"Strange" Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation - art. no. 052101

This study advocates the application of fractional dynamics to the descript ion of anomalous acceleration processes in self-organized turbulent systems . Such processes (termed "strange" accelerations) involve both the non-Mark ovian fractal. time acceleration events associated with a generalized stoch astic Fermi mechanism, and the velocity-space Levy flights identified with nonlocal violent accelerations in turbulent media far from the (quasi)equil ibrium. The "strange" acceleration processes are quantified by a fractional extension of the velocity-space transport equation with fractional time an d phase space derivatives. A self-consistent nonlinear fractional kinetic e quation is proposed for the stochastic fractal time accelerations near the turbulent nonequilibrium saturation state. The ensuing self-consistent ener gy distribution reveals a power-law superthermal tail psi(epsilon) proporti onal to epsilon (-eta) with slope 6 less than or equal to eta less than or equal to7 depending on the type of acceleration process (persistent or anti persistent). The results obtained are in close agreement with observational data on the Earth's magnetotail.