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Particle contamination can greatly affect the performance of X-ray focusing mirror. In this paper, we analyze the influence of particle contamination on X-ray focusing mirror. The model of interaction between contaminant particles and incident light is established from Mie scattering theory in the wavelength range of X-ray. And the relationship between them is mainly influenced by the complex refractive index of the particles
$m$ and the scale factor$\alpha$ . Therefore, the reaction cross section and scattering function of particle contamination are calculated. Then, in order to obtain the effect of particle contamination on Einstein probe follow-up X-ray telescope (EP-FXT) focusing mirror, we carry out Monte Carlo simulation based on the design parameters of EP-FXT focusing mirror. Finally, the relationships among effective area, HEW, W90 and particle contamination density are calculated to characterize the influence of particle contamination on the performance of the focusing mirror. In this paper, structural and thermal model (STM) and qualification model (QM) are simulated simultaneously to make full use of their test data. By comparing the simulation results of STM effective area with the measured results, we find that the simulation results of STM effective area are accurate. When the EP-FXT is in orbit (the contamination amount is limited to less than 1.1 × 10–3), the effective area and angle resolution (HEW) meet the development requirements of EP-FXT. For the simulation of HEW, both QM and STM are in good agreement with the test results. The simulation results of HEW and effective area can be used to quantitatively analyze the effect of particle contamination on the performance of the focusing mirror. These quantitative analysis results provide a theoretical basis for the contamination prevention requirements of EP-FXT.-
Keywords:
- particle contamination /
- X-ray focusing mirror /
- Einstein probe /
- follow-up X-ray telescope
[1] Wolter H 1952 Ann. Phys. 445 94
[2] 袁为民, 张臣, 陈勇, 等 2018 中国科学: 物理 力学 天文学 48 039502
Yuan W M, Zhang C, Chen Y, et al. 2018 Sci. Sin.-Phys. Mech. As. 48 039502
[3] Chen Y, Cui W W, Han D W, et al. 2020 Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray, December 13, 2020 p114445
[4] Yang Y J, Wang Y S, Han D W, et al. 2023 Exp. Astron. DOI: 10.1007/s10686-022-09870-9
[5] O'Dell S L, Elsner R F, Oosterbroek T 2010 Space Telescopes and Instrumentation 2010: Ultraviolet to Gamma Ray San Diego, California, USA, July 29, 2010 p77322V
[6] Elsner R F, Joy M K, O'Dell S L, Ramsey B D, Weisskopf M C 1994 Advances in Multilayer and Grazing Incidence X-Ray/EUV/FUV Optics San Diego, California, USA, November 11, 1994 p332
[7] Zhu Y X, Lu J B, Yang Y J, et al. 2021 Opt. Eng. 60 025102
[8] Mie G 1908 Ann. Phys. 25 377
Google Scholar
[9] 柯熙政, 马冬冬, 刘佳妮 2009 光散射学报 21 104
Google Scholar
Ke X J, Ma D D, Liu J N 2009 Chin. J. Light Scatt. 21 104
Google Scholar
[10] 麻金继, 陈瑾 2005 原子与分子物理学报 22 701
Google Scholar
Ma J J, Chen J 2005 J. Atom. Mol. Phys. 22 701
Google Scholar
[11] Bedareva T V, Sviridenkov M A, Zhuravleva T B 2014 J. Quant. Spectrosc. Ra. 146 140
[12] Su M Y 1987 Inverse Problems in Optics Hague, Netherlands, September 10, 1987 p112
[13] Slane P O, McLaughlin E R, Schwartz D A, et al. 1989 Reflective Optics II Orlando, FL, USA, October 11, 1989 p12
[14] Weisskopf M C, O'Dell S L, van Speybroeck L P 1996 Multilayer and Grazing Incidence X-Ray/EUV Optics III Denver, CO, USA, July 19, 1996 p2
[15] Henke B L, Gullikson E M, Davis J C 1993 Atom Data Nucl. Data 54 181
Google Scholar
[16] Aschenbach B 2005 Optics for EUV, X-Ray, and Gamma-Ray Astronomy II San Diego, California, USA, September 8, 2005 p59000
[17] O'Dell S L, Brissenden R J, Davis W N, et al. 2010 Adaptive X-Ray Optics San Diego, California, USA, October 22, 2010 p78030
[18] Wiscombe W J 1980 Appl. Opt. 19 1505
Google Scholar
[19] 沈建琪 1999 博士学位论文 (上海: 上海理工大学)
Shen J Q 1999 Ph. D. Dissertation (Shanghai: University of Shanghai for Science and Technology) (in Chinese)
[20] Hagemann H J, Gudat W, Kunz C 1975 J. Opt. Soc. Am. B 65 742
Google Scholar
[21] Friedrich P, Brauninger H, Budau B, et al. 2008 Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray Marseille, France, July 15, 2008 p70112
[22] 郑钢镖, 康天合, 柴肇云, 尹志宏 2006 太原理工大学学报 3 317
Google Scholar
Zheng G B, Kang T H, Chai Z Y, Yin Z H 2006 J. Taiyuan Univ. Technol. 3 317
Google Scholar
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图 1 污染物颗粒在聚焦镜镜片上对X射线的遮挡
Figure 1. X-ray shielding of contaminant particles on the surface of the focusing mirrors.
图 2 三维坐标系下的方程参数
Figure 2. Equation parameters in a three-dimensional coordinate system.
图 3 EP-FXT聚焦镜粒子污染仿真流程图
Figure 3. Flow chart of particle contamination simulation for EP-FXT focusing mirror.
图 4 不同
$ \delta $ 下效率因子Q与尺度因子$ \alpha $ 的关系Figure 4. Relationship between efficiency factor Q and scale factor
$ \alpha $ under different$ \delta $ .
图 5 不同
$ \beta $ 下效率因子Q与尺度因子$ \alpha $ 的关系Figure 5. Relationship between efficiency factor Q and scale factor
$ \alpha $ under different$ \beta $ .
图 6 散射角分布函数随
$ \delta $ 变化情况($ \alpha = 10000 $ )Figure 6. Variation of scattering angle distribution function with
$ \delta $ ($ \alpha = 10000 $ ).
图 7 散射角分布函数90%概率宽度随
$ \delta $ 的变化 ($\alpha = $ $ 10000$ )Figure 7. Variation of 90% probability width of scattering angle distribution function with
$ \delta $ ($\alpha = 10000$ ).
图 8 散射角分布函数随
$ \beta $ 的变化情况 ($ \alpha = 10000 $ )Figure 8. Variation of scattering angle distribution function with
$ \beta $ ($ \alpha = 10000 $ ).
图 9 散射角分布函数90%概率宽度随
$ \beta $ 的变化 ($\alpha = $ $ 10000$ )Figure 9. Variation of 90% probability width of scattering angle distribution function with
$ \beta $ ($\alpha = 10000$ ).
图 10 散射角分布函数随
$ \alpha $ 的变化情况 ($ \delta = 0.1 $ ,$ \beta = 0.1 $ )Figure 10. Variation of scattering angle distribution function with
$ \alpha $ ($ \delta = 0.1 $ ,$ \beta = 0.1 $ ).
图 11 散射角分布函数90% 概率宽度随
$ \alpha $ 的变化($ \delta = 0.1 $ ,$ \beta = 0.1 $ )Figure 11. Variation of 90% probability width of scattering angle distribution function with
$ \alpha $ ($ \delta = 0.1 $ ,$ \beta = 0.1 $ )
图 12 碳单质的散射角分布函数(
$ \alpha = 10000 $ )Figure 12. Scattering angle distribution function of simple substance carbon (
$ \alpha = 10000 $ )
图 13 污染物颗粒的粒径分布
Figure 13. Particle diameter distribution of contaminant particles.
图 14 污染物粒径分布拟合残差
Figure 14. Residual error of fitting particle diameter distribution of contaminant.
图 15 QM件有效面积随粒子污染密度变化
Figure 15. Effective area of the QM varies with particle contamination density.
图 16 STM件有效面积随粒子污染密度变化
Figure 16. Effective area of the STM varies with particle contamination density.
图 17 QM件的HEW随污染物密度变化关系
Figure 17. Relationship between HEW and contaminant density of the QM.
图 18 QM件的W90随污染物密度变化关系
Figure 18. Relationship between W90 and contaminant density of the QM.
图 19 STM件的角分辨随污染物密度变化关系
Figure 19. Relationship between angle resolution and contaminant density of the STM.
Energy/keV $Q_{\rm abs}$ 1.49 0.800 2.98 0.728 4.50 0.586 4.95 0.544 6.40 0.430 
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表 2 STM的污染物颗粒尺度分布
Table 2. Particle size distribution of contamination on STM
粒径范围/μm 颗粒数 < 25 220 25—50 156 50—100 71 100—150 59 150—200 37 200—400 12 400—600 4 600—1000 2
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表 3 STM件有效面积的仿真与实测结果
Table 3. Simulation and measurement results of effective area on the STM
能量/keV 仿真结果/${\rm {cm^{2}}}$ 实测结果/${\rm {cm^{2}}}$ 0.277 $42.43\pm0.25$ $42.34\pm0.19$ 1.49 $41.57\pm0.24$ $41.11\pm0.55$ 8.04 $0.91\pm0.01$ $0.92\pm0.01$
DownLoad: CSV
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[1] Wolter H 1952 Ann. Phys. 445 94
[2] 袁为民, 张臣, 陈勇, 等 2018 中国科学: 物理 力学 天文学 48 039502
Yuan W M, Zhang C, Chen Y, et al. 2018 Sci. Sin.-Phys. Mech. As. 48 039502
[3] Chen Y, Cui W W, Han D W, et al. 2020 Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray, December 13, 2020 p114445
[4] Yang Y J, Wang Y S, Han D W, et al. 2023 Exp. Astron. DOI: 10.1007/s10686-022-09870-9
[5] O'Dell S L, Elsner R F, Oosterbroek T 2010 Space Telescopes and Instrumentation 2010: Ultraviolet to Gamma Ray San Diego, California, USA, July 29, 2010 p77322V
[6] Elsner R F, Joy M K, O'Dell S L, Ramsey B D, Weisskopf M C 1994 Advances in Multilayer and Grazing Incidence X-Ray/EUV/FUV Optics San Diego, California, USA, November 11, 1994 p332
[7] Zhu Y X, Lu J B, Yang Y J, et al. 2021 Opt. Eng. 60 025102
[8] Mie G 1908 Ann. Phys. 25 377
Google Scholar
[9] 柯熙政, 马冬冬, 刘佳妮 2009 光散射学报 21 104
Google Scholar
Ke X J, Ma D D, Liu J N 2009 Chin. J. Light Scatt. 21 104
Google Scholar
[10] 麻金继, 陈瑾 2005 原子与分子物理学报 22 701
Google Scholar
Ma J J, Chen J 2005 J. Atom. Mol. Phys. 22 701
Google Scholar
[11] Bedareva T V, Sviridenkov M A, Zhuravleva T B 2014 J. Quant. Spectrosc. Ra. 146 140
[12] Su M Y 1987 Inverse Problems in Optics Hague, Netherlands, September 10, 1987 p112
[13] Slane P O, McLaughlin E R, Schwartz D A, et al. 1989 Reflective Optics II Orlando, FL, USA, October 11, 1989 p12
[14] Weisskopf M C, O'Dell S L, van Speybroeck L P 1996 Multilayer and Grazing Incidence X-Ray/EUV Optics III Denver, CO, USA, July 19, 1996 p2
[15] Henke B L, Gullikson E M, Davis J C 1993 Atom Data Nucl. Data 54 181
Google Scholar
[16] Aschenbach B 2005 Optics for EUV, X-Ray, and Gamma-Ray Astronomy II San Diego, California, USA, September 8, 2005 p59000
[17] O'Dell S L, Brissenden R J, Davis W N, et al. 2010 Adaptive X-Ray Optics San Diego, California, USA, October 22, 2010 p78030
[18] Wiscombe W J 1980 Appl. Opt. 19 1505
Google Scholar
[19] 沈建琪 1999 博士学位论文 (上海: 上海理工大学)
Shen J Q 1999 Ph. D. Dissertation (Shanghai: University of Shanghai for Science and Technology) (in Chinese)
[20] Hagemann H J, Gudat W, Kunz C 1975 J. Opt. Soc. Am. B 65 742
Google Scholar
[21] Friedrich P, Brauninger H, Budau B, et al. 2008 Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray Marseille, France, July 15, 2008 p70112
[22] 郑钢镖, 康天合, 柴肇云, 尹志宏 2006 太原理工大学学报 3 317
Google Scholar
Zheng G B, Kang T H, Chai Z Y, Yin Z H 2006 J. Taiyuan Univ. Technol. 3 317
Google Scholar
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