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等离子体层嘶声波(plasmaspheric hiss)是地球辐射带中一种常见的电磁波动. 嘶声波可以通过波粒相互作用将辐射带电子散射进入损失锥进而沉降到中性大气, 因此是导致辐射带电子损失的重要波动源. 作为电子能量和投掷角的变化函数, 嘶声波对辐射带电子的散射系数受到太阳风和地磁活动水平的显著影响, 还强烈依赖于空间位置、背景磁场和等离子体密度分布. 为了快速获取嘶声波对辐射带电子的投掷角散射系数以用于辐射带全球动态变化过程建模, 本文利用FDC(full diffusion code)系统计算了嘶声波对辐射带电子的散射系数, 建立了空间区域L = 1.5—6、冷等离子体参数α* = 3—30、电子能量1 keV—10 MeV、电子投掷角0°—90°范围内的四维散射系数矩阵数据库. 基于该数据库, 可通过线性插值快速得到不同L和α*参数下的嘶声波对辐射带电子的散射系数. 通过对比FDC计算的散射系数与线性插值的结果, 验证了基于数据库线性插值得到散射系数的准确性, 大部分误差位于10%以内. 本文建立的嘶声波对辐射带电子的投掷角散射系数四维数据库和验证的线性插值方法, 可以大幅降低获取嘶声波散射系数全球信息的时间, 从而快速提升开展长时间辐射带时空变化模拟的计算效率, 进而有望为开发地球辐射带动态预报模型提供有利条件.Plasmaspheric hiss is an important wave mode in the Earth’s radiation belts. Hiss waves can scatter energetic electrons into loss cones to precipitate into the atmosphere, and therefore become an important source of fluctuations, leading the radiation belt to lose electrons . As a function of electron energy and pitch angle, the diffusion coefficient of hiss waves for radiation belt electrons is significantly influenced by the solar wind and geomagnetic activity, and also strongly depends on the spatial position, the background magnetic field, and the plasma density distribution. In order to quickly obtain the diffusion coefficients of hiss waves on electrons in the radiation belt for modelling the global dynamics of the radiation belt, we systematically calculate the diffusion coefficients of hiss waves on electrons in the radiation belt by using the full diffusion code (FDC), and build a four-dimensional matrix database of diffusion coefficients for the spatial region L = 1.5–6, the cold plasma parameter α* = 3–30, electron energy 1 keV–10 MeV, and electron throw angle 0°–90°. According to the database, we can quickly obtain diffusion coefficients with different L and α* values through linear interpolations. By comparing the errors between diffusion coefficients calculated by the FDC code and those linearly interpolated from the diffusion coefficient database, the accuracies of interpolated coefficients are validated, showing that most of the errors lie in 10%. The four-dimensional database of hiss wave pitch angle diffusion coefficients for radiation belt electrons and the validated linear interpolation method established in this paper can significantly reduce the time required to obtain global information about hiss wave diffusion coefficients, thereby rapidly improving the computational efficiency of carrying out simulations of spatial and temporal changes in the radiation belts over long periods of time, which in turn is expected to provide favourable conditions for the development of dynamic forecasting models of the Earth's radiation belts.
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Keywords:
- radiation belt electrons /
- plasmaspheric hiss /
- diffusion coefficients /
- linear interpolation /
- wave-particle interactions
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图 1 (a) 不同的L和α*条件下对应等离子体密度的数值; (b) 不同L下α*的值, 蓝线表示位于等离子体层以内, 黄线表示位于等离子体层以外
Fig. 1. (a) The values of the density at different L and α* values; (b) the values of α* at different L, the blue line indicates inside the plasmapause and the yellow line indicates outside the plasmapause.
图 2 L = 2时常数传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 2. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with constant wave normal angle model at L = 2, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 3 L = 3时固定传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 3. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with constant wave normal angle model at L = 3, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 4 L = 4时常数传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 4. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with constant wave normal angle model at L = 4, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 5 L = 5时固定传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 5. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with constant wave normal angle model at L = 5, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 7 L = 3时随纬度变化传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 7. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle$ of hiss waves for electrons with latitudinally varying wave normal angle model at L = 3, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 8 L = 4时随纬度变化传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 8. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with latitudinally varying wave normal angle model at L = 4, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 6 L = 2时随纬度变化传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)分别对应不同α*条件下的散射系数Fig. 6. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with latitudinally varying wave normal angle model at L = 2, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 9 L = 5时随纬度变化传播角模型的嘶声波对电子的弹跳平均散射系数
$\langle $ Dαα$\rangle $ , 其中(a1)—(d7)对应不同α*条件下的散射系数Fig. 9. Bounce averaged diffusion coefficients
$\langle $ Dαα$\rangle $ of hiss waves for electrons with latitudinally varying wave normal angle model at L = 5, where (a1)–(d7) corresponds to the diffusion coefficients under different α* conditions, respectively.
图 10 (a1)—(a3) 当α* = 4时, L = 3.25, L = 4.35, L = 5.55处计算得到的嘶声波散射系数; (b1)—(b3) 通过数据库进行线性插值计算得到的嘶声波散射系数; (c1)—(c3) 二者相对误差分析
Fig. 10. (a1)–(a3) The diffusion coefficients of hiss waves calculated at L = 3.25, L = 4.35, L = 5.55 when α* = 3; (b1)–(b3) the hiss wave diffusion coefficients calculated by linear interpolation from the database; (c1)–(c3) the relative error analysis.
图 11 (a)—(c) 当α* = 4时, L = 3.25, L = 4.35, L = 5.55处选取能级为50 keV, 200 keV, 400 keV以及700 keV的散射系数对比结果; (d)—(f) 数值的比值, 虚线表示FDC计算结果, 点画线表示线性插值结果, 不同颜色代表不同能级
Fig. 11. (a1)–(a3) Comparison of the diffusion coefficients at α* = 4, L = 3.25, L = 4.35, L = 5.55 for selected energy levels of 50 keV, 200 keV, 400 keV and 700 keV; (d)–(f) the ratio of values, the dashed line shows the result of the FDC calculation, the dotted lines shows the result of linear interpolation, different colors represent different energy levels.
图 12 (a1)—(a3) 当L = 4时, α* = 3.25, α* = 4.35, α* = 5.55处计算得到的嘶声波散射系数; (b1)—(b3) 通过数据库进行线性插值计算得到的嘶声波散射系数; (c1)—(c3) 表示对二者进行相对误差分析
Fig. 12. (a1)–(a3) The diffusion coefficients of hiss waves calculated at α* = 3.25, α* = 4.35, α* = 5.55 when L = 4; (b1)–(b3) the hiss wave diffusion coefficients calculated by linear interpolation from the database; (c1)–(c3) the relative error analysis.
图 13 (a)—(c) 当L = 4时, α* = 3.25, α* = 4.35, α* = 5.55处选取能级为50 keV, 200 keV, 400 keV和700 keV的散射系数对比结果; (d)—(f) 数值的比值, 虚线表示FDC计算结果, 点画线表示线性插值结果, 表示不同颜色代表不同能级
Fig. 13. (a)–(c) The comparison of the diffusion coefficients at α* = 3.25, α* = 4.35, α* = 5.55 for L = 4 for selected energy levels of 50 keV, 200 keV, 400 keV and 700 keV; (d)–(f) the ratio of values, the dashed line shows the result of the FDC calculation, the dotted lines shows the result of linear interpolation, different colors represent different energy levels.
表 1 随纬度变化的传播角模型主要参数
Table 1. Parameters of the varying latitudinal wave normal angle model.
λ/(º) $ \varphi $m/(º) δ$ \varphi $/(º) $ \varphi $/(º) 0—5 0 15 0—25 5—10 20 15 0—40 10—15 40 20 0—55 15—20 50 30 15—70 20—25 60 40 30—75 25—30 70 50 50—80 30—35 80 60 65—85 35—40 80 70 75—85 40—45 80 80 80—85 
下载: 导出CSV
表 2 不同L的磁纬度选取范围
Table 2. Range of magnetic latitude at different L values
L λ/(°) 1.5—2.2 0—30 2.3—2.9 0—40 3.0—6.0 0—45
下载: 导出CSV
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