Regularized $\kappa$-distributions with non-diverging moments

TL;DR

This paper introduces a regularized $ppa$-distribution that ensures all velocity moments are finite, enabling comprehensive macroscopic descriptions of plasmas with suprathermal particles.

Contribution

The authors propose a new regularized $ppa$-distribution that overcomes divergence issues of moments in standard $ppa$-distributions, facilitating better plasma modeling.

Findings

Derived a general analytical expression for all velocity moments.

Enabled a macroscopic description of plasmas with $ppa$-distributions.

Addressed limitations of the standard $ppa$-distribution regarding moment divergence.

Abstract

For various plasma applications the so-called (non-relativistic) $\kappa$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its reputation the standard $\kappa$-distribution as a concept is still disputable, mainly due to the velocity moments $M_{l}$ which make possible a macroscopic characterization, but whose existence is restricted only to low orders $l < 2\kappa-1$. In fact, the definition of the $\kappa$-distribution itself is conditioned by the existence of the moment of order $l=2$ (i.e., kinetic temperature) satisfied only for $\kappa > 3/2$. In order to resolve these critical limitations we introduce the regularized $\kappa$-distribution with non-diverging moments. For the evaluation of all velocity moments a general analytical expression is provided enabling a significant step towards a macroscopic (fluid-like) description of space plasmas, and, in general, any system of $\kappa$-distributed particles.