甚低频台站信号对地球内辐射带和槽区能量电子的散射效应分析

刘阳希子; 项正; 郭建广; 顾旭东; 付松; 周若贤; 花漫; 朱琪; 易娟; 倪彬彬

doi:10.7498/aps.70.20202029

摘要

人工地面甚低频台站发射的10—30 kHz信号主要在地球—低电离层波导传播, 部分能量会泄露进入内磁层, 进而会影响近地空间中高能电子的动态变化过程. 本文详细研究了NWC, NAA和DHO38三个人工甚低频台站信号对内辐射带和槽区高能电子的散射作用. 基于准线性理论, 分别计算了三个甚低频台站信号单独和共同作用时对高能电子的弹跳平均投掷角扩散系数, 并进一步利用Fokker-Planck扩散方程模拟内辐射带及槽区的高能电子在200 d内的动态演化过程. 结果表明, 在低L-shell (L ≤ 1.8), NWC台站信号对电子的损失占主导作用, 可以使能量在100 keV附近、投掷角小于60°的电子出现明显损失; 在较高的L-shell (2.2 ≤ L ≤ 2.7), 主要是NAA和DHO38台站信号占主导作用, 可以使能量小于20 keV、投掷角小于70°的电子通量显著下降; 三个甚低频台站信号对高投掷角(> 80°)的电子均无显著影响.

关键词:

Abstract

Whistler mode very low frequency (VLF) waves from man-made ground-based transmitters in a frequency range of 10–30 kHz are mainly used for submarine communication, and they propagate primarily in the Earth-lower ionosphere waveguide and part of their energy can leak into the inner magnetosphere, leading the energetic electrons in inner radiation belt and slot region to precipitate into atmosphere and then affect the energetic electron dynamics in the near-Earth space. The scattering effects of artificial VLF signals from NWC, NAA and DHO38 transmitters on energetic electrons in Earth’s inner belt and slot region are investigated in detail in this work. Based on the quasi-linear theory and the Full Diffusion Code, we calculate the bounce-average pitch angle diffusion coefficients induced by NWC, NAA and DHO38 VLF transmitter signals, for which the resonance harmonics |N| ≤ 10 are considered, respectively. We further implement the one-dimensional Fokker-Planck diffusion simulations by using the available pitch angle diffusion rates to model the dynamic evolutions of energetic electrons caused by the scattering of the VLF transmitter signals in the inner belt and slot region in 200 d. The simulation results indicate that the NWC VLF transmitter signals are dominant in scattering ~100 keV electrons with pitch angles less than 60° at L ≤ 1.8, and the mainly scattered electron energy values increase with L-shell decreasing , from L = 1.8 to L = 1.5, the mainly scattered electron energy increases from 90–120 keV to 550–650 keV. The NAA and DHO38 VLF transmitter signals are important in scattering < 20 keV electrons with pitch angles less than 70° at higher L-shells (2.2 ≤ L ≤ 2.7), from L = 2.2 to L = 2.7, the mainly scattered electron energy decreases from 10–20 keV to several keV. The VLF transmitter signals are found to have a slight influence on the loss of energetic electrons with pitch angles larger than 80°.

Keywords:

Earth’s radiation belts /
artificial very low frequency transmitter signals /
wave-particle interactions /
electron pitch angle diffusion coefficient

作者及机构信息

1.
武汉大学电子信息学院, 武汉　430072

2.
中国气象局国家空间天气监测预警中心, 北京　100081

3.
中国科学院比较行星学卓越创新中心, 合肥　230026

通信作者: 项正, xiangzheng@whu.edu.cn ; 郭建广, guojg@cma.gov.cn ;

基金项目: 国家自然科学基金(批准号: 42025404, 41704162, 41974186, 41674163, 41904144, 41904143)、中国科学院先导B计划(批准号: XDB41000000)、国家航天局民用航天预研项目(批准号: D020303, D020308, D020104)和中国博士后科学基金(批准号: 2019M662700)资助的课题

Authors and contacts

1.
Department of Space Physics, School of Electronic Information, Wuhan University, Wuhan 430072, China

2.
Key Laboratory of Space Weather, National Center for Space Weather, China Meteorological Administration, Beijing 100081, China

3.
Center for Excellence in Comparative Planetology, Chinese Academy of Sciences, Hefei 230026, China

Corresponding author: Xiang Zheng, xiangzheng@whu.edu.cn ; Guo Jian-Guang, guojg@cma.gov.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 42025404, 41704162, 41974186, 41674163, 41904144, 41904143), the B-type Strategic Priority Program of the Chinese Academy of Sciences (Grant No. XDB41000000), the Pre-research Projects on Civil Aerospace Technologies funded by the China National Space Administration (Grant Nos. D020303, D020308, D020104), and the China Postdoctoral Science Foundation (Grant No. 2019M662700)

文章全文

参考文献

[1]	Xiang Z, Tu W, Li X, Ni B, Morley S K, Baker D N 2017 J. Geophys. Res. Space Phys. 122 9858 Google Scholar
[2]	Xiang Z, Tu W, Ni B, Henderson M G, Cao X 2018 Geophys. Res. Lett. 45 8035 Google Scholar
[3]	Ma X, Xiang Z, Ni B, Fu S, Cao X, Hua M, Guo D, Guo Y, Gu X, Liu Z, Zhu Q 2020 Earth Planet. Phys. 4 598 Google Scholar
[4]	Rosen A, Sanders N L 1971 J. Geophys. Res. 76 110 Google Scholar
[5]	Selesnick R S 2015 J. Geophys. Res. Space Phys. 120 2912 Google Scholar
[6]	Xiang Z, Li X, Selesnick R, Temerin M A, Ni B, Zhao H, Zhang K, Khoo L Y 2019 Geophys. Res. Lett. 46 1919 Google Scholar
[7]	Xiang Z, Li X, Temerin M A, Ni B, Zhao H, Zhang K, Khoo L Y 2020 J. Geophys. Res. Space Phys. 125 e2019JA027678
[8]	Xiang Z, Li X, Ni B, Temerin M A, Zhao H, Zhang K, Khoo L Y 2020 J. Geophys. Res. Space Phys. 125 e2020JA028042
[9]	Zhang K, Li X, Zhao H, Schiller Q, Khoo L Y, Xiang Z, Selesnick R, Temerin M A, Sauvaud J A 2019 Geophys. Res. Lett. 46 544 Google Scholar
[10]	Ni B, Hua M, Zhou R, Yi J, Fu S 2017 Geophys. Res. Lett. 44 3465 Google Scholar
[11]	Hua M, Ni B, Fu S, Gu X, Xiang Z, Cao X, Zhang W, He Y, Huang H, Lou Y, Zhang Y 2018 Geophys. Res. Lett. 45 10057 Google Scholar
[12]	Rodger C J, Clilverd M A, McCormick R J 2003 J. Geophys. Res. 108 1462 Google Scholar
[13]	Clilverd M A, Rodger C J, Nunn D 2004 J. Geophys. Res. A 109 12208 Google Scholar
[14]	Green A, Li W, Ma Q, Shen X C, Bortnik J, Hospodarsky G B 2020 Geophys. Res. Lett. 47 e2020GL089584
[15]	Ma Q, Li W, Thorne R M, Bortnik J, Kletzing C A, Kurth W S, Hospodarsky G B 2016 J. Geophys. Res. Space Phys. 121 274 Google Scholar
[16]	顾旭东, 何颖, 倪彬彬, 付松, 花漫, 项正 2020 地球物理学报 63 2121 Google Scholar Gu X D, He Y, Ni B B, Fu S, Hua M, Xiang Z 2020 Chin. J. Geophys. 63 2121 Google Scholar
[17]	Ni B, Yan L, Fu S, Gu X, Cao X, Xiang Z, Zhang Y 2020 Geophys. Res. Lett. 47 e2019GL086487
[18]	Ma Q, Mourenas D, Li W, Artemyev A, Thorne R M 2017 Geophys. Res. Lett. 44 6483 Google Scholar
[19]	Ross J P J, Meredith N P, Glauert S A, Horne R B, Clilverd M A 2019 J. Geophys. Res. Space Phys. 124 5260 Google Scholar
[20]	Hua M, Li W, Ni B, Ma Q, Green A, Shen X, Claudepierre S G, Bortnik J, Gu X, Fu S, Xiang Z, Reeves G D 2020 Nat. Commun. 11 4847 Google Scholar
[21]	Chen Y P, Yang G B, Ni B B, Zhao Z Y, Gu X D, Zhou C, Wang F 2016 Adv. Space Res. 57 1871 Google Scholar
[22]	Chen Y, Ni B, Gu X, Zhao Z, Yang G, Zhou C, Zhang Y 2017 Sci. Chin. Technol. Sci. 60 166 Google Scholar
[23]	易娟, 顾旭东, 李志鹏, 林仁桐, 蔡毅徽, 陈隆, 倪彬彬, 乐新安 2019 地球物理学报 62 3223 Google Scholar Yi J, Gu X D, Li Z P, Lin R T, Cai Y H, Chen L, Ni B B, Yue X A 2019 Chin. J. Geophys. 62 3223 Google Scholar
[24]	Yi J, Gu X, Cheng W, Tang X, Chen L, Ni B, Zhou R, Zhao Z, Wang Q, Zhou L 2020 Earth Planet. Phys. 4 238 Google Scholar
[25]	Zhou R, Gu X, Yang K, Li G, Ni B, Yi J, Chen L, Zhao F, Zhao Z, Wang Q, Zhou L 2020 Earth Planet. Phys. 4 120 Google Scholar
[26]	Vampola A L, Kuck G A 1978 J. Geophys. Res. 83 2543 Google Scholar
[27]	Koons H C, Edgar B C, Vampola A L 1981 J. Geophys. Res. 86 640 Google Scholar
[28]	Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397 Google Scholar
[29]	Gamble R J, Rodger C J, Clilverd M A, Sauvaud J A, Thomson N R, Stewart S L, McCormick R J, Parrot M, Berthelier J J 2008 J. Geophys. Res. A 113 10211 Google Scholar
[30]	Graf K L, Inan U S, Piddyachiy D, Kulkarni P, Parrot M, Sauvaud J A 2009 J. Geophys. Res. A 114 07205 Google Scholar
[31]	Selesnick R S, Albert J M, Starks M J 2013 J. Geophys. Res. Space Phys. 118 628 Google Scholar
[32]	Agapitov O V, Artemyev A V, Mourenas D, Kasahara Y, Krasnoselskikh V 2014 J. Geophys. Res. Space Phys. 119 2876 Google Scholar
[33]	Claudepierre S G, Ma Q, Bortnik J, O'Brien T P, Fennell J F, Blake J B 2020 Geophys. Res. Lett. 47 e2019GL086056 Google Scholar
[34]	Imhof W L, Reagan J B, Voss H D, Gaines E E, Datlowe D W, Mobilia J, Helliwell R A, Inan U S, Katsufrakis J, Joiner R G 1983 Geophys. Res. Lett. 10 361 Google Scholar
[35]	Inan U S, Chang H C, Helliwell R A, Imhof W L, Reagan J B, Walt M 1985 J. Geophys. Res. 90 359 Google Scholar
[36]	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 物理学报 60 039401 Google Scholar 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 Google Scholar
[37]	Sauvaud J A, Maggiolo R, Jacquey C, Parrot M, Berthelier J J, Gamble R J, Rodger C J 2008 Geophys. Res. Lett. 35 L09101 Google Scholar
[38]	Clilverd M A, Rodger C J, Gamble R, Meredith N P, Parrot M, Berthelier J J, Thomson N R 2008 J. Geophys. Res. A 113 04211 Google Scholar
[39]	Kulkarni P, Inan U S, Bell T F, Bortnik J 2008 J. Geophys. Res. A 113 07214 Google Scholar
[40]	张振霞, 王辰宇, 李强, 吴书贵 2014 物理学报 63 079401 Google Scholar Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401 Google Scholar
[41]	罗旭东, 牛胜利, 左应红 2015 物理学报 64 069401 Google Scholar Luo X D, Niu S L, Zuo Y H 2015 Acta Phys. Sin. 64 069401 Google Scholar
[42]	Meredith N P, Horne R B, Clilverd M A, Ross J P J 2019 J. Geophys. Res. Space Phys. 124 5246 Google Scholar
[43]	Ozhogin P, Tu J, Song P, Reinisch B W 2012 J. Geophys. Res. A 117 06225 Google Scholar
[44]	Ni B, Thorne R M, Meredith N P, Shprits Y Y, Horne R B 2011 J. Geophys. Res. A 116 10207 Google Scholar
[45]	Ni B, Thorne R M, Shprits Y Y, Bortnik J 2008 Geophys. Res. Lett. 35 L11106 Google Scholar
[46]	Ma Q, Artemyev A V, Mourenas D, Li W, Thorne R M, Kletzing C A, Kurth W S, Hospodarsky G B, Reeves G D, Spence H E, Wygant J 2017 Geophys. Res. Lett. 44 12057
[47]	Xiao F, Su Z, Zheng H, Wang S 2009 J. Geophys. Res. A 114 03201 Google Scholar
[48]	Xiao F, Shen C, Wang Y, Zheng H, Wang S 2008 J. Geophys. Res. A 113 05203 Google Scholar

施引文献

图 1 计算得到的三个台站的波幅

Fig. 1. Calculated wave amplitudes from three VLF transmitters.

下载: 全尺寸图片幻灯片

图 2 NWC台站信号在L = 1.5—2.2导致的电子弹跳平均投掷角扩散系数$\left\langle {{D_{\alpha \alpha }}} \right\rangle $. 图中横坐标为赤道投掷角${\alpha _{{\rm{eq}}}}$, 纵坐标为电子能量${E_{\rm{k}}}$, 颜色表示扩散系数的大小

Fig. 2. The color-code bounce-averaged pitch angle diffusion coefficients $\left\langle {{D_{\alpha \alpha }}} \right\rangle $ as a function of equatorial pitch angle ${\alpha _{{\rm{eq}}}}$ and electron kinetic energy ${E_{\rm{k}}}$ induced by VLF transmitter signals from NWC at L = 1.5–2.2.

下载: 全尺寸图片幻灯片

图 3 NAA台站信号在L = 1.7—3.0导致的电子弹跳平均投掷角扩散系数. 格式同图2

Fig. 3. Same as in Fig. 2 except for VLF transmitter signals from NAA at L = 1.7–3.0.

下载: 全尺寸图片幻灯片

图 4 DHO38台站信号在L = 1.7−2.9导致的电子弹跳平均投掷角扩散系数. 格式同图2

Fig. 4. Same as in figure 2 except for VLF transmitter signals from DHO38 at L = 1.7−2.9.

下载: 全尺寸图片幻灯片

图 5 在L = 1.8处, 不同VLF台站信号对电子散射效果的模拟, 从左至右分别为NWC, NAA, DHO38台站信号单独散射和三个台站信号联合散射　(a1)−(d4)不同模拟时间的电子相空间密度分布二维图, 颜色表示电子相空间密度的大小; (e1)−(h4)指定能级电子的相空间密度随时间演化的过程图, 线条颜色表示不同的时间

Fig. 5. (a1)−(d4) Two dimensional distributions of color-code electron phase space density (PSD) as a function of equatorial pitch angle ${\alpha _{{\rm{eq}}}}$ and electron kinetic energy ${E_{\rm{k}}}$ at the indicated interaction time stamps at L = 1.8 induced by different VLF transmitter signals (from left to right): NWC, NAA, DHO38 individual scattering and combined scattering; (e1)−(h4) temporal evolution of electron PSD distribution as a function of ${\alpha _{{\rm{eq}}}}$ for the indicated four electron energies at the color-coded interaction time stamps.

下载: 全尺寸图片幻灯片

图 6 在L = 2.2处, 不同VLF台站信号对电子的散射效果模拟, 格式同图5

Fig. 6. Same as in Fig. 5 except for at L = 2.2.

下载: 全尺寸图片幻灯片

图 7 在L = 2.6处, 不同VLF台站信号对电子的散射效果模拟. 格式同图5

Fig. 7. Same as in Fig. 5 except for at L = 2.6.

下载: 全尺寸图片幻灯片

表 1 选取计算的台站信息

Table 1. The information of the three selected VLF transmitters.

台站频率/kHz 功率/kW 经纬度 L-shell 磁层中波
幅范围/L

NWC 19.8 1000 21.8°S
114.2°E 1.42 1.5—2.2
NAA 24.0 1000 44.6°N
67.3°W 2.74 1.7—3.0
DHO38 23.4 300 53.1°N
7.6°E 2.38 1.7—2.9

下载: 导出CSV

[1]	Xiang Z, Tu W, Li X, Ni B, Morley S K, Baker D N 2017 J. Geophys. Res. Space Phys. 122 9858 Google Scholar
[2]	Xiang Z, Tu W, Ni B, Henderson M G, Cao X 2018 Geophys. Res. Lett. 45 8035 Google Scholar
[3]	Ma X, Xiang Z, Ni B, Fu S, Cao X, Hua M, Guo D, Guo Y, Gu X, Liu Z, Zhu Q 2020 Earth Planet. Phys. 4 598 Google Scholar
[4]	Rosen A, Sanders N L 1971 J. Geophys. Res. 76 110 Google Scholar
[5]	Selesnick R S 2015 J. Geophys. Res. Space Phys. 120 2912 Google Scholar
[6]	Xiang Z, Li X, Selesnick R, Temerin M A, Ni B, Zhao H, Zhang K, Khoo L Y 2019 Geophys. Res. Lett. 46 1919 Google Scholar
[7]	Xiang Z, Li X, Temerin M A, Ni B, Zhao H, Zhang K, Khoo L Y 2020 J. Geophys. Res. Space Phys. 125 e2019JA027678
[8]	Xiang Z, Li X, Ni B, Temerin M A, Zhao H, Zhang K, Khoo L Y 2020 J. Geophys. Res. Space Phys. 125 e2020JA028042
[9]	Zhang K, Li X, Zhao H, Schiller Q, Khoo L Y, Xiang Z, Selesnick R, Temerin M A, Sauvaud J A 2019 Geophys. Res. Lett. 46 544 Google Scholar
[10]	Ni B, Hua M, Zhou R, Yi J, Fu S 2017 Geophys. Res. Lett. 44 3465 Google Scholar
[11]	Hua M, Ni B, Fu S, Gu X, Xiang Z, Cao X, Zhang W, He Y, Huang H, Lou Y, Zhang Y 2018 Geophys. Res. Lett. 45 10057 Google Scholar
[12]	Rodger C J, Clilverd M A, McCormick R J 2003 J. Geophys. Res. 108 1462 Google Scholar
[13]	Clilverd M A, Rodger C J, Nunn D 2004 J. Geophys. Res. A 109 12208 Google Scholar
[14]	Green A, Li W, Ma Q, Shen X C, Bortnik J, Hospodarsky G B 2020 Geophys. Res. Lett. 47 e2020GL089584
[15]	Ma Q, Li W, Thorne R M, Bortnik J, Kletzing C A, Kurth W S, Hospodarsky G B 2016 J. Geophys. Res. Space Phys. 121 274 Google Scholar
[16]	顾旭东, 何颖, 倪彬彬, 付松, 花漫, 项正 2020 地球物理学报 63 2121 Google Scholar Gu X D, He Y, Ni B B, Fu S, Hua M, Xiang Z 2020 Chin. J. Geophys. 63 2121 Google Scholar
[17]	Ni B, Yan L, Fu S, Gu X, Cao X, Xiang Z, Zhang Y 2020 Geophys. Res. Lett. 47 e2019GL086487
[18]	Ma Q, Mourenas D, Li W, Artemyev A, Thorne R M 2017 Geophys. Res. Lett. 44 6483 Google Scholar
[19]	Ross J P J, Meredith N P, Glauert S A, Horne R B, Clilverd M A 2019 J. Geophys. Res. Space Phys. 124 5260 Google Scholar
[20]	Hua M, Li W, Ni B, Ma Q, Green A, Shen X, Claudepierre S G, Bortnik J, Gu X, Fu S, Xiang Z, Reeves G D 2020 Nat. Commun. 11 4847 Google Scholar
[21]	Chen Y P, Yang G B, Ni B B, Zhao Z Y, Gu X D, Zhou C, Wang F 2016 Adv. Space Res. 57 1871 Google Scholar
[22]	Chen Y, Ni B, Gu X, Zhao Z, Yang G, Zhou C, Zhang Y 2017 Sci. Chin. Technol. Sci. 60 166 Google Scholar
[23]	易娟, 顾旭东, 李志鹏, 林仁桐, 蔡毅徽, 陈隆, 倪彬彬, 乐新安 2019 地球物理学报 62 3223 Google Scholar Yi J, Gu X D, Li Z P, Lin R T, Cai Y H, Chen L, Ni B B, Yue X A 2019 Chin. J. Geophys. 62 3223 Google Scholar
[24]	Yi J, Gu X, Cheng W, Tang X, Chen L, Ni B, Zhou R, Zhao Z, Wang Q, Zhou L 2020 Earth Planet. Phys. 4 238 Google Scholar
[25]	Zhou R, Gu X, Yang K, Li G, Ni B, Yi J, Chen L, Zhao F, Zhao Z, Wang Q, Zhou L 2020 Earth Planet. Phys. 4 120 Google Scholar
[26]	Vampola A L, Kuck G A 1978 J. Geophys. Res. 83 2543 Google Scholar
[27]	Koons H C, Edgar B C, Vampola A L 1981 J. Geophys. Res. 86 640 Google Scholar
[28]	Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397 Google Scholar
[29]	Gamble R J, Rodger C J, Clilverd M A, Sauvaud J A, Thomson N R, Stewart S L, McCormick R J, Parrot M, Berthelier J J 2008 J. Geophys. Res. A 113 10211 Google Scholar
[30]	Graf K L, Inan U S, Piddyachiy D, Kulkarni P, Parrot M, Sauvaud J A 2009 J. Geophys. Res. A 114 07205 Google Scholar
[31]	Selesnick R S, Albert J M, Starks M J 2013 J. Geophys. Res. Space Phys. 118 628 Google Scholar
[32]	Agapitov O V, Artemyev A V, Mourenas D, Kasahara Y, Krasnoselskikh V 2014 J. Geophys. Res. Space Phys. 119 2876 Google Scholar
[33]	Claudepierre S G, Ma Q, Bortnik J, O'Brien T P, Fennell J F, Blake J B 2020 Geophys. Res. Lett. 47 e2019GL086056 Google Scholar
[34]	Imhof W L, Reagan J B, Voss H D, Gaines E E, Datlowe D W, Mobilia J, Helliwell R A, Inan U S, Katsufrakis J, Joiner R G 1983 Geophys. Res. Lett. 10 361 Google Scholar
[35]	Inan U S, Chang H C, Helliwell R A, Imhof W L, Reagan J B, Walt M 1985 J. Geophys. Res. 90 359 Google Scholar
[36]	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 物理学报 60 039401 Google Scholar 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 Google Scholar
[37]	Sauvaud J A, Maggiolo R, Jacquey C, Parrot M, Berthelier J J, Gamble R J, Rodger C J 2008 Geophys. Res. Lett. 35 L09101 Google Scholar
[38]	Clilverd M A, Rodger C J, Gamble R, Meredith N P, Parrot M, Berthelier J J, Thomson N R 2008 J. Geophys. Res. A 113 04211 Google Scholar
[39]	Kulkarni P, Inan U S, Bell T F, Bortnik J 2008 J. Geophys. Res. A 113 07214 Google Scholar
[40]	张振霞, 王辰宇, 李强, 吴书贵 2014 物理学报 63 079401 Google Scholar Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401 Google Scholar
[41]	罗旭东, 牛胜利, 左应红 2015 物理学报 64 069401 Google Scholar Luo X D, Niu S L, Zuo Y H 2015 Acta Phys. Sin. 64 069401 Google Scholar
[42]	Meredith N P, Horne R B, Clilverd M A, Ross J P J 2019 J. Geophys. Res. Space Phys. 124 5246 Google Scholar
[43]	Ozhogin P, Tu J, Song P, Reinisch B W 2012 J. Geophys. Res. A 117 06225 Google Scholar
[44]	Ni B, Thorne R M, Meredith N P, Shprits Y Y, Horne R B 2011 J. Geophys. Res. A 116 10207 Google Scholar
[45]	Ni B, Thorne R M, Shprits Y Y, Bortnik J 2008 Geophys. Res. Lett. 35 L11106 Google Scholar
[46]	Ma Q, Artemyev A V, Mourenas D, Li W, Thorne R M, Kletzing C A, Kurth W S, Hospodarsky G B, Reeves G D, Spence H E, Wygant J 2017 Geophys. Res. Lett. 44 12057
[47]	Xiao F, Su Z, Zheng H, Wang S 2009 J. Geophys. Res. A 114 03201 Google Scholar
[48]	Xiao F, Shen C, Wang Y, Zheng H, Wang S 2008 J. Geophys. Res. A 113 05203 Google Scholar

[1]	刘阳希子, 项正, 周晨, 倪彬彬, 董俊虎, 胡景乐, 王建行, 郭浩智. NWC人工甚低频台站信号产生“条缕状”准捕获电子能谱的模拟研究. 物理学报, 2024, 73(20): 209401. doi: 10.7498/aps.73.20240975
[2]	王敬之, 马新, 项正, 顾旭东, 焦鹿怀, 雷良建, 倪彬彬. 等离子体层嘶声波对辐射带电子投掷角散射系数的多维建模. 物理学报, 2022, 71(22): 229401. doi: 10.7498/aps.71.20220655
[3]	杨巨涛, 李清亮, 王建国, 郝书吉, 潘威炎. 双频双波束加热电离层激发甚低频/极低频辐射理论分析. 物理学报, 2017, 66(1): 019401. doi: 10.7498/aps.66.019401
[4]	罗旭东, 牛胜利, 左应红. 典型甚低频电磁波对辐射带高能电子的散射损失效应. 物理学报, 2015, 64(6): 069401. doi: 10.7498/aps.64.069401
[5]	常珊珊, 倪彬彬, 赵正予, 汪枫, 李金星, 赵晶晶, 顾旭东, 周晨. 基于试验粒子模拟的电离层人工调制激发的极低频和甚低频波对磁层高能电子的散射效应. 物理学报, 2014, 63(6): 069401. doi: 10.7498/aps.63.069401
[6]	郝书吉, 李清亮, 杨巨涛, 吴振森. 电离层调制加热产生极低频/甚低频波定向辐射的理论分析. 物理学报, 2013, 62(22): 229402. doi: 10.7498/aps.62.229402
[7]	吕耀平, 顾国锋, 陆华春, 戴瑜, 唐国宁. 在不同扩散系数下反应扩散平面波的折射. 物理学报, 2009, 58(5): 2996-3000. doi: 10.7498/aps.58.2996
[8]	顾旭东, 赵正予, 倪彬彬, 王翔, 邓峰. 地基高频加热激励ELF/VLF波对辐射带高能电子的准线性散射. 物理学报, 2008, 57(10): 6673-6682. doi: 10.7498/aps.57.6673
[9]	倪彬彬, 赵正予, 顾旭东, 汪枫. 场向传播的内磁层哨声波对辐射带高能电子的共振扩散. 物理学报, 2008, 57(12): 7937-7949. doi: 10.7498/aps.57.7937
[10]	刘志明, 崔田, 马琰铭, 刘冰冰, 邹广田. Nb2H 的电子结构和相互作用. 物理学报, 2007, 56(8): 4877-4883. doi: 10.7498/aps.56.4877
[11]	颜利芬, 王红成, 佘卫龙. 扩散效应对光伏孤子相互作用的影响. 物理学报, 2006, 55(10): 5257-5262. doi: 10.7498/aps.55.5257
[12]	徐妙华, 梁天骄, 张杰. 利用韧致辐射诊断激光等离子体相互作用产生的超热电子. 物理学报, 2006, 55(5): 2357-2363. doi: 10.7498/aps.55.2357
[13]	卫青, 王奇, 施解龙, 陈园园. 孤子和辐射场的非线性相互作用. 物理学报, 2002, 51(1): 99-103. doi: 10.7498/aps.51.99
[14]	赵东焕. 自由电子激光中电子与辐射波相互作用有效时间的分析. 物理学报, 1996, 45(4): 573-579. doi: 10.7498/aps.45.573
[15]	赵东焕. 自由电子激光器中电子与波的相互作用及其增益分析. 物理学报, 1994, 43(9): 1447-1454. doi: 10.7498/aps.43.1447
[16]	张希清, 赵家龙, 秦伟平, 窦凯, 黄世华. 用非相干光时间延迟四波混频测量二极扩散系数. 物理学报, 1993, 42(3): 417-421. doi: 10.7498/aps.42.417
[17]	孙鑫, 陈洪奕, 吴长勤, 傅荣堂, 傅柔励. 高分子中电子相互作用矩阵元. 物理学报, 1991, 40(1): 102-108. doi: 10.7498/aps.40.102
[18]	贺贤土. 等离子体中大幅波与低频振荡粒子非线性相互作用效应. 物理学报, 1982, 31(10): 1317-1336. doi: 10.7498/aps.31.1317
[19]	潘威炎. 关于地球曲率对低频电波电离层反射系数计算的影响. 物理学报, 1981, 30(5): 661-670. doi: 10.7498/aps.30.661
[20]	孙鑫. 铁磁体中导电电子与自旋波的相互作用. 物理学报, 1964, 20(3): 193-206. doi: 10.7498/aps.20.193

计量

文章访问数: 5566
PDF下载量: 102
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

甚低频台站信号对地球内辐射带和槽区能量电子的散射效应分析