Scaling of spontaneous rotation with temperature and plasma current in tokamaks

TL;DR

This paper derives a simple theoretical scaling law for intrinsic plasma rotation in tokamaks, showing it depends on ion temperature difference and inversely on plasma current, consistent with experimental data across various devices.

Contribution

It introduces a new theoretical scaling law for intrinsic rotation in tokamaks, linking rotation velocity to ion temperature difference and plasma current, independent of device size.

Findings

Scaling law fits data from multiple tokamaks

Rotation velocity proportional to ion temperature difference

Inverse relation between rotation and plasma current

Abstract

Using theoretical arguments, a simple scaling law for the size of the intrinsic rotation observed in tokamaks in the absence of 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 $10\,\mathrm{km \cdot s^{-1} \cdot MA \cdot keV^{-1}}$. When the intrinsic rotation profile is hollow, i.e. it is counter-current in the core of the tokamak and co-current 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.