The plasma particle velocity distributions observed in the solar wind generally show enhanced (non-Maxwellian) suprathermal tails, decreasing as a power law of the velocity and well described by the family of Kappa distribution functions. The presence of non-thermal populations at different altitudes in space plasmas suggests a universal mechanism for their creation and important consequences concerning plasma fluctuations, the resonant and nonresonant wave -particle acceleration and plasma heating. These effects are well described by the kinetic approaches where no closure requires the distributions to be nearly Maxwellian. This paper summarizes and analyzes the various theories proposed for the Kappa distributions and their valuable applications in coronal and space plasmas.

Estimating the temperature of the solar wind particles and their anisotropies is particularly important for understanding the origin of these deviations from thermal equilibrium as well as their effects. In the absence of energetic events the velocity distribution of electrons reveal a dual structure with a thermal (Maxwellian) core and a suprathermal (Kappa) halo. This paper presents a detailed observational analysis of these two components, providing estimations of their temperatures and temperature anisotropies and decoding any potential interdependence that their properties may indicate. The data set used in this study includes more than 120 000 the events detected by three missions in the ecliptic within an extended range of heliocentric distances from 0.3 to over 4 AU. The anti-correlation found for the core and halo temperatures is consistent with the radial evolution of the Kappa model, clarifying an apparent contradiction in previous observational analysis and providing valuable clues about the temperature of the Kappa-distributed populations. However, these two components manifest a clear tendency to deviate from isotropy in the same direction, that seems to confirm the existence of mechanisms with similar effects on both components, e.g., the solar wind expansion, or the particle heating by the fluctuations. On the other hand, the existence of plasma states with anti-correlated anisotropies of the core and halo populations suggests a dynamic interplay of these components, mediated, most probably, by the anisotropy-driven instabilities.

Context. Suprathermal populations are ubiquitous in the solar wind, indicating plasma states out of thermal equilibrium, and an excess of free energy expected to enhance the kinetic instabilities. However, recent endeavors to disclose the effects of these populations on the electromagnetic instabilities driven by the temperature anisotropy do not confirm this expectation, but mainly show that these instabilities are inhibited by the suprathermals. Aims. In an attempt to clarify the effect of the suprathermals, we propose to revisit the existing models for the anisotropic velocity distributions of plasma particles and to provide an alternative comparative analysis that unveils the destabilizing effects of the suprathermal populations. Methods. Suprathermal tails of the observed distributions are best fitted by the Kappa power laws (with the bi-Kappa variant to model temperature anisotropies), which are nearly Maxwellian at low speeds (thermal core) and decrease as a power law at high speeds (suprathermal halo). To unveil the destabilizing effects of the suprathermal populations, the existing methods (A) compare Kappa and Maxwellian distributions of the same effective temperature, while the alternative comparative method (B) proposed in this paper allows for an increase of the effective temperature with increasing the suprathermal populations. Both of these two methods are invoked here to quantify and compare the effects of suprathermal electrons on the electromagnetic electron-cyclotron (EMEC) instability, driven by the temperature anisotropy T e,⊥ > T e, of the electrons (where , ⊥ are directions with respect to the magnetic field). Results. Only the Maxwellian limit of lower effective temperature shapes the Kappa model at low energies (method B), enabling a realistic comparison between the Maxwellian core and the global best-fitting Kappa, which incorporates both the core and suprathermal tails. In this case, the EMEC instability is found to be markedly and systematically enhanced by the suprathermal populations for any level of the temperature anisotropy. The results of the present study may provide valuable premises for a realistic description of the suprathermal populations and their destabilizing effects for the whole spectrum of kinetic instabilities in the solar wind.

Context. The generally accepted representation of κ-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be κ-independent. Aims. The present paper aims to clarify the issue concerning which of the two possible choices and the related physical interpretation is correct. Methods. A quantitative comparison of the consequences of the use of both distributions for specific physical systems leads to their correct interpretation. Results. It is found that both alternatives can be realized, but they are valid for principally different physical systems. Conclusions. The investigation demonstrates that, before employing one of the two alternatives, one should be conscious about the nature of the physical system one intends to describe, otherwise one would possibly obtain unphysical results.

New arguments are given here in favor of Weibel-type instabilities as one of the most plausible sources of the cosmological magnetic field. The Weibel instability has recently been proposed as one of the secondary mechanisms of relaxation for the large interpenetrating formations of galactic and intergalactic plasma. Here, these investigations are extended to counterstreaming plasmas which have, in addition, intrinsic temperature anisotropies, and where any form of the Weibel-type instability can be excited. This can be a simple filamentation instability due to the relative motion of counterstreaming plasmas, or a Weibel-like instability when it is generated by an excess of transverse temperature with respect to the streaming direction. But it can also be a cumulative filamentation/Weibel instability when the plasma is hotter along the streaming direction. Such plasma systems are relevant for the relative motions of filaments and sheets of galaxies, and are expected to exist at large scales and any age of our Universe. For such counterstreaming plasmas with internal temperature anisotropies, any Weibel-type instability mentioned before can become the primary wave relaxation mechanism of the plasma anisotropy, because it develops easily faster than the principal competitor, which is the two-stream electrostatic instability. The estimations made here for typical parameters of intergalactic plasmas, provide micro-Gauss levels of the magnetic field of Weibel type, which are consistent with magnetic field values, 10 −7 -10 −5 G, derived from Faraday rotation measure of the linearly polarized emission of galactic or extragalactic sources.

In the solar wind electron velocity distributions reveal two counter-moving populations which may induce electromagnetic (EM) beaming instabilities known as heat flux instabilities. Depending on plasma parameters two distinct branches of whistler and firehose instabilities can be excited. These instabilities are invoked in many scenarios, but their interplay is still poorly understood. An exact numerical analysis is performed to resolve the linear Vlasov-Maxwell dispersion and characterize these two instabilities, e.g., growth rates, wave frequencies and thresholds, enabling to identify their dominance for conditions typically experienced in space plasmas. Of particular interest are the effects of suprathermal Kappa-distributed electrons which are ubiquitous in these environments. The dominance of whistler or firehose instability is highly conditioned by the beam-core relative velocity, core plasma beta and the abundance of suprathermal electrons. Derived in terms of relative drift velocity the instability thresholds show an inverse correlation with the core plasma beta for the whistler modes, and a direct correlation with the core plasma beta for the firehose instability. Suprathermal electrons reduce the effective (beaming) anisotropy inhibiting the firehose modes while the whistler instability is stimulated.

Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index κ. Each of them can obtain justification in different scenarios involving Kappa-distributed plasmas, but direct evidences supporting any of these two alternatives with measurements from laboratory or natural plasmas are not available yet. Aims. This paper aims to provide more facts on this intriguing issue from direct fitting measurements of suprathermal electron populations present in the solar wind, as well as from their destabilizing effects predicted by these two alternating approaches. Methods. Two fitting models are contrasted, namely, the global Kappa and the dual Maxwellian-Kappa models, which are currently invoked in theory and observations. The destabilizing effects of suprathermal electrons are characterized on the basis of a kinetic approach which accounts for the microscopic details of the velocity distribution. Results. In order to be relevant, the model is chosen to accurately reproduce the observed distributions and this is achieved by a dual Maxwellian-Kappa distribution function. A statistical survey indicates a κ-dependent temperature of the suprathermal (halo) electrons for any heliocentric distance. Only for this approach the instabilities driven by the temperature anisotropy are found to be systematically stimulated by the abundance of suprathermal populations, i.e., lowering the values of κ-index.

For various plasma applications the so-called (nonrelativistic) κ-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 κ-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 < 2κ − 1. In fact, the definition of the κ-distribution itself is conditioned by the existence of the moment of order l = 2 (i.e., kinetic temperature) satisfied only for κ > 3/2. In order to resolve these critical limitations we introduce the regularized κ-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 κ-distributed particles.