A Fractional Kinetic Transport Theory for Energetic Particle Acceleration and Propagation in Dynamic Small-scale Flux Rope Regions in the Solar Wind.

Abstract:

Solar energetic particles (SEPs) from impulsive solar flare events were observed by Mazur et al. (2000) to exhibit "dropout" events on intermediate MHD scales of the order a turbulence correlation scale at 1 AU. One potential explanation is that these SEPs were temporarily trapped in small-scale magnetic flux rope (SMFR) structures indicating subdiffusive perpendicular transport of SEPs (Ruffolo et al. 2003). The distinctive spectral features observed for lower-energy suprathermal particles accelerated by SMFRs at 1 AU and beyond the solar wind termination shock were also interpreted in terms of particle trapping in SMFRs (e.g., Zank et al. 2015; Khabarova et al. 2016). Furthermore, analysis of energetic test particle trajectories on MHD scales by Isliker et al. (2017, 2019) in a plasma simulation exhibiting turbulent current sheet magnetic reconnection suggests anomalous spatial transport and that these particles undergo Levy flights in energy space which might be interpreted as superdiffusive acceleration. Such anomalous transport in energy space was detected both when particles are accelerated in contracting magnetic islands and in the turbulent motional electric fields generated in the vicinity of current sheet reconnection zones. In response, we developed a more general version of our existing focused transport equation for energetic particle acceleration in and transport through a collection of dynamic MHD-scale SMFRs in the solar wind, thus allowing for an anomalous description of the transport of particles in both ordinary and momentum space. In the derivation, the classical quasi-linear kinetic transport theory perturbation approach was extended to a fully non-linear level of particle trajectories disturbed by SMFRs so that anomalous transport processes can be modeled generally in terms of fractional derivatives (Sanchez et al. 2006). We argue that such a more flexible renormalization theory can in principle account for particle trapping in dynamic SMFRs (subdiffusion) in the solar wind during which efficient particle acceleration might acquire superdiffusive characteristics.