Magnetic Field Line Random Walk and Solar Energetic Particle Path Lengths: Stochastic Theory and PSP/ISoIS Observation

Abstract

Context:In 2020 May-June, six solar energetic ion events were observed by the Parker Solar Probe/ISoIS instrument suite at 0.35 AU from the Sun. From standard velocity-dispersion analysis, the apparent ion path length is 0.625 AU at the onset of each event. Aims:We develop a formalism for estimating the path length of random-walking magnetic field lines, to explain why the apparent ion pathlength at event onset greatly exceeds the radial distance from the Sun for these events. Methods:We developed analytical estimates of the average increase in pathlength of random-walking magnetic field lines, relative to the unperturbed mean field. Monte Carlo simulations of fieldline and particle trajectories in a model of solar wind turbulence are used to validate the formalism and study the path lengths of particle guiding-center and full-orbital trajectories. The formalism is implemented in a global solar wind model, and results are compared with ion pathlengths inferred from ISoIS observations. Results:Both a simple estimate and a rigorous theoretical formulation are obtained for fieldlines' pathlength increase as a function of pathlength along the large-scale field. From simulated fieldline and particle trajectories, we find that particle guiding centers can have pathlengths somewhat shorter than the average fieldline pathlength, while particle orbits can have substantially larger pathlengths due to their gyromotion with a nonzero effective pitch angle. Conclusions:The long apparent path length during these solar energetic ion events can be explained by 1) a magnetic field line path length increase due to the field line random walk, and 2) particle transport about the guiding center with a nonzero effective pitch angle. Our formalism for computing the magnetic field line path length, accounting for turbulent fluctuations, may be useful for application to solar particle transport in general.

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• The radial variation of the solar wind turbulence spectra near the kinetic break scale from Parker Solar Probe measurements
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• Connecting solar flare hard X-ray spectra to in situ electron spectra. A comparison of RHESSI and STEREO/SEPT observations
• Parker Solar Probe Observations of Helical Structures as Boundaries for Energetic Particles
• An analytical model of turbulence in Parker spiral geometry and associated magnetic field line lengths
• Solar Energetic Particle event onsets at different heliolongitudes: The effect of turbulence in Parker Spiral Geometry
• Simulation of the Solar Energetic Particle Event on 2020 May 29 Observed by Parker Solar Probe
• Evidence of Time-Dependent Diffusive Shock Acceleration in the 2022 September 5 Solar Energetic Particle Event
• Widespread 1-2 MeV Energetic Particles Associated with Slow and Narrow Coronal Mass Ejections: Parker Solar Probe and STEREO Measurements
• The effect of turbulence on the angular momentum of the solar wind
• Variable Ion Compositions of Solar Energetic Particle Events in the Inner Heliosphere: A Field-line Braiding Model with Compound Injections
• On the Turbulent Reduction of Drifts for Solar Energetic Particles