The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.

中文翻译：

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Kappa 分布描述的空间等离子体特性的统计不确定性


空间等离子体粒子的速度通常遵循卡伯分布函数，其具有特征性的高能尾部。这些分布的尾部与低粒子通量相关，因此，在等离子体测量中精确解析它们具有挑战性。另一方面，准确确定广泛能量范围内的卡伯分布函数对于理解物理机制至关重要。血浆观察的标准分析根据下划线分布的统计矩确定血浆体参数。然而，量化得出的等离子体整体参数的不确定性也很重要，这决定了科学结论的置信度。我们研究了通过理想静电分析仪的观察来确定等离子体本体参数。我们推导出简单的公式来估计计算的体积参数的统计不确定性。然后，我们使用正演建模方法来模拟典型顶帽静电分析仪的等离子体观测结果。我们分析模拟观测结果，以获得等离子体本体参数及其不确定性。我们的模拟验证了我们的简化公式。我们进一步检查了等离子体速度分布函数的几种形状的等离子体体参数的统计误差。