Scaling trends of the critical E x B shear for edge harmonic oscillation onset in DIII-D quiescent H-mode plasmas

Quiescent H-mode (QH-mode) has been identified as an attractive stationary operational regime in tokamaks due to its lack of edge localized modes (ELMs), along with good particle and impurity control aided by the presence of magnetohydrodynamic modes such as the edge harmonic oscillation (EHO) or edge turbulence. Experiments on the DIII-D tokamak explore local access conditions for QH-mode through measurements of the critical edge rotational shear necessary for the transition from a QH-mode with a coherent EHO to a typical ELMy H-mode. The critical E x B shear and EHO frequency are predicted by a nonlinear phase-dynamics model relating the pressure and velocity perturbations in the edge pedestal region. The reduced theoretical model predicts a linear relationship between critical shearing rate and c(s)/root L-p Delta x, where c(s) is the ion acoustic velocity, L-p the pressure gradient scale length, and Delta x the radial width of the mode. This scaling of the critical shearing rate agrees with the experimental trend, although the absolute magnitude of the shearing rate threshold is over-predicted by the model. Through a normalized predicted scaling, the model demonstrates the dynamic transition into and out of QH-mode qualitatively, within a single plasma discharge. The experimental comparison lends insight into improving the theoretical model by including more accurate geometry and toroidal mode number physics for more accurate quantitative predictions.