Size Scaling of Intrinsic Rotation in DIII-D

Despite the richness in the variety of the profiles of intrinsic rotation in axisymmetric tokamaks, a common feature is a co-Ip directed toroidal velocity on the outboard midplane in the region of $\rho\sim 0.8$ in DIII-D. This feature showed a ``Rice scaling'' (RS) in DIII-D and led to similarity experiments with C-Mod [1]. RS correlates toroidal velocity with W/Ip, where W is the total plasma kinetic energy and Ip the plasma current. Subsequent analysis from DIII-D shows a clear $\rho\ast$ dimensionless scaling of this intrinsic velocity in DIII-D, where $\rho\ast\sim\surd T_i/aB$, multiplying the $\beta$q scaling indicative of RS [1]. The DIII-D scaling is $M_A\sim\beta_N\rho\ast$, where $M_A$ is the Alfv\'en ``Mach'' value and $\beta_N$ is normalized $\beta$. In machine parameters it is very similar to the theoretical ``Parra scaling,'' [2] which emphasizes the correlation of toroidal velocity with ion temperature as seen experimentally, but in this DIII-D scaling having an additional critical dependence on $\surd\beta$. Published data from C-Mod and low power ICRF in JET also fit with this DIII-D scaling. The relation to the RS will be described.\\[4pt] [1] J.S. deGrassie et al., Phys. Plasmas 14, 056115 (2007).\\[0pt] [2] F. Parra et al, Phys. Rev. Lett. 108, 095001 (2012)