Measurement of Turbulence-driven Reynolds Stress and Its Contribution to Toroidal Intrinsic Rotation in the DIII-D Tokamak*

Intrinsic rotation is important in fusion plasmas because rotation and its shear are known to suppress turbulent transport, stabilize MHD modes, and affect L-H transitions. Turbulence-driven Reynolds stress, $\langle \tilde{v}_r \tilde{v}_\phi \rangle$, is theoretically predicted to generate intrinsic toroidal rotation via symmetry breaking. To investigate this, the radial profile of Reynolds stress is experimentally determined using fluctuation measurements from Beam Emission Spectroscopy (BES) and Ultra-Fast Charge Exchange Recombination Spectroscopy (UF-CHERS). BES measures long-wavelength density fluctuations and can use velocimetry to infer the radial and poloidal velocity fluctuations, $\tilde{v}_r$ and $\tilde{v}_\theta$. UF-CHERS is located on the same plane as BES and measures the correlated toroidal velocity fluctuations from carbon impurities, $\tilde{v}_\phi$. In otherwise matched DIII-D plasmas, Electron Cyclotron Heating (ECH) is applied to alter the ion and electron heat fluxes, changing the long-wavelength turbulence composition from dominantly electron modes to a mixture of electron and ion modes. In addition, the bulk of the toroidal rotation profile reverses from counter-current to co-current in the plasmas with ECH. A radially non-uniform residual stress is extracted from the measured Reynolds stress near the plasma edge, which develops in response to changes in turbulence and generates a strong co-current intrinsic torque. Rotation profiles are reconstructed from the momentum balance equation with and without this intrinsic torque, and are compared with measurements, showing that the turbulence-generated intrinsic torque is required to reproduce the observed rotation profiles. These results provide important insights into the relationship between turbulence and flow generation in fusion plasmas, consistent with theories of turbulence-driven intrinsic rotation, and support the use of turbulence models to predict rotation profiles for ITER and other magnetic fusion facilities.