Experimental Evidence for the Intimate Interaction among Sheared Flows, Eddy Structures, Reynolds Stress, and Zonal Flows across a Transition to Improved Confinement

Dedicated experiments have been carried out at the TEXTOR tokamak in biasing-induced improved confinement regimes using Langmuir probe and GPI measurements. The results show the first evidence for the intimate interaction among sheared flows, eddy structures, Reynolds stress, zonal flows, and ambient fluctuations during a transition to an improved confinement. The sheared flows impose dynamic effects on turbulence structures, resulting in generation of Reynolds stress and zonal flows and eventually the suppression of background fluctuation levels via nonlinear energy transfer processes. The latter may therefore trigger a transition to the $H$ mode.

Figure 1

Typical waveforms of biasing $H$-mode discharges at TEXTOR. Time traces of (a) biasing voltages $V_{\mathrm{bias}}$ in different $V_{\mathrm{bM}}$ discharges; (b) ${\overline{n}}_e$ and $D_{\alpha }$ emission on the limiter in three $V_{\mathrm{bM}}$ shots; (c) radial position of reciprocating probes and the GPI exposure time window.

Figure 2

Radial dependence of (a) $E_r$ and (b) $E_r\times B$ flow shear (${\omega }_s$) in different $V_{\mathrm{bM}}$ shots.

Figure 3

(a)–(b) GPI frames and (c)–(d) their 2D wave number spectra measured in two $V_{\mathrm{bM}}$ discharges. (a), (c) $V_{\mathrm{bM}}=0\mathrm{V}$ and (b), (d) $V_{\mathrm{bM}}=60\mathrm{V}$.

Figure 4

(a)–(f) Contour plots of 2D wave number spectra in different $V_{\mathrm{bM}}$ shots. (g)–(l) Frequency spectra of potential fluctuations. The red dashed curve is the spectrum for $V_{\mathrm{bM}}=0$. Bottom row: A schematic view of the eddy shape under different $V_{\mathrm{bM}}$.

Figure 5

(a) Radial profiles of Reynolds stress measured by GPI at different $V_{\mathrm{bM}}$ discharges. (b) Time traces of the turbulence energy and the $V_{E\times B}$ velocity at $V_{\mathrm{bM}}=150\mathrm{V}$. (c) The energy transfer parameters in the power balance model as a function of $V_{\mathrm{bM}}$.