Investigating 1st and 2nd order Fermi acceleration of energetic particles by small-scale magnetic flux ropes at 1AU

Abstract

A new telegrapher-type Parker transport equation was derived from the existing underlying focused transport equation to model the acceleration of energetic particles by contracting and reconnecting small-scale magnetic flux ropes (SMFRs) in the large-scale solar wind. Time-dependent and steady-state analytical solutions were found that unify all SMFR acceleration mechanisms present in the transport equation, showing that SMFR acceleration by the parallel reconnection electric field in the mixed spatial and momentum derivative transport term is constrained by and requires the presence of 2nd order Fermi SMFR acceleration. We explore the potential of these solutions in reproducing energetic proton flux enhancements and spectral evolution between ∼50 keV-5 MeV in dynamic SMFR regions near large-scale reconnecting current sheets in the solar wind at 1 AU. It is shown that both 2nd order Fermi SMFR acceleration involving the variance in SMFR compression and incompressible parallel shear flow, and 1st order SMFR Fermi acceleration due to mean SMFR compression are both workable options in reproducing observed flux amplification factors when using reasonable SMFR parameters. However, the predicted substantial quantitative differences in the spatial evolution of the accelerated spectra through the SMFR region might provide a diagnostic to distinguish between 1st and 2nd order Fermi SMFR acceleration in observations.