Thermal diffusivities in DIII-D show evidence of critical gradients

The ion thermal diffusivities ${\mathrm{(\chi }}_i)$ in DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] discharges exhibit a strong nonlinear dependence on the measured temperature gradients. In low confinement mode (L-mode) discharges with low toroidal rotation, the ion thermal diffusivity, ${\chi }_i,$ has an approximately Heaviside function dependence on the major radius divided by the radial scale length of the ion temperature, ${\mathrm{R/L}}_{\mathrm{Ti}}.$ When ${\mathrm{R/L}}_{\mathrm{Ti}}$ is less than a critical value, the ${\chi }_i’\mathrm{s}$ are very small. When ${\mathrm{R/L}}_{\mathrm{Ti}}$ is about equal to the critical value, ${\chi }_i$ increases rapidly. Although the gradient profiles for high confinement (H-mode) have a different shape, they still show a critical gradient type of behavior. This type of dependence is consistent with the predictions for transport, which is dominated by ion temperature gradient modes and is a strong indicator that these modes are the main contributors toward L-mode transport in DIII-D and a major contributor to transport in a certain region of DIII-D H-mode discharges. When strong rotational shear is present, the thermal confinement is improved in regions of the plasma. In these regions, the dependence of the diffusivities on the gradients is changed. The type of change is consistent with the physical picture that when the $\mathrm{E\times B}$ shearing frequency is greater than the maximum linear growth rate of the modes as calculated without shear, then the modes are stabilized and the transport is reduced.