Relativistic regularized kappa distributions

TL;DR

This paper derives a relativistic version of regularized kappa distributions, compares it to the standard form, and analyzes their properties, including the limits of the kappa parameter and the pressure moments, enhancing understanding of relativistic plasma models.

Contribution

It introduces a relativistic generalization of isotropic regularized kappa distributions and compares their properties to the standard kappa distributions, expanding the theoretical framework for relativistic plasma physics.

Findings

Relativistic regularized kappa distributions allow all positive kappa values.

Standard kappa distributions have more limited kappa parameter ranges.

Pressure calculations reveal differences between relativistic and non-relativistic distributions.

Abstract

The special relativistic generalization of isotropic regularized kappa distributions is derived and compared to that of the original Olbertian (or standard) kappa distributions. It is demonstrated that for the latter the kappa parameter is even stronger limited than in the non-relativistic case, while for the former all positive kappa values remain possible. After a derivation of the non-relativistic limits, the pressures of the distributions are studied as a specific case of the moments of both the relativistic standard and regularized kappa distributions.