Simulating the field-line random walk process

Abstract

The nature and structure of the heliospheric magnetic field play an important role in the transport of energetic particles throughout the heliosphere. In order to further knowledge about turbulence-particle interactions, especially the diffusive motion of charged particles perpendicular to the mean field, a greater understanding of the field-line random walk process is needed. This study summarises the fundamental physics encapsulating the meandering of magnetic field-lines due to turbulence within the solar wind, and develops a numerical model with which to simulate the turbulent heliospheric magnetic field. This is done by employing stochastic differential equations to numerically solve the convection diffusion equation for field-line diffusion, which is derived from the focused transport equation for particles. Assuming purely 2D turbulence and adopting turbulence quantities derived from observations, the numerical model is applied to the Parker heliospheric magnetic field. The model results show a probability distribution possessing a nearGaussian shape, which is narrower when close to the Sun and grows wider with the increase in radial distance. The most likely path of the heliospheric magnetic field is calculated from the probability distribution for different field-line diffusion coefficients. Comparing the model results with the turbulence-free Parker heliospheric magnetic field shows that the calculated most likely paths are similar to the turbulence-free Parker heliospheric magnetic field model for smaller diffusion coefficients, while becoming more underwound as the diffusion coefficient increases. This corresponds well with recent observations