Self-regulation of turbulence bursts and transport barriers

The interplay between turbulent bursts and transport barriers is analyzed with a simplified model of interchange turbulence in magnetically confined plasmas. The turbulent bursts spread into the transport barriers and, depending on the competing magnitude of the burst and stopping capability of the barrier, can burn through. Simulations of two models of transport barriers are presented: a hard barrier where interchange turbulence modes are stable in a prescribed region and a soft barrier with external plasma biasing. The response of the transport barriers to the non-linear perturbations of the turbulent bursts, addressed in a predator–prey approach, indicates that the barriers monitor an amplification factor of the turbulent bursts, with amplification smaller than one for most bursts and, in some cases, amplification factors that can significantly exceed unity. The weak barriers in corrugated profiles and magnetic structures, as well as the standard barriers, are characterized by these transmission properties, which then regulate the turbulent burst transport properties. The interplays of barriers and turbulent bursts are modeled as competing stochastic processes. For different classes of the probability density function (PDF) of these processes, one can predict the heavy tail properties of the bursts downstream from the barrier, either exponential for a leaky barrier, or with power laws for a tight barrier. The intrinsic probing of the transport barriers by the turbulent bursts thus gives access to the properties of the barriers. The main stochastic variables are the barrier width and the spreading distance of the turbulent bursts within the barrier, together with their level of correlation. One finds that in the case of a barrier with volumetric losses, such as radiation or particle losses as addressed in our present simulations, the stochastic model predicts a leaky behavior with an exponential PDF of escaping turbulent bursts in agreement with the simulation data.