Description
In magnetic-confinement-fusion devices, turbulent transport is an essential constraint on the confinement of the plasma. In tokamak edge-pedestals formed in the high-confinement mode of operation (H-mode), electron-scale turbulence is found to be the main source of anomalous transport, and the parameter $\eta_e = L_{n_e}/L_{T_e}$ is strongly correlated with the structure of the pedestal. Here, $L_{n_e}$ and $L_{T_e}$ are the equilibrium gradient length scales of the electron density and temperature, respectively.
Using a model for electron-scale, collisional, drift-kinetic turbulence, we investigate the dependence of the nonlinear heat transport on $\eta_e$. Linearly, this model describes unstable drift waves driven by the electron-temperature gradients of the underlying equilibrium. The inclusion of a finite density gradient affects the linear modes by inducing a drift that changes the relative phase between the perturbed electron temperature $T_e$ and electron-density $n_e$, suppressing the instability.
We study the nonlinear behaviour of this system using simulations in shear-less slab geometry with periodic boundary conditions. The suppression of the instability by finite $\eta_e$ quenches the heat transport in the nonlinearly saturated state. This is also accompanied by a qualitative change in the turbulence: the decoherence of waves caused by the density-gradient drift increases the injection-scale anisotropy, which manifests itself by a longer radial coherence of streamers. In the marginal limit, where $\eta_e$ approaches $\eta_{e,\mathrm{crit}}$, the critical value for linear stability, the system saturates in a streamer-dominated low-Reynolds-number state that is nearly monochromatic around the injection scale, imitating the linear solution.
We identify the root causes of the nonlinear suppression of turbulence by describing the turbulent cascade and anisotropy in the weakly suppressed limit ($\eta_e \rightarrow \infty$), and we show a solution describing the saturation of the system in the marginal limit ($\eta_e \rightarrow \eta_{e,\mathrm{crit}}$). By describing the system in the intermediate stages and identifying the $\eta_e$ value at which the radial correlation length of streamers diverges, we identify the physical roots of the transition our system undergoes.