A Focused Transport-based Kinetic Fractional Diffusion-advection Equation for Energetic Particle Trapping and Reconnection-related Acceleration by Small-scale Magnetic Flux Ropes in the Solar Wind

J A Le Roux,G P Zank

doi:10.3847/1538-4357/abf3c6

Abstract

Abstract Analysis of energetic particle inner heliospheric spacecraft data increasingly suggests the existence of anomalous diffusion phenomena that should be addressed to achieve a better understanding of energetic particle transport and acceleration in the expanding solar wind medium. Related to this is fast-growing observational evidence supporting the long-standing prediction from magnetohydrodynamic (MHD) theory and simulations of the presence of an inner heliospheric, dominant quasi-two-dimensional MHD turbulence component that contains coherent contracting and merging (reconnecting) small-scale magnetic flux rope (SMFR) structures. This suggests that energetic particle trapping in SMFRs should play a role in anomalous diffusion in the solar wind that warrants further investigation. However, progress in studying such anomalous energetic particle transport phenomena in the solar wind is hampered by the lack of a fundamental derivation of a general fractional kinetic transport equation linking macroscopic energetic particle fractional transport to the microscopic physics of energetic particle interaction with SMFR structures. Here, we outline details of how one can derive a closed ensemble-averaged focused transport equation in the form of a general kinetic fractional diffusion-advection equation from first principles following the nonlinear Eulerian correlation function closure approach of Sanchez et al. With this equation one can model the anomalous diffusion of energetic particles in ordinary, momentum, and pitch-angle space in response to particle trapping in numerous SMFRs advected with the solar wind flow.

Highlights

The number of studies finding potential anomalous transport features in energetic particle spacecraft data in the solar wind have been steadily increasing
SEPs that propagate to 1 au while being trapped in closed small-scale quasi-helical magnetic field structures or small-scale magnetic flux ropes (SMFRs) will retain a relatively high counting rate, while those SEPs propagating along adjacent open magnetic field lines that spread efficiently in latitude and longitude will arrive at 1 au with a strongly reduced counting rate
The idea of particle trapping in SMFRs in the solar wind being responsible for observed potentially anomalous energetic particle transport behavior has received a considerable boost from the identification of unprecedented numbers of SMFRs in the inner heliosphere from ∼0.3–7 au using Helios, Advanced Composition Explorer (ACE), Wind, Ulysses, and Voyager data (e.g., Hu et al 2018; Zheng & Hu 2018; Chen et al 2019; Zhao et al 2019a; Chen & Hu 2020)

Summary

Introduction

The number of studies finding potential anomalous transport features in energetic particle spacecraft data in the solar wind have been steadily increasing. Evidence is increasing that in a space plasma with a significant guide/background magnetic field like the solar wind, SMFRs naturally form as part of a self-generated quasi-two-dimensional (quasi-2D) MHD turbulence component that might dominate other MHD wave turbulence modes This is supported by observations in the slow solar wind near 1 au (e.g., Matthaeus et al 1990; Bieber et al 1996; Greco et al 2009; Zheng & Hu 2018), MHD simulations (e.g., Shebalin et al 1983; Dmitruk et al 2004) and nearly incompressible MHD turbulence transport theory (e.g., Zank & Matthaeus 1992, 1993; Zank et al 2017, 2018, 2020). Observational evidence is accumulating that SMFRs form locally in the solar wind near the heliospheric current sheet, large-scale current sheets associated with interplanetary coronal mass ejections, and corotating interaction regions through turbulent magnetic reconnection, and that neighboring SMFRs undergo merging through small-scale magnetic reconnection and large-scale compression (Khabarova et al 2015, 2016; Hu et al 2018; Zheng & Hu 2018; Chen et al 2019; Chen & Hu 2020)

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Conclusion