Focused Transport of Solar Energetic Particles in Interplanetary Space and the Formation of the Anisotropic Beam-like Distribution of Particles in the Onset Phase of Large Gradual Events


In the onset phase of large gradual solar energetic particle (SEP) events, the first particles of a given rigidity to arrive at Earth are accelerated in the low corona, focused into a narrow cone of pitch angles by the diverging magnetic field, and transported from near the Sun to 1 au with minimal scattering. The effects of focused transport on the evolution of the beam-like SEPs are investigated analytically. The model assumes for simplicity a constant focusing length and a constant pitch-angle diffusion coefficient for SEPs at small pitch angles. Cross-field transport is ignored. This analytical approximation provides a reasonable representation of the spatial and pitch-angle distribution of the beam-like SEPs. Assuming an instantaneous injection of SEPs near the Sun, the model naturally reproduces several features of the SEP onset profiles observed at 1 au, including a spike-like time–intensity profile with rapid rising and declining edges that resemble a Reid–Axford profile. By assuming an extended injection profile with the shape of an isosceles triangle, we fit the onset phase data of the 2005 January 20 GLE event to our model. The derived mean free path (∼4 au) for relativistic protons is much larger than the theoretical prediction based on the standard quasilinear theory but consistent with our assumption of nearly scatter-free transport and can be explained by a reduced scattering rate, due to particles interacting with ambient turbulence with a Goldreich–Sridhar spectrum. Assuming that the SEPs that are scattered out of the beam are governed by spatial diffusive transport in interplanetary space, we perform an illustrative calculation to account for the nearly isotropic phase following the anisotropic onset as a natural result of the interplanetary transport of SEPs.

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The Astrophysical Journal



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