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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

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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

Scattering effect of very low frequency transmitter signals on energetic electrons in Earth’s inner belt and slot region

Liu Yang-Xi-Zi, Xiang Zheng, Guo Jian-Guang, Gu Xu-Dong, Fu Song, Zhou Ruo-Xian, Hua Man, Zhu Qi, Yi Juan, Ni Bin-Bin
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  • 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.
    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°.
      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
      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)
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    Xiang Z, Tu W, Ni B, Henderson M G, Cao X 2018 Geophys. Res. Lett. 45 8035Google Scholar

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    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 598Google Scholar

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    Rosen A, Sanders N L 1971 J. Geophys. Res. 76 110Google Scholar

    [5]

    Selesnick R S 2015 J. Geophys. Res. Space Phys. 120 2912Google 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 1919Google 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 544Google Scholar

    [10]

    Ni B, Hua M, Zhou R, Yi J, Fu S 2017 Geophys. Res. Lett. 44 3465Google Scholar

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    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 10057Google Scholar

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    Rodger C J, Clilverd M A, McCormick R J 2003 J. Geophys. Res. 108 1462Google Scholar

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    Clilverd M A, Rodger C J, Nunn D 2004 J. Geophys. Res. A 109 12208Google Scholar

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    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 274Google Scholar

    [16]

    顾旭东, 何颖, 倪彬彬, 付松, 花漫, 项正 2020 地球物理学报 63 2121Google Scholar

    Gu X D, He Y, Ni B B, Fu S, Hua M, Xiang Z 2020 Chin. J. Geophys. 63 2121Google 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 6483Google 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 5260Google 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 4847Google 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 1871Google Scholar

    [22]

    Chen Y, Ni B, Gu X, Zhao Z, Yang G, Zhou C, Zhang Y 2017 Sci. Chin. Technol. Sci. 60 166Google 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 3223Google 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 3223Google 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 238Google 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 120Google Scholar

    [26]

    Vampola A L, Kuck G A 1978 J. Geophys. Res. 83 2543Google Scholar

    [27]

    Koons H C, Edgar B C, Vampola A L 1981 J. Geophys. Res. 86 640Google Scholar

    [28]

    Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397Google 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 10211Google Scholar

    [30]

    Graf K L, Inan U S, Piddyachiy D, Kulkarni P, Parrot M, Sauvaud J A 2009 J. Geophys. Res. A 114 07205Google Scholar

    [31]

    Selesnick R S, Albert J M, Starks M J 2013 J. Geophys. Res. Space Phys. 118 628Google Scholar

    [32]

    Agapitov O V, Artemyev A V, Mourenas D, Kasahara Y, Krasnoselskikh V 2014 J. Geophys. Res. Space Phys. 119 2876Google Scholar

    [33]

    Claudepierre S G, Ma Q, Bortnik J, O'Brien T P, Fennell J F, Blake J B 2020 Geophys. Res. Lett. 47 e2019GL086056Google 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 361Google Scholar

    [35]

    Inan U S, Chang H C, Helliwell R A, Imhof W L, Reagan J B, Walt M 1985 J. Geophys. Res. 90 359Google 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 039401Google 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 039401Google 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 L09101Google 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 04211Google Scholar

    [39]

    Kulkarni P, Inan U S, Bell T F, Bortnik J 2008 J. Geophys. Res. A 113 07214Google Scholar

    [40]

    张振霞, 王辰宇, 李强, 吴书贵 2014 物理学报 63 079401Google Scholar

    Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401Google Scholar

    [41]

    罗旭东, 牛胜利, 左应红 2015 物理学报 64 069401Google Scholar

    Luo X D, Niu S L, Zuo Y H 2015 Acta Phys. Sin. 64 069401Google Scholar

    [42]

    Meredith N P, Horne R B, Clilverd M A, Ross J P J 2019 J. Geophys. Res. Space Phys. 124 5246Google Scholar

    [43]

    Ozhogin P, Tu J, Song P, Reinisch B W 2012 J. Geophys. Res. A 117 06225Google Scholar

    [44]

    Ni B, Thorne R M, Meredith N P, Shprits Y Y, Horne R B 2011 J. Geophys. Res. A 116 10207Google Scholar

    [45]

    Ni B, Thorne R M, Shprits Y Y, Bortnik J 2008 Geophys. Res. Lett. 35 L11106Google 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 03201Google Scholar

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    Xiao F, Shen C, Wang Y, Zheng H, Wang S 2008 J. Geophys. Res. A 113 05203Google Scholar

  • 图 1  计算得到的三个台站的波幅

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

    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.

    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.

    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.

    图 5  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.

    图 6  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.

    图 7  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.

    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
    NWC19.8100021.8°S
    114.2°E
    1.421.5—2.2
    NAA24.0100044.6°N
    67.3°W
    2.741.7—3.0
    DHO3823.430053.1°N
    7.6°E
    2.381.7—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 9858Google Scholar

    [2]

    Xiang Z, Tu W, Ni B, Henderson M G, Cao X 2018 Geophys. Res. Lett. 45 8035Google 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 598Google Scholar

    [4]

    Rosen A, Sanders N L 1971 J. Geophys. Res. 76 110Google Scholar

    [5]

    Selesnick R S 2015 J. Geophys. Res. Space Phys. 120 2912Google 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 1919Google 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 544Google Scholar

    [10]

    Ni B, Hua M, Zhou R, Yi J, Fu S 2017 Geophys. Res. Lett. 44 3465Google 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 10057Google Scholar

    [12]

    Rodger C J, Clilverd M A, McCormick R J 2003 J. Geophys. Res. 108 1462Google Scholar

    [13]

    Clilverd M A, Rodger C J, Nunn D 2004 J. Geophys. Res. A 109 12208Google 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 274Google Scholar

    [16]

    顾旭东, 何颖, 倪彬彬, 付松, 花漫, 项正 2020 地球物理学报 63 2121Google Scholar

    Gu X D, He Y, Ni B B, Fu S, Hua M, Xiang Z 2020 Chin. J. Geophys. 63 2121Google 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 6483Google 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 5260Google 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 4847Google 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 1871Google Scholar

    [22]

    Chen Y, Ni B, Gu X, Zhao Z, Yang G, Zhou C, Zhang Y 2017 Sci. Chin. Technol. Sci. 60 166Google 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 3223Google 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 3223Google 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 238Google 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 120Google Scholar

    [26]

    Vampola A L, Kuck G A 1978 J. Geophys. Res. 83 2543Google Scholar

    [27]

    Koons H C, Edgar B C, Vampola A L 1981 J. Geophys. Res. 86 640Google Scholar

    [28]

    Abel B, Thorne R M 1998 J. Geophys. Res. 103 2397Google 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 10211Google Scholar

    [30]

    Graf K L, Inan U S, Piddyachiy D, Kulkarni P, Parrot M, Sauvaud J A 2009 J. Geophys. Res. A 114 07205Google Scholar

    [31]

    Selesnick R S, Albert J M, Starks M J 2013 J. Geophys. Res. Space Phys. 118 628Google Scholar

    [32]

    Agapitov O V, Artemyev A V, Mourenas D, Kasahara Y, Krasnoselskikh V 2014 J. Geophys. Res. Space Phys. 119 2876Google Scholar

    [33]

    Claudepierre S G, Ma Q, Bortnik J, O'Brien T P, Fennell J F, Blake J B 2020 Geophys. Res. Lett. 47 e2019GL086056Google 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 361Google Scholar

    [35]

    Inan U S, Chang H C, Helliwell R A, Imhof W L, Reagan J B, Walt M 1985 J. Geophys. Res. 90 359Google 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 039401Google 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 039401Google 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 L09101Google 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 04211Google Scholar

    [39]

    Kulkarni P, Inan U S, Bell T F, Bortnik J 2008 J. Geophys. Res. A 113 07214Google Scholar

    [40]

    张振霞, 王辰宇, 李强, 吴书贵 2014 物理学报 63 079401Google Scholar

    Zhang Z X, Wang C Y, Li Q, Wu S G 2014 Acta Phys. Sin. 63 079401Google Scholar

    [41]

    罗旭东, 牛胜利, 左应红 2015 物理学报 64 069401Google Scholar

    Luo X D, Niu S L, Zuo Y H 2015 Acta Phys. Sin. 64 069401Google Scholar

    [42]

    Meredith N P, Horne R B, Clilverd M A, Ross J P J 2019 J. Geophys. Res. Space Phys. 124 5246Google Scholar

    [43]

    Ozhogin P, Tu J, Song P, Reinisch B W 2012 J. Geophys. Res. A 117 06225Google Scholar

    [44]

    Ni B, Thorne R M, Meredith N P, Shprits Y Y, Horne R B 2011 J. Geophys. Res. A 116 10207Google Scholar

    [45]

    Ni B, Thorne R M, Shprits Y Y, Bortnik J 2008 Geophys. Res. Lett. 35 L11106Google 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 03201Google Scholar

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    Xiao F, Shen C, Wang Y, Zheng H, Wang S 2008 J. Geophys. Res. A 113 05203Google Scholar

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出版历程
  • 收稿日期:  2020-12-01
  • 修回日期:  2021-02-27
  • 上网日期:  2021-07-09
  • 刊出日期:  2021-07-20

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