proposed strategy and method.
It is pointed out that there are some deficiencies when directly applying artificial intelligence (AI) algorithms to the linear lattice design. This is because it is very difficult to give a complete set of constraint conditions and objective functions for the linear lattice design. To solve this problem, a method called locating method is proposed, which uses the multi-objective AI algorithms to quickly search for all regions of the lattice solutions satisfying the constraint conditions, thus providing a variety of lattice solutions for storage ring lattice design and optimization. The reason that there are some deficiencies in the step-by-step chromaticity compensation method is explained, and it is pointed out that the deficiencies can be cured by introducing AI algorithms. Thus, a new method used for nonlinear lattice optimization, called chromatic sextupole pair optimization method, is proposed, which overcomes the deficiencies in the step-by-step chromaticity compensation method and thus can obtain better optimization results. Additionally, it is pointed out that the formula of sextupole compensating chromaticity connects the two methods of optimizing chromatic sextupole pair related quantities and chromatic sextupole strengths, respectively, using AI algorithms, and the equivalence of the two AI algorithm based numerical methods is demonstrated.
首先应用全局扫描法得到了合肥光源改造储存环线性lattice解与参数数据库,从而方便了lattice研究,并筛选出了几个具有较好线性参数与非线性表现的lattice候选解。接着应用粒子群优化算法同样研究了合肥光源改造储存环线性lattice。先通过与全局扫描法的对比,表明了粒子群优化算法可以用于高效率地搜索线性lattice的全局最优信息；之后应用粒子群优化算法研究了多变量情况下的合肥光源改造储存环超周期结构lattice,结果表明其lattice灵活性有限。然后将粒子群优化算法应用于非线性lattice优化。在优化动力学孔径时,为了比较不同动力学孔径的优劣,提出了一种动力孔径量化判据；根据动力学孔径跟踪计算中的变化特点,提出了多圈与少圈策略来降低计算量；为了更容易地搜索到质量较好的动力学孔径,提出可以在优化时设置一个专门用于粒子跟踪的孔径,并对其尺寸选择做了说明。还提出了一种动量孔径量化判据,并同时优化了动力学孔径与动量孔径。以合肥光源改造储存环和上海光源储存环为例进行了非线性lattice优化,优化结果表明应用粒子群优化算法以及所提出的策略与方法可以较快地搜索到非线性表现较好的lattice解。
指出了在线性lattice设计时直接应用智能优化算法的不足之处,这主要是由于在线性lattice设计中一般很难给出优化问题的完备的约束条件与目标函数的集合。接着提出了定位方法来加以解决。定位方法通过应用多目标智能优化算法来快速得到满足约束条件的所有lattice解域,从而为储存环lattice设计与优化提供多样性的lattice解。解释说明了逐步补偿色品方法存在不足之处的原因,并指出可以通过引入智能优化算法来加以解决,由此提出用于非线性lattice优化的色品六极铁对优化方法。色品六极铁对优化方法克服掉了逐步补偿色品方法的不足之处,因此优化效果好于逐步补偿色品方法。还指出了六极铁补偿色品公式可以把智能优化算法优化色品六极铁对相关的量和优化色品六极铁强度两种方法联系起来,并进一步说明了这两种基于智能优化算法的数值优化方法的等价性。
For a synchrotron radiation light source, its main performance is directly determined by the parameters in electron storage ring lattice design and optimization. The work of the electron storage ring lattice design and optimization can be divided into two parts:linear lattice design and nonlinear lattice optimization. For synchrotron radiation light sources, the main objectives in the linear lattice design are to obtain electron beam natural emittance as low as possible and satisfactory linear optics functions mainly for increasing synchrotron radiation brightness. The main objectives in the nonlinear lattice optimization are to obtain large enough dynamic aperture (DA) and acceptable momentum aperture for increasing beam injection efficiency and beam lifetime. In this dissertation, the particle swarm optimization (PSO) algorithm, widely used for quickly searching for global optimal solutions, is applied to the electron storage ring lattice design and optimization, and some related methods are proposed.
First, the global scan method is applied to study the storage ring of the upgraded Hefei Light Source (HLS) named HLS-II, and the database of its linear lattice solutions and parameters is obtained, which is helpful for lattice study. Several candidate lattice solutions are selected from the database, which have both better linear parameters and better nonlinear performance. Then the PSO algorithm is applied to study the linear lattice of the HLS-Ⅱ storage ring. The comparison of the results obtained by the PSO algorithm and the global scan method, respectively, shows that the PSO algorithm can be used for searching for global optimal information highly efficiently for linear lattice design. The PSO algorithm is naturally applied to study the case of the superperiod lattice for the HLS-Ⅱ storage ring, in which there are more variables, and the results show that the flexibility of the HLS-Ⅱ storage ring lattice is limited. Then the PSO algorithm is also applied to nonlinear lattice optimization. To optimize the DA, a quantitative criterion of DA is proposed for the comparison of different DAs. Based on the characteristic of the change of DA in particle tracing, a strategy named more turns and less turns is proposed for reducing the amount of computation. To more easily search for DAs of better quality, a method is proposed of setting up one aperture specially used for particle tracking in nonlinear lattice optimization, and the determination of the dimensions of the aperture is demonstrated. In addition, a quantitative criterion of momentum aperture is proposed, and the PSO algorithm is applied to simultaneously optimize DA and momentum aperture. As examples of application, the nonlinear lattices of the storage rings of HLS-II and Shanghai Synchrotron Radiation Facility are optimized, and the optimization results show that some lattice solutions with better nonlinear performance can be found more quickly using the PSO algorithm combined with the proposed strategy and method.
It is pointed out that there are some deficiencies when directly applying artificial intelligence (AI) algorithms to the linear lattice design. This is because it is very difficult to give a complete set of constraint conditions and objective functions for the linear lattice design. To solve this problem, a method called locating method is proposed, which uses the multi-objective AI algorithms to quickly search for all regions of the lattice solutions satisfying the constraint conditions, thus providing a variety of lattice solutions for storage ring lattice design and optimization. The reason that there are some deficiencies in the step-by-step chromaticity compensation method is explained, and it is pointed out that the deficiencies can be cured by introducing AI algorithms. Thus, a new method used for nonlinear lattice optimization, called chromatic sextupole pair optimization method, is proposed, which overcomes the deficiencies in the step-by-step chromaticity compensation method and thus can obtain better optimization results. Additionally, it is pointed out that the formula of sextupole compensating chromaticity connects the two methods of optimizing chromatic sextupole pair related quantities and chromatic sextupole strengths, respectively, using AI algorithms, and the equivalence of the two AI algorithm based numerical methods is demonstrated.
引文
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[2]国家同步辐射实验室实验线站介绍.http://www.nsrl.ustc.edu.cn/yonghu/syxz/.
[3]LIU Gui-Min, et al. Lattice Design for SSRF Storage Ring. High Energy Physics and Nuclear Physics,2006,30, Supp.Ⅰ:144-146.
[4]M. Eriksson, et al. The MAX IV Synchrotron Light Source. Proceedings of DPAC 2011, San Sebastian, Spain,2011, p.3026-3028.
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[6]M. Bei, et al. The Potential of an Ultimate Storage Ring for Future Light Sources. Nuclear Instruments and Methods in Physics Research A,2010,622:518-535.
[7]Yunhai Cai. Future synchrotron light sources based on ultimate storage rings. SLAC-PUB-14890,2012.
[8]Y. Nosochkov, et al. Lattice design for PEP-X ultimate storage ring light source. Proceedings of IPAC 2011, San Sebastian, Spain,2011, p.3068-3070.
[9]K. Soutome. SPring-8 Upgrade:Lattice Design of a Very Low-Emittance Storage Ring. Low Emittance Rings 2011,2011.
[10]XU Gang, JIAO Yi. Towards the ultimate storage ring:The lattice design for Beijing Advanced Photon Source. Chinese Physics C,2013,37(5):057003.
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