For collisionless (or collision-poor) plasma populations which are well described by the κ-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 κ-distribution, which resolves this critical limitation. Regularization is here applied to the anisotropic forms of κ-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 κ, opening promising perspectives for a macroscopic (fluid-like) characterization of non-ideal plasmas.

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 parameterization without any constraint for the power-law exponent κ.

Observations in space plasmas reveal particle velocity distributions out of thermal equilibrium, with anisotropies (e.g., parallel drifts or/and different temperatures, T∥ - parallel and T⊥ - perpendicular, with respect to the background magnetic field), and multiple quasithermal and suprathermal populations with different properties. The recently introduced (isotropic) κ-cookbook is generalized in the present paper to cover all these cases of anisotropic and multi-component distributions reported by the observations. We derive general analytical expressions for the velocity moments and show that the common (bi-)Maxwellian and (bi-)κ −distributions are obtained as limiting cases of the generalized anisotropic κ-cookbook (or recipes). Based on this generalization, a new 2D fitting procedure is introduced, with an improved level of confidence compared to the 1D fitting methods widely used to quantify the main properties of the observed distributions. The nonlinear least-squares fit is applied to electron data sets measured by the Ulysses spacecraft confirming the existence of three different populations, a quasithermal core and two suprathermal (halo and strahl) components. In general, the best overall fit is given by the sum of a Maxwellian and two generalized κ-distributions.

The velocity particle distributions measured in-situ in space plasmas deviate from Maxwellian (thermal) equilibrium, showing enhanced suprathermal tails which are well described by the standard Kappa-distribution (SKD). Despite its successful application, the SKD is frequently disputed due to a series of unphysical implications like diverging velocity moments, preventing a macroscopic description of the plasma. The regularized Kappa-distribution (RKD) has been introduced to overcome these limitations, but the dispersion properties of RKD-plasmas are not explored yet.In the present paper we compute the wavenumber dispersion of the frequency and damping or growth rates for the electromagnetic modes in plasmas characterized by the RKD. This task is accomplished by using the grid-based kinetic dispersion solver LEOPARD developed for arbitrary gyrotropic distributions [Ref. 1]. By reproducing previous results obtained for the SKD and Maxwellian, we validate the functionality of the code. Furthermore, we apply the isotropic as well as the anisotropic RKDs to investigate stable electromagnetic electron-cyclotron (EMEC) and ion-cyclotron (EMIC) modes as well as temperature-anisotropy-driven instabilities, both for the case T ⊥ /T > 1 (EMEC and EMIC instabilities) and for the case T ⊥ /T < 1 (proton and electron firehose instabilities), where and ⊥ denote directions parallel and perpendicular to the local time-averaged magnetic field. Provided that the cutoff parameter α is small enough, the results show that the RKDs reproduce the dispersion curves of the SKD plasmas at both qualitative and quantitative levels. For higher values, however, physically significant deviation occurs.

Context. In heliospheric plasmas, such as the solar wind and planetary magnetospheres, the transport of energy and particles is governed by various fluxes (e.g., heat flux, particle flux, current flow) triggered by different forces, electromagnetic fields, and gradients in density or temperature. In the outer corona and at relatively low heliocentric distances in the solar wind (i.e., < 1 AU), particle-particle collisions play an important role in the transport of energy, momentum, and matter, described within classical transport theory by the transport coefficients, which relate the fluxes to their sources. Aims. The aim of the present paper is to improve the evaluation of the main transport coefficients in such nonequilibrium plasmas, on the basis of an implicit realistic characterization of their particle velocity distributions, in accord with the in situ observations. Of particular interest is the presence of suprathermal populations and their influence on these transport coefficients. Methods. Using the Boltzmann transport equation and macroscopic laws for the energy and particle fluxes, we derived transport coefficients, namely, electric conductivity, thermoelectric coefficient, thermal conductivity, diffusion, and mobility coefficients. These are conditioned by the electrons, which are empirically well described by the Kappa distribution, with a nearly Maxwellian (quasi-thermal) core and power-law tails enhanced by the suprathermal population. Here we have adopted the original Kappa approach that has the ability to outline and quantify the contribution of suprathermal populations. Results. Without exception, the transport coefficients are found to be systematically and markedly enhanced in the presence of suprathermal electrons (i.e., for finite values of the κ parameter), due to the additional kinetic energy with which these populations contribute to the dynamics of space plasma systems. The present results also show how important an adequate Kappa modeling of suprathermal populations is, which is in contrast to other modified interpretations that underestimate the effects of these populations.