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.

Since observed velocity distributions of particles in the magnetosphere generally have a suprathermal tail instead of an exponential one, we propose to recalculate the density and temperature distributions in a nonrotating ion exosphere with a Lorentzian velocity distribution function (VDF) instead of a Maxwellian. The number density, the flux of particles, parallel and perpendicular pressures, and energy flux of the different classes of particles in the exosphere have been determined for any value of the index κ characterizing the Lorentzian VDF. The barometric density and temperature distributions for a Maxwellian VDF and for a Lorentzian VDF are compared. It is shown that for particles in an attractive potential, the barometric density decreases more slowly with altitude for the Lorentzian VDF. Furthermore, the temperature increases with altitude in this case, while for a Maxwellian VDF, it is independent of altitude. It is suggested that positive gradients of the ion and electron temperatures observed between the topside ionosphere and the outer plasmasphere can be explained by this effect, that is, a non‐Maxwellian VDF with an enhanced suprathermal tail.

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