Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?

Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.