基于卡方分布函数的辐射带电子蝴蝶状投掷角分布的优化判别方法

受不同物理过程影响，辐射带电子呈现多种投掷角分布类型，其中蝴蝶状分布尤为引人关注，其特征为通量在90°投掷角附近有极小值、在较低投掷角处达到峰值.现有研究普遍通过对几个特定投掷角间的通量比值进行限定来识别蝴蝶状分布，然而，该方法所挑选的电子分布并不一定符合蝴蝶状分布特征，这为准确研究电子蝴蝶状分布的现象学规律及其背后物理机制带来了一定困难.针对该问题，本文建立了一个基于卡方分布函数的判别模型，通过比较电子观测通量剖面与模型模拟的理想蝴蝶状分布剖面的相似性来判别电子蝴蝶状分布.使用范艾伦卫星上REPT仪器提供的L-shell > 3空间区域内两组不同投掷角分辨率的电子通量数据对该判别方法进行验证，结果表明该方法能明显提升判别效果，分别使基于17个投掷角和36个投掷角的电子通量数据判别蝴蝶状分布的误判率下降12.6%和27.5%.本文的分析结果证实了提高投掷角精度有利于准确确定辐射带电子的投掷角分布类型，发展的模型方法也对深入开展地球与行星磁层中电子蝴蝶状分布的统计学研究具有重要价值.

An optimized identification method for radiation belt electron butterfly pitch angle distributions based on the chi-square distribution function

Due to different physical mechanisms,radiation belt electrons exhibit types of pitch angle distribution.Recently,the characterful butterfly pitch angle distribution has received extensive attentions with the flux minimum around 90°pitch angles and the flux peak at lower pitch angles.To identify the butterfly pitch angle distributions,previous studies usually set the threshold for the electron flux ratio between several specific pitch angles.However,such criterion will bring some uncertainties to distinguish butterfly-distribution profile.Therefore,it was difficult to accurately investigate the phenomenological law and physical mechanisms of the butterfly distribution.In this study,we develop an identification method based on the chi-square distribution function to identify butterfly distribution,by comparing the similarity between the observed flux profile and the ideal butterfly distribution profiles simulated by the model.Using two sets of electron flux data with different pitch-angle resolutions measured by Van Allen Probes REPT instrument at L-shell>3,we find that our method can significantly improve the identification on butterfly distributions.By using two flux datasets with 17 pitch angles and 36 pitch angles,our method can reduce the false identification rates by 12.6%and 27.5%,respectively.Our results demonstrate that increasing the pitch-angle resolutions is effective to accurately identify the radiation belt electron distributions.Moreover,the developed method is of great importance for further statistical research on electron butterfly distribution in the Earth and planetary magnetospheres.