Transport of Solar Energetic Particles along Stochastic Parker Spirals

It was recently shown that, owing to the turbulent nature of the solar wind, the interplanetary magnetic field lines can be well described by stochastic Parker spirals. These are realizations of Brownian diffusion on a sphere of increasing radius, superimposed on the angular drift due to the solar rotation. In this work, we present a model for the transport of solar energetic particles along stochastic Parker spirals in the inner heliosphere. The transport model is governed by a set of four stochastic differential equations for the heliographic position ( r , α = cos θ , ϕ ) of the guiding centers and the cosine of the pitch angle between the velocity vector and the Parker field. The model accounts for the role played by the combination of pitch angle scattering and magnetic focusing in the interplanetary medium. The effects of the dynamical evolution of the turbulence are included in the model by taking the field line angular diffusivity to be a function of the radial distance from the Sun. The heliolongitudinal distribution of particles propagating along stochastic Parker spirals is given by the wrapped Gaussian distribution. This angular distribution can also well be represented by the von Mises distribution that interpolates between the Gaussian distribution at small angular spread and the uniform distribution at large distances from the acceleration region of energetic particles in the aftermath of a solar eruption.