Strange Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation

This study advocates the application of fractional dynamics to the description of anomalous acceleration processes in self-organized turbulent systems. Such processes (termed "strange" accelerations) involve both the non-Markovian fractal. time acceleration events associated with a generalized stochastic Fermi mechanism, and the velocity-space Levy flights identified with nonlocal violent accelerations in turbulent media far from the (quasi)equilibrium. The "strange" acceleration processes are quantified by a fractional extension of the velocity-space transport equation with fractional time and phase space derivatives. A self-consistent nonlinear fractional kinetic equation is proposed for the stochastic fractal time accelerations near the turbulent nonequilibrium saturation state. The ensuing self-consistent energy distribution reveals a power-law superthermal tail psi(epsilon) proportional 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 antipersistent). The results obtained are in close agreement with observational data on the Earth's magnetotail.