Predicting the Z-pinch Dimits shift through gyrokinetic tertiary instability analysis of the entropy mode

Abstract

The Dimits shift, an upshift in the onset of turbulence from the linear instability threshold, caused by self-generated zonal flows, can greatly enhance the performance of magnetic confinement plasma devices. Except in simple cases, using fluid approximations and model magnetic geometries, this phenomenon has proved difficult to understand and quantitatively predict. To bridge the large gap in complexity between simple models and realistic treatment in toroidal magnetic geometries (e.g. tokamaks or stellarators), the present work uses fully gyrokinetic simulations in a Z-pinch geometry to investigate the Dimits shift through the lens of tertiary instability analysis, which describes the emergence of drift waves from a zonally dominated state. Several features of the tertiary instability, previously observed in fluid models, are confirmed to remain. Most significantly, an efficient reduced-mode tertiary model, which previously proved successful in predicting the Dimits shift in a gyrofluid limit (Hallenbert & Plunk, J. Plasma Phys., vol. 87, issue 05, 2021, 905870508), is found to be accurate here, with only slight modifications to account for kinetic effects.

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

“…GENE results are obtained using the same Fourier modes as the gyromoment simulation and a velocity grid resolution of N v × N μ = 32 × 12 points for the (v , μ) velocity space in a box of dimension L v × L μ = 6 × 4. This ensures convergence of GENE results and that the results obtained by Hallenbert & Plunk (2022) are retrieved. It is worth noting that FIGURE 3.…”

“…The time traces are presented on figure 5. Hallenbert & Plunk (2022) present the velocity space resolution we use as the minimum necessary not to compromise key results. We confirm their claim by observing spurious predator-prey cycles when running lower resolution simulations at κ N = 1.6.…”

“…For the intermediate values of the equilibrium gradient strength, we perform two simulations with GENE. The first simulation considers a constant level of numerical diffusion, while the second takes advantage of the adaptive numerical diffusion feature in GENE, as described in Hallenbert & Plunk (2022). This is done to ensure that the effect of the adaptive diffusion feature is not significant.…”

“…We now turn to the nonlinear results that include finite collisionality, and we discuss two scans of simulations, for ν = 0.1 and ν = 0.01, where the drive value is varied from κ N = 1.6 to κ N = 2.5, being η = 0.25. The results are shown in figure 11, where they are compared with the collisionless limit, which shows a Dimits threshold value κ N 2, similarly to Hallenbert & Plunk (2022), below which ZF suppress turbulence. We observe that the effect of collisions vanishes at large drive values, where the ZF do not play a crucial role, in agreement with the observations in Ricci et al (2006a).…”

“…This allows the numerical prediction of the Dimits threshold, i.e. the gradient level below which transport is strongly reduced by the presence of ZF (Hallenbert & Plunk 2022). The prediction is confirmed by comparison with GENE simulations.…”