H-mode transition in the TJ-II stellarator plasmas

TL;DR

This study investigates the L-H transition in TJ-II stellarator plasmas, focusing on how turbulence suppression and edge flow dynamics drive confinement improvement. It combines a comprehensive diagnostic suite with advanced analysis tools to resolve fast, localized turbulence–flow interactions, emphasizing $E_r$ and $E\times B$ dynamics. The results demonstrate that fluctuating $E\times B$ flows, i.e., zonal flows, correlate with and likely trigger the transition, revealing a predator–prey relationship between turbulence and flows through nonlinear bicoherence analyses and the observation of a Limit Cycle Oscillation (LCO). The work also highlights scale-dependent turbulence suppression, magnetic topology effects, and potential fast-particle influences, providing a framework for predictive modeling and guiding future TJ-II and broader toroidal-device research.

Abstract

Since the first H-mode transitions were observed in TJ-II plasmas in 2008, an extensive experimental effort has been done aiming a better physics understanding of confinement transitions. In this paper, an overview of the main findings related to the L-H transition in TJ-II is presented including how the radial electric field is driven, which are the possible mechanisms for turbulence suppression, and what are the related temporal and spatial scales which can impact the transition. The trigger of the L-H transition in TJ-II plasmas is found to be more correlated with the development of fluctuating $E\times B$ flows than with steady-state $E_r$ effects, pointing to the role played by zonal flows in mediating the transition. Experimental evidence supporting the predator-prey relationship between turbulence and flows as the basis for the L-H transition, found for the first time in TJ-II, reinforces this conclusion. Besides, the reduction in the turbulent transport at the transition is detected at the barrier region but also in a wider radial range with weak or even zero $E\times B$ flow shear, what points to other mechanisms beyond the turbulence suppression by local sheared flows.

Figures (4)

• Figure 1: Turbulence and $E\times B$ flow shear measured using Doppler reflectometry during the L-H transition in the TJ-II stellarator. (a) Time evolution of $E_r$ measured at two adjacent radial positions right at the $E\times B$ flow shear location: ch1 at $\rho$ = 0.86 and ch2 at $\rho$ = 0.82. (b) $E_r$ shear (in red) and density fluctuations (in green), and (c) the low frequency components (1-10 kHz) of the fluctuating $E_r$ shear. The vertical line indicates the time of the L-H transition. Figure reproduced with permission from Estrada:2009. Copyright 2009 IOP Publishing.
• Figure 2: Radially resolved auto-bicoherence measured during the L-H transition in the TJ-II stellarator. The vertical dashed line indicates the L-H transition time defined as in figure 1. The $E_r$ shear position is marked in the figure. Figure reproduced with permission from Milligen:2013. Copyright 2013 IAEA, Vienna.
• Figure 3: Time evolution of $E\times B$ flow and density fluctuations measured by Doppler reflectometry during the I-phase in the TJ-II stellarator. Top: Spectrogram of the Doppler reflectometer signal measured at $\rho \sim 0.8$, in a magnetic configuration with $\iota/2\pi = 1.53$. The color code reflects the density fluctuation level and the frequency of the Doppler peak gives $E_r$. Middle: Time evolution of $E_r$ (red solid line) and density fluctuation level (green broken line) obtained from the spectrogram. Bottom: Relation between density fluctuation level and $E_r$ in phase space during the I-phase; only two of the cycles are displayed. The time interval between consecutive points is 12.8 $\mu s$. Figure reproduced with permission from Estrada:2010c. Copyright 2010 Europhysics Letters Association.
• Figure 4: Density fluctuation wavenumber spectra measured during the I-phase by Doppler reflectometry in the TJ-II stellarator. The extreme values of the turbulence level measured during the oscillatory phase are represented: maxima (in blue) and minima (in red). The spectral indexes are shown for each spectrum and the normalized wave-numbers $k_\perp \rho_s = 1$$\&$$2$ are marked in the figure. Figure reproduced with permission from Estrada:2012b. Copyright 2012 IOP Publishing.