Delay-time Distributions of Solar Energetic Particles. II. Effects of Magnetic Focusing

We extend a recently published analytic model for the intensity–time profile of solar energetic particle (SEP) events, in which the dominant physical mechanism is turbulent pitch-angle scattering of a collimated distribution of particles accelerated at the Sun. The present model includes the effect of magnetic focusing in the expanding magnetic field geometry of the inner heliosphere. For a power-law variation of the magnetic field strength with distance (B ∼ s ^−α) that lacks a characteristic focusing length scale, the fundamental shape of the intensity–time profile (i.e., a Lévy distribution at times up to and just past the time of peak intensity, followed by an exponential decay) is preserved. The effect of magnetic focusing is essentially to produce a rescaling of the stochastic process describing the angular diffusion of the particles, making the typical time that characterizes the SEP time profile quantitatively lower by a factor of (α + 1), 3 for the radial field geometry B ∼ s ⁻².