月球表面电场环境的数值模拟
摘要
本文深入地模拟了月球表面的电场环境。由于月球表面不同的太空环境,月球表面形成了多种性质不同的鞘层。在同一鞘层中,由于太阳光子的入射角度的不同,在月球表面形成的电场环境也是不同的。
月球处于太阳风的环境中,如果只考虑这一因素,在其表面会形成玻姆鞘层。太阳风中的电子入射到月球表面,会使月球表面的电势为负。在月球的阳面,由于太阳光子的入射,月球表面会产生光电效应,发射出光电子,这样会增加月球表面的电势。根据月球所处的不同的太空环境,本文建立了三种鞘层模型:存在势垒的鞘层A;主要由光电子作用,电势单调上升的鞘层B;主要由太阳风中的电子作用,电势单调下降的鞘层C。在电子和光电子满足半麦克斯韦速度分布的初始条件下,给出了各个粒子的密度分布函数。然后对每一种鞘层模型进行分析推导,得出边界条件方程,泊松方程以及电场的表达式。
鞘层模型中的有些参数是未知的,需要通过边界方程进行求解。在得出所有的参数后可以通过龙格-库塔法对泊松方程进行求解,得到表面的电场强度和电势,以及在不同位置不同离子的密度。由于太阳光子入射到月球的表面的角度是不断变化的,我们通过改变在月球表面的光电子的密度来比较分析月球表面的电场环境。通过数值模拟和结果分析,我们认为在月球的夜面形成的是鞘层C,太阳光子入射到月球的表面的角度对鞘层C的电场强度和电势都会产生比较大的影响。在月球的阳面,鞘层A、B和C都有可能形成。在光电子密度比较小的时候会形成鞘层C,在光电子密度变大时既可以形成鞘层A,又可以形成鞘层B。在引入势能判断法之后就可以决定鞘层的类型。我们又发现马赫数对鞘层有很大的影响。结合不同鞘层所选择的初始光电子密度的范围和势能判断法则,我们最终给出了对于不同的光电子密度和马赫数的不通过鞘层之间的临界曲线。
In this paper, we have simulated the electrical field environment of the lunar surface in depth. Different kinds of sheaths are formed on the lunar surface for the different space environment. Even for the same kind of sheath, because of different angles the photons flux hitting the Moon, electrical field environment is different from each other.
The Moon stays in the solar wind, so the Bohm sheath is formed on the lunar surface. The electrons in the solar wind hit the surface and make the potential of the surface to be negative. On the day-side of the Moon, because of photons to the surface, photoelectric effect is happened, and which will increase the potential of lunar surface. According to these conditions, we model three kinds of sheaths: sheath A, which have a potential barrier; sheath B in which the potential decreases monotonically, and the photoelectrons play the domain role; sheath C in which the potential increases monotonically. We get the densities of different particles in the condition that the electrons and photoelectrons satisfy half-Maxwellian distribution. By derivation, we get the boundary condition equations, Poisson’s equation and the expression of electrical field intensity for every sheath model.
Some of parameters in the sheath models are unknown, but they can be solved by boundary condition equations. After all parameters obtained, we can get the electrical potential and electrical field intensity by solving the Poisson’s equation with Runge-Kutta method. We change the density of photoelectrons on the lunar surface to simulate the different angle of photons hitting the Moon. By numerical simulation and data analysis, we believe that on the night-side of the Moon, sheath C is formed and the angle of photons hitting the Moon has large impact on the electrical potential and electrical field intensity. On the day-side, both sheath A B and C could be formed. When the photoelectrons density at origin is small, sheath C will be formed; when n_(p,o)grows bigger, both sheath A and B could be formed. For the sheath which contains a smaller energy is more stable. Then we can compute the potential energy to decide which sheath would be formed. We also find the Mach number M has a great influence on the sheath A. Combining the range of n(p,o), we can give the critical curve between A B and C for different n(p,o) and M.
月球处于太阳风的环境中,如果只考虑这一因素,在其表面会形成玻姆鞘层。太阳风中的电子入射到月球表面,会使月球表面的电势为负。在月球的阳面,由于太阳光子的入射,月球表面会产生光电效应,发射出光电子,这样会增加月球表面的电势。根据月球所处的不同的太空环境,本文建立了三种鞘层模型:存在势垒的鞘层A;主要由光电子作用,电势单调上升的鞘层B;主要由太阳风中的电子作用,电势单调下降的鞘层C。在电子和光电子满足半麦克斯韦速度分布的初始条件下,给出了各个粒子的密度分布函数。然后对每一种鞘层模型进行分析推导,得出边界条件方程,泊松方程以及电场的表达式。
鞘层模型中的有些参数是未知的,需要通过边界方程进行求解。在得出所有的参数后可以通过龙格-库塔法对泊松方程进行求解,得到表面的电场强度和电势,以及在不同位置不同离子的密度。由于太阳光子入射到月球的表面的角度是不断变化的,我们通过改变在月球表面的光电子的密度来比较分析月球表面的电场环境。通过数值模拟和结果分析,我们认为在月球的夜面形成的是鞘层C,太阳光子入射到月球的表面的角度对鞘层C的电场强度和电势都会产生比较大的影响。在月球的阳面,鞘层A、B和C都有可能形成。在光电子密度比较小的时候会形成鞘层C,在光电子密度变大时既可以形成鞘层A,又可以形成鞘层B。在引入势能判断法之后就可以决定鞘层的类型。我们又发现马赫数对鞘层有很大的影响。结合不同鞘层所选择的初始光电子密度的范围和势能判断法则,我们最终给出了对于不同的光电子密度和马赫数的不通过鞘层之间的临界曲线。
In this paper, we have simulated the electrical field environment of the lunar surface in depth. Different kinds of sheaths are formed on the lunar surface for the different space environment. Even for the same kind of sheath, because of different angles the photons flux hitting the Moon, electrical field environment is different from each other.
The Moon stays in the solar wind, so the Bohm sheath is formed on the lunar surface. The electrons in the solar wind hit the surface and make the potential of the surface to be negative. On the day-side of the Moon, because of photons to the surface, photoelectric effect is happened, and which will increase the potential of lunar surface. According to these conditions, we model three kinds of sheaths: sheath A, which have a potential barrier; sheath B in which the potential decreases monotonically, and the photoelectrons play the domain role; sheath C in which the potential increases monotonically. We get the densities of different particles in the condition that the electrons and photoelectrons satisfy half-Maxwellian distribution. By derivation, we get the boundary condition equations, Poisson’s equation and the expression of electrical field intensity for every sheath model.
Some of parameters in the sheath models are unknown, but they can be solved by boundary condition equations. After all parameters obtained, we can get the electrical potential and electrical field intensity by solving the Poisson’s equation with Runge-Kutta method. We change the density of photoelectrons on the lunar surface to simulate the different angle of photons hitting the Moon. By numerical simulation and data analysis, we believe that on the night-side of the Moon, sheath C is formed and the angle of photons hitting the Moon has large impact on the electrical potential and electrical field intensity. On the day-side, both sheath A B and C could be formed. When the photoelectrons density at origin is small, sheath C will be formed; when n_(p,o)grows bigger, both sheath A and B could be formed. For the sheath which contains a smaller energy is more stable. Then we can compute the potential energy to decide which sheath would be formed. We also find the Mach number M has a great influence on the sheath A. Combining the range of n(p,o), we can give the critical curve between A B and C for different n(p,o) and M.
引文
1. S. A. Stern. Worlds Beyond: The Thrill of Planetary Exploration as told by Leading Experts. Cambridge University Press, 2003: 76-84
2. ESA SP-1150, Report: Mission to the Moon, 1992
3. T. Yamada, K. Takita. Japan’s Rocket Program Finds Success but Has a Way to Go. Mainichi Shimbun, February 28,2005
4. J. N. Goswami, M. Annadurai. Chandrayaan-1: India’s First Planetary Science Mission to the Moon. Current Science, 25 February 2009, Vol. 96, NO. 4: 486-491
5. H. X. Sun, S. W. Dai. Mission Objectives and payloads for the First Lunar Exploration if China. Acta Astronautica, 2005, 57: 561-565
6. F. F. Chen. Introduction to Plasma and Controlled Fusion, Vol. 1: plasma Physics. New York, 1983
7. D. A. Gurnett, A. Bhattacharjee. Introduction to Plasma Physics: With Space and Laboratory Applications. Cambridge University Press, 2005
8. P. M. Bellan. Fundamentals of Plasma Physics. Cambridge University Press, 2006
9. D. R. Nicholson. Introduction to Plasma Theory. New York, 1983: Chapter 1
10. T. J. Stubbs. Characterizing the Near Lunar Plasma Environment.
11.欧阳自远.月球科学概论.中国宇航出版社, 2005
12. T. J. Stubbs, R. R. Vondrak. Impact of Dust on Lunar Exploration. ESA SP-643, January 2007: 239-243
13.邹永廖,欧阳自远,徐琳.月球表面的环境特征.第四纪研究, 2002年11月,第二十二卷,第六期: 533-539
14. M. Nicole. Basics of the Solar Wind. Cambridge University Press, 2007
15. A. R. Serway. Physics for Scientists & Engineers (3rd ed.). Saunders, 1990:1150
16. W. F. Sears, M. W. Zemansky. University Physics (6th ed.). Addison-Wesley: 843-844
17. T. Nitter, O. Havenes. Levitation and Dynamics of Charged Dust in the Photoelectron Sheath above Surfaces in Space. Journal of Geophysical Research, April 1,1998, Vol. 103, NO. A4: 6605-6620
18. S. F. Singer, E. H. Walker, Photoelectric Screening of Bodies in Interplanetary Space. Icarus, 1962, Vol. 1: 7-12
19. J.-P. J. Lafon. On the Sheath Surrounding a Conductor Emitting Photoelectrons in an Isotropic Collisionless Plasma. Radio Sci., 1976, Vol. 11, 483-493
20. E. Walbridge. Lunar Photoelectron Layer. J. Geophys. Res., 1973, Vol. 78: 3668-3687
21. B. G. Goldstein. Observation of Electrons at the Lunar Surface. J. Geophys. Res., 1974, Vol. 79: 23-35
22. E. C. Jr. Whipple. Theory of the Spherically Symmetric Photoelectron Sheath: A Thick Sheath Approximation and Comparison with the ATS 6 Observation of a Potential Barrier, J. Geophys. Res. 1976, Vol. 81: 601-607
23. R. J. L. Grard, J. K. E. Tunaley. Photoelectron Sheath neat a Planar Probe in Interplanetary Space. J. Geophys. Res. 1971, Vol. 76: 2498-2505
24. R. L. Guernsey, J. H. M. Fu. Potential Distribution Surrounding a Photo-emitting Plate in a Dilute Plasma. J. Geophys. Res. 1970, Vol. 75:3193-3199
25. J. H. M. Fu. Surface Potential of a Photoemitting Plate. J. Geophys. Res. 1971, Vol. 76:2506-2509
26. K. Knott. Electrostatic Charging of the Lunar Surface and Possible Consequences. J. Geophys. Res.. 1973, Vol. 78: 3172-3175
27. D. L. Reasoner, W. J. Burke. Characteristics of the Lunar Photoelectron Layer in the Geomagnetic Tail. J. Geophys. Res.. 1972, Vol. 77: 6671-6687
28. J. W. Jr. Freeman. Energetic Ion Bursts on the Nightside of the Moon. J. Geophys. Res.. 1972, Vol. 77: 239-243
29. J. W. Freeman, M. Ibrahim. Lunar Electric Fields, Surface Potential and Associated Plasma Sheaths. The Moon. 1975, Vol. 14: 103-114
30. J. S. Halekas, G. T. Delory. Lunar Prospector Observation of the Electrostatic Potential of the Lunar Surface and Its Response to Incident Current. Geophys. Res.. 2008, Vol. 113: A09102
31. J. S. Halekas, G. T. Delory. Lunar Prospector Measurement of Secondary Electron Emisson from Lunar Regolith. Planetary and Space Science. 2009, 57: 78-82
32. J. S. Halekas, D. L. Mitchell. Evidence for Negative Charging of the Lunar Surface in Shadow. Geophys. Res.. 2002, Vol. 29, NO. 10: 1435-1438
33. J. S. Halekas, R. P. Lin. Large Negative Lunar Surface Potential in Sunlight and Show. Geophys. Res.. 2005, Vol. 32: L09102
34. J. Wang, X. M. He. Modeling Electrostatic Levitation of Dust Particle on Lunar Surface. IEEE Transactions on Plasma Science. 2008, Vol. 36, NO. 5: 2459-2466
35. T. Nitter, O. Havenes. Dynamics of Dust in a Plasma Sheath and Injection of Dust into the Plasma Sheath above Moon and Asteroidal Surface. Earth, Moon, and Planets. 1992, 56: 7-34
36. F. W. Crawford, A. B. Cannara. Structure of the Double Sheath in Hot Cathode. J. Appl. Phys. 1965, 36: 3135-3142
37. D. Leonard, Y. Edgar. Lithium-Fed Hollow Cathode Theory. 40th Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, 2004: AIAA 2004-3431
38. Y. R. Li, J. X. Ma. Measurement of Potential Distributions in Sheath and Presheath near a Mesh and Metal Plate. J. Phys.. 2008, 41: 225210
39. B. Feuerbacher, B. Fitton. Experimental Investigation of Photoemission from Satellite Surface Materials. J. Appl. Phys.. 1972, Vol. 43, NO. 4: 1563-1572
40. B. Feuerbacher, M. Anderegg. Photoemission from Lunar Surface Fines and the Lunar Photoelectron Sheath. The Third Lunar Science Conference. The M. I. T. press, 1972. Vol. 3: 2655-2663
41. N. R. Mukherjee. Solar-wind Interactions with the Moon: Nature and Composition of Nitrogen Compounds. Earth, Moon, and Planets. 1981, Vol. 25, NO. 4: 451-463
42. J. Geiss, P. Hirt. On Accelearation and Motion of Ions in Corona and Solar Wind. Solar Physics. 1970, 12: 458-483
43. R. S. Lindzen, S. S. Hong. Effects of Mean Winds and Horizontal Temperature Gradients on Solar and Lunar Semidiurnal Tides in the Atmosphere. Journal of the Atmosphere. 1974, Vol. 31: 1421-1446
44.谷云鹏,马腾才.粒子束对玻姆鞘层判据的影响.物理学报. 2003年5月,Vol. 52, NO. 5: 1906-1912
45.王正汹,刘金远.尘埃等离子体鞘层的玻姆判据.物理学报. 2004年3月,Vol. 53, NO. 3: 793-797
46. J. R. Reitz, J. F. Milford. Foundations of Electromagnetic Theory (4th ed.). Addison-Wesley, Reading, Mass., 1993: 141-148
2. ESA SP-1150, Report: Mission to the Moon, 1992
3. T. Yamada, K. Takita. Japan’s Rocket Program Finds Success but Has a Way to Go. Mainichi Shimbun, February 28,2005
4. J. N. Goswami, M. Annadurai. Chandrayaan-1: India’s First Planetary Science Mission to the Moon. Current Science, 25 February 2009, Vol. 96, NO. 4: 486-491
5. H. X. Sun, S. W. Dai. Mission Objectives and payloads for the First Lunar Exploration if China. Acta Astronautica, 2005, 57: 561-565
6. F. F. Chen. Introduction to Plasma and Controlled Fusion, Vol. 1: plasma Physics. New York, 1983
7. D. A. Gurnett, A. Bhattacharjee. Introduction to Plasma Physics: With Space and Laboratory Applications. Cambridge University Press, 2005
8. P. M. Bellan. Fundamentals of Plasma Physics. Cambridge University Press, 2006
9. D. R. Nicholson. Introduction to Plasma Theory. New York, 1983: Chapter 1
10. T. J. Stubbs. Characterizing the Near Lunar Plasma Environment.
11.欧阳自远.月球科学概论.中国宇航出版社, 2005
12. T. J. Stubbs, R. R. Vondrak. Impact of Dust on Lunar Exploration. ESA SP-643, January 2007: 239-243
13.邹永廖,欧阳自远,徐琳.月球表面的环境特征.第四纪研究, 2002年11月,第二十二卷,第六期: 533-539
14. M. Nicole. Basics of the Solar Wind. Cambridge University Press, 2007
15. A. R. Serway. Physics for Scientists & Engineers (3rd ed.). Saunders, 1990:1150
16. W. F. Sears, M. W. Zemansky. University Physics (6th ed.). Addison-Wesley: 843-844
17. T. Nitter, O. Havenes. Levitation and Dynamics of Charged Dust in the Photoelectron Sheath above Surfaces in Space. Journal of Geophysical Research, April 1,1998, Vol. 103, NO. A4: 6605-6620
18. S. F. Singer, E. H. Walker, Photoelectric Screening of Bodies in Interplanetary Space. Icarus, 1962, Vol. 1: 7-12
19. J.-P. J. Lafon. On the Sheath Surrounding a Conductor Emitting Photoelectrons in an Isotropic Collisionless Plasma. Radio Sci., 1976, Vol. 11, 483-493
20. E. Walbridge. Lunar Photoelectron Layer. J. Geophys. Res., 1973, Vol. 78: 3668-3687
21. B. G. Goldstein. Observation of Electrons at the Lunar Surface. J. Geophys. Res., 1974, Vol. 79: 23-35
22. E. C. Jr. Whipple. Theory of the Spherically Symmetric Photoelectron Sheath: A Thick Sheath Approximation and Comparison with the ATS 6 Observation of a Potential Barrier, J. Geophys. Res. 1976, Vol. 81: 601-607
23. R. J. L. Grard, J. K. E. Tunaley. Photoelectron Sheath neat a Planar Probe in Interplanetary Space. J. Geophys. Res. 1971, Vol. 76: 2498-2505
24. R. L. Guernsey, J. H. M. Fu. Potential Distribution Surrounding a Photo-emitting Plate in a Dilute Plasma. J. Geophys. Res. 1970, Vol. 75:3193-3199
25. J. H. M. Fu. Surface Potential of a Photoemitting Plate. J. Geophys. Res. 1971, Vol. 76:2506-2509
26. K. Knott. Electrostatic Charging of the Lunar Surface and Possible Consequences. J. Geophys. Res.. 1973, Vol. 78: 3172-3175
27. D. L. Reasoner, W. J. Burke. Characteristics of the Lunar Photoelectron Layer in the Geomagnetic Tail. J. Geophys. Res.. 1972, Vol. 77: 6671-6687
28. J. W. Jr. Freeman. Energetic Ion Bursts on the Nightside of the Moon. J. Geophys. Res.. 1972, Vol. 77: 239-243
29. J. W. Freeman, M. Ibrahim. Lunar Electric Fields, Surface Potential and Associated Plasma Sheaths. The Moon. 1975, Vol. 14: 103-114
30. J. S. Halekas, G. T. Delory. Lunar Prospector Observation of the Electrostatic Potential of the Lunar Surface and Its Response to Incident Current. Geophys. Res.. 2008, Vol. 113: A09102
31. J. S. Halekas, G. T. Delory. Lunar Prospector Measurement of Secondary Electron Emisson from Lunar Regolith. Planetary and Space Science. 2009, 57: 78-82
32. J. S. Halekas, D. L. Mitchell. Evidence for Negative Charging of the Lunar Surface in Shadow. Geophys. Res.. 2002, Vol. 29, NO. 10: 1435-1438
33. J. S. Halekas, R. P. Lin. Large Negative Lunar Surface Potential in Sunlight and Show. Geophys. Res.. 2005, Vol. 32: L09102
34. J. Wang, X. M. He. Modeling Electrostatic Levitation of Dust Particle on Lunar Surface. IEEE Transactions on Plasma Science. 2008, Vol. 36, NO. 5: 2459-2466
35. T. Nitter, O. Havenes. Dynamics of Dust in a Plasma Sheath and Injection of Dust into the Plasma Sheath above Moon and Asteroidal Surface. Earth, Moon, and Planets. 1992, 56: 7-34
36. F. W. Crawford, A. B. Cannara. Structure of the Double Sheath in Hot Cathode. J. Appl. Phys. 1965, 36: 3135-3142
37. D. Leonard, Y. Edgar. Lithium-Fed Hollow Cathode Theory. 40th Joint Propulsion Conference and Exhibit, Fort Lauderdale, Florida, 2004: AIAA 2004-3431
38. Y. R. Li, J. X. Ma. Measurement of Potential Distributions in Sheath and Presheath near a Mesh and Metal Plate. J. Phys.. 2008, 41: 225210
39. B. Feuerbacher, B. Fitton. Experimental Investigation of Photoemission from Satellite Surface Materials. J. Appl. Phys.. 1972, Vol. 43, NO. 4: 1563-1572
40. B. Feuerbacher, M. Anderegg. Photoemission from Lunar Surface Fines and the Lunar Photoelectron Sheath. The Third Lunar Science Conference. The M. I. T. press, 1972. Vol. 3: 2655-2663
41. N. R. Mukherjee. Solar-wind Interactions with the Moon: Nature and Composition of Nitrogen Compounds. Earth, Moon, and Planets. 1981, Vol. 25, NO. 4: 451-463
42. J. Geiss, P. Hirt. On Accelearation and Motion of Ions in Corona and Solar Wind. Solar Physics. 1970, 12: 458-483
43. R. S. Lindzen, S. S. Hong. Effects of Mean Winds and Horizontal Temperature Gradients on Solar and Lunar Semidiurnal Tides in the Atmosphere. Journal of the Atmosphere. 1974, Vol. 31: 1421-1446
44.谷云鹏,马腾才.粒子束对玻姆鞘层判据的影响.物理学报. 2003年5月,Vol. 52, NO. 5: 1906-1912
45.王正汹,刘金远.尘埃等离子体鞘层的玻姆判据.物理学报. 2004年3月,Vol. 53, NO. 3: 793-797
46. J. R. Reitz, J. F. Milford. Foundations of Electromagnetic Theory (4th ed.). Addison-Wesley, Reading, Mass., 1993: 141-148