# Moments of the anisotropic regularized $\kappa$-distributions

## TL;DR

This paper extends the regularization of $ppa$-distributions to anisotropic plasma models, enabling well-defined moments for all positive $ppa$, which facilitates macroscopic plasma analysis.

## Contribution

It introduces a regularization method for anisotropic $ppa$-distributions, ensuring finite moments and improving the macroscopic description of non-ideal plasmas.

## Key findings

- Regularized anisotropic $ppa$-distributions have finite moments for all positive $ppa$.
- The approach allows for a fluid-like macroscopic characterization of collisionless plasmas.
- The method applies to temperature anisotropies and beam-plasma systems.

## Abstract

For collisionless (or collision-poor) plasma populations which are well described by the $\kappa$-distribution functions (also known as the Kappa or Lorentzian power-laws) a macroscopic interpretation has remained largely questionable, especially because of the diverging moments of these distributions. Recently significant progress has been made by introducing a generic regularization for the isotropic $\kappa$-distribution, which resolves this critical limitation. Regularization is here applied to the anisotropic forms of $\kappa$-distributions, commonly used to describe temperature anisotropies, and skewed or drifting distributions of beam-plasma systems. These regularized distributions admit non-diverging moments which are provided for all positive $\kappa$, opening promising perspectives for a macroscopic (fluid-like) characterization of non-ideal plasmas.