Authors: Gang Li (University of Alabama in Huntsville), Nic Bian (University of Alabama in Huntsville)

In the 1960’s, Leighton developed a diffusion model for the transfer of magnetic flux on the photosphere, and hence, for the turbulent motions of magnetic footpoints on the solar wind source surface. The Leighton’s model is the basis of the stochastic solar wind magnetic field line model put forth by Jokipii and Parker. They assume a Brownian diffusion on the source surface yielding an infinite path length of the boundary-driven magnetic field lines. Here, we extend these models by describing the magnetic footpoint motions by a spherical Ornstein–Uhlenbeck process with a drift due to the Sun’s rotation. The boundary-driven interplanetary magnetic field (IMF) lines become smooth differentiable curves with finite path lengths. The model is parameterized by two measurable quantities, the Lagrangian integral timescale and the root-mean-square footpoint velocity. It reduces to Leighton’s model in the singular Markov limit when the Lagrangian integral timescale tends to zero while keeping the footpoint diffusivity finite. The joint velocity and position of the magnetic footpoints on the source surface are the solutions of a set of stochastic differential equations which are solved numerically. The path-lengths of the IMF lines and their probability distributions at 1 au are computed numerically and their dependency with respect to the two controlling parameters is determined.