Zonal Flows and Transient Dynamics of the $L\mathrm{\text{−}}H$ Transition

We elucidate the role of zonal flows in transient phenomena observed during $L\mathrm{\text{−}}H$ transition by studying a simple $L\mathrm{\text{−}}H$ transition model which contains the evolution of zonal flows, mean $\mathbf{E}\times \mathbf{B}$ flows, and the ion pressure gradient. Zonal flows are shown to trigger the $L\mathrm{\text{−}}H$ transition and cause time-transient behavior through the self-regulation of turbulence before a mean shearing, due to a steep pressure profile, secures a quiescent $H$ mode. Surprisingly, this self-regulation lowers the power threshold for the ultimate transition to a quiescent $H$-mode state.

Figure 1

Evolution of $\mathcal{E}$ (solid line), $V_{\mathrm{Z}\mathrm{F}}$ (dotted line), and $\mathcal{N}/5$ (dashed line) as a function of input power $Q=0.01t$. Parameter values are $a_1=0.2$, $a_2=a_3=0.7$, $b_1=1.5$, $b_2=b_3=1$, $c_1=1$, $c_2=0.5$, and $d=1$.

Figure 2

The same as Fig. 1 besides $b_2=0$.

Figure 3

Evolution of $\mathcal{E}$ (solid line) and $\mathcal{N}$ (dashed line) as a function of input power $Q=0.01t$ with $V_{\mathrm{Z}\mathrm{F}}=0$. Parameter values are the same as Fig. 1. For comparison, $\mathcal{E}$ (dotted line) and $\mathcal{N}$ (dash-dotted line) in Fig. 1 are superimposed.