Nonequilibrium stationary states in the earthʹs magnetotail: Stochastic acceleration processes and nonthermal distribution functions Original Research Article

A self-consistent kinetic description of turbulent plasma and fields at the nonequilibrium stationary states (NESSʹs) of the Earthʹs magnetotail is proposed. We argue that the inherent dynamics of the NESSʹs is manifested in the low-frequency power law fluctuation spectrum ∼ ƒ−1 (i.e., the flicker noise). At the higher frequebcies, the fluctuation spectrum has a steeper shape ∼ ƒ−73 and is related to the structural characteristics of the magnetotail turbulence. The basic dynamical processes operating at the NESS are described by a nonlinear fractional kinetic equation which includes the following principal effects: (1) stochastic particle acceleration in the turbulent magnetic field varying with time, and (2) self-interaction of the medium associated with the reproduction of the turbulent field by the energetic particles accelerated therein. We find that the particle energy distribution in presence of the self-interaction events reveals a high-energy nonthermal tail ƒ(ε) ∝ ε−η. The slope of the distribution, η, obeys the condition 6 ≤ η < 7; this reflects the fundamental dynamical properties underlying magnetic field and plasma coupling in self-organized electromagnetic systems. The results obtained are in close agreement with spacecraft observational data on the Earthʹs magnetotail.