We have proposed a one-dimensional transport model based on critical-gradient fluctuation dynamics to describe some of the properties of plasma turbulence induced transport [1]. This model has the characteristic properties of a self-organized critical (SOC) system. In this model, the flux is self-regulated by the stability properties of the fluctuations. A high-gradient edge region emerges where transport dynamics is close to marginal stability. The core remains at the subcritical gradient that is typical of a SOC system.
There is a different dynamical behavior of the fluxes above and below the transition point. Between the transition point and the edge, there is continuous activity. In the inner region, there are quasi-periodic flux bursts which we call avalanches. They are the dominant transport mechanism. These avalanches are triggered in the outer region, and they propagate inward. The avalanches are arranged in groups in which the first avalanche of the group reaches all the way to the center and every successive avalanche runs to a shorter distance inward. When the termination point of the avalanches has moved all the way to the edge pedestal, a new avalanche goes all the way to the center and the process starts again with a new group. The inward penetration point of the avalanches of successive groups appears to have a sawtooth-like envelope.
During an avalanche, the functional form of the flux at a given time is a front-like structure and it propagates inwards at a practically constant speed. Near the termination point, the flux propagation slows down. This front-like structure is driven by a supercritical value of the gradient at a single cell, just at the position of the front.
We have done a sequence of calculations varying the system size and the particle source. The power spectrum of the flux across a fixed radial position shows two clear peaks associated to the frequency of the groups of avalanches and the frequency of the individual avalanches, respectively. For frequencies above this second peak, the spectrum shows the 1/f decay characteristic of SOC systems. The probability distribution function of the length and duration of these avalanches is practically flat. These results are explained using a simple model for the front-like structure of avalanches.

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