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Radiation belt energetic electrons can interact with very low frequency (VLF) electromagnetic wave due to wave-particle resonance; then the particles are imposed to enter into the loss cone and sink to dense atmosphere resulting from changing of its pitch angle. To investigate the diffusion mechanism of interaction of VLF electromagnetic wave with radiation belt energetic electrons, according to quasi-linear diffusion theory, in this paper we use a physical model to calculate diffusion coefficients of Coulomb scatting and wave-particle resonance interaction. Bounce-averaged pitch angle diffusion coefficients of energetic electrons due to the interaction of wave-particle resonance with two groups of VLF electromagnetic waves are obtained. The influence of interaction caused by VLF electromagnetic wave and Coulomb scatting on diffusion of radiation belt energetic electrons for different L shells and various energies are analyzed. Take the case for example, where L equals 2.2 and electron energy E equals 0.5 MeV, the diffusion equation of energetic electrons are solved by using the finite difference method. The time evolutions of precipitation of directional particle flux and omnidirectional particle flux are analyzed. The results show that the resonance interaction caused by VLF electromagnetic wave plays a dominant role when E>0.5 MeV and L>1.6; the higher the L shell or electron energy value, the more significant the high order resonance interaction caused by the oblique propagation VLF electromagnetic wave will be; approximately, the omnidirectional particle flux of radiation belt energetic electrons decreases exponentially with time.
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Keywords:
- radiation belt /
- wave-particle resonance diffusion /
- diffusion coefficient /
- very low frequency electromagnetic wave
[1] Horne R B, Thorne R M, Shprits Y Y, Meredith N P, Glauert S A, Smith A J, Kanekal S G, Baker D N, Engebretson M J, Posch J L, Spasojevic M, Inan U S, Pickett J S, Decreau P M E 2005 Nature 437 227
[2] Chang S S, Ni B B, Zhao Z Y, Gu X D, Zhou C 2014 Chin. Phys. B 23 089401
[3] Dupont D G 2004 Scientific American 290 100
[4] Graf K L, Inan U S, Piddyachiy D 2009 J. Geophys. Res. 38 114
[5] Kennel C F, Petschek H E 1966 J. Geophys. Res. 7 1
[6] Summers D 2005 J. Geophys. Res. A 110 08213
[7] Shprits Y Y, Thorne R M, Horne R B, Summers D 2006 J. Geophys. Res. A 111 10225
[8] Gu X D, Zhao Z Y, Ni B B, Wang X, Deng F 2008 Acta Phys. Sin. 57 6673 (in Chinese) [顾旭东, 赵正予, 倪彬彬, 王翔, 邓峰 2008 57 6673]
[9] Wang P, Wang H Y, Ma Y Q, Li X Q, Lu H, Meng X C, Zhang J L, Wang H, Shi F, Xu Y B, Yu X X, Zhao X Y, Wu F 2011 Acta Phys. Sin. 60 039401 (in Chinese) [王平, 王焕玉, 马宇蒨, 李新乔, 卢红, 孟祥承, 张吉龙, 王辉, 石峰, 徐岩冰, 于晓霞, 赵小芸, 吴峰 2011 60 039401]
[10] Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401 (in Chinese) [张振霞, 王辰宇, 李强, 吴书贵 2014 63 079401]
[11] Walt M, MacDonald W 1964 Rev. Geophys. 2 543
[12] Schulz M, Lanzerotti L J 1974 Particle Diffusion in the Radiation Belts (New York: Springer-Verlag Press) pp60
[13] Kennel C F, Engelmann F 1966 Phys. Fluids 9 2377
[14] Lyons L R 1974 J. Plasma Phys. 12 417
[15] Walt M 1994 Introduction to Geomagnetically Trapped Radiation (London: Cambridge University Press) pp64, 115
[16] Glauert S A Horne R B 2005 J. Geophys. Res. A 110 04206
[17] Chen F F (Translated by Lin G H) 1980 Introduction to Plasma Physics (Beijing: People's Education Press) p77 (in Chinese) [Chen F F 著 (林光海 译) 1980等离子体物理学导论(北京: 人民教育出版社)第77页]
[18] Lyons L R, Thorne R M, Kennel C F 1971 J. Plasma Phys. 6 589
[19] Lyons L R, Thorne R M, Kennel C F 1972 J. Geophys. Res. 77 3455
[20] Niu S L, Luo X D, Wang J G, Qiao D J 2011 Chin. J. Comput. Phys. 28 645 (in Chinese) [牛胜利, 罗旭东, 王建国, 乔登江 2011 计算物理 28 645]
[21] Albert J M, Young S L 2005 Geophys. Res. Ett. 32L 14110
[22] Abel B, Thorne R M 1998 J. Geophys. Res. 103 2385
[23] Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397
[24] Shprits Y, Subbotin D, Ni B B, Horne R, Baker D, Cruce P 2011 Pace Weather 9 S08007
[25] Lu J F, Guan Z 2004 Numerical Methods for Partial Differential Equations (2nd Ed.) (Beijing: Tsinghua University Press) pp83, 109 (in Chinese) [陆金甫, 关冶2004偏微分方程数值解法(第2版) (北京: 清华大学出版社)第83, 109页]
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[1] Horne R B, Thorne R M, Shprits Y Y, Meredith N P, Glauert S A, Smith A J, Kanekal S G, Baker D N, Engebretson M J, Posch J L, Spasojevic M, Inan U S, Pickett J S, Decreau P M E 2005 Nature 437 227
[2] Chang S S, Ni B B, Zhao Z Y, Gu X D, Zhou C 2014 Chin. Phys. B 23 089401
[3] Dupont D G 2004 Scientific American 290 100
[4] Graf K L, Inan U S, Piddyachiy D 2009 J. Geophys. Res. 38 114
[5] Kennel C F, Petschek H E 1966 J. Geophys. Res. 7 1
[6] Summers D 2005 J. Geophys. Res. A 110 08213
[7] Shprits Y Y, Thorne R M, Horne R B, Summers D 2006 J. Geophys. Res. A 111 10225
[8] Gu X D, Zhao Z Y, Ni B B, Wang X, Deng F 2008 Acta Phys. Sin. 57 6673 (in Chinese) [顾旭东, 赵正予, 倪彬彬, 王翔, 邓峰 2008 57 6673]
[9] Wang P, Wang H Y, Ma Y Q, Li X Q, Lu H, Meng X C, Zhang J L, Wang H, Shi F, Xu Y B, Yu X X, Zhao X Y, Wu F 2011 Acta Phys. Sin. 60 039401 (in Chinese) [王平, 王焕玉, 马宇蒨, 李新乔, 卢红, 孟祥承, 张吉龙, 王辉, 石峰, 徐岩冰, 于晓霞, 赵小芸, 吴峰 2011 60 039401]
[10] Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401 (in Chinese) [张振霞, 王辰宇, 李强, 吴书贵 2014 63 079401]
[11] Walt M, MacDonald W 1964 Rev. Geophys. 2 543
[12] Schulz M, Lanzerotti L J 1974 Particle Diffusion in the Radiation Belts (New York: Springer-Verlag Press) pp60
[13] Kennel C F, Engelmann F 1966 Phys. Fluids 9 2377
[14] Lyons L R 1974 J. Plasma Phys. 12 417
[15] Walt M 1994 Introduction to Geomagnetically Trapped Radiation (London: Cambridge University Press) pp64, 115
[16] Glauert S A Horne R B 2005 J. Geophys. Res. A 110 04206
[17] Chen F F (Translated by Lin G H) 1980 Introduction to Plasma Physics (Beijing: People's Education Press) p77 (in Chinese) [Chen F F 著 (林光海 译) 1980等离子体物理学导论(北京: 人民教育出版社)第77页]
[18] Lyons L R, Thorne R M, Kennel C F 1971 J. Plasma Phys. 6 589
[19] Lyons L R, Thorne R M, Kennel C F 1972 J. Geophys. Res. 77 3455
[20] Niu S L, Luo X D, Wang J G, Qiao D J 2011 Chin. J. Comput. Phys. 28 645 (in Chinese) [牛胜利, 罗旭东, 王建国, 乔登江 2011 计算物理 28 645]
[21] Albert J M, Young S L 2005 Geophys. Res. Ett. 32L 14110
[22] Abel B, Thorne R M 1998 J. Geophys. Res. 103 2385
[23] Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397
[24] Shprits Y, Subbotin D, Ni B B, Horne R, Baker D, Cruce P 2011 Pace Weather 9 S08007
[25] Lu J F, Guan Z 2004 Numerical Methods for Partial Differential Equations (2nd Ed.) (Beijing: Tsinghua University Press) pp83, 109 (in Chinese) [陆金甫, 关冶2004偏微分方程数值解法(第2版) (北京: 清华大学出版社)第83, 109页]
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