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Statistical properties of small-amplitude Langmuir waves in the Earth's electron foreshock

机译：地球电子前震中小振幅朗缪尔波的统计特性

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摘要

We present the results of a statistical study of Langmuir waves observed by the Cluster spacecraft in the Earth's electron foreshock. To classify the probability density distributions of the logarithms of the wave energies, a Pearson technique is used. We show that experimental distributions can be better approximated, in a statistical sense, by Beta distribution or Pearson Type IV distribution rather than by a normal distribution predicted by the stochastic growth theory. This conclusion agrees with the results of numerical simulations that were previously performed with the use of a model for Langmuir wave propagation in unstable plasma with random inhomogeneities. The main reason for deviations of empirical distributions from a normal distribution is probably related to the effective number of regions, where the waves grow, which is not sufficiently large for the central limit theorem to be applicable under typical conditions in the Earth's electron foreshock. For two of seven events such deviations may be partially attributed to the effects of thermal Langmuir waves.
机译：我们介绍了由簇状航天器在地球电子前震中观测到的Langmuir波的统计研究结果。为了对波能量的对数的概率密度分布进行分类，使用了Pearson技术。我们显示，在统计意义上，通过Beta分布或Pearson Type IV分布可以更好地近似实验分布，而不是通过随机增长理论预测的正态分布更好。这一结论与先前使用朗格缪尔波模型在具有随机非均匀性的不稳定等离子体中传播的模型进行的数值模拟结果相吻合。经验分布偏离正态分布的主要原因可能与波的生长区域的有效数量有关，该区域的有效数量不足以使中心极限定理在地球电子前震的典型条件下适用。对于七个事件中的两个，这种偏差可能部分归因于热朗缪尔波的影响。

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