The κ-cookbook: a novel generalizing approach to unify κ-like distributions for plasma particle modelling

• Published in: Monthly notices of the Royal Astronomical Society 2020-09, Vol.497 (2), p.1738-1756
• Main Authors: Scherer, K, Husidic, E, Lazar, M, Fichtner, H
• Format: Article
• Language: English
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/staa1969

ABSTRACT In the literature different so-called κ-distribution functions are discussed to fit and model the velocity (or energy) distributions of solar wind species, pickup ions, or magnetospheric particles. Here, we introduce a generalized (isotropic) κ-distribution as a ‘cookbook’, which admits as special cases, or ‘recipes’, all the other known versions of κ-models. A detailed analysis of the generalized distribution function is performed, providing general analytical expressions for the velocity moments, Debye length, and entropy, and pointing out a series of general requirements that plasma distribution functions should satisfy. From a contrasting analysis of the recipes found in the literature, we show that all of them lead to almost the same macroscopic parameters with a small standard deviation between them. However, one of these recipes called the regularized κ-distribution provides a functional alternative for macroscopic parametrization without any constraint for the power-law exponent κ.