Main-Ion Intrinsic Toroidal Rotation Profile Driven by Residual Stress Torque from Ion Temperature Gradient Turbulence in the DIII-D Tokamak

Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. The prediction of the velocity profile by integrating the momentum balance equation produces a rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.

Figure 1

Experimental main-ion toroidal rotation profiles displaying a reversed rotation profile upon increasing the heating power from 0.5, 1.0, and 1.7 MW of ECH.

Figure 2

Experimental (a) electron and (b) ion temperature profiles and (c) electron density profiles for 0.5, 1.0, and 1.7 MW of ECH. Above 1.0 MW of ECH, the profiles are resilient to changes and the energy confinement (d) degrades.

Figure 3

Linear turbulence stability at displaying excitation of linearly unstable ITG turbulence upon power step from (a) 0.5 MW to (b) 1.0 MW with appearance of (c),(d) midradius finite growth rate with negative frequency. The dashed boxes indicate (a),(b) growth rate and (b),(c) frequency at low wave number $k_{\theta }{\rho }_s<1.0$.

Figure 4

Residual stress displaying dipolar structure that produces the hollow rotation profile.

Figure 5

Ion heat and momentum diffusivity used to validate $\mathrm{Pr}\approx 0.7$. At the off-axis peak of the rotation profile, $\partial {\mathrm{\Omega }}_{\phi }/\partial \rho$ is 0 and ${\chi }_{\phi }$ is undefined.

Figure 6

Momentum flux from three simulations used to separate residual stress, momentum diffusion, and pinch.

Figure 7

Main-ion toroidal rotation and gts simulation for (a) 1.0 and (b) 1.7 MW heating with experimental data taken from Fig. 1. In (a), we include the prediction including a later time average and Prandtl numbers within the variation of the gts simulation.