Abstract
le Roux and Zank [25] showed previously how one can derive from first principles a pitch-angle dependent fractional diffusion-advection kinetic equation to model the anomalous diffusion of energetic particles interacting with small-scale magnetic flux ropes (SMFRs) in the inner heliosphere on the basis of the standard focused transport equation. This equation has the following limitations: (1) The asymptotic power law of a Lévy distribution was specified to model the non-Gaussian statistics of the disturbed energetic particle trajectories generated during energetic particle interaction with numerous SMFRs. The second moment (variance) and higher moments of the Lévy distribution are infinite, indicating over-efficient non-local transport that is scale-free. (2) The theory does not naturally allow for a transition of anomalous transport to normal diffusion, or to a different anomalous diffusion state. An outline of a derivation is presented in which an exponentially truncated Lévy distribution was specified instead, resulting in a tempered fractional diffusion-advection kinetic equation that addresses these two concerns.
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