Hot plasma effects on the dispersion properties of plasmaspheric hiss and its electron diffusion
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摘要: 由等离子体层嘶声波引起的电子散射效应是地球内磁层电子损失的重要机制，也是地球内外辐射带间槽区形成的主要原因. 在量化嘶声波对高能电子散射效应的研究过程中，冷等离子体近似下的嘶声波色散关系被广泛应用. 然而在实际磁层等离子体环境中，热等离子体成分的存在会修正嘶声波的色散特性，进而也会影响嘶声波对高能电子的散射效应. 本文主要介绍了热等离子体影响嘶声波色散特性及其对电子散射效应的相关研究. 基于卫星波动观测数据的统计分析结果证实了热等离子体效应对嘶声波色散特性的修正作用；通过典型事例分析以及基于准线性理论的数值计算，分析了嘶声波散射高能电子对地磁活动条件和热等离子体参数（电子温度各向异性、热电子温度以及热电子占比）的依赖性. 结果表明，冷等离子体假设会高估100 keV以下能量电子以及较大投掷角范围内100 keV以上能量电子的散射系数，而低估较低投掷角范围内100 keV以上能量电子的散射系数. 此外，冷等离子体假设下共振区间会扩展到更低能量的电子，而基于观测的色散曲线结果则使100 keV以上电子与嘶声波的共振范围扩展到更小的投掷角区间. 随着热等离子体参数的增大，冷等离子体近似与热等离子体环境下的散射系数差异也逐渐增大. 相关研究结果对于模拟实际等离子体环境中嘶声波对电子的散射过程以及辐射带的动态演化具有重要意义.Abstract: Electron diffusion caused by plasmaspheric hiss is an important mechanism for the loss of electrons in Earth's inner magnetosphere; it has also been considered responsible for the formation of the slot region between inner and outer radiation belts. The cold plasma dispersion relation of plasmaspheric hiss is widely used to quantify the scattering effect of energetic electrons. However, the existence of hot plasma in a realistic magnetospheric plasma environment modifies the dispersion relation of plasmaspheric hiss, thereby affecting wave-induced energetic electron scattering. This paper presents the results of some recent studies on the influence of hot plasma on the dispersion relation and electron scattering effects of plasmaspheric hiss. Using statistical analysis results based on satellite wave observations, the modification of the hiss dispersion relation under the effects of hot plasma was verified. Furthermore, based on typical case analyses and numerical calculations using the quasi-linear diffusion theory, we investigated the dependence of the hiss-driven electron scattering rates on the geomagnetic activities and hot plasma parameters (i.e., temperature anisotropy, hot electron temperature, and hot electron abundance). The results revealed that the cold plasma dispersion relation overestimates the scattering rate of energetic electrons below 100 keV. For electrons above 100 keV, the differences between the cold plasma and hot plasma dispersion relations in terms of the induced scattering rates are somewhat smaller; this indicates that using the cold plasma dispersion relation can lead to the underestimation of the hiss-driven rates of electron pitch angle diffusion at smaller pitch angles and the overestimation of the rates at higher pitch angles. In addition, the cold plasma assumption can cause resonant diffusion down to lower electron energies; however, when the observed hiss wave dispersion curves are used, the resonant electron diffusion tends to extend to smaller pitch angles with a broader range. Notably, the differences in the scattering rates between the cold plasma and hot plasma dispersion relations increase with the hot plasma parameters. Therefore, our results are important for future simulations of the hiss wave-induced electron diffusion processes in the actual magnetospheric plasma environment and the dynamic variability of radiation belt electrons.
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图 1 Van Allen Probe A 在2014年1月4日17:30—21:30观测到的等离子体层嘶声事例. 由上到下分别为（a）背景等离子体密度；（b）AE和SYM-H指数；（c）观测电场功率谱强度；（d）观测磁场功率谱强度；（e）反演磁场功率谱强度；（f）波动传播角；（g）波动极化率；（h）波动平面度；（i）观测与反演的嘶声波幅值（修改自Ma et al., 2021）
Figure 1. Overview of plasmaspheric hiss event observed by Van Allen Probe A on January 4, 2014. (a) Ambient electron density inferred from upper hybrid frequency, fUHR. (b) Time series of AE index and SYM_H index. Observed power spectral intensities of the (c) electric field and (d) magnetic field. (e) Converted power spectral intensity of the magnetic field based on the cold plasma dispersion relation. (f) Wave normal angle. (g) Wave ellipticity. (h) Wave planarity. (i) Observed (red) and converted (blue) hiss wave amplitudes (modified from Ma et al., 2021)
图 2 （a-c）利用冷等离子体色散关系反演得到的嘶声波波动强度与卫星观测波动强度的对比. 横坐标表示观测波动强度，纵坐标表示反演得到的波动强度. 每个色块表示相应的观测波动强度对应的反演波动强度的归一化事件数. （d-f）观测嘶声波强度与反演波动强度之比（ratio）的对数的概率分布. 相应的方差绘制在每个面板上标注在子图左侧，上方色块表示数据出现在不同比值区间内的概率（修改自Ma et al., 2021）
Figure 2. (a-c) Comparisons of observed and converted wave intensities using cold plasma dispersion relation for plasmaspheric hiss with different levels of substorm activity. The color indicates the number of points in each bin, which is normalized to the maximum number of points in each observed wave power column (x-axis). (d-f) Probability distributions of the logarithm of the ratio between the observed and converted wave intensities. The corresponding variance is also plotted in each panel, along with the percentages of the data that occur in the discreet ratio (modified from Ma et al., 2021)
图 3 （a-c）不同地磁活动强度下观测嘶声波强度与反演嘶声波强度比值的方差在不同L-MLT区域内的全球分布. （d-f）不同地磁活动强度下观测嘶声波强度与反演嘶声波强度比值的方差随波动频率的变化（修改自Ma et al., 2021）
Figure 3. (a-c) Global distribution of variance in the distributions for the ratio of observed and converted wave intensities in the L-MLT domain, under different levels of substorm activity. (d-f) Variance as a function of the hiss wave frequency (modified from Ma et al., 2021)
图 4 不同地磁活动水平下，嘶声波观测强度与反演强度比值的均值和方差随L-MLT 的全球统计分布，（a-c）均值；（d-f）方差（修改自Zhu et al., 2022）
Figure 4. From left to right, global distribution of mean value and variance in the ratio of the observed hiss amplitude and converted amplitude as a function of L-shell and MLT, under different geomagnetic conditions: (a-c) mean value and (d-f) variance in the ratio (modified from Zhu et al., 2022)
图 5 （a-c）不同地磁活动条件下嘶声波事件的磁场强度与色散曲线. 色图对应每个波动事件的磁场强度，蓝色虚线表示冷等离子体近似假设下的色散曲线，红色实线为基于观测数据得到的色散曲线，黑色虚线是对观测数据频谱进行高斯拟合后的色散曲线. 不同地磁活动条件下嘶声波对高能电子的散射效应差异对比. （d-f）冷等离子体近似下嘶声波对高能电子的局地投掷角散射系数. （g-i）基于观测数据色散关系拟合的嘶声波对辐射带电子的局地投掷角散射系数. 图（j-l）为两种色散关系下指定电子能级的局地投掷角散射系数对比（修改自Ma et al., 2021）
Figure 5. (a-c) Observed hiss magnetic field spectral intensities at L = 4 as a function of the wave frequency and data-based wavenumber, under different substorm conditions. The dashed blue line corresponds to the cold plasma dispersion curve, and the solid red line corresponds to the averaged data-based dispersion curve. The averaged data-based dispersion curve was further linearly fitted, as indicated by the dashed black line. Electron local pitch angle diffusion coefficients as a function of the electron pitch angle kinetic energy corresponding to (d-f) cold plasma and (g-i) linearly fitted data-based dispersion relations. (j-l) Line plots of electron local pitch angle diffusion coefficients corresponding to the cold plasma (dashed lines) and linear fitted data-based (solid lines) dispersion relations for four indicated electron energies (modified from Ma et al., 2021)
图 6 不同热等离子体参数情况下，等离子体层嘶声波的色散曲线. （a-c）分别对应色散曲线随热电子温度各向异性、热电子温度和热电子占比的变化. 实线对应不同热等离子体参数下色散曲线，虚线对应冷等离子体假设下的色散曲线
Figure 6. Dispersion curves of plasmaspheric hiss under different thermal plasma parameters. (a-c) Variation in dispersion curve with temperature anisotropy, hot electron temperature, and hot electron abundance, respectively. The solid and dotted lines correspond to the dispersion curves under the hot plasma and cold plasma assumptions, respectively
图 7 等离子体层嘶声波对电子的弹跳平均投掷角散射系数随电子能级和赤道投掷角的变化. （a-c）冷等离子体条件下的投掷角散射系数；（d-f）不同热电子温度各向异性下的投掷角散射系数；（g-h）不同热电子温度下的投掷角散射系数；（j-l）不同热电子占比下的投掷角散射系数
Figure 7. 2-D plots of bounce-averaged pitch angle diffusion rates as a function of the electron energy and equatorial pitch angle. From top to bottom, we show the results corresponding to (a-c) cold plasma approximation, (d-f) hot plasma approach for different temperature anisotropic behaviors, (g-h) different hot electron temperatures, and (j-l) different hot electron abundances
图 8 等离子体层嘶声波对四种不同能量的电子的弹跳平均投掷角散射系数. （a-c）不同热电子温度各向异性下的投掷角散射系数；（d-f）不同热电子温度下的投掷角散射系数；（g-i）不同热电子占比下的投掷角散射系数. 虚线表示冷等离子体假设下的投掷角散射系数，实线表示热等离子体条件下的投掷角散射系数
Figure 8. Bounce-averaged pitch angle scattering rates of electrons at four different energies induced by plasmaspheric hiss under different thermal plasma parameters: (a-c) different sets of hot electron temperature anisotropic behaviors, (d-f) different hot electron temperatures, and (g-h) different hot electron abundances. The solid and dotted lines correspond to the pitch angle scattering rates under the hot plasma and cold plasma assumptions, respectively
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