Shear flow effects on ion thermal transport in tokamaks

From various laboratory and numerical experiments, there is clear evidence that under certain conditions the presence of sheared flows in a tokamak plasma can significantly reduce the ion thermal transport. In the presence of plasma fluctuations driven by the ion temperature gradient, the flows of energy and momentum parallel and perpendicular to the magnetic field are coupled with each other. This coupling manifests itself as significant off-diagonal coupling coefficients that give rise to new terms for anomalous transport. The authors derive from the gyrokinetic equation a set of velocity moment equations that describe the interaction among plasma turbulent fluctuations, the temperature gradient, the toroidal velocity shear, and the poloidal flow in a tokamak plasma. Four coupled equations for the amplitudes of the state variables radially extended over the transport region by toroidicity induced coupling are derived. The equations show bifurcations from the low confinement mode without sheared flows to high confinement mode with substantially reduced transport due to strong shear flows. Also discussed is the reduced version with three state variables. In the presence of sheared flows, the radially extended coupled toroidal modes driven by the ion temperature gradient disintegrate into smaller, less elongated vortices. Such a transition to smaller spatial correlation lengths changes the transport from Bohm-like to gyrobohm-like. The properties of these equations are analyzed. The conditions for the improved confined regime are obtained as a function of the momentum-energy deposition rates and profiles. The appearance of a transport barrier is a consequence of the present theory.