System Size Effects on Gyrokinetic Turbulence

The scaling of turbulence-driven heat transport with system size in magnetically confined plasmas is reexamined using first-principles based numerical simulations. Two very different numerical methods are applied to this problem, in order to resolve a long-standing quantitative disagreement, which may have arisen due to inconsistencies in the geometrical approximation. System size effects are further explored by modifying the width of the strong gradient region at fixed system size. The finite width of the strong gradient region in gyroradius units, rather than the finite overall system size, is found to induce the diffusivity reduction seen in global gyrokinetic simulations.

Figure 1

Ion heat diffusivity ${\chi }_i/{\chi }_{\mathrm{GB}}$ (${\chi }_{\mathrm{GB}}={\rho }_s^2{c}_s/a$) obtained with global-GENE and ORB5 as function of $1/{\rho }^{*}$. A radial window, $r\in [0.4,0.6]$ is used, and a time average over $t{c}_s/R\in [210,450]$. The results are compared with the corresponding GENE flux-tube simulation. The error bar represents simulation-to-simulation variability.

Figure 2

Logarithmic temperature gradients plotted against radius for simulations with ${\rho }^{*}=1/280$, and ${\Delta }_r=0.2$, 0.4, 0.8, in order of increasing width of the plotted peak. The dashed lines show initial gradients, and the solid lines show the late time average over the last half of the simulation time.

Figure 3

Average flux levels $r\in [0.4,0.6]$ for $t\in [150,410]R/c_s$ versus the width of the strong gradient region, $1/{\rho }_{\mathrm{eff}}^{*}$, in gyroradius units.