Kappa distributions in the framework of superstatistics

TL;DR

This paper reviews how superstatistics can derive and analyze kappa velocity distributions in collisionless plasmas, offering an alternative to non-extensive statistics and exploring implications for plasma properties.

Contribution

It presents a comprehensive derivation of kappa distributions using superstatistics and discusses their physical implications, providing a new perspective beyond Tsallis' framework.

Findings

Superstatistics effectively derives kappa distributions for collisionless plasmas.

The framework aids in computing expectation values for kappa-distributed particles.

Implications for plasma correlations, temperature, and entropy are discussed.

Abstract

The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified through the use of Tsallis' non-extensive statistics, nowadays there are alternative frameworks that provide insight into these distributions, such as superstatistics. In this work we review the derivation of the multi-particle and single-particle kappa distributions for collisionless plasmas within the framework of superstatistics, as an alternative to the use of non-extensive statistics. We also show the utility of the superstatistical framework in the computation of expectation values under kappa distributions. Some consequences of the superstatistical formalism regarding correlations, temperature and entropy of kappa-distributed plasmas are also discussed.