Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold

Abstract

It is shown that ITG turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows and, consequently, the numerical dissipation on these flows must be sufficient small. Close to the nonlinear threshold for turbulence generation, a relatively small dissipation can maintain a turbulent state with a sizeable heat flux, through the damping of the zonal flow. Lowering the dissipation causes the turbulence, for temperature gradients close to the threshold, to be subdued. The heat flux then does not go smoothly to zero when the threshold is approached from above. Rather, a finite minimum heat flux is obtained below which no fully developed turbulent state exists. The threshold value of the temperature gradient length at which this finite heat flux is obtained is up to 30% larger compared with the threshold value obtained by extrapolating the heat flux to zero, and the cyclone base case is found to be nonlinearly stable. Transport is subdued when a fully developed staircase structure in the ExB shearing rate forms. Just above the threshold, an incomplete staircase develops, and transport is mediated by avalanche structures which propagate through the marginally stable regions.

Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit

“…(2010), Kobayashi & Rogers (2012) or Peeters et al. (2016), quickly develops, which can then efficiently suppress the amplitude of drift waves, typically on the order of 2 magnitudes (but occasionally much more). All that then remains are the localised tertiary modes which will eventually die if stable or grow back if unstable.…”

Nonlinear electromagnetic interplay between fast ions and ion-temperature-gradient plasma turbulence

“…It is worth mentioning that the results of this paper were obtained in a realistic plasma scenario, which includes the effects of inter-species collisions, kinetic electrons, electromagnetic effects and complex magnetic plasma geometry. Therefore, each of these terms can affect the minimum heat-flux threshold for the non-physical results discussed in Peeters et al (2016) and Rath et al (2016). In particular, collisions can act on the zonal flow evolution as a natural damping mechanism, suppressing or delaying its long-time secular growth.…”

“…Certain turbulent systems that approach the nonlinear ITG threshold have recently been shown to exhibit a long-time evolution of the zonal flow amplitude (Peeters et al 2016;Rath et al 2016). In particular, a minimum main-ion heat flux value of Q i = 10 in gyro-Bohm units has been identified for the collisionless electrostatic CYCLONE base case parameters with adiabatic electrons.…”

Benchmarking of flux-driven full-F gyrokinetic simulations

“…In addition, the time-averaged temperature profile spontaneously corrugates leading to zonal flows and the interplay between zonal flows and avalanches gives rise to the socalled E Â B staircase. 4,5,34,35 Figure 16 shows the spatio-temporal evolutions of the ion heat flux Q i , the normalized ion temperature gradient R 0 =L ti and the radial electric field shear dE r =dr. In a source free region (q ¼ 0:5-0:9), the turbulent heat transport shows the avalanche-like feature in both codes [see Figs.…”