How turbulence fronts induce plasma spin-up

A calculation which describes the spin-up of toroidal plasmas by the radial propagation of turbulence fronts with broken parallel symmetry is presented. The associated flux of parallel momentum is calculated by using a two-scale direct-interaction approximation in the weak turbulence limit. We show that fluctuation momentum spreads faster than mean flow momentum. Specifically, the turbulent flux of wave momentum is stronger than the momentum pinch. The scattering of fluctuation momentum can induce edge-core coupling of toroidal flows, as observed in experiments.

Figure 1

A schematic picture of the edge-core coupling of toroidal flows. In the conventional view, the change in the mean flow can influence the change in core flows through an inward pinch. Here, in contrast, we argue that the spreading of fluctuation momentum into the core plasmas is a dominant process.

Figure 2

A contour plot for the coupling coefficient $F_1$, for $k_{1x}=0.8$ and $k_{1y}=0.9$. The dotted (red) curve is the resonant manifold, defined by ${\omega }_{{\mathbf{k}}_1+{\mathbf{k}}_2}-{\omega }_{{\mathbf{k}}_1}-{\omega }_{{\mathbf{k}}_2}=0$. The summation must be evaluated along the curve. A triad that gives a dominant contribution is also indicated.

Figure 3

Jogging the edge flows results in a core flow change by spreading the edge fluctuation momentum into the core.