Linear gyrokinetic calculations of toroidal momentum transport in a tokamak due to the ion temperature gradient mode

It is shown from a symmetry in the gyrokinetic equation that for up–down symmetric tokamak equilibria and for $u_{\varphi }⪢\rho {\upsilon }_{\mathrm{thi}}∕r$ (where $u_{\varphi }$ is the toroidal velocity, ${\upsilon }_{\mathrm{thi}}$ is the thermal ion velocity, $\rho$ is the Larmor radius, and $r$ is the radius of the flux surface), the transport of parallel momentum can be written as the sum of a diffusive and a pinch contribution with no off-diagonal terms due to temperature and pressure gradients. The measured parallel velocity gradient in ASDEX Upgrade [O. Gruber, H.-S. Bosch, S. Günter et al., Nucl. Fusion 39, 1321 (1999)] is insufficient to drive the parallel velocity shear instability. The parallel velocity is then transported by the ion temperature gradient mode. The diffusive contribution to the transport flux is investigated using a linear gyrokinetic approach, and it is found that the diffusion coefficient for parallel velocity transport divided by the ion heat conductivity coefficient is close to 1, and only weakly dependent on plasma parameters.