"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 or =eta< or =7 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.