Influence of energy spread on the transverse profile of the focused electron beam
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摘要: 介绍了均方根（RMS）、半高全宽（FWHM）和50%调制传递函数（MTF）等效均匀分布等焦斑尺寸评价方法。针对一台直线感应加速器，通过建立理论模型和开展逐束片PIC模拟研究了长脉冲（约100 ns）电子束的聚焦过程，分析了能量、流强与平顶区差异较大的脉冲上升/下降沿对FWHM和MTF焦斑尺寸的影响。研究结果表明：能散度较大的束流上升/下降沿会导致束流焦斑，尤其是MTF焦斑显著增长，在模拟结果中FWHM尺寸增长约9%，而MTF尺寸增长达到约24%，是目前导致束流底宽偏大的主要因素之一。Abstract: A brief introduction to evaluating the beam size with the Root-Mean-Square (RMS) value, the full-width-half-maximum (FWHM) value and the modulation-transfer-function (MTF) value is given in this paper. The focusing of the long pulse electron beam (～100 ns) in an induction linear accelerator is studied by both theoretical analysis and numerical simulation, the contribution of the energy and current difference of the rising edge and the falling edge to the final beam size are discussed. In our results, the rising edge and the falling edge of the beam with large energy deviation may lead to a significant increase of the beam size, especially the MTF beam size, i.e. the FWHM beam size is increased by about 9% while the MTF beam size is increased by about 24%.
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Key words:
- linear induction accelerator /
- bunch size /
- energy spread /
- beam slice
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图 1 均匀分布、高斯分布、本涅特分布曲线(a)，及对应的空间频域曲线F(k)(b)
Figure 1. The curvatures of Kapchiskij-Vladimirskij (KV) distribution, Gaussian distribution, Bennett distribution (a), and their spatial Fourier expansion (b)
图 2 焦距差异导致的束流横向位置差异示意图
Figure 2. The position deviation of electrons induced by focusing length difference
图 3 根据实验数据获得的束流的能量和流强分布
Figure 3. Current and energy distribution of the electron beam measured in experiment
图 4 根据公式（1）计算得到的中心束片和整个束流聚焦后的横向分布
Figure 4. Transverse profiles of the center slice and of the whole beam calculated with formula (1)
图 5 根据公式（1）计算得到第#(46−n) 至 #(46+n)号束片叠加后的MTF尺寸（右），其中#46为中心束片
Figure 5. MTF size of the electron bunch composed with slice #(46−n) to #(46+n) (right), the results are calculated with formula (1)
图 6 PIC模拟得到的中心束片和整个束流聚焦后的横向分布
Figure 6. Transverse profiles of the center slice and of the whole beam simulated with ASTRA
图 7 PIC模拟得到的第#(46−n) 至 #(46+n)号束片叠加后的MTF尺寸，其中#46为中心束片
Figure 7. MTF size of the electron bunch composed with slice #(46−n) to #(46+n) , the results are calculated with the PIC code ASTRA
表 1 不同分布函数下，FWHM尺寸与MTF尺寸的对应关系
Table 1. Relationship between the FWHM beam size and the MTF beam size in various distributions
$\;\mathit{f}\left(\mathit{x}\right)$ $ {\rm{\sigma }}_{\rm{F}\rm{W}\rm{H}\rm{M}} $/mm $ {\mathit{k}}_{0} $/mm−1 $ {\rm{\sigma }}_{\rm{M}\rm{T}\rm{F}} $/mm KV 1.00 0.705 1.00 Gaussian 1.00 0.441 1.60 Bennett 1.00 0.258 2.70 
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