Statistical Uncertainties of Space Plasma Properties Described by Kappa Distributions

Abstract

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.

Resolving Space Plasma Species With Electrostatic Analyzers

“…We demonstrate the use of an appropriate forward model simulating the expected response of an electrostatic analyzer in the presence of plasma of heavy, negative ions. The development of forward models is not only useful in dataanalyses (e.g., Nicolaou et al, 2014b;Nicolaou et al, 2021;Wilson et al, 2008;Wilson et al, 2017, Elliott et al, 2016, but also in testing the performance of the instrument in a range of expected conditions (Kessel et al, 1989;Cara et al, 2017;Nicolaou et al, 2014c;Nicolaou et al, 2014b;Nicolaou et al, 2020a;Nicolaou et al, 2020b;Nicolaou and Livadiotis, 2016). In this study we focus on the ability to resolve key species for plasma science in the vicinity of Enceladus and Titan.…”

Radial evolution of thermal and suprathermal electron populations in the slow solar wind from 0.13 to 0.5 au : Parker Solar Probe Observations

“…The fitting technique is widely used in solar and space plasma physics in order to derive plasma bulk parameters from observations (Halekas et al 2020;Berčič et al 2020;Nicolaou et al 2020;Stansby et al 2018;Štverák et al 2009;Maksimovic et al 2005).To capture the properties of the electrons, we analytically describe the anticipated distribution function and then fit to the measured data. Once fitted, we obtain parameters such as density, temperature, and bulk speed of each modelled population.…”

Deriving the bulk properties of solar wind electrons observed by Solar Orbiter

“…The development of such models is not just extremely useful for the analysis of the observations, but also for the quantification of the errors in the derived parameters that define the confidence level of the scientific results (Nicolaou & Livadiotis 2020;Criton et al 2020). The basic principle is to simulate the observations of a specific instrument in given plasma conditions.…”