Stationary Zonal Flows during the Formation of the Edge Transport Barrier in the JET Tokamak

High spatial resolution Doppler backscattering measurements in JET have enabled new insights into the development of the edge $E_r$. We observe fine-scale spatial structures in the edge $E_r$ well with a wave number $k_r{\rho }_i\approx 0.4–0.8$, consistent with stationary zonal flows, the characteristics of which vary with density. The zonal flow amplitude and wavelength both decrease with local collisionality, such that the zonal flow $E\times B$ shear increases. Above the minimum of the $L\text{−}H$ transition power threshold dependence on density, the zonal flows are present during $L$ mode and disappear following the $H$-mode transition, while below the minimum they are reduced below measurable amplitude during $L$ mode, before the $L\text{−}H$ transition.

Figure 1

Comparison of $E_r$ measured with CXRS (uncertainties indicated by shaded area) and DBS in $L$ mode. DBS data shown both assuming $v_{\mathrm{ph}}=0$ and $v_{\mathrm{ph}}=v_{\mathrm{dia},e}$. DBS data are shifted radially by 2.1 cm. Shown in the inset panel are the the polynomial fits for each of the CXRS $E_r$ terms and their sum.

Figure 2

$E_r$ profile measured with three consecutive 200 ms sweeps during a steady-state Ohmic time period.

Figure 3

(a) Ohmic $E_r$ profiles for six shots at different densities, $t=12.4–12.6\mathrm{s}$. For clarity, for each density increment the $E_r$ profile is offset by an additional $3\mathrm{kV}/\mathrm{m}$ (annotated). (b) Averaged $n_e$ profile 12.4–12.6 s, from a profile reflectometer.

Figure 4

Local scaling of the zonal flow radial wavelength and amplitude with collisionality.

Figure 5

(a)–(c) $E_r$ and density fluctuation (d)–(f) profiles for Ohmic conditions and several hundred milliseconds before and after the $L\text{−}H$ transition at three densities: (a),(d) $⟨n_e⟩=1.6\times {10}^{19}{\mathrm{m}}^{-3}$, (b),(e) $⟨n_e⟩=2.0\times {10}^{19}{\mathrm{m}}^{-3}$, and (c),(f) $⟨n_e⟩=2.6\times {10}^{19}{\mathrm{m}}^{-3}$. Density fluctuations measured at $k_{\perp }\approx 3{\mathrm{cm}}^{-1}$ ($k_{\perp }{\rho }_i\approx 0.2$) and normalized to Ohmic values.