Dynamical Field Line Connectivity in Magnetic Turbulence

Abstract:

Point-to-point magnetic connectivity has a stochastic character whenever magnetic fluctuations cause a field line random walk, with observable manifestations such as dropouts of solar energetic particles and upstream events at Earth’s bow shock. This can also change due to dynamical activity. Comparing the instantaneous magnetic connectivity to the same point at two different times, we provide a nonperturbative analytic theory for the ensemble average perpendicular displacement of the magnetic field line, given the power spectrum of magnetic fluctuations. For simplicity, the theory is developed in the context of transverse turbulence, and is numerically evaluated for two specific models: reduced magnetohydrodynanmics (RMHD), a quasi-two dimensional model of anisotropic turbulence that is applicable to low-beta plasmas, and two-dimensional (2D) plus slab turbulence, which is a good parameterization for solar wind turbulence. We take into account the dynamical decorrelation of magnetic fluctuations due to wave propagation, nonlinear distortion, random sweeping, and convection by a bulk wind flow relative to the observer. The mean squared time-differenced displacement increases with time and with parallel distance, becoming twice the field line random walk displacement at long distances and/or times, corresponding to a pair of uncorrelated random walks. These results are relevant to a variety of astrophysical processes, such as electron transport and heating patterns in coronal loops and the solar transition region, changing magnetic connection to particle sources near the Sun or at a planetary bow shock, and thickening of coronal hole boundaries. Partially supported by the Thailand Research Fund, the US NSF (AGS-1063439 and SHINE AGS-1156094), NASA (Heliophysics Theory NNX11AJ44G), and by the Solar Probe Plus Project through the ISIS Theory team.