The self-organization is one of the most interesting phenomena in the non-equilibrium complex system, generating ordered structures of different sizes and durations. In tokamak plasmas, various self-organized phenomena have been reported, and two of them, coexisting in the near-marginal (interaction dominant) regime, are avalanches and the E × B staircase. Avalanches mean the ballistic flux propagation event through successive interactions as it propagates, and the E × B staircase means a globally ordered pattern of self-organized zonal flow layers. Various models have been suggested to understand their characteristics and relation, but experimental researches have been mostly limited to the demonstration of their existence. Here we report detailed analyses of their dynamics and statistics and explain their relation. Avalanches influence the formation and the width distribution of the E × B staircase, while the E × B staircase confines avalanches within its mesoscopic width until dissipated or penetrated. Our perspective to consider them the self-organization phenomena enhances our fundamental understanding of them as well as links our findings with the self-organization of mesoscopic structures in various complex systems.
Staircase formation by resonant and non-resonant transport of potential vorticity