Simulation of harmonic lasing self-seeded free electron laser
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摘要: 在自由电子激光（FEL）中，谐波驱动自种子（HLSS）可以减小自放大自发辐射（SASE）机制的辐射带宽、提高X射线波段FEL的谱亮度，其原理已被FLASH、PAL、European XFEL等实验室验证。HLSS可改善SASE FEL的相干性，但同时相对SASE并没有提出新的硬件需求，因此可以很方便地应用于国内在建或运行在SASE机制的自由电子激光装置。本文对HLSS方案实现窄带宽效果的原理进行了归纳，给出了波荡器参数的定量条件；随后使用深圳中能高重复频率X射线自由电子激光的典型参数进行模拟，模拟结果表明在出光波长为4.5 nm与6.75 nm时，HLSS的带宽减小至SASE的1/2左右，同时谱亮度提高至2倍左右。Abstract: Among free electron laser (FEL) schemes, the Harmonic Lasing Self-Seeded (HLSS) scheme can reduce the radiation bandwidth of self amplified spontaneous emission (SASE) and improve the spectral brightness of FEL in X-ray band. The principle of HLSS has been verified at FLASH, PAL, European XFEL and other laboratories. The HLSS scheme can improve the coherence of a SASE FEL without additional hardware, so it can be easily applied to domestic facilities under construction or running in SASE scheme. In this paper, the principle of the HLSS scheme to achieve narrow bandwidth is summarized, and the quantitative conditions of the undulator parameters are given. Typical parameters of Shenzhen superconducting soft X-ray free electron laser are used to simulate the HLSS scheme. Simulation results show that the bandwidth in the HLSS scheme can be reduced to about 1/2 of the bandwidth in SASE, and the spectral brightness can increase to about 2 times, when the output wavelengths are 4.5 nm and 6.75 nm.
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图 2 特定辐射波长分别由3次谐波辐射与基波辐射产生时，相干长度之比
Figure 2. Ratio of coherent lengths at a certain wavelength, for lasing at the third harmonic and at the fundamental wavelength
图 4 三次谐波辐射(THG)与基波辐射能量和带宽演化过程对比(10发平均)
Figure 4. Comparison of the pulse energy and the bandwidth of FEL (10 shots average), from the third harmonic generation (THG) and from the resonant wavelength
图 5 HLSS 方案中，扫描第一级波荡器共振波长导致最终出光的能量和带宽(10发平均)的变化
Figure 5. Variation of the energy and bandwidth (10 shots average) when scanning resonance wavelength in the HLSS scheme
图 6 在4.5 nm，HLSS与SASE的对比（10发平均）
Figure 6. Comparison of HLSS and SASE (10 shots average) when lasing at 4.5 nm
图 7 在6.75 nm，HLSS与SASE在波荡器出口的光谱对比（10发平均）
Figure 7. Comparison of the spectrum (10 shots average) at 6.75 nm from HLSS and SASE at different distance from the undulator exit
表 1 模拟用到的参数
Table 1. Parameters for simulation
beam energy/GeV energy spread/% current/A beam length/$ {\text{μ}}$m normalized emittance /$ {\text{μ}}$rad period/cm period number FODO length/m 2.53 0.012 800 65 0.39 4.3 93 10 
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