Speaker
Description
In most cases, micro-turbulence is the main source of heat and particle transport in tokamaks, leading to a degradation of the fusion performence. Ion Temperature Gradient (ITG) instability is one of the major micro-instabilities responsible for ion heat and particle transport. In the present work, the transition between a highly turbulent regime and a zonal-flow dominated regime is investigated for ITG turbulence, using the local, gradient driven version of the gyrokinetic code GENE, considering adiabatic electrons and electrostatic turbulence, for simplicity. Using the zonal to total fraction of free energy, we propose to interpret the Dimits shift, as a phase transition in a thermodynamical sense between a disordered, turbulent phase, and an ordered zonal dominated phase. A careful scan in temperature gradient $R/L_{T,i}$ is performed to characterize the two phases : for large $R/L_{T,i}$, the system exhibits high heat flux characteristic of fully developped turbulence, whereas at lower $R/L_{T,i}$ the heat flux is strongly reduced and quasi null. To elucidate the nature of this transition, chained simulations are performed with the parameters of the Cyclone Base Case, but with the effective control parameter $R/L_{T,i}$, initialized at a high value resulting in a disordered turbulent phase, is then slowly decreased to enter into the zonal flow dominated state and then increased again to go back to the disordered phase. Comparing these simulations to independent runs at each value of $R/L_{T,i}$, reveals a hysteresis behavior for the zonal to total free energy fraction, which plays the role of the order parameter, or the heat flux. The mechanism for the hysteresis seems to be that once established, zonal flows persist at higher temperature gradients and continue to supress turbulence, making the threshold for the transition from the turbulent to the zonal phase different from that of the reverse transition.