Scaling of Spontaneous Rotation with Temperature and Plasma Current in Tokamaks

Using theoretical arguments, a simple scaling law for the size of the intrinsic rotation observed in tokamaks in the absence of a momentum injection is found: The velocity generated in the core of a tokamak must be proportional to the ion temperature difference in the core divided by the plasma current, independent of the size of the device. The constant of proportionality is of the order of $10\text{ }\text{ }\mathrm{km}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{s}}^{\ensuremath{-}1}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{MA}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{keV}}^{\ensuremath{-}1}$. When the intrinsic rotation profile is hollow, i.e., it is countercurrent in the core of the tokamak and cocurrent in the edge, the scaling law presented in this Letter fits the data remarkably well for several tokamaks of vastly different size and heated by different mechanisms.