Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles propagate systematically along meandering field lines, and only later reach the time-asymptotic diffusive cross-field propagation. In this paper, we analyse cross-field propagation of 1--100 MeV protons in composite 2D-slab turbulence superposed on a constant background magnetic field, using full-orbit particle simulations, to study the non-diffusive phase of particle propagation with a wide range of turbulence parameters. We show that the early-time non-diffusive propagation of the particles is consistent with particle propagation along turbulently meandering field lines. This results in a wide cross-field extent of the particles already at the initial arrival of particles to a given distance along the mean field direction, unlike when using spatial diffusion particle transport models. The cross-field extent of the particle distribution remains constant for up to tens of hours in turbulence environment consistent with the inner heliosphere during solar energetic particle events. Subsequently, the particles escape from their initial meandering field lines, and the particle propagation across the mean field reaches time-asymptotic diffusion. Our analysis shows that in order to understand solar energetic particle event origins, particle transport modelling must include non-diffusive particle propagation along meandering field lines.
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We study the ratio of the numbers of interplanetary to interacting protons, Γ, using a model of stochastic acceleration on open magnetic field lines in solar corona. The impact of diverging coronal magnetic field lines is incorporated into the particle transport operator and shown to be unavoidable, no matter how small the mean free path may be. We calculate the energy spectra of protons precipitating into the subcoronal regions (interacting protons) and the spectra of protons escaping into the interplanetary medium (interplanetary protons). In the case in which both injection and the magnetic field exponentially decrease with altitude, the proton spectra for interacting particles are steeper than the corresponding spectra in interplanetary space. The deduced high-energy ratio Γ varies from 1 to ≈5, being almost independent on a magnetic mirror ratio beneath the acceleration region if the latter ratio does not exceed typically ≈10. A quantitative relation between the interplanetary to interacting proton ratio and the magnetic field change from the top of the interaction region to the top of the acceleration region is established. The model results are qualitatively consistent with patterns of energetic protons, γ-rays, and neutrons produced during the approximately 40 minutes after the impulsive phase of the 1990 May 24 solar flare.
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