Model analysis of edge relaxation phenomena in tokamak plasmas

Based on a transition transport model with hysteresis nature, the heat transport in the plasma edge region is investigated. A hysteresis type flux-force relation is incorporated into the model of local heat diffusivity. A one-dimensional heat transport equation is solved numerically for a given influx. The time evolution of the heat flux oscillation due to the nature of the hysteresis and the parameter dependences of its amplitude and frequency are examined. The oscillatory characteristics of the outflux are found to alter depending on (1) the time scale ratio of the local limit cycle period and the spatial propagation time of successive transitions (avalanche) and (2) whether the induced avalanche can reach and make the transition at the very edge of the plasma or not. Different characteristic power law relations are obtained in the parameter dependences. The critical behaviour of the transition between two transport mechanisms, i.e. the hysteresis type and the discontinuous, is analyzed and compared. The self-organized criticality like behaviour, i.e. power spectrum obeying power law, is obtained in a limiting case of the hysteresis model.