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

Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, delta B/B-0, 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 B-0 = B(0)e(z) and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B-0. The energy density spectrum is a power law, and in k space it is described by the correlation lengths l(x), l(y), l(z), which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R = (delta B/B-0)(l(z)/l(x)). For small Kubo numbers, R << 1, anomalous, non-Gaussian transport regimes (both sub- and superdiffusive) are found, which can be described as a Levy random walk. Increasing the Kubo number, i.e. the fluctuation level, delta B/B-0, or the ratio l(z)/l(x), 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, delta B/B-0 similar or equal to 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 l(z)/l(x) < 1, with a Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for l(z)/l(x) > 1 normal Gaussian diffusion is found. A possible expression for generalized double diffusion is discussed.