Fractional diffusion in plasma turbulence

Transport of tracer particles is studied in a model of three-dimensional, resistive, pressure-gradient-driven plasma turbulence. It is shown that in this system transport is anomalous and cannot be described in the context of the standard diffusion paradigm. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit superdiffusive scaling. To model these results we present a transport model with fractional derivatives in space and time. The model incorporates in a unified way nonlocal effects in space (i.e., non-Fickian transport), memory effects (i.e., non-Markovian transport), and non-Gaussian scaling. There is quantitative agreement between the turbulence transport calculations and the fractional diffusion model. In particular, the model reproduces the shape and space-time scaling of the pdf, and the superdiffusive scaling of moments.