The Earth’s magnetosphere represents a natural plasma laboratory that allows us to study the behavior of particle distribution functions in the absence of Coulomb collisions, typically described by the kappa distributions. We have investigated the properties of these functions for ions and electrons in different magnetospheric regions, thereby making it possible to reveal the κ-parameters for a wide range of plasma beta (β) values (from 10⁻³ to 10²). This was done using simultaneous ion and electron measurements from the five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft spanning the years 2008–2018. It was found that for a fixed plasma β, the κ-index and core energy (E _c ) of the distribution can be modeled by the power law for both species, and the relation between β, κ, and E _c is much more complex than earlier reported: both A and γ exhibit systematic dependencies with β. Our results indicate that β ∼ 0.1–0.3 is a range where the plasma is more dynamic, since it is influenced by both the magnetic field and temperature fluctuations, which suggests that the transition between magnetically and kinetically dominated plasmas occurs at these values of β. For β > 1, both A and γ take nearly constant values, a feature that is especially notable for the electrons and might be related to their demagnetization. The relation between β, κ, and E _c that we present is an important result that can be used by theoretical models in the future.

地球磁层代表了一个天然的等离子体实验室，它使我们能够研究在没有库仑碰撞的情况下粒子分布函数的行为，通常由 kappa 分布描述。我们已经研究了不同磁层区域中离子和电子的这些函数的特性，从而可以揭示大范围等离子体β ( β ) 值（从10 ^-3到10 ²）的κ参数。这是使用来自 2008 年至 2018 年亚暴 (THEMIS) 航天器期间事件和宏观相互作用的五个时间历史的同步离子和电子测量值完成的。发现对于固定的等离子体β，κ分布的指数和核心能量 ( E _c ) 可以通过两种物质的幂律建模，β、κ和E _c之间的关系比之前报道的要复杂得多：A和γ 都表现出系统依赖性β。我们的结果表明β ∼ 0.1-0.3 是等离子体更具动态性的范围，因为它受磁场和温度波动的影响，这表明磁性和动力学主导等离子体之间的转变发生在这些β值处。对于β > 1，A 和γ取几乎恒定的值，这一特征对于电子尤其显着，可能与它们的退磁有关。我们提出的β、κ和E _c之间的关系是一个重要的结果，可以在未来的理论模型中使用。