Multi-dimensional modeling of radiation belt electron pitch-angle diffusion coefficients caused by plasmaspheric hiss

Wang Jing-Zhi; Ma Xin; Xiang Zheng; Gu Xu-Dong; Jiao Lu-Huai; Lei Liang-Jian; Ni Bin-Bin

doi:10.7498/aps.71.20220655

Abstract

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.

Keywords:

Authors and contacts

1.
Department of Space Physics, School of Electronic Information, Wuhan University, Wuhan 430072, China
2.
Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

Corresponding author: Ma Xin, whumaxin@whu.edu.cn ; Xiang Zheng, xiangzheng@whu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 42025404, 42188101, 42174190, 41904143, 42274199, 42204160), the Pre-research Projects on Civil Aerospace Technologies (Grant Nos. D020308, D020104) funded by the China National Space Administration, and the B-type Strategic Priority Program of the Chinese Academy of Sciences (Grant Nos. XDB41000000) and the Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences (Grant No. DQXX2021-04), and the Fundamental Research Funds for the Central Universities (Grant No. 2042021kf0016).

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Cited By

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

Figure 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.

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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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 2. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

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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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 3. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

DownLoad: Full-Size Img PowerPoint

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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 4. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

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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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 5. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

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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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 7. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

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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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 8. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

DownLoad: Full-Size Img PowerPoint

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 $D_αα$\rangle $, 其中(a₁)—(d₇)分别对应不同α^*条件下的散射系数

Figure 6. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

DownLoad: Full-Size Img PowerPoint

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 $D_αα$\rangle $, 其中(a₁)—(d₇)对应不同α^*条件下的散射系数

Figure 9. Bounce averaged diffusion coefficients $\langle $D_αα$\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.

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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

Figure 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.

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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

Figure 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.

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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

Figure 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.

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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

Figure 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.

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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

DownLoad: 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

DownLoad: CSV

map

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[2]	Lou Y, Cao X, Ni B, Tu W, Gu X, Fu S, Xiang Z, Ma X 2021 Geophys. Res. Lett. 48 e2020GL092208
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[8]	Liu S, Xie Y, Zhang S, Shang X, Yang C, Zhou Q, He Y, Xiao F 2020 Geophys. Res. Lett. 47 e2020GL089994
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