Candidate Lattice Design of the HEPS Booster Consisting of Combined-Function Dipoles-猫眼课题宝

DOI：

10.18429/jacow-ipac2017-wepab053

发表时间：

2017-05

期刊：

影响因子：

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中科院分区：

其他

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作者：

Y. Jiao;Yuemei Peng;Gang Xu

高能光子源（HEPS）是一个6 gev、超低发射度、千米尺度的存储环形光源，将在中国建设。计划使用300兆电子伏直线加速器和全能量助推器作为注入器。在本文中，我们提出了HEPS助推器的候选晶格设计之一，其中大多数偶极子与四极子和六极子梯度相结合。对晶格进行了全局优化，讨论了晶格性能与各种参数的关系，包括最小极面场、阻尼分配数、偶极子数等。高能光子源（HEPS）是一个6-GeV、超低发射度的存储环形光源，将在中国北京郊区建设。HEPS测试设备（HEPS- tf）的研发项目于2016年启动。基于“混合MBA”概念开发了一个7BA环晶格，并作为HEPS-TF的基线晶格，其周长约为1296 m，在6 GeV下的自然发射度约为60 pm。由于HEPS的晶格正在设计和优化中，尚未最终确定，因此HEPS的其他相关物理研究，包括助推器设计，都是基于这种60 pm设计。对于助推器，有两种选择。一种是将助推器与储存环定位在同一隧道中，另一种是设计一个周长为储存环1/3的助推器，放置在单独的隧道中。对于后一种选择，我们设计了一个15BA晶格，在6 GeV[3]下自然发射度为~4.5 nm。在这个晶格中，我们只将水平离焦梯度组合成偶极，而使用分离函数水平聚焦的四极和六极。一个与预算相关的问题出现了，那么我们是否可以将更多的梯度组合到偶极子中，类似于NSLS-II助推器[4]，从而大大减少磁体的数量，从而降低成本。为此，我们对这种类型的晶格进行了详细的设计和优化研究。虽然在2016年底决定不再使用这种类型的晶格，但展示设计这种晶格的潜在考虑是有意义的，可以为其他类似的晶格设计提供有用的参考。线性光学相关问题类似于为HEPS助推器设计的15BA晶格，该晶格假定具有4个超周期，提供4个长直段以容纳注入，提取和射频系统。这种晶格的主要特性是大部分四极和六极梯度组合成偶极。然而，这将对可用的最小发射度引入几个限制。首先，在这种情况下，每个单元格由两个偶极子组成，分别结合聚焦和散焦梯度。这导致了一个问题，即人们不能同时将两个偶极子中的光学函数降低到接近所谓的“理论最小发射度”条件[5]。其次，为了达到低发射度，它需要大量的偶极子（因此弯曲角度小）和强聚焦，然而，对于固定的周长，这意味着短偶极子结合强聚焦梯度和强六极子梯度（以纠正自然色度）。这将使偶极子的极面场迅速接近其上限或下限。初步研究表明，降低发射度更容易达到极面电场的下限（而不是上限）。因此，我们研究了在特定数量的偶极子下，可用最小发射度与偶极子极面场下限之间的关系。对于单晶胞，我们导出了偶极子参数下的发射度和极面场表达式（不考虑偶极子的六极梯度）。这样，对于任意一组偶极子参数，我们可以快速计算出相应的发射度和极面场，而不需要将这些参数放在实际的晶格模型中。通过比较研究验证了这一点，在每个超周期41个偶极子的情况下，分别基于解析表达式和实晶格模型进行了超过1000代的PSO（粒子群优化）进化。两种粒子群演化的最终解如图1所示。看来这两种方法产生的结果基本相同。此外，基于解析表达式的粒子群到达所谓的帕累托前沿的速度要快得多。基于解析表达式的粒子群优化得到了最小发射度与偶极子最小极面场的关系曲线，如图2所示。对于不同的偶极子数（即一个超周期内不同的单体胞数），认为可用的最大胞长为84 m/No。单位细胞。同时，在优化过程中对调谐、beta函数等进行了约束，以保证得到的解具有满意的光学参数。从图2可以清楚地看到，它并不一定导致较低的发射率与大量的偶极子。___________________________________________ *由国家自然科学基金资助（11475202,11405187）†jiaoyi@ihep.ac.cn WEPAB053 IPAC2017, Copenhagen, Denmark， Proceedings of IPAC2017 ISBN 978-3-95450-182-3 2700版权所有©2017 CC -B Y3。最后，我们选择一个超周期内的偶极子数为45个。在偶极子数量较多的情况下，进一步降低发射度的空间有限，但代价是成本较高（偶极子数量较多）。此外，我们有些随意地将偶极极面场的下限设定为0.2 T，为6 GeV（对应于注入能量为300 MeV时的100高斯）。从图2中可以看出，这样的最小极面场对应于~5 nm的最小发射度。图1：基于解析表达式和实际格模型的PSO进化解。图2：基于解析表达式的粒子群优化得到的一个超周期内不同数量的偶极子，有效发射度相对于最小偶极子面场的变化。非线性优化相关问题根据上述估计，我们将每个超周期的偶极子数固定为45。然后，我们对实际晶格模型进行非线性优化，计算偶极子的六极梯度，校正色度为（+1,+1），并计算长直截面中心的动态孔径（DA）。采用MOPSO和多目标遗传算法（MOGA）[6]，以发射度和DA两个目标依次迭代优化晶格，直到种群达到较好的收敛性。结果（此处未显示）表明，在6 GeV下可以达到4~5 nm的自然发射度，同时实现与物理孔径（假设x和y平面均为18 mm）相比的DA。然而，我们注意到，尽管所有解的最小极面场都在0.2 T以上（假设极宽为18 mm），但晶格中使用的四极和六极梯度相当大。表1给出了一种典型解的偶极子参数，其中也给出了NSLS-II助推器[4]的偶极子参数。表1:HEPS和NSLS-II中使用的偶极子参数

The High Energy Photon Source (HEPS) is a 6-GeV, ultralow-emittance, kilometer-scale storage ring light source to be built in China. It is planned to use a 300 MeV linac and a full energy booster as the injector. In this paper we present one of the candidate lattice designs for the HEPS booster, where most of the dipoles are combined with quadrupole and sextupole gradients. Global optimization of the lattice has been done, where the dependencies of the lattice performance on various parameters, including the minimum pole face field, damping partition number, number of dipoles, etc. are discussed. INTRODUCTION The High Energy Photon Source (HEPS) is a 6-GeV, ultralow-emittance storage ring light source to be built in the suburb of Beijing, China. The R&D project, HEPS test facility (HEPS-TF) started in 2016. A 7BA ring lattice was developed [1] based on the ‘hybrid MBA’ concept [2] and used as the baseline lattice of the HEPS-TF, with a circumference of about 1296 m and a natural emittance of about 60 pm at 6 GeV. Since the lattice for the HEPS is under design and optimization and not finally determined yet, other related physics studies for the HEPS, including the booster design, are based on this 60-pm design. For the booster, there are two options. One is to locate the booster in the same tunnel with the storage ring, while the other is to design a booster with circumference of 1/3 of the storage ring and place it in a separate tunnel. For the latter option, we have designed a 15BA lattice, with a natural emittance of ~4.5 nm at 6 GeV [3]. In this lattice, we combine only the horizontally defocusing gradients into the dipoles, while using separate-function horizontally focusing quadrpoles and sextupoles. A question related to the budget arises then whether we can combine more gradients into the dipoles, similar to the NSLS-II booster [4], so as to greatly reduce the number of the magnets and hence the cost. To this end, we did detailed design and optimization studies on this type of lattice. Although at the end of 2016, it was decided to not use this type of lattice, it is meaningful to show the underlying considerations for designing such a lattice, which may provide useful reference for other similar lattice designs. LINEAR OPTICS RELATED ISSUES Similar to the 15BA lattice designed for the HEPS booster, this lattice is assumed to have 4 super-periods, providing 4 long straight sections to accommodate injection, extraction, and RF systems. The main property of this type of lattice is that most of the quadrupole and sextupole gradients are combined into the dipoles. This, however, will introduce several constraints on the available minimum emittance. First, in this case each unit cell is consisted of two dipoles combined with focusing and defocusing gradients, respectively. This leads to a backward that one cannot simultaneously reduce the optical functions in the two dipoles to be close to the so-called ‘theoretical minimum emittance’ conditions [5]. Secondly, to reach a low emittance it calls for a large number of dipoles (and hence small bending angles) and strong focusing, which however, for a fixed circumference, implies short dipoles combined with strong focusing gradients and also strong sextupole gradients (to correct the natural chromaticity). This will make the pole face filed of the dipole quickly approaching its upper or lower limit. Preliminary studies show that it is easier to reach the lower limit (than to reach the upper limit) of the pole face filed, when reducing the emittance. So, we investigate the relationship between the available minimum emittance and the lower limit of the dipole pole face field, for a specific number of dipoles. For the unit cell, we derive the expressions of the emittance and the pole face field in terms of dipole parameters (not taking into account the sextupole gradients of dipoles). In this way, for an arbitrary set of dipole parameters, we can quickly calculate the corresponding emittance and pole face filed, and do not need to put these parameters in a real lattice model. This is verified with a comparison study, where two PSO (particle swarm optimization) evolutions are performed over 1000 generations based on the analytical expressions and real lattice models respectively, for the case with 41 dipoles in each super-period. The final solutions of two PSO evolutions are shown in Fig. 1. It appears that these two approaches generate basically the same results. Furthermore, it is much faster for the PSO based on the analytical expressions to reach the so-called Pareto front. From the PSO optimizations based on analytical expressions, we obtain the dependence curves of minimum emittance versus the minimum pole face field of the dipole, as shown in Fig. 2. For different dipole numbers (namely, different number of unit cells in one superperiod), the available maximum cell length is considered to be 84 m/No. of unit cells. And, constraints on tunes, beta functions, etc., were imposed in the optimization, to ensure that the found solutions have satisfying optical parameters. One can see clearly from Fig. 2 that it does not definitely result in lower emittance with larger number of dipoles. ___________________________________________ * Work supported by NSFC (11475202, 11405187) † jiaoyi@ihep.ac.cn WEPAB053 Proceedings of IPAC2017, Copenhagen, Denmark ISBN 978-3-95450-182-3 2700 Co py rig ht © 20 17 CC -B Y3. 0 an d by th er es pe ct iv ea ut ho rs 02 Photon Sources and Electron Accelerators A05 Synchrotron Radiation Facilities Finally, we choose the number of dipoles in one superperiod to be 45. In the case with larger number of dipoles, there is just a limited room for further-reduction of the emittance, but with a price of higher cost (more dipoles). In addition, we somewhat arbitrarily set the lower limit of the dipole pole face field to 0.2 T at 6 GeV (corresponding to 100 Gauss at the injection energy 300 MeV). From Fig. 2, such a minimum pole face field corresponds to a minimum emittance of ~5 nm. Figure 1: Solutions of PSO evolutions based on anlyatical expression and actual lattice model. Figure 2: Variation of the available emittance with respect to the minimum dipole pole face filed, for different numbers of dipoles in one super-period, obtained from PSO optimizations based on analytical expressions. NONLINEAR OPTIMIZATION RELATED ISSUES From the above estimations, we fix the dipole numbers of each super-period to 45. Then, we perform nonlinear optimizations with the actual lattice model, where the sextupole gradients of dipoles are calculated for corrected chromaticities of (+1, +1), and the dynamic aperture (DA) at the center of the long straight section is also calculated. The lattice is optimized by iteratively and successively implementing the MOPSO and multi-objective genetic algorithm (MOGA) [6], with two objectives, i.e., the emittance and DA, until the population reaches a good convergence. The results (not shown here) suggest that it is possible to reach a natural emittance of 4~5 nm at 6 GeV, and simultaneously achieve a DA comparative to the physical aperture (assumed to be 18 mm in both x and y planes). Nevertheless, we noticed that although the minimum pole face fields of all the solutions are above 0.2 T (assuming the pole width is 18 mm), the quadrupole and sextupoles gradients used in the lattice are quite large. Table 1 lists the dipole parameters of one typical solution, where the dipole parameters of the NSLS-II booster [4] are also presented. Table 1: Dipole Parameters UUUused in HEPS and NSLS-II

Candidate Lattice Design of the HEPS Booster Consisting of Combined-Function Dipoles

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