Magnetic field line transport in three dimensional turbulence: Lévy random walk and spectrum models

The transport of magnetic field lines is investigated numerically by summing an isotropic spectrum of randomly phased magnetic fluctuations to a uniform background field. The aim of this study is to clarify the dependence of transport properties on the fluctuation correlation length lc, which ideally should be much smaller than the periodicity scale L, and to eliminate the effects due to periodicity. Two types of spectra are considered: in the first, the longest turbulence wavelength equals L, and lc is varied in order to describe either the injection zone or the inertial range of turbulence. In this case, strong anisotropy of transport and, for moderate fluctuation levels, Lévy random walk in the y direction only is found. When lc is decreased, both transport and anisotropy are reduced. In the second type of spectrum the longest wavelengths in the spectrum are excluded in order to have lc≪L and to reduce the influence of periodicity of the magnetic field model. In this case transport is isotropic for all fluctuation levels, and the Lévy random walk is independent of periodicity, since it is found even when the transverse displacement Δr is within the periodicity box, lc<Δr