We study the turbulent dynamics of a helium plasma in a nonconfining cylindrical configuration. Our experimental setup allows us to analyze particle transport in different plasma regions. We find that, whereas the transport is diffusive in the innermost regions of the plasma, distinctive non-diffusive features appear in regions away from the center. Indeed, at the plasma edge we find that particle flux exhibits a power-law distribution of avalanche durations, intermittency, and long-term correlations.