Assessing Zonal-Flow Impact in Turbulence Simulations

Zonal flows saturate turbulence, lower transport levels, and are ubiquitous in fusion plasmas. Common non-invasive methods of determining zonal-flows importance in a nonlinear simulations are a visual inspection of contours in the perpendicular plane or an evaluation of the shearing rate. It will be discussed how these approaches can fail to answer the question of zonal-flow impact correctly. Direct evaluation of nonlinear energy transfer and the evaluation of transfer efficiency via triplet correlation times provide more reliable results.

Zonal-flow deletion, i.e., zeroing out $\Phi(n=m=0)$ at every time step, has been employed as an assessment of whether zonal flows are important in saturation. However, often this technique produces features in the electrostatic potential or density fluctuations that mimic zonal properties but are poorly conditioned numerically. The efficacy of two alternate approaches to avoid such features is discussed, namely deleting $\Phi(n=0)$ and gradual zonal-mode damping. These techniques are tested for three applications: a transition from trapped-electron-mode to ion-temperature-gradient-driven turbulence, a scan from strong negative to strong positive triangularity, and a density-gradient-dominated scenario in stellarator geometry.