X射线辐照典型材料出射电子特征规律研究

韩立会; 朱金辉; 王建国; 牛胜利; 刘利; 左应红

doi:10.11884/HPLPB202537.250215

X射线辐照典型材料出射电子特征规律研究

doi: 10.11884/HPLPB202537.250215

西北核技术研究所，西安 710024

基金项目: 国家重点研发计划资助项目(2020YFA0709800)

详细信息

作者简介:
韩立会，hanlihui@nint.ac.cn

通讯作者:
王建国，wangjianguo@nint.ac.cn。

中图分类号: O571.33
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- 被引次数: 0
出版历程
- 收稿日期: 2025-07-15
- 修回日期: 2025-08-21
- 录用日期: 2025-08-21
- 网络出版日期: 2025-09-02
- 刊出日期: 2025-10-15

Investigation of emitted electron characteristics from typical materials under X-ray irradiation

Northwest Institute of Nuclear Technology, Xi’an 710024, China

摘要

摘要: 电子发射参数是研究X射线辐照下腔体结构产生系统电磁脉冲（SGEMP）效应的关键电流源项。采用基于浓缩历史方法与单事件方法建立的电子输运模块开展光子-电子耦合输运蒙特卡罗模拟计算。通过分析光子、电子与物质相互作用特点，系统分析了不同能量X射线正入射辐照典型材料时产生的背向及前向电子发射特性，包括电子能谱、角分布规律。建立基于光子平均自由程的背向电子产额计算方法，提出了饱和产额计算公式与饱和厚度；针对前向电子产额，结合光子衰减规律和电子最大射程建立了计算模型，并引入累积因子进行修正，进一步提升了准确性。在SGEMP关注的X射线能量范围及典型材料厚度范围内进行验证，结果显示，与蒙特卡罗直接模拟相比，计算公式给出的背向、前向电子产额相对偏差在10%以内，研究结果为SGEMP的电子产额计算提供了一种高效便捷的求解方法。
- X射线 /
- 光电子 /
- 康普顿散射电子 /
- 蒙特卡罗 /
- 系统电磁脉冲 /
- 电子产额 /
- 分析模型
Abstract: Background
System-generated electromagnetic pulse (SGEMP) effects induced by X-ray irradiation pose a significant threat to electronic systems in aerospace and nuclear environments. Accurate quantification of electron emission parameters, which are critical current sources for SGEMP simulations, remains challenging because of the complex coupled photon-electron transport processes involved.
Purpose
This study aims to systematically investigate the characteristics of backward- and forward-emitted electrons from typical materials (e.g., aluminum) under X-ray irradiation and develop efficient analytical models for predicting electron yields without relying on computationally intensive Monte Carlo (MC) simulations for each new scenario.
Methods
Photon-electron coupled transport simulations were performed using a Monte Carlo module combining the condensed history and single-event methods. The energy and angular distributions of emitted electrons were analyzed for X rays (0.1–100 keV) normally incident on aluminum plates of varying thicknesses. Analytical models for backward and forward electron yields were derived based on photon mean free path, electron maximum range, and attenuation laws, with a cumulative correction factor introduced to improve forward yield accuracy.
Results
Backward electron energy spectra exhibited a double-peak structure (Compton and photoelectron peaks), with angular distributions following a cosine law. A saturation thickness of about 3 photon mean free paths was identified for backward yield, beyond which yields remained constant. For forward emission, yields peaked at the electron maximum range thickness and decreased with further increasing plate thickness. The proposed analytical formulas for both backward and forward yields achieved relative errors within 10% compared to direct MC simulations across the studied energy and thickness ranges.
Conclusions
The derived analytical models provide efficient and accurate predictions of electron emission coefficients for SGEMP source terms, reducing the need for repeated MC simulations. The methodology is generalizable to other materials and supports rapid assessment of X-ray-induced electron emission in complex systems. Future work will explore machine learning techniques to further enhance computational efficiency for broader applications.
- X-ray /
- photoelectron /
- Compton electron /
- Monte Carlo simulation /
- system-generated electromagnetic pulse /
- electron yield /
- analytical model

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图 1 计算模型示意图

Figure 1. Schematic diagram of the computational model

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图 2 光子与铝原子的相互作用参数

Figure 2. Photon interaction parameters with aluminum atoms

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图 3 电子在铝介质中的射程图

Figure 3. Electron range in aluminum medium

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图 4 平板内部对表面出射电子有贡献的区域示意图

Figure 4. Schematic of regions contributing to surface-emitted electrons within the plate

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图 5 背向出射光子、电子能谱

Figure 5. Energy distributions of backward-emitted photons and electrons

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图 6 背向出射电子角分布

Figure 6. Angular distribution of backward-emitted electrons

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图 7 不同能量X射线入射背向出射电子的饱和产额

Figure 7. Saturation yields of backward-emitted electrons under X rays of varying energies

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图 8 前向出射电子特征

Figure 8. Characteristics of forward-emitted electrons

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图 9 前向最大电子产额

Figure 9. Maximum forward electron yield

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图 10 累积因子修正函数曲线

Figure 10. Cumulative factor correction function curve

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表 1 不同能量X射线入射不同厚度铝板背向出射电子产额

Table 1. Backward electron yields for aluminum plates of varying thicknesses under different X-ray energies

E/keV	r_max/cm	$ \lambda /{\text{cm}} $	$ {Y_{{r_{\max }}}} $	$ {Y_{0.25\lambda }} $	$ {Y_{0.5\lambda }} $	$ {Y_{0.75\lambda }} $	$ {Y_\lambda } $	$ {Y_{3\lambda }} $	$ {Y_{5\lambda }} $
1	2.93×10⁻⁶	3.13×10⁻⁴	1.33×10⁻³	1.33×10⁻³	1.33×10⁻³	1.33×10⁻³	1.33×10⁻³	1.33×10⁻³	1.33×10⁻³
5	4.05×10⁻⁵	1.92×10⁻³	2.45×10⁻³	2.46×10⁻³	2.46×10⁻³	2.46×10⁻³	2.46×10⁻³	2.46×10⁻³	2.46×10⁻³
10	1.31×10⁻⁴	1.41×10⁻²	1.23×10⁻³	1.24×10⁻³	1.24×10⁻³	1.24×10⁻³	1.24×10⁻³	1.24×10⁻³	1.24×10⁻³
20	4.34×10⁻⁴	1.08×10⁻¹	4.12×10⁻⁴	4.18×10⁻⁴	4.21×10⁻⁴	4.22×10⁻⁴	4.23×10⁻⁴	4.24×10⁻⁴	4.24×10⁻⁴
40	1.44×10⁻³	6.52×10⁻¹	1.50×10⁻⁴	1.67×10⁻⁴	1.73×10⁻⁴	1.77×10⁻⁴	1.78×10⁻⁴	1.80×10⁻⁴	1.80×10⁻⁴
60	2.91×10⁻³	1.33	7.42×10⁻⁵	9.43×10⁻⁵	1.04×10⁻⁴	1.10×10⁻⁴	1.12×10⁻⁴	1.16×10⁻⁴	1.16×10⁻⁴
80	4.76×10⁻³	1.84	4.53×10⁻⁵	6.58×10⁻⁵	7.52×10⁻⁵	7.98×10⁻⁵	8.25×10⁻⁵	8.62×10⁻⁵	8.65×10⁻⁵
100	6.94×10⁻³	2.17	3.13×10⁻⁵	5.33×10⁻⁵	6.43×10⁻⁵	7.08×10⁻⁵	7.40×10⁻⁵	7.88×10⁻⁵	7.88×10⁻⁵

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表 2 给定能量、平板厚度条件下背向产额的蒙卡模拟值与计算公式对比

Table 2. Comparison between Monte Carlo simulations and analytical formula predictions for backward electron yields at given energies and plate thicknesses

E/keV	Y_MC	Y_Eq	relative error/%	Y_MC	Y_Eq	relative error/%	Y_MC	Y_Eq	relative error/%
E/keV	t=0.075 mm			t=0.5 mm			t=2.5 mm
0.5	2.99×10⁻³	3.07×10⁻³	2.78	2.99×10⁻³	3.07×10⁻³	2.78	2.99×10⁻³	3.07×10⁻³	−2.71
3	3.78×10⁻³	3.74×10⁻³	−1.06	3.78×10⁻³	3.74×10⁻³	−1.06	3.78×10⁻³	3.74×10⁻³	−1.06
6	2.09×10⁻³	2.13×10⁻³	1.73	2.09×10⁻³	2.13×10⁻³	1.72	2.09×10⁻³	2.13×10⁻³	1.72
9	1.38×10⁻³	1.36×10⁻³	−1.44	1.38×10⁻³	1.36×10⁻³	−1.51	1.38×10⁻³	1.36×10⁻³	−1.51
15	6.24×10⁻⁴	6.58×10⁻⁴	5.35	6.29×10⁻⁴	6.58×10⁻⁴	4.64	6.29×10⁻⁴	6.58×10⁻⁴	4.61
35	1.84×10⁻⁴	1.95×10⁻⁴	6.03	1.90×10⁻⁴	2.01×10⁻⁴	5.33	2.02×10⁻⁴	2.15×10⁻⁴	5.98
55	8.86×10⁻⁵	8.59×10⁻⁵	−3.07	9.39×10⁻⁵	8.95×10⁻⁵	−4.72	1.07×10⁻⁴	1.02×10⁻⁴	−4.61
75	5.17×10⁻⁵	5.05×10⁻⁵	−2.38	5.50×10⁻⁵	5.31×10⁻⁵	−3.37	6.61×10⁻⁵	6.36×10⁻⁵	−3.80
95	3.47×10⁻⁵	3.83×10⁻⁵	10.11	3.75×10⁻⁵	4.04×10⁻⁵	7.67	4.66×10⁻⁵	4.91×10⁻⁵	5.57

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表 3 40 keV光子入射不同厚度平板三种方式得到前向出射电子产额结果对比

Table 3. Comparison of forward electron yields obtained via three methods for 40 keV photons incident on plates of varying thicknesses

t/mm	Y_MC	Y_Eq6	Y_Eq8	Y_Eq6 relative error/%	Y_Eq8 relative error/%
0.10	3.01×10⁻⁴	3.03×10⁻⁴	3.04×10⁻⁴	0.96	1.10
0.25	2.98×10⁻⁴	2.96×10⁻⁴	2.99×10⁻⁴	−0.55	0.37
0.50	2.92×10⁻⁴	2.85×10⁻⁴	2.92×10⁻⁴	−2.18	0.01
0.75	2.85×10⁻⁴	2.75×10⁻⁴	2.84×10⁻⁴	−3.51	−0.11
1.00	2.77×10⁻⁴	2.64×10⁻⁴	2.77×10⁻⁴	−4.73	−0.16
2.00	2.49×10⁻⁴	2.27×10⁻⁴	2.49×10⁻⁴	−8.95	−0.14
3.00	2.22×10⁻⁴	1.94×10⁻⁴	2.22×10⁻⁴	−12.41	0.08
4.00	1.97×10⁻⁴	1.67×10⁻⁴	1.98×10⁻⁴	−15.57	0.11
5.00	1.75×10⁻⁴	1.43×10⁻⁴	1.75×10⁻⁴	−18.44	0.01
10.00	9.30×10⁻⁵	6.64×10⁻⁵	9.26×10⁻⁵	−28.63	−0.44

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表 4 给定能量、平板厚度条件下前向电子产额的蒙卡模拟值与计算公式对比

Table 4. Comparison between Monte Carlo simulations and analytical formula predictions for forward electron yields at given energies and plate thicknesses

E/keV	Y_MC	Y_eq	relative error/%	Y_MC	Y_eq	relative error/%	Y_MC	Y_eq	relative error/%
E/keV	t=0.075 mm			t=0.5 mm			t=2.5 mm
3	0	4.42×10⁻¹⁰	−	0	2.40×10⁻⁴⁹	−	0	0	−
6	1.98×10⁻⁴	1.99×10⁻⁴	0.86	0	3.66×10⁻¹⁰	−	0	3.65×10⁻³⁷	−
9	6.79×10⁻⁴	6.36×10⁻⁴	−6.41	8.80×10⁻⁶	8.05×10⁻⁶	−8.52	0	9.37×10⁻¹⁵	−
15	8.18×10⁻⁴	7.40×10⁻⁴	−9.56	3.40×10⁻⁴	3.04×10⁻⁴	−10.79	4.88×10⁻⁶	4.53×10⁻⁶	−7.21
35	3.57×10⁻⁴	3.58×10⁻⁴	0.32	3.43×10⁻⁴	3.32×10⁻⁴	−3.19	2.45×10⁻⁴	2.30×10⁻⁴	−6.08
55	2.12×10⁻⁴	2.08×10⁻⁴	−1.82	2.09×10⁻⁴	2.05×10⁻⁴	−2.02	1.94×10⁻⁴	1.89×10⁻⁴	−2.64
75	1.56×10⁻⁴	1.58×10⁻⁴	1.20	1.58×10⁻⁴	1.58×10⁻⁴	−0.02	1.54×10⁻⁴	1.53×10⁻⁴	−0.25
95	1.40×10⁻⁴	1.42×10⁻⁴	1.21	1.41×10⁻⁴	1.42×10⁻⁴	0.99	1.37×10⁻⁴	1.41×10⁻⁴	3.07

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