Authors: Jakobus A. le Roux (University of Alabama in Hunstville), Rubaiya K. Shikha (University of Alabama in Huntsville)

Solar wind magnetic turbulence, being intermittent, can statistically be better modeled with an exponentially truncated Lévy distribution, e.g., than with a Gaussian or a standard Lévy distribution (Bruno et al. 2004). Solar wind turbulence is thought to be intermittent because of coherent magnetic structures, such as small-scale magnetic flux ropes (SMFRs) separated by small-current sheets that to belong to a prominent non-propagating quasi-2D MHD turbulence component advected with the solar wind flow. Energetic particles undergo gyro-resonant interactions with small (gyro)-scale parallel propagating Alfvèn waves with random phases that obey Gaussian statistics. These interactions result in energetic particle normal pitch-angle and momentum diffusion as indicated by standard quasi-linear theory. However, because small-scale Alfvèn waves propagate in a solar wind medium with intermittent quasi-2D turbulence, the Alfvén wave magnetic and electric fields are expected to become statistically non-Gaussian when viewed on intermediate scales. This is expected to yield intermittent fluctuations in the pitch-angle and momentum diffusion coefficients for energetic particles interacting gyro-resonantly with parallel-propagating Alfvén waves. By assuming that the statistics of the intermittent fluctuations in the particle pitch-angle and momentum diffusion coefficients is an exponentially truncated Lévy distribution, we derived a new focused transport equation that includes additional terms for anomalous diffusion of energetic particles. The derived equation reveals that energetic particle interaction with Alfvén waves in such an intermittent solar wind medium results in new anomalous pitch-angle and momentum diffusion transport terms featuring tempered fractional derivatives. In the limit of Alfven waves propagating in solar wind medium with Gaussian quasi-2D turbulence, the tempered fractional derivatives in the new transport terms become normal, featuring 3^rd and 4^th order derivatives where the latter indicates the occurrence of compound diffusion in pitch-angle and momentum space.