Av. Milovanov et Lm. Zelenyi, "Strange" Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation - art. no. 052101, PHYS REV E, 6405(5), 2001, pp. 2101
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.