We recently extended our Parkertype transport equation for energetic particle interaction with numerous dynamic smallscale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the secondorder Fermi mechanism for particle acceleration by SMFRs is more important than firstorder Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find thatmore »
It has been suggested before that smallscale magnetic flux rope (SMFR) structures in the solar wind can temporarily trap energetic charged particles. We present the derivation of a new fractional Parker equation for energeticparticle interaction with SMFRs from our pitchangledependent fractional diffusionadvection equation that can account for such trapping effects. The latter was derived previously in le Roux & Zank from the first principles starting with the standard focused transport equation. The new equation features anomalous advection and diffusion terms. It suggests that energeticparticle parallel transport occurs with a decaying efficiency of advection effects as parallel superdiffusion becomes more dominant at late times. Parallel superdiffusion can be linked back to underlying anomalous pitchangle transport, which might be subdiffusive during interaction with quasihelical coherent SMFRs. We apply the new equation to timedependent superdiffusive shock acceleration at a parallel shock. The results show that the superdiffusiveshockacceleration timescale is fractional, the net fractional differential particle flux is conserved across the shock ignoring particle injection at the shock, and the accelerated particle spectrum at the shock converges to the familiar powerlaw spectrum predicted by standard steadystate diffusiveshockacceleration theory at late times. Upstream, as parallel superdiffusion progressively dominates the advection of energetic particles, their more »
 Award ID(s):
 2148653
 Publication Date:
 NSFPAR ID:
 10366823
 Journal Name:
 The Astrophysical Journal
 Volume:
 930
 Issue:
 2
 Page Range or eLocationID:
 Article No. 125
 ISSN:
 0004637X
 Publisher:
 DOI PREFIX: 10.3847
 Sponsoring Org:
 National Science Foundation
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Abstract 
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