Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation

Gyrokinetic simulation of tokamak transport has evolved sufficiently to allow direct comparison of numerical results with experimental data. It is to be emphasized that only with the simultaneous inclusion of many distinct and complex effects can this comparison realistically be made. Until now, numerical studies of tokamak microturbulence have been restricted to either (a) flux tubes or (b) electrostatic fluctuations. Using a newly developed global electromagnetic solver, we have been able to recover via direct simulation the Bohm-like scaling observed in DIII-D L-mode discharges. We also match, well within experimental uncertainty, the measured energy diffusivities.

Figure 1

Box-size study showing time-averaged ${\chi }_i$ profiles for ${\rho }_{*}=0.0026$ (a) and ${\rho }_{*}=0.004$ (b). These simulations include all physics effects, but with reduced mass ratio $(m_i/m_e=400)$. At the reference point, $r/a=0.6$, the small-box simulation is a good approximation to the full-domain calculation, but at substantially reduced computational expense.

Figure 2

Impact of selected physical effects on ion (a) and electron (b) energy transport, and comparison with experimental estimates.

Figure 3

Dependence of ion (a) and electron (b) transport on temperature gradient. Very close agreement in both electron and ion channel transport occurs for a 10% reduction in the baseline ion temperature gradient, whereas a 15% reduction eliminates transport entirely. Note that the actual experimental uncertainty in this gradient is estimated to be 30%.

Figure 4

Heat-flux avalanches induced by toroidal rotation. The upper frame shows the flux intensity (normalized) for a simulation with no toroidal rotation. When sheared rotation is switched on, avalanches of outward-directed heat-flux propagate inwards, as seen in the lower frame.