Scaling of Energy Confinement with Rotation for Advanced Inductive Plasmas in DIII-D

We report the scaling of the energy confinement time in moderately high beta ($2.2\leq\beta_N\leq3.3$) advanced inductive plasmas in DIII-D, based on an analysis of a database of 630 discharges that have stationary conditions for $\geq 1$ s ($\sim\tau_R$). In dedicated experiments it was found that $\tau_E$ decreases by $\sim$40\% from the highest to the lowest accessible rotation, prompting this study. Both power-law and offset-linear models are fit to the data, with the rotation represented by either $M_A$ or $M_S$, the Mach number based on the Alfv\'en or the sound speed. A power-law ($\tau = C\, B^{a_B}\, n^{a_n}...\, M^{a_M}$) is the most commonly used model, but there are strong physical arguments for a model that does not yield zero confinement for zero rotation, e.g., offset-linear ($\tau = C_a\, B^{a_B}\, n^{a_n}...+C_b\, B^{b_B}\, n^{b_n}...\, M$). As there are values in the dataset that fall outside the general trend, the fitting is done by minimizing the mean absolute deviation, a method more robust than the common $\chi^2$ minimization. There is no significant statistical difference between fits using $M_A$ or $M_S$. Also no significant difference is found between the power-law and offset-linear models.