  From Liouville's equation, a phase-space multi-scale transport equation is
systematically derived. The proposed phase-space multi-scale transport equation
based on the first principle indicates that the nonlinear stochastic transport
is due to the micro-turbulence scattering while the familiar quasilinear
transport is due to the long-range correlation of the meso-scale coherent
modes; and more interestingly, it demonstrates a systematic derivation of the
fractional transport equation that may provide a new view-angle to understand
the anomalous transport observed in plasma turbulence. The multi-scale kinetics
suggests a new approach to confinement improvement through the formation of
nonlinearly self-organized stable large-scale structures.
