Effect of work function on dust charging and dynamics near lunar surface

Liu Zhi-Gui; Song Zhi-Ying; Quan Rong-Hui

doi:10.7498/aps.73.20241281

Abstract

Charged dust on the lunar surface poses a threat to space missions. Research into charged dust is essential for the safety of future space missions. When calculating the charging currents related to photoelectrons, a single constant work function is assumed in the conventional lunar dust charging theory. However, the components of lunar regolith exhibit considerable diversity, including plagioclase, pyroxene, and ilmenite. Because the ability of the lunar surface or lunar dust to emit photoelectrons strongly depends on its work function, it is necessary to analyze the effect of the work function on dust charging and dynamics near the lunar surface. In this work, we use a novel method that can predict the photoelectric yield of materials with different work functions to recalculate the surface charging currents of four types of dust particles and derive their subsequent charging and dynamic results at different solar zenith angles (SZAs). As SZA varies from 0° to 90°, the work function value of dust decreases into 6 eV (Apollo lunar soil), 5.58 eV (plagioclase), 5.14 eV (pyroxene), and 4.29 eV (ilmenite), correspondingly. With each decrement in work function, the equilibrium charging current of dust particles increases about 0.25 times, the equilibrium charge number increases about 120–170 elemental charges, and the equilibrium height increases about 0.3–2 m. It is found that dust particles cannot levitate stably at a critical SZA, and the critical SZAs for the four types of dust particles are 28°, 76°, 85.8°, and 89.6°, respectively (arranged in decreasing order of work functions). These results indicate that the equilibrium heights, equilibrium currents, and critical SZAs all have an inverse relationship with the work function of dust particles as the SZA varies from 0° to 90°. Furthermore, a higher photoelectron density in areas with lower work functions leads energy losses to decrease, thus causing dust particles to take longer time to reach equilibrium. This means that the equilibrium time follows the pattern similar to that of the work function.

Keywords:

Authors and contacts

College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Corresponding author: Quan Rong-Hui, quanrh@nuaa.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 42241148, 51877111).

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References

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[2]	Xia Q, Cai M H, Xu L L, Han R L, Yang T, Han J W 2022 Chin. Phys. B 31 045201 Google Scholar
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[21]	Zelenyi L M, Popel S I, Zakharov A V 2020 Plasma Phys. Rep. 46 527 Google Scholar
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[35]	Kimura H 2016 Mon. Not. R. Astron. Soc. 459 2751 Google Scholar
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[37]	Senshu H, Kimura H, Yamamoto T, Wada K, Kobayashi M, Namiki N, Matsui T 2015 Planet. Space Sci. 116 18 Google Scholar
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[41]	Colwell J E, Gulbis A A, Horányi M, Robertson S 2005 Icarus 175 159 Google Scholar
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[44]	Zhao J, Wei X, Du X, He X, Han D 2021 IEEE Trans. Plasma Sci. 49 3036 Google Scholar
[45]	Nitter T, Aslaksen T K, Melandso F, Havnes O 1994 IEEE Trans. Plasma Sci. 22 159 Google Scholar
[46]	Qian X Y, Zhang Y Y, Fang Z, Yang J F, Fang Y W, Li S Q 2024 J. Astronaut. 45 613 Google Scholar
[47]	Poppe A, Horányi M 2010 J. Geophys. Res.: Space Phys. 115 A08106 Google Scholar
[48]	Hartzell C M 2019 Icarus 333 234 Google Scholar
[49]	Popel S I, Golub’ A P, Kassem A I, Zelenyi L M 2022 Phys. Plasmas 29 013701 Google Scholar

Cited By

图 1 阿波罗任务带回的样品的光电子产率

Figure 1. Photoelectric yield measured on samples returned by Apollo missions.

DownLoad: Full-Size Img PowerPoint

图 2 最小太阳活动周期下的太阳辐射光谱

Figure 2. Wavelength dependence of solar radiation spectrum under minimum solar activity conditions.

DownLoad: Full-Size Img PowerPoint

图 3 4种不同功函数尘埃的光电子产率. 实线表示使用Kimura方法计算的产率, 红色实线代表阿波罗月球土壤, 蓝色实线代表斜长石, 黄色实线代表辉石, 绿色实线代表钛铁矿. 红色虚线表示阿波罗月球土壤的实验产率

Figure 3. Photoelectric yield for four different types of dust particles. Solid lines represent yield calculated by using Kimura’s method. Red line represents Apollo lunar soil, blue line represents plagioclase, yellow line represents pyroxene, and green line represents ilmenite. Red dash line represents experimental yield of Apollo lunar soil.

DownLoad: Full-Size Img PowerPoint

图 4 4个区域内正午时分的电势、电场与高度的函数关系, 为方便比较, 绘制了半对数横坐标形式的内插图　(a) 电势与高度的函数关系; (b) 电场与高度的函数关系

Figure 4. Height dependence of surface potential and electric field at noon. For clarity, the semilogx form has been plotted: (a) Potential; (b) electric field.

DownLoad: Full-Size Img PowerPoint

图 5 正午时分悬浮尘埃颗粒的充电电流　(a) 光电子发射电流; (b) 光电子收集电流; (c) 太阳风电子电流

Figure 5. Charging currents of suspended dust particles at noon: (a) Photoemission current; (b) photoelectron collection current; (c) solar wind electron current.

DownLoad: Full-Size Img PowerPoint

图 6 正午时分4种尘埃颗粒的电流能, 0—60 s内的结果已被绘制为内插图

Figure 6. Energy created by charging currents at noon. Current energy from 0–60 s has been magnified.

DownLoad: Full-Size Img PowerPoint

图 7 正午时分悬浮尘埃颗粒的表面电荷数

Figure 7. Charge numbers of suspended dust particles at noon.

DownLoad: Full-Size Img PowerPoint

图 8 正午时分悬浮尘埃颗粒的高度, 内插图为900—1000 s的结果

Figure 8. Vertical height of suspended dust particles at noon, results at 900–1000 s have been magnified.

DownLoad: Full-Size Img PowerPoint

图 9 悬浮尘埃颗粒的平衡态　(a) 平衡高度; (b) 平衡电荷数

Figure 9. Equilibria of suspended dust particles: (a) equilibrium height; (b) equilibrium charge numbers.

DownLoad: Full-Size Img PowerPoint

表 1 4个区域中的材料参数及正午时分的光电子浓度

Table 1. Material parameters and photoelectron density of four areas at noon.

尘埃类型	密度/(g·cm^–3)	功函数/eV	浓度/(10⁷ m^–3)
阿波罗月壤	1.5	6.00	6.6943
斜长石	2.7	5.58	6.9190
辉石	3.2	5.14	7.1508
钛铁矿	4.4	4.29	7.5901

DownLoad: CSV

表 2 初始参数

Table 2. Initial parameters.

参数	参数值
日心距$ {d} $/AU	1
重力加速度$ g_{\mathrm{a}}/({\mathrm{m}} \cdot {\mathrm{s}}^{-2}) $	1.63
尘埃质量$ m_{\mathrm{d}}/{\mathrm{kg}} $	6.28318$ \times 10^{-18} $
初始电荷$ Q_0 /{\mathrm{C}}$	3.20424$ \times 10^{-17} $
初始速度$ v_{\mathrm{d0}}/({\mathrm{m}} \cdot {\mathrm{s}}^{-1}) $	2

DownLoad: CSV

[1]	Zakharov A V, Popel S I, Kuznetsov I A, Borisov N D, Rosenfeld E V, Skorov Y, Zelenyi L M 2022 Phys. Plasmas 29 110501 Google Scholar
[2]	Xia Q, Cai M H, Xu L L, Han R L, Yang T, Han J W 2022 Chin. Phys. B 31 045201 Google Scholar
[3]	Grard R, Tunaley J 1971 J. Geophys. Res. 76 2498 Google Scholar
[4]	Nitter T, Havnes O 1992 Earth Moon and Planets 56 7 Google Scholar
[5]	Nitter T, Havnes O, Melands F 1998 J. Geophys. Res.: Space Phys. 103 6605 Google Scholar
[6]	Colwell J, Batiste S, Horányi M, Robertson S, Sture S 2007 Rev. Geophys. 45 RG2006 Google Scholar
[7]	Lee P 1996 Icarus 124 181 Google Scholar
[8]	Walbridge E 1973 J. Geophys. Res. 78 3668 Google Scholar
[9]	Whipple E C 1981 Rep. Prog. Phys. 44 1197 Google Scholar
[10]	Wang X, Horányi M, Robertson S 2009 J. Geophys. Res.:Space Phys. 114 A05103 Google Scholar
[11]	Wang X, HoráNyi M, Robertson S 2010 J. Geophys. Res.: Space Phys. 115 A11102 Google Scholar
[12]	Wang X, Horányi M, Robertson S 2011 Planet. Space Sci. 59 1791 Google Scholar
[13]	Wang X, Schwan J, Hsu H W, Grün E, Horányi M 2016 Geophys. Res. Lett. 43 6103 Google Scholar
[14]	Wang X, Pilewskie J, Hsu H W, Horányi M 2016 Geophys. Res. Lett. 43 525 Google Scholar
[15]	Schwan J, Wang X, Hsu H W, Grün E, Horányi M 2017 Geophys. Res. Lett. 44 3059 Google Scholar
[16]	Zimmerman M I, Farrell W M, Hartzell C M, Wang X, Horanyi M, Hurley D M, Hibbitts K 2016 J. Geophys. Res.: Planets 121 2150 Google Scholar
[17]	Hartzell C, Zimmerman M, Hergenrother C 2022 Planet. Sci. J. 3 85 Google Scholar
[18]	Golub’ A P, Dol’nikov G G, Zakharov A V, Zelenyi L M, Izvekova Y N, Kopnin S I, Popel S I 2012 Jetp. Lett. 95 182 Google Scholar
[19]	Popel S I, Kopnin S I, Golub’ A P, Dol’nikov G G, Zakharov A V, Zelenyi L M, Izvekova Y N 2013 Sol. Syst. Res. 47 419 Google Scholar
[20]	Popel S I, Golub’ A P, Zakharov A V, Zelenyi L M 2019 J. Phys. : Conf. Ser. 1147 012110 Google Scholar
[21]	Zelenyi L M, Popel S I, Zakharov A V 2020 Plasma Phys. Rep. 46 527 Google Scholar
[22]	Hess S L G, Sarrailh P, Mateo-Velez J C, Jeanty-Ruard B, Cipriani F, Forest J, Hilgers A, Honary F, Thiebault B, Marple S R, Rodgers D 2015 IEEE Trans. Plasma Sci. 43 2799 Google Scholar
[23]	Kuznetsov I A, Hess S L G, Zakharov A V, Cipriani F, Seran E, Popel S I, Lisin E A, Petrov O F, Dolnikov G G, Lyash A N, Kopnin S I 2018 Planet. Space Sci. 156 62 Google Scholar
[24]	Davari H, Farokhi B, Ali Asgarian M 2023 Sci. Rep. 13 1111 Google Scholar
[25]	Piquette M, Horányi M 2017 Icarus 291 65 Google Scholar
[26]	李梦谣, 夏清, 蔡明辉, 杨涛, 许亮亮, 贾鑫禹, 韩建伟 2024 物理学报 73 155201 Google Scholar Li M Y, Xia Q, Cai M H, Yang T, Xu L L, Jia X Y, Han J W 2024 Acta Phys. Sin. 73 155201 Google Scholar
[27]	Zhao C, Gan H, Xie L, Wang Y, Wang Y, Hong J 2023 Sci. China: Earth Sci. 66 2278 Google Scholar
[28]	Gan H, Wei G F, Zhang W W, Li X Y, Jiang S Y, Wang C, Ma J N, Zhang X P 2023 Sci. China: Phys. Mech. Astron. 53 127 Google Scholar
[29]	Li L, Zhang Y T, Zhou B, Feng Y Y 2016 Sci. China: Earth Sci. 59 2053 Google Scholar
[30]	Popel S I, Golub’ A P, Izvekova Y N, Afonin V V, Dol’nikov G G, Zakharov A V, Zelenyi L M, Lisin E A, Petrov O F 2014 Jetp. Lett. 99 115 Google Scholar
[31]	Mishra S K 2020 Phys. Plasmas 27 082906 Google Scholar
[32]	Feuerbacher B, Anderegg M, Fitton B, Laude L D, Willis R F, Grard R J L 1972 Lunar and Planetary Science Conference Proceedings 3 2655
[33]	Sternovsky Z, Robertson S, Sickafoose A, Colwell J, Horányi M 2002 J. Geophys. Res.: Planets 107 5105 Google Scholar
[34]	Sternovsky Z, Chamberlin P, Horanyi M, Robertson S, Wang X 2008 J. Geophys. Res.: Space Phys. 113 A10104 Google Scholar
[35]	Kimura H 2016 Mon. Not. R. Astron. Soc. 459 2751 Google Scholar
[36]	Seah M P, Dench W 1979 Surf. Interface Anal. 1 2 Google Scholar
[37]	Senshu H, Kimura H, Yamamoto T, Wada K, Kobayashi M, Namiki N, Matsui T 2015 Planet. Space Sci. 116 18 Google Scholar
[38]	Chamberlin P C, Woods T N, Eparvier F G 2007 Space Weather 5 S07005 Google Scholar
[39]	Rakesh Chandran S B, Veenas C L, Asitha L R, Parvathy B, Rakhimol K R, Abraham A, Rajesh S R, Sunitha A P, Renuka G 2022 Adv. Space Res. 70 546 Google Scholar
[40]	Stubbs T J, Farrell W M, Halekas J S, Burchill J K, Collier M R, Zimmerman M I, Vondrak R R, Delory G T, Pfaff R F 2014 Planet. Space Sci. 90 10 Google Scholar
[41]	Colwell J E, Gulbis A A, Horányi M, Robertson S 2005 Icarus 175 159 Google Scholar
[42]	Gan H, Li X, Wei G, Wang S 2015 Adv. Space Res. 56 2432 Google Scholar
[43]	Willis R F, Anderegg M, Feuerbacher B, Fitton B (Grard R J L Ed.) 1973 Astrophys. Space Sci. Libr. 37 389
[44]	Zhao J, Wei X, Du X, He X, Han D 2021 IEEE Trans. Plasma Sci. 49 3036 Google Scholar
[45]	Nitter T, Aslaksen T K, Melandso F, Havnes O 1994 IEEE Trans. Plasma Sci. 22 159 Google Scholar
[46]	Qian X Y, Zhang Y Y, Fang Z, Yang J F, Fang Y W, Li S Q 2024 J. Astronaut. 45 613 Google Scholar
[47]	Poppe A, Horányi M 2010 J. Geophys. Res.: Space Phys. 115 A08106 Google Scholar
[48]	Hartzell C M 2019 Icarus 333 234 Google Scholar
[49]	Popel S I, Golub’ A P, Kassem A I, Zelenyi L M 2022 Phys. Plasmas 29 013701 Google Scholar

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