Anomalous particle transport in the heliosphere

The transport of energetic particles in the presence of magnetic turbulence can exhibit a variety of regimes different from the standard quasilinear diffusion. Here we discuss a number of solar and space problems where nonquasilinear diffusion is found, and then we illustrate anomalous transport regimes, for which the mean square deviation grows nonlinearly with time. In particular, we concentrate on superdiffusive regimes, and show what is the theoretical framework which is to be used to describe superdiffusion. We discuss the results of numerical simulations which show that superdiffusive and subdiffusive regimes are possible, and describe data analyses which allow to single out the superdiffusive transport from the observation of energetic particle profiles upstream of interplanetary shocks. The implications of superdiffusion on the efficiency of wave particle interactions are also discussed.