Turbulent diffusion of magnetic field lines in astrophysical plasmas

We calculate the Kolmogorov entropy for the exponential divergence of two neighboring field lines of an astrophysically relevant stochastic magnetic field. We take the approach of using the standard nonlinear map to approximate the diffusive random-walk process that is described by the Fokker-Planck equation, to diagnose any chaotic behavior in the process. We employ an expression for the diffusion coefficient of the standard map that includes higher order correlations, along with a numerical solution to the Fokker-Planck equation. For turbulent fields with Kolmogorov-like power spectra, we find that the diffusion process exhibits a non-Gaussian or turbulent regime, as has been suggested by a recent MHD numerical calculation. For weak to moderate turbulence strengths, this signature is in sharp contrast with simple quasi-linear predictions. For moderate to strong turbulence, however, a Gaussian-like diffusion is recovered, consistent with quasi-linear predictions.