Importance of gyrokinetic exact Fokker-Planck collisions in fusion plasma turbulence

Gyrokinetic simulations of turbulence are fundamental to understanding and predicting particle and energy loss in magnetic fusion devices. Previous works have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius effects. This work moves beyond models to demonstrate important corrections using a gyrokinetic Fokker-Planck collision operator with the exact field-particle terms, in realistic simulations of turbulence in magnetically confined fusion plasmas. The exact operator shows significant corrections for temperature-gradient-driven trapped electron mode turbulence and zonal flow damping, and for microtearing modes in a Joint European Torus pedestal under ITER-like wall conditions. Analysis of the corrections using parameter scans motivates an accurate model which closely reproduces the exact results while reducing computational demands.

Figure 1

Gyrokinetic simulations of TEM linear growth rates and nonlinear electron heat fluxes for ${\eta }_e=1$. (a) Growth rates and (b) frequencies given by the exact operator (solid), the Sugama model (dotted), and the proposed GTDF model (pluses); (c) electron heat fluxes (normalized to gyroBohm) of the exact operator and the Sugama model; and (d) flux comparison of the exact operator with its GTDF model. In (a) and (b), the red (blue) lines are for cases with (without) FLR effects, and the exact and Sugama GTDF data are overlaid on their respective full-operator (i.e., with FLR effects) data. The horizontal lines in (c) and (d) represent the mean values of the indicated intervals.

Figure 2

(a) Summary of the mean nonlinear particle flux ($\mathrm{\Gamma }$), and ion ($Q_i$) and electron ($Q_e$) heat fluxes in normalized units. The error bar indicates the standard deviation of the means of nonoverlapping windows based on autocorrelation time [20]. (b) Zonal flow decay time as a function of the radial wave number.

Figure 3

Dependence of TEM growth rates on collisionality and ${\eta }_e$ at fixed $k_y{\rho }_s=0.5$ and $R/L_n=5$. (a) Growth rates given by the exact operator, (b) relative difference of growth rates given by exact and Sugama operators, (c) growth rates and relative difference at ${\widehat{\nu }}_{ei}=1$, and (d) growth rates and relative difference at ${\eta }_e=1.25$. The pluses in (a) and (b) indicate the parameters used in Fig. 1.

Figure 4

Dependence in growth rates and frequencies vs central $k_x$ at ${\rho }_{\text{tor}}=0.98$, comparing the exact operator (colored) with the Sugama (dashed) and Xu–Rosenbluth (XR) (crosses) models. Growth rates at (a) $k_y{\rho }_s=0.1$, (b) $k_y{\rho }_s=0.15$, and (c) $k_y{\rho }_s=0.2$; (d) frequencies shown in blue, green, and red colors, corresponding to the three binormal wave numbers shown in (a), (b), and (c), respectively.