Toroidal momentum confinement in neoclassical quasilinear theory in tokamaks

The neoclassical quasilinear theory is employed to study the toroidal momentum confinement in tokamaks. The electrostatic fluctuation-induced toroidal stress is calculated. It is found that besides the conventional diffusion term, there is also a convective term in the toroidal momentum equation. In the case of a weak toroidal momentum source, the logarithmic gradient of the toroidal flow is proportional to the linear combination of the logarithmic gradients of the plasma pressure and the temperature. This conclusion is insensitive to both the renormalization procedure and the magnitude of the fluctuations. The theory is applied to explain the changing of the toroidal flow direction after low mode (L-mode) to high mode (H-mode) transition observed in some experiments.