Anomalous particle diffusion and Lévy random walk of magnetic field lines in three-dimensional solar wind turbulence

Abstract

Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, δB/B0, the ratio between the particle Larmor radius and the turbulence correlation length, and the turbulence anisotropy. In this paper, we present the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B0 = B0 ez and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B0. The energy density spectrum is a power law, and in k space it is described by the correlation lengths lx, ly, lz, which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R = (δB/B0) (lz/lx). For small Kubo numbers, R ≪ 1, anomalous, non-Gaussian transport regimes (both sub- and superdiffusive) are found, which can be described as a Lévy random walk. Increasing the Kubo number, i.e. the fluctuation level, δB/B0, or the ratio lz/lx, we find first a quasilinear regime and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field depends heavily on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, δB/B0≃ 0.5–1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case lz/lx ⩽ 1, with a Lévy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for lz/lx > 1 normal Gaussian diffusion is found. A possible expression for generalized double diffusion is discussed.