Zonally dominated dynamics and the transition to strong turbulence in ion-scale plasma turbulence
Keywords: fusion plasma
plasma nonlinear phenomena
plasma instabilities

We present a study of the low-transport Dimits state (Dimits et al., 2000) and the transition to a high-transport saturated state in plasma turbulence driven by the ion-temperature-gradient instability. This thesis focuses on a fluid model derived in the cold-ion, long-wavelength asymptotic limit of the ion gyrokinetic equation in a magnetic field with constant curvature (a Z-pinch) and in the presence of an equilibrium temperature gradient. Numerical simulations reveal that the Dimits state is dominated by a quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows which have patch-wise constant shear. Such a structure is reminiscent of the so-called "ExB staircase" observed in global gyrokinetic numerical simulations (Dif-Pradalier et al., 2010). It suppresses turbulence in two complementary ways: first, by shearing turbulent eddies in the regions of strong zonal shear, and, secondly, by flattening the background temperature gradient at the turning points of the zonal flow, where the shear vanishes. 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 (van Wyk et al., 2016). The breakup 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 ExB flow. The former acts to support the staircase by providing a net negative turbulent viscosity for the zonal flows and is opposed by the latter. The winner of this competition decides the type of saturated state. When the Reynolds stress dominates, the system enters the Dimits regime which is characterised by the aforementioned zonal staircase. Otherwise, if the diamagnetic stress prevails, strong turbulence-suppressing zonal flows cannot be maintained and turbulence reigns supreme. We show that the transition from low to high transport can be understood by analysing the linearly unstable ion-temperature-gradient modes. This is demonstrated by a semi-analytic model for the Dimits threshold in 2D and at large collisionality. In 3D, unless the system is restricted in the magnetic-field direction, a Dimits state arises for all values of the equilibrium parameters. This is explained by the existence of a "parasitic" small-scale slab-ITG instability which is driven by the gradients of large-scale 2D perturbation. The modes of this parasitic instability provide an effective thermal diffusion at large scales and act to move energy from large scales to small viscous scales where dissipation takes place, thus providing a mechanism for saturation. Although such a saturation mechanism was investigated as early as (Cowley et al., 1991), it is not part of the conventional discourse on strong ITG turbulence, which often follows simpler scenarios (e.g., critical balance, see Barnes et al., 2011).