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摘要: 为了研究史密斯-帕塞尔自由电子激光的输出频率和光栅槽深、光栅槽长、光栅槽宽的关系，对于基于矩形光栅的史密斯-帕塞尔自由电子激光利用粒子模拟软件进行模拟和理论分析。首先，利用粒子模拟软件模拟对于基于矩形光栅的史密斯-帕塞尔自由电子激光进行了研究，发现史密斯-帕塞尔自由电子激光的输出频率随光栅槽深、光栅槽长、光栅槽宽的增大而减少。接着，对史密斯-帕塞尔自由电子激光的光栅槽进行了理论分析，发现每个光栅槽都可以等效为一个LC谐振电路，并发现在史密斯-帕塞尔自由电子激光中存在两种辐射，一种是史密斯-帕塞尔辐射，另一种是LC振荡辐射。最后，对光栅槽的LC振荡辐射进行了估算，发现史密斯-帕塞尔自由电子激光输出频率的模拟值与光栅槽的LC振荡辐射估算值的数量级均为102 GHz，且变化规律上一致。据此推测决定史密斯-帕塞尔自由电子激光输出频率的应该是光栅槽，而不是谐振腔。Abstract: In order to study the relationship between the output frequency of Smith-Purcell free-electron laser and the depth, length and width of grating groove, the rectangular grating size of Smith-Purcell free-electron laser is discussed by means of theoretical analysis and particle simulation methods. First, by particle simulation, we found that the output frequency of Smith-Purcell free-electron laser decreases with the increase of grating groove depth, grating groove length and grating groove width. Then, the grating groove of Smith-Purcell free-electron laser is discussed by means of theoretical analysis. It is found that each grating groove can be equivalent to an LC resonant circuit. There are two kinds of radiation in Smith-Purcell free-electron laser, one is Smith-Purcell radiation and the other is LC oscillatory radiation. Finally, the LC oscillatory radiation of grating groove is estimated as well. It is found that the simulated values of output frequency of Smith-Purcell free-electron laser and the estimation values of LC oscillatory radiation of grating groove are both on the order of 102 GHz, and the variation is consistent. It is inferred that the output frequency of Smith-Purcell free-electron laser should be determined by grating groove rather than resonator.
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Key words:
- physical electronics /
- free-electron laser /
- grating /
- resonator /
- Smith-Purcell radiation /
- LC resonance circuit
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图 1 基于矩形光栅的SP FEL的原理图
Figure 1. Schematic diagram of the SP FEL based on rectangular grating
图 2 基于矩形光栅的SP FEL的模拟图
Figure 2. Simulation graph of the SP FEL based on rectangular grating
图 3 在不同光栅槽深时SP FEL中电子注的动能沿z轴分布图
Figure 3. Kinetic energy of beams in bunching state of SP FEL at different slot depths of grating
图 4 在不同光栅槽深时SP FEL的频谱分布图
Figure 4. Frequency spectra of the SP FEL at different depths of grating groove
表 1 基于矩形光栅的SP FEL的谐振腔参数和电子束参数
Table 1. Resonator parameters and electron beam parameters of the SP FEL based on rectangular grating
Parameters Value Parameters Value Width of resonator/mm 1.5 Transverse size of beam/mm 0.5 Length of resonator/mm 36.9 Beam voltage/kV 50 Height of resonator/mm 0.75 Current/A 10 
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表 2 在不同光栅槽深时SP FEL输出频率的模拟值
Table 2. Simulation values of output frequency of SP FEL at different depths of grating groove
Parameters Values Number of periods 32 Period length of grating/mm 0.3 Slot length of grating/mm 1.5 Slot width of grating/mm 0.1 Slot depth of grating/mm 0.15 0.2 0.25 0.3 0.35 0.4 Simulation value of output frequency / GHz 723.379 529.786 483.632 436.827 400.121 370.060
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表 3 在不同光栅槽长时SP FEL输出频率的模拟值
Table 3. Simulation values of output frequency of SP FEL at different lengths of grating groove
Parameters Values Number of periods 32 Period length of grating/mm 0.3 Slot width of grating/mm 0.1 Slot depth of grating/mm 0.2 Slot length of grating/mm 0.75 1.5 Simulation value of output frequency/GHz 727.255 529.786
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表 4 在不同光栅槽宽时SP FEL输出频率的模拟值
Table 4. Simulation values of output frequency of SP FEL at different widths of grating groove
Parameters Values Number of periods 32 Period length of grating/mm 0.3 Slot length of grating/mm 1.5 Slot depth of grating/mm 0.2 Slot width of grating/mm 0.1 0.15 0.2 Simulation value of output frequency / GHz 529.786 515.823 508.692
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表 5 不同光栅槽深时光栅槽的LCR估算值
Table 5. Estimation values of LCR of grating groove at different groove depths
Slot depth of grating/mm Estimation value of LCR/GHz 0.15 302.849 0.2 224.843 0.25 178.800 0.3 148.412 0.35 126.854 0.4 110.765
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表 6 不同光栅槽长时光栅槽的LCR估算值
Table 6. Estimation values of LCR of grating groove at different groove lengths
Slot length of grating/mm Estimation value of LCR/GHz 0.75 317.976 1.5 224.843
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表 7 不同光栅槽宽时光栅槽的LCR估算值
Table 7. Estimation values of LCR of grating groove at different groove widths
Slot width of grating/mm Estimation value of LCR/GHz 0.1 224.843 0.15 150.806 0.2 137.482
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