A Tempered Fractional Focused and Parker Transport Theory Approach to Model the Transport and Acceleration of Energetic Particles interacting with Dynamic Small-Scale Magnetic Flux Rope Structures in the Large-scale Solar Wind

Evidence is mounting that the intermittent nature of magnetic turbulence in the solar wind can partly be explained by the strong presence of a non-propagating quasi-2D magnetic turbulence component that consists of closed magnetic structures in the form of small-scale magnetic flux ropes (SMFRs) interspersed with open field meandering lines in the perpendicular direction. It appears that the PDF of the magnetic field strength increments of the quasi-2D component can best be modeled by an exponentially truncated Lévy distribution suggestive of magnetic field-line meandering characterized by tempered Lévy flights. Thus, perpendicular energetic particle transport in the solar wind might feature tempered Lévy flights characterized by superdiffusive behavior on intermediate time scales with a transition to more normal diffusive behavior at later times. Newly developed focused and Parker-type tempered fractional diffusion-advection equations derived from first principles that model the tempered anomalous diffusive propagation and energization of energetic particles in a dynamic SMFR field will be presented. Explorative solutions of the tempered fractional Parker transport equation to investigate tempered superdiffusive shock acceleration of energetic particles at a perpendicular shock imbedded in a SMFR field will be discussed.