The Importance of the Ubiquitous 'Kappa' Distributions in Space Plasmas (Invited)

The kappa model for f(v) was originally derived by Olbert (1966) to provide frugal but informative fits to observed particle fluxes from which moments of the underlying plasma could be extracted. Olbert's new fit parameter (kappa) allowed for the ambient plasma to possess reduced kurtosis, which a Gaussian does not. The universality of kappa can easily be overstated, since it cannot fit distributions with a heat flux which is generally important in astrophysical plasmas. Geophysically the frequent use of such a parametrization for the zeroth order energy distribution in the comoving frame acknowledges that the observed plasmas of nature are generally non-thermal, hence kurtotic, which for this author is their principal significance. A key question remains whether the analytically convenient kappa function's kurtotic form is required by the laws of physics, or rather a deft representative of all possible distributions with non-negligible kurtosis and other higher moments. This paper develops why the non-thermal kurtotic f(v) should generally be expected in astrophysical plasmas structured by gravity, driven by their tendency to achieve quasi-neutrality. It will demonstrate the essential role of runaway phenomena in the origin of this kurtosis while showing consistency with observables. This approach provides a rationale why such kurtotic distributions should occur without arguing what its precise shape should be, beyond possessing non-zero skewness and kurtosis. Initial results will be shown that the kappa model for such kurtotic distributions, while better than an Gaussian, may be too rigid to describe the non-thermal distributions of nature at all radial distances from the sun.