Zonally dominated dynamics and the transition to strong turbulence in ion-scale plasma turbulence*

Since the discovery of the Dimits shift (Dimits et al. 2000), the role of zonal flows (ZFs) for the turbulence in tokamak plasmas has been an area of intense research. We attempt to shed some light on this problem by studying the transition to turbulence in a cold-ion fluid model for ion-scale turbulence. Our equations are obtained in an asymptotic cold-ion limit of the ion gyrokinetic equation and capture the two ion-temperature-gradient (ITG) instabilities driven by either magnetic curvature or parallel compression. We find that this model has a well-defined Dimits (low-transport, ZF-dominated) state characterised by a staircase-like arrangement of ZFs that suppresses turbulence. Viscous decay of the ZFs leads to turbulent bursts that reconstitute the staircase by providing a negative zonal turbulent viscosity. In 2D, at large equilibrium temperature gradients, the zonal turbulent viscosity switches sign and the Dimits state is destroyed. In 3D, the Dimits state is much more resilient and can always be sustained provided sufficient parallel extent of the system. This is because the large-scale curvature-driven perturbations go unstable to small-scale "parasitic" 3D slab-ITG modes that always give rise to a negative zonal turbulent viscosity. If we restrict the parallel extent of the system, a strongly turbulent, high-transport state emerges. In this state, energy is injected into large-scale perturbations by the curvature-ITG instability, then transferred into the parasitic small-scale modes, and finally dissipated by the finite collisionality. We also find that insufficient parallel resolution can result in a non-physical breakup of the Dimits regime.