Optimization design of photocathode injector assisted by deep Gaussian process
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摘要: 环形正负电子对撞机（CEPC）对注入器出口处的束团的电荷量、横向发射度、纵向长度等指标提出了严格的要求，设计开发高性能的电子枪及注入器成为了重要挑战。为了得到满足指标的束流，必须同时考虑众多非线性且相互耦合的变量。基于光阴极微波电子枪，提出了一种用多目标遗传算法在高维参数空间进行搜索的方法，对束团的横向归一化发射度和纵向长度进行优化，以期将电子枪的性能发挥至极限。由于考虑空间电荷效应后的束团传输过程模拟计算非常耗时，我们构建了一个3层的深度高斯过程作为替代模型，以解决目标值计算开销大的问题。通过对影响束流横、纵向相空间演化的关键因素分析，共确定了16个几何参数和10个束流元件参数。最后，展示了对由一个L-band的常温微波电子枪、一对螺线管和一个行波加速管组成的注入器，在初始电荷量为10 nC的优化结果。在计算了8 000个有效解后，观察到在两个优化目标上均表现良好的解，其对应的横向归一化发射度为19.8 π·mm·mrad，束团长度（RMS）为1.0 mm，与当前的设计结果比较，横向归一化发射度压低了约70%。Abstract: The Circular Electron-Positron Collider (CEPC) has high requirements for bunch charge, transverse emittance, and longitudinal length at the injector exit. Consequently, designing a high-performance electron gun and injector has become a challenge. To design an injector that meets the targets, many nonlinear and mutually coupled parameters need to be considered simultaneously. Therefore, we propose a method of searching in a high-dimensional parameter space using a multi-objective genetic algorithm to optimize the normalized transverse emittance and longitudinal bunch length, thus to maximize the performance of the electron gun. Since the full simulation of bunch transportaion with spacecharge effect is extremly time consuming, we adopted the deep Gaussian process as an surrogate model to solve high-dimensional parameter optimization problem. Through the analysis of key factors affecting the evolution of beam transverse and longitudinal phase space, a total of 16 geometric parameters and 10 beam element parameters have been determined in this paper. we present a design optimization for an injector consisting of an L-band radio frequency electron gun, a pair of solenoids, and a traveling wave tube, with an initial charge of 10 nC. After calculating 8000 effective solutions, we acquired a good approximation to the Pareto front between two objectives. The corresponding transverse normalized emittance is 19.8 π·mm·mrad, and the RMS beam length is 1.0 mm. Compared with the design requirement, the transverse normalized emittance is reduced by about 70%.
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图 4 电子枪的几何结构示意图
Figure 4. Schematic diagram of the geometric structure of the electron gun
图 5 算法优化束团发射度和纵向长度的演化情况
Figure 5. Evolution of transverse RMS normalized emittance and longitudinal length
图 6 种群的发射度和纵向长度的演化过程
Figure 6. Evolution of the normalized transverseemittance and longitudinal length of bunch
图 7 两种方法辅助后的NSGA-III算法的收敛指标比较
Figure 7. Negative value of Hyper Volume fromNSGA-III with GP and DeepGP
表 1 几何参数的范围
Table 1. Range of geometric parameters
parameter unit range width of nose cm [0.5 , 1.5] radius of arc-1 cm [0.0 , 1.0] angle of arc-1 ° [0 , 90] radius of iris cm [3.0 , 5.0] width of iris cm [1.0 , 2.6] angle of arc-3 ° [30 , 90] radius of arc-3 cm [0.5,1.0] length of gun cm [27.0 , 36.0] width of gun cm [1.0 , 2.5] length of first cell cm [4.4 ,8.4] length of second cell cm [10 , 12] radius of first cell cm [8.5 , 9.5] radius of second cell cm [8.5,9.5] radius of arc-2 cm [0.5 , 2.0] angle of arc-2 ° 90 radius of arc-4 cm [0.5, 2.0] angle of arc-4 ° 90 radius of arc-5 cm [0.5,2.0] angle of arc-5 ° 30 
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表 2 束流元件参数范围
Table 2. Beam element parameter range
parameter unit range peak gun field MV/m [30 , 80] cavity phase ° [0 , 360] solenoid 1 peak field T [0.1 , 0.5] solenoid 1 position m [0.05, 0.2] solenoid 1 length m [0.05, 0.1] solenoid 2 peak field T [0.0 , 0.5] solenoid 2 length m [0.05, 0.15] solenoid 2 radius m [0.02 , 0.1] peak TWT field MV/m 30 TWT phase ° [0 , 360] TWT position m [0.02, 2.0]
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表 3 该优化解对应主要的参数值
Table 3. Main parameter values of a solution
parameter unit range peak gun field MV/m 80 cavity phase ° 243 solenoid 1 peak field T 0.3 solenoid 1 position m 0.12 solenoid 2 peak field T 0.28 peak TWT field MV/m 30 TWT phase ° 104 TWT position m 0.6 radius of iris cm 4.9 width of iris cm 1.0 length of gun cm 24 width of gun cm 1.5 length of first cell cm 6.2 length of second cell cm 11.0 radius of first cell cm 9.11 radius of second cell cm 8.71
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