Modeling Energetic Particle Acceleration by Small-Scale Flux Ropes at 1 AU

Based on observations from spacecraft at 1 AU and ~5 AU, it is strongly suspected that contracting and merging (reconnecting) small-scale magnetic flux ropes (SMFRs) form locally near turbulently reconnecting, strong, large-scale current sheets. Energetic particle acceleration in SMFR regions has been identified in the form of energetic particle flux enhancements with amplification factors increasing with particle energy and accelerated spectra that harden with distance through the SMFR region. Detailed kinetic focused and Parker transport type equations have been developed by Zank et al. (2014) and le Roux et al. (2015, 2018) that contain the main SMFR acceleration mechanisms identified in particle simulations in terms of a number of first and second-order Fermi acceleration mechanisms. Analytical solutions to the Parker transport equation have been derived in planar geometry, and solutions emphasizing first-order Fermi SMFR acceleration were able to reproduce energetic ion SMFR acceleration event characteristics observed at 1 AU and 5 AU (Zhao et al., 2018; Adhikari et al., 2019). We present a new analytical solution in spherical geometry that includes all SMFR acceleration mechanisms. This solution is used to model observations of energetic particle acceleration in SMFR regions at 1 AU (Khabarova and Zank, 2017) for cases where second-order Fermi acceleration dominates first-order Fermi acceleration, vice versa, and where both contribute. In all three cases, results are generated that resemble observational data. Therefore, energetic particle acceleration in SMFR regions could be the result of only first-order Fermi acceleration mechanisms, only second-order Fermi acceleration mechanisms, or some combination of both.