Dependencies of Kappa Parameter on the Core Energy of Kappa Distributions and Plasma Parameter in the Case of the Magnetosphere of the Earth

Abstract

Abstract Formation of kappa distribution functions and their relaxation to Maxwellian distributions are the main feature of astrophysical and space collisionless plasmas. In this work, we use the magnetosphere of the Earth as a giant plasma laboratory to study the properties of ion kappa distribution functions. Four years of measurements, performed by the multi-satellite Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission during quiet geomagnetic conditions, at geocentric distances from three Earth radii (R E) to the magnetopause at daytime (of the order of 10R E), and up to 20R E at night time are used for the analyses. We find a dependence of the k parameter on the core energy E 0 of a single kappa distribution inside the magnetospheric ring current and in the plasma sheet, for different values of the plasma parameter (the ratio between the plasma and magnetic pressures). We show that k increases with E 0 for all values of plasma parameter, which supports earlier results obtained for the magnetospheres of the Earth, Jupiter, and Saturn, but using lower statistics. However, contrary to previous results, our studies show that the relation between k and E 0 is nonlinear, and most probably is a power law with a nearly constant index. The results obtained are relevant to solve the problem of thermalization of kappa distributions.