Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence

Abstract

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations. A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear. The break up of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system -- the Reynolds stress and the advection of the diamagnetic flow by the $\mathbf{E}\times \mathbf{B}$ flow. By analysing the linear ITG modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

63 pages, 30 figures, to be submitted to J. Plasma Phys

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• Dimits transition in three-dimensional ion-temperature-gradient turbulence
• Theory of the tertiary instability and the Dimits shift within a scalar model
• Dimits shift, avalanche-like bursts, and Solitary propagating structures in the two-field Flux-Balanced Hasegawa-Wakatani model for plasma edge turbulence
• Bistable turbulence in strongly magnetised plasmas with a sheared mean flow
• Predicting the Z-pinch Dimits shift through gyrokinetic tertiary instability analysis of the entropy mode
• Nearly integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence
• Resistive instabilities in sinusoidal shear flows with a streamwise magnetic field
• An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field
• Suppression of temperature-gradient-driven turbulence by sheared flows in fusion plasmas
• Scale invariance and critical balance in electrostatic drift-kinetic turbulence
• Flux-driven turbulent transport using penalisation in the Hasegawa-Wakatani system
• The gyrokinetic field invariant and electromagnetic temperature-gradient instabilities in `good-curvature' plasmas
• Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit