In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (or `Gaussian'). The term `superdiffusive' refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. The mathematical treatment of anomalous transport leads to both nonlinear and so-called fractional differential equations.
|Schematical overview of anomalous diffusion, associated Fokker-Planck equations, and stochastic processes. The quantity ζ is defined via <(Δ x)2> ∼ t ζ. [click to enlarge]|