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Plasma, as a special state of matter, has an effect on its inner conductors. Practically in the plasma environment, the effect may induce surface to charge and discharge, and may degrade the performance of spacecraft. Therefore, this effect needs to be further studied in the electromagnetic compatibility. The energy in a conductors' system is a key factor of the effect, which can also be used to depict the system consisting of relevant conductors and plasma environment. In order to investigate the essence of the system, the variational method is adopted. So with considering the electromagnetic compatibility and protection of this system, the energy of related conductors should be estimated by the theoretical method in the plasma environment. In the stochastic movement, electrons are faster than the irons. Therefore, the negative energy is cumulated. Considering the definition of capacitance, the system energy can be represented by the conductor capacitance and charging potential. Meanwhile, from the plasma kinetic theory, the potential can be obtained in the steady state. Thus, the relations among electromagnetic parameters of conductors, environmental features of plasma, and systematic energy are established, from which the corresponding Collin principle is also investigated. The principle indicates the system essence in the complex electromagnetic environment. In order to illustrate the utility of the variational principle, a simple cubic model is theoretically analyzed directly. From the typical instance, the relation between the geometric dimension and electric energy is illustrated, which is in consistence with the results in the early literature. The relation between secondary electrons and systematic energy is also analyzed. Starting from these theoretical investigations, in order to estimate the complicated structures, the analysis needs to be generalized further. With the assistance of discrete technology, the numerical method is established for analyzing the system energy of the complex conductive system in plasma environment. The generalized method is based on the equation with integral operator, in the calculation of which the method of moment is practically employed. As an application, the estimated energy of cube in plasma environment is compared with the theoretical estimation and the numerical estimation, which are in good agreement with each other. And then a composited structure is numerically analyzed. Obviously, the vairational analysis is beneficial to investigating the physical and principal regulation for conductors in the plasma environment, and the generalized method has wide potential applications in controlling the energy of complex charged conductors, electromagnetic protection, compatibility engineering in plasma environment, etc.
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Keywords:
- plasma /
- charged conductor /
- electrostatic energy /
- variational
[1] Higgins A B, Starling R L C, Gtz D, Mereghetti S, Wiersema K, Maccarone T, Osborne J P, Tanvir N R, O'Brien P T, Bird A J, Rowlinson A, Gehrels N 2017 MNRAS 470 314
[2] Chen F F 2006 Introduction to Plasma Physics and Controlled Fusion (New York: Springer) pp120-203
[3] Hu T P, Luo Q 2007 Chin. Phys. B 16 179
[4] Liu W Z, Wang H, Zhang D J, Zhang J 2014 Plasma Sci. Technol. 16 344
[5] Jiao J, Tong J S, Ma C G, Guo J Y, Bo Y, Zhao Q 2018 Acta Phys. Sin. 67 015202 (in Chinese)[焦蛟, 童继生, 马春光, 郭佶玙, 薄勇, 赵青 2018 物理学报 67 015202]
[6] Ma H J, Wang G L, Luo J, Liu L P, Pan D X, Zhang J, Xing Y L, Tang F 2018 Acta Phys. Sin. 67 025201 (in Chinese)[马昊军, 王国林, 罗杰, 刘丽萍, 潘德贤, 张军, 邢英丽, 唐飞 2018 物理学报 67 025201]
[7] Li Q, Chen Q, Zhong J 2018 Acta Phys. Sin. 67 027303 (in Chinese)[李群, 陈谦, 种景 2018 物理学报 67 027303]
[8] Cao J B, Wang X Y, Zhou G C, Chen T 2000 Chin. J. Geophys. 43 459 (in Chinese)[曹晋滨, 汪学毅, 周国成, 陈涛 2000 地球物理学报 43 459]
[9] Cai M H, Han J W, Li X Y, Li H W, Zhang Z L 2009 Acta Phys. Sin. 58 6659 (in Chinese)[蔡明辉, 韩建伟, 李小银, 李宏伟, 张振力 2009 物理学报 58 6659]
[10] Huang J G, Chen D 2004 Acta Phys. Sin. 53 961 (in Chinese)[黄建国, 陈东 2004 物理学报 53 961]
[11] Huang J G, Chen D 2004 Acta Phys. Sin. 53 1611 (in Chinese)[黄建国, 陈东 2004 物理学报 53 1611]
[12] Huang J G, Han J W 2010 Acta Phys. Sin. 59 2907 (in Chinese)[黄建国, 韩建伟 2010 物理学报 59 2907]
[13] Huang B C, Tong J Y 2010 Space Environment Engineering (Beijing: Chinese Science and Technology Press) p451 (in Chinese)[黄本诚, 童靖宇 2010 空间环境工程学(北京: 中国科学技术出版社)第451页]
[14] Cao H F, Liu S H, Sun Y W, Yuan Q Y 2013 Acta Phys. Sin. 62 149401 (in Chinese)[曹鹤飞, 刘尚合, 孙永卫, 原青云 2013 物理学报 62 149401]
[15] Cao H F, Liu S H, Sun Y W, Yuan Q Y 2013 Acta Phys. Sin. 62 149402 (in Chinese)[曹鹤飞, 刘尚合, 孙永卫, 原青云 2013 物理学报 62 149402]
[16] Witze A 2016 Nature 539 15
[17] Goldstein H 1950 Classical Mechanics (Cambridge, MA: Addison-Wesley) pp68-96
[18] Courant R, Hilbert D (translated by Qian M, Guo D R) 1958 Methods of Mathematical Physics vol. I (Beijing: Science Press) p129-210 (in Chinese)[柯朗 R, 希尔伯特 D 著 (钱敏, 郭敦仁 译) 1958 数学物理方法 卷I (北京: 科学出版社)第129210页]
[19] Chien W Z 2000 Applications of Green Functions and Variational Methods in Electromagnetic Field and Wave Computation (Shanghai: Shanghai University Press) pp1-85 (in Chinese)[钱伟长 2000 格林函数和变分法在电磁场和电磁波计算中的应用(上海: 上海大学出版社)第185页]
[20] Mei F X 1988 Special Problems of Analytical Mechanics (Beijing: Beijing Institute of Technology Press) pp68-158 (in Chinese)[梅凤翔 1988 分析力学专题(北京: 北京工业学院出版社)第68158页]
[21] Ding G T 2011 Acta Phys. Sin. 60 044503 (in Chinese)[丁光涛 2011 物理学报 60 044503]
[22] Stratton J A 1941 Electromagnetic Theory (New York: McGraw-Hill) pp104-136
[23] Jackson J D 1975 Classical Electrodynamics (New York: Wiley) pp236-240
[24] Collin R E 1960 Field Theory of Guided Waves (New York: McGraw-Hill) pp338-348
[25] Liang C H, Su T, Wan J X 2004 Acta Phys. Sin. 53 0001 (in Chinese)[梁昌洪, 苏涛, 万继响 2004 物理学报 53 0001]
[26] Murali S 2000 J. Electron Spectrosc. Relat. Phenom. 106 93
[27] Kazami Y, Junichiro K, Norio O, Michikazu K, Naoki H, Ryuji S, Kenichirou S, Takeshi T 2009 Appl. Surf. Sci. 256 958
[28] Harrington R F 1993 Field Computation by Moment Methods (New York: Wiley-IEEE Press) pp1-50
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[1] Higgins A B, Starling R L C, Gtz D, Mereghetti S, Wiersema K, Maccarone T, Osborne J P, Tanvir N R, O'Brien P T, Bird A J, Rowlinson A, Gehrels N 2017 MNRAS 470 314
[2] Chen F F 2006 Introduction to Plasma Physics and Controlled Fusion (New York: Springer) pp120-203
[3] Hu T P, Luo Q 2007 Chin. Phys. B 16 179
[4] Liu W Z, Wang H, Zhang D J, Zhang J 2014 Plasma Sci. Technol. 16 344
[5] Jiao J, Tong J S, Ma C G, Guo J Y, Bo Y, Zhao Q 2018 Acta Phys. Sin. 67 015202 (in Chinese)[焦蛟, 童继生, 马春光, 郭佶玙, 薄勇, 赵青 2018 物理学报 67 015202]
[6] Ma H J, Wang G L, Luo J, Liu L P, Pan D X, Zhang J, Xing Y L, Tang F 2018 Acta Phys. Sin. 67 025201 (in Chinese)[马昊军, 王国林, 罗杰, 刘丽萍, 潘德贤, 张军, 邢英丽, 唐飞 2018 物理学报 67 025201]
[7] Li Q, Chen Q, Zhong J 2018 Acta Phys. Sin. 67 027303 (in Chinese)[李群, 陈谦, 种景 2018 物理学报 67 027303]
[8] Cao J B, Wang X Y, Zhou G C, Chen T 2000 Chin. J. Geophys. 43 459 (in Chinese)[曹晋滨, 汪学毅, 周国成, 陈涛 2000 地球物理学报 43 459]
[9] Cai M H, Han J W, Li X Y, Li H W, Zhang Z L 2009 Acta Phys. Sin. 58 6659 (in Chinese)[蔡明辉, 韩建伟, 李小银, 李宏伟, 张振力 2009 物理学报 58 6659]
[10] Huang J G, Chen D 2004 Acta Phys. Sin. 53 961 (in Chinese)[黄建国, 陈东 2004 物理学报 53 961]
[11] Huang J G, Chen D 2004 Acta Phys. Sin. 53 1611 (in Chinese)[黄建国, 陈东 2004 物理学报 53 1611]
[12] Huang J G, Han J W 2010 Acta Phys. Sin. 59 2907 (in Chinese)[黄建国, 韩建伟 2010 物理学报 59 2907]
[13] Huang B C, Tong J Y 2010 Space Environment Engineering (Beijing: Chinese Science and Technology Press) p451 (in Chinese)[黄本诚, 童靖宇 2010 空间环境工程学(北京: 中国科学技术出版社)第451页]
[14] Cao H F, Liu S H, Sun Y W, Yuan Q Y 2013 Acta Phys. Sin. 62 149401 (in Chinese)[曹鹤飞, 刘尚合, 孙永卫, 原青云 2013 物理学报 62 149401]
[15] Cao H F, Liu S H, Sun Y W, Yuan Q Y 2013 Acta Phys. Sin. 62 149402 (in Chinese)[曹鹤飞, 刘尚合, 孙永卫, 原青云 2013 物理学报 62 149402]
[16] Witze A 2016 Nature 539 15
[17] Goldstein H 1950 Classical Mechanics (Cambridge, MA: Addison-Wesley) pp68-96
[18] Courant R, Hilbert D (translated by Qian M, Guo D R) 1958 Methods of Mathematical Physics vol. I (Beijing: Science Press) p129-210 (in Chinese)[柯朗 R, 希尔伯特 D 著 (钱敏, 郭敦仁 译) 1958 数学物理方法 卷I (北京: 科学出版社)第129210页]
[19] Chien W Z 2000 Applications of Green Functions and Variational Methods in Electromagnetic Field and Wave Computation (Shanghai: Shanghai University Press) pp1-85 (in Chinese)[钱伟长 2000 格林函数和变分法在电磁场和电磁波计算中的应用(上海: 上海大学出版社)第185页]
[20] Mei F X 1988 Special Problems of Analytical Mechanics (Beijing: Beijing Institute of Technology Press) pp68-158 (in Chinese)[梅凤翔 1988 分析力学专题(北京: 北京工业学院出版社)第68158页]
[21] Ding G T 2011 Acta Phys. Sin. 60 044503 (in Chinese)[丁光涛 2011 物理学报 60 044503]
[22] Stratton J A 1941 Electromagnetic Theory (New York: McGraw-Hill) pp104-136
[23] Jackson J D 1975 Classical Electrodynamics (New York: Wiley) pp236-240
[24] Collin R E 1960 Field Theory of Guided Waves (New York: McGraw-Hill) pp338-348
[25] Liang C H, Su T, Wan J X 2004 Acta Phys. Sin. 53 0001 (in Chinese)[梁昌洪, 苏涛, 万继响 2004 物理学报 53 0001]
[26] Murali S 2000 J. Electron Spectrosc. Relat. Phenom. 106 93
[27] Kazami Y, Junichiro K, Norio O, Michikazu K, Naoki H, Ryuji S, Kenichirou S, Takeshi T 2009 Appl. Surf. Sci. 256 958
[28] Harrington R F 1993 Field Computation by Moment Methods (New York: Wiley-IEEE Press) pp1-50
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