Simulation analysis and design of electron deflector for eXTP focusing telescope

ZHENG Renzhou; QIANG Pengfei; YANG Yanji; YAN Yongqing; LI Yue; SHENG Lizhi; CHEN Yong

doi:10.7498/aps.74.20241649

Abstract

X-ray focusing telescope is the core equipment for space X-ray observation. In order to ensure the accuracy of the observation results, it is necessary to deflect the low-energy electrons entering the focusing telescope to effectively reduce the background noise. In this work, the electron deflector for enhanced X-ray timing and polarimetry mission (eXTP) focusing telescope is developed to meet the deflection requirements of low-energy electrons in the focusing telescope optical system, with the lightweight, ability to deflect electrons , and electromagnetic compatibility considered. The finite element analysis software COMSOL Multiphysics is used to establish the full physical simulation model of the electron deflector and focusing telescope mirrors. The magnetic flux density distribution, electron deflection trajectories and the effect of magnetic field on focusing telescope mirrors are analyzed, and the electromagnetic parameters of the electron deflector are designed. The simulation results show that the closer to the magnet and the center of electron deflector, the greater the magnetic flux density, and the maximum magnetic flux density in the middle of the two spokes can reach 0.027 T. When the radius is larger than 280 mm, the longitudinal distance is larger than 60 mm, the magnetic flux density is less than 5×10^–5 T (0.5 Gs), i.e. the geomagnetic intensity, which meets the design requirements of electromagnetic compatibility performance. When the incidence angle is ≤10°, the electron deflection efficiency decreases with the increase of electron energy and incidence angle, and the deflection efficiency of electrons below 50 keV energy can reach 100%, which meets the design requirements of electron deflection. In addition, as the focusing telescope mirrors are away from the electron deflector, the area of mirrors affected by the magnetic field becomes smaller and smaller. When the distance between the mirror bottom and electron deflector is 130 mm, the magnetic flux density at the mirror bottom only reaches 10^–4 T. Similarly, as the focusing telescope mirrors are away from the electron deflector, the stress at the mirror bottom decreases from 10³ N/m² at 10 mm to 10^–2 N/m² at 60 mm, and the deformation at mirror bottom decreases from ~nm at 10 mm to 10^–4 nm at 60 mm. When the distance between the mirror bottom and electron deflector is 130 mm, the stress is only 10^–3 N/m², and the deformation is only 10^–5 nm, indicating that the magnetic field does not affect the optical properties of the focusing telescope. The above simulation analyses show that the design parameters of NdFeB magnet structure of the electron deflector fully meet the requirements of the eXTP focusing telescope optical system for the deflection of low-energy electrons. And the deflection efficiency of electrons with 25 keV energy, incidence angle within ±5°, and deflection distance of 5250 mm is 100%. These results provide an important reference for developing electron deflector of eXTP focusing telescope.

Keywords:

Authors and contacts

1.
State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China
2.
Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: YAN Yongqing, yanyongqing@opt.ac.cn ; SHENG Lizhi, lizhi_sheng@opt.ac.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 42327802, 62271483), the National Key Laboratory Foundation of China (Grant No. SKLIPR2021), the Natural Science Basic Research Program of Shaanxi Province, China (Grant Nos. 2023-JC-ZD-40, 2024JC-YBQN-0003), and the 76th General Program of the China Postdoctoral Science Foundation (Grant No. 2024M763511).

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References

[1]	袁为民, 张臣, 陈勇, 孙胜利, 张永合, 崔伟, 凌志兴, 黄茂海, 赵冬华, 王文昕, 裘予雷, 刘柱, 潘海武, 蔡洪波, 邓劲松, 贾振卿, 金驰川, 孙惠, 胡海波, 刘飞飞, 张墨, 宋黎明, 卢方军, 贾淑梅, 李承奎, 赵海升, 葛明玉, 张娟, 崔苇苇, 王于仨, 王娟, 孙小进, 金戈, 黎龙辉, 陈凡胜, 蔡志鸣, 郭彤, 刘国华, 刘华秋, 冯骅, 张双南, 张冰, 戴子高, 吴雪峰, 苟利军 2018 中国科学: 物理学力学天文学 48 039502 Google Scholar Yuan W M, Zhang C, Chen Y, Sun S L, Zhang Y H, Cui W, Lin Z X, Huang M H, Zhao D H, Wang W X, Qiu Y L, Liu Z, Pan H W, Cai H B, Deng J S, Jia Z Q, Jin C C, Sun H, Hu H B, Liu F F, Zhang M, Song L M, Lu F J, Jia S M, Li C K, Zhao H S, Ge M Y, Zhang J, Cui W W, Wang Y S, Wang J, Sun X J, Jin G, Li L H, Chen F S, Cai Z M, Guo T, Liu G H, Liu H Q, Feng H, Zhang S N, Zhang B, Dai Z G, Wu X F, Gou L J 2018 Sci. China: Phys. Mech. 48 039502 Google Scholar
[2]	Jeong S, Panasyuk M I, Reglero V 2018 Space Sci. Rev. 214 25 Google Scholar
[3]	Zhang S N, Santangelo A, Feroci M 2019 Sci. China Phys. Mech. 62 25
[4]	Zand J J M, Bozzo E, Qu J L 2019 Sci. China Phys. Mech. 62 029506 Google Scholar
[5]	Aslanyan V, Keresztes K, Feldman C, Pearson J F, Willingale R, Martindale A, Sembay S, Osborne J P, Sachdev S S, Bicknell C L, Houghton P R, Crawford T, Chornay D 2019 Rev. Scientif. Inst. 90 124502 Google Scholar
[6]	Zhang S N, Santangelo A, Feroci M, et al. 2018 Sci. China: Phys. Mech. 62 029502
[7]	Yuan W M, Zhang C, Feng H, et al. 2015 Swift: 10 Years of Discovery
[8]	Yuan W M, Chen Z, Ling Z, et al. 2018 Proc. SPIE: Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray 2018 1069925
[9]	Chen Y, Cui W W, Han D W, et al. 2020 Proc. SPIE: Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray 2020 11444B
[10]	Gehrels N, Chincarini G, Giommi P, et al. 2004 Astrophys. J. 611 1309
[11]	Willingale R 2000 An electron diverter for the Swift Telescope XRA study note XRT-LUX-RE-011/1 (University of Leicester
[12]	Friedrich P, Bräuninger H, Budau B, et al. 2012 Proc. SPIE 8443 84431S Google Scholar
[13]	Spiga D, Fioretti V, Bulgarelli A, et al. 2008 Proc. SPIE: Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray 7011 70112Y
[14]	Wang L, Qin L, Cheng J, et al. 2020 IEEE Trans. Appl. Supercond. 30 1
[15]	Lotti S, Mineo T, Jacquey C, et al. 2018 Exp. Astron. 45 411 Google Scholar
[16]	Fioretti V, Bulgarelli A, Molendi S, et al. 2018 Astrophys. J. 867 9 Google Scholar
[17]	Qi L Q, Li G, Xu Y P, et al. 2020 Nucl. Instrum. Meth. A 963 163702 Google Scholar
[18]	Qi L Q, Li G, Xu Y P, Chen Y, He H L, Wang Y S, Yang Y J, Zhang J, Lu F J 2021 Exp. Astron. 51 475 Google Scholar
[19]	Aguilar M, Alcaraz J, Allaby J, et al. 2002 Phys. Rep. 366 331 Google Scholar
[20]	Aguilar M, Cavasonza L A, Ambrosi G, et al. 2021 Phys. Rep. 894 1 Google Scholar

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图 1 聚焦镜及电子偏转器结构示意图^[6]

Figure 1. Schematic diagram of the structure of focusing telescope and electron deflector^[6].

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图 2 电子偏转器及聚焦镜镜片全物理仿真模型

Figure 2. Full physical simulation model of the electron deflector and focusing telescope mirrors.

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图 3 电子偏转器周围空间　(a)磁感应强度分布, 右侧彩色图例表示磁感应强度; (b)磁场方向

Figure 3. (a) Distribution of magnetic flux density, the color legend on the right represents the magnetic flux density; (b) magnetic field direction around the electron deflector.

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图 4 磁铁中心所在平面　(a)磁感应强度; (b)磁感应强度x分量; (c)磁感应强度y分量分布

Figure 4. Distribution of (a) magnetic flux density; (b) x component of magnetic flux density; (c) y component of magnetic flux density in the magnet center plane.

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图 5 磁感应强度沿两根辐条之间半径的分布情况

Figure 5. Distribution of magnetic flux density along the radius between two spokes.

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图 6 半径500 mm范围内磁感应强度平面分布

Figure 6. Plane distribution of magnetic flux density within a radius of 500 mm.

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图 7 磁感应强度纵向分布

Figure 7. Longitudinal distribution of magnetic flux density.

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图 8 电子偏转效率与电子能量和入射角的关系

Figure 8. Variations of electron deflection efficiency dependent on the electron energy and incidence angle.

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图 9 20°入射角极限情况　(a) 60 keV; (b) 80 keV; (c) 100 keV电子偏转轨迹

Figure 9. For the 20° incident angle limit case: (a) 60 keV; (b) 80 keV; (c) 100 keV electron deflection trajectories.

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图 10 入射角为5°时电子偏转效率与钕铁硼磁铁高度的关系

Figure 10. Variations of electron deflection efficiency dependent on the NdFeB magnet height at incident angle of 5°.

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图 11 聚焦镜镜片磁感应强度分布

Figure 11. Distribution of magnetic flux density of the focusing telescope mirrors.

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图 12 电子偏转器及聚焦镜镜片周围空间磁感应强度分布

Figure 12. Distribution of magnetic flux density around the electron deflector and focusing telescope mirrors.

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图 13 聚焦镜镜片应力分布

Figure 13. Stress distribution of the focusing telescope mirrors.

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图 14 聚焦镜镜片　(a)形变大小; (b)形变x分量; (c)形变y分量; (d)形变z分量

Figure 14. (a) Deformation, (b) x component of deformation, (c) y component of deformation, and (d) z component of deformation of the focusing telescope mirrors.

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图 15 聚焦镜镜片底端距离电子偏转器　(a) 10 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm时聚焦镜镜片磁感应强度分布

Figure 15. Distribution of magnetic flux density of the focusing telescope mirrors when the distance between the mirror bottom and electron deflector is (a) 10 mm, (b) 20 mm, (c) 40 mm, and (d) 60 mm.

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图 16 聚焦镜镜片底端距离电子偏转器　(a) 10 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm时电子偏转器及聚焦镜镜片周围空间磁感应强度分布

Figure 16. Distribution of magnetic flux density around the electron deflector and focusing telescope mirrors when the distance between the mirror bottom and electron deflector is (a) 10 mm, (b) 20 mm, (c) 40 mm, and (d) 60 mm.

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图 17 聚焦镜镜片底端距离电子偏转器　(a) 10 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm时聚焦镜镜片应力分布

Figure 17. Stress distribution of the focusing telescope mirrors when the distance between the mirror bottom and electron deflector is (a) 10 mm, (b) 20 mm, (c) 40 mm, and (d) 60 mm.

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图 18 聚焦镜镜片底端距离电子偏转器　(a) 10 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm时聚焦镜镜片形变

Figure 18. Deformation of the focusing telescope mirrors when the distance between the mirror bottom and electron deflector is (a) 10 mm, (b) 20 mm, (c) 40 mm, and (d) 60 mm.

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表 1 电子偏转器各材料参数

Table 1. Material parameters of the electron deflector.

名称	材料/型号	数量	密度/(kg·m^–3)	杨氏模量/(N·mm^–2)	泊松比	质量/kg
电子偏转器法兰	AA7075	1	2800	70000	0.33	0.339
磁铁	NdFeB	120	7400	140000	—	0.224
螺丝	TC4	—	7900	210000	0.3	0.003
粘合胶	EC2216	—	—	—	—	—

DownLoad: CSV

表 2 电子偏转器钕铁硼(NdFeB)磁铁结构设计参数

Table 2. Structure design parameters of the electron deflector NdFeB magnet.

序号	长度/mm	宽度/mm	高度/mm	剩磁/T
#1	26	1.8	5	1.4
#2	26	2.5	5	1.4
#3	26	3	5	1.4
#4	26	3.5	5	1.4
#5	30	4	5	1.4

DownLoad: CSV

[1]	袁为民, 张臣, 陈勇, 孙胜利, 张永合, 崔伟, 凌志兴, 黄茂海, 赵冬华, 王文昕, 裘予雷, 刘柱, 潘海武, 蔡洪波, 邓劲松, 贾振卿, 金驰川, 孙惠, 胡海波, 刘飞飞, 张墨, 宋黎明, 卢方军, 贾淑梅, 李承奎, 赵海升, 葛明玉, 张娟, 崔苇苇, 王于仨, 王娟, 孙小进, 金戈, 黎龙辉, 陈凡胜, 蔡志鸣, 郭彤, 刘国华, 刘华秋, 冯骅, 张双南, 张冰, 戴子高, 吴雪峰, 苟利军 2018 中国科学: 物理学力学天文学 48 039502 Google Scholar Yuan W M, Zhang C, Chen Y, Sun S L, Zhang Y H, Cui W, Lin Z X, Huang M H, Zhao D H, Wang W X, Qiu Y L, Liu Z, Pan H W, Cai H B, Deng J S, Jia Z Q, Jin C C, Sun H, Hu H B, Liu F F, Zhang M, Song L M, Lu F J, Jia S M, Li C K, Zhao H S, Ge M Y, Zhang J, Cui W W, Wang Y S, Wang J, Sun X J, Jin G, Li L H, Chen F S, Cai Z M, Guo T, Liu G H, Liu H Q, Feng H, Zhang S N, Zhang B, Dai Z G, Wu X F, Gou L J 2018 Sci. China: Phys. Mech. 48 039502 Google Scholar
[2]	Jeong S, Panasyuk M I, Reglero V 2018 Space Sci. Rev. 214 25 Google Scholar
[3]	Zhang S N, Santangelo A, Feroci M 2019 Sci. China Phys. Mech. 62 25
[4]	Zand J J M, Bozzo E, Qu J L 2019 Sci. China Phys. Mech. 62 029506 Google Scholar
[5]	Aslanyan V, Keresztes K, Feldman C, Pearson J F, Willingale R, Martindale A, Sembay S, Osborne J P, Sachdev S S, Bicknell C L, Houghton P R, Crawford T, Chornay D 2019 Rev. Scientif. Inst. 90 124502 Google Scholar
[6]	Zhang S N, Santangelo A, Feroci M, et al. 2018 Sci. China: Phys. Mech. 62 029502
[7]	Yuan W M, Zhang C, Feng H, et al. 2015 Swift: 10 Years of Discovery
[8]	Yuan W M, Chen Z, Ling Z, et al. 2018 Proc. SPIE: Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray 2018 1069925
[9]	Chen Y, Cui W W, Han D W, et al. 2020 Proc. SPIE: Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray 2020 11444B
[10]	Gehrels N, Chincarini G, Giommi P, et al. 2004 Astrophys. J. 611 1309
[11]	Willingale R 2000 An electron diverter for the Swift Telescope XRA study note XRT-LUX-RE-011/1 (University of Leicester
[12]	Friedrich P, Bräuninger H, Budau B, et al. 2012 Proc. SPIE 8443 84431S Google Scholar
[13]	Spiga D, Fioretti V, Bulgarelli A, et al. 2008 Proc. SPIE: Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray 7011 70112Y
[14]	Wang L, Qin L, Cheng J, et al. 2020 IEEE Trans. Appl. Supercond. 30 1
[15]	Lotti S, Mineo T, Jacquey C, et al. 2018 Exp. Astron. 45 411 Google Scholar
[16]	Fioretti V, Bulgarelli A, Molendi S, et al. 2018 Astrophys. J. 867 9 Google Scholar
[17]	Qi L Q, Li G, Xu Y P, et al. 2020 Nucl. Instrum. Meth. A 963 163702 Google Scholar
[18]	Qi L Q, Li G, Xu Y P, Chen Y, He H L, Wang Y S, Yang Y J, Zhang J, Lu F J 2021 Exp. Astron. 51 475 Google Scholar
[19]	Aguilar M, Alcaraz J, Allaby J, et al. 2002 Phys. Rep. 366 331 Google Scholar
[20]	Aguilar M, Cavasonza L A, Ambrosi G, et al. 2021 Phys. Rep. 894 1 Google Scholar

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