The neoclassical theory of poloidal flow damping in a tokamak

The damping rate of the poloidal flow uθ in a tokamak is determined in the banana regime as an initial value problem. The bounce averaged drift kinetic equation is solved analytically for early times and numerically for longer time scales of the order of the ion–ion collision time τii. Initial conditions are chosen for the ion distribution function fi(t=0) describing states with similar flows uθ(t=0), but varying structures in pitch angle velocity space. At early times an analytical treatment shows that the damping characteristics of uθ(t) depend sensitively on whether or not the ions resposible for the flow are close to the trapped–passing boundary. Initial decay is shown to be of the form duθ/dt∼(νiiε/t)1/2. A numerical treatment then confirms this early time result and extends the solution to the long term asymptotic decay, which is found to be independent of the initial preparation of the system. This long term evolution is also found to tend to independence of inverse aspect ratio ε as t→0.