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

Abstract

The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite–Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a two-dimensional Z-pinch is considered within a flux-tube configuration. In the collisionless regime, our gyromoment approach shows very good agreement with nonlinear simulations carried out with the continuum gyrokinetic code GENE, even with fewer gyromoments than required for the convergence of the linear growth rate. By using advanced linear collision operators, the role of collisions in setting the level of turbulent transport is then analysed. The choice of collision operator model is shown to have a crucial impact when turbulence is quenched by the presence of zonal flows. The convergence properties of the gyromoment approach improve when collisions are included.

Gyrokinetic moment-based simulations of the Dimits shift

“…Second, we recall that the Laguerre polynomials are involved in the Bessel-Laguerre decomposition of (2.21), which converges non-monotonically with respect to the maximal Laguerre degree, explaining the non-monotonic convergence at the highest Laguerre modes in figure 3. We note that the convergence of the nonlinear GM simulations is set by the convergence of the peak linear growth rate of the ITG mode, which is in agreement with the findings of our previous work (Hoffmann et al 2023). In fact, the overestimate of the linear growth rates observed for the (4, 2) basis (see figure 1a) corresponds to an increased saturated transport value (see figure 2b) and a high amplitude of the GM spectrum on figure 3.…”

“…Similarly to our previous work on the entropy mode (Hoffmann et al 2023), we observe a non-monotonic convergence of the GM growth rates with P and J. The GM approach converges to the correct growth rate with a smaller number of polynomials in the long-wavelength limit, k y ρ s 1, than at short wavelengths.…”

“…The convergence behaviour exhibits typical characteristics of spectral methods, that is an exponential and non-monotonic trend with P and J. It is worth noting that figure 1(b) reveals optimal convergence properties when P ∼ 2J, which justifies this choice also in previous works (Mandell et al 2022;Frei et al 2023;Hoffmann et al 2023). This is possibly related to the fact that H n is a Hermite polynomial of degree n in the parallel velocity coordinate, whereas L n is a Laguerre polynomial of degree 2n in the perpendicular velocity coordinate.…”

“…N pj = 0 for p > P or j > J. The truncation closure is the most straightforward to apply and shows good results in Frei et al (2022), Frei et al (2023) and Hoffmann et al (2023). We must note that, in collisionless simulations, the Hermite parallel coupling in (2.24), combined with the closure by truncation, may lead to recurrence effects, which yields a non-physical energy transfer from the highest to the lowest Hermite modes.…”

“…The details of these operators and their projection onto the Hermite-Laguerre basis can be found in Frei et al (2021). For an overview of the qualitative differences between the aforementioned collision operators we also refer to Hoffmann et al (2023). We set the intensity of the collisions through the non-dimensional parameter ν, normalized by the ion-ion collision frequency…”