Correlations and non-local transport in a critical-gradient fluctuation model

Abstract

A one-dimensional model based on critical-gradient fluctuation dynamics is used to study turbulent transport in magnetically confined plasmas. The model exhibits the selforganized criticality (SOC) dynamics. At the steady state, two regions are found: the outer one is close to critical state and the inner one remaining at the subcritical gradient. The gradient- flux relation exhibits a parabola-like profile centered in the most probable gradient following experimental studies. This is a signature of the non-locality of particle transport driven by avalanches: at the given position transport is due to gradients situated into closer but different positions. The R/S analysis, applied to the fluxes dynamics reveals memory and correlation. Different H exponents corresponding to different dynamical behavior are obtained. The flux at the edge exhibits long time correlations, which can be suppressed if the external drive or the system size is modified. On the other hand, we found that in the sub-critical region the quasiperiodicity is present in the avalanches.