Mesoscopic transport in KSTAR plasmas: avalanches and the $E \times B$ staircase

TL;DR

This study probes the coexistence and mutual influence of avalanches and the $E \times B$ staircase in KSTAR plasmas operating near the nonlinear regime. By combining high-resolution electron temperature measurements, beam emission spectroscopy, and advanced time-series analyses, the authors demonstrate that avalanches propagate ballistically at $60.5 \pm 24.5$ m/s and seed/modify mesoscopic staircases that act as transport barriers, confining smaller events while being penetrated by rare large avalanches. The staircase formation is linked to seed perturbations and exhibits a Fréchet-like width distribution near large avalanches, consistent with extreme-value statistics, while the avalanche statistics show power-law behavior, $P(S) \propto S^{-\alpha}$, enabling a unified view of self-organization in the near-marginal regime. The results advance understanding of mesoscopic transport, offer pathways to validate transport models across machines, and highlight the interplay between localized perturbations, zonal-flow structures, and turbulence through regimes characterized by long-range correlations and multi-scale dynamics.

Abstract

The self-organization is one of the most interesting phenomena in the non-equilibrium complex system, generating ordered structures of different sizes and durations. In tokamak plasmas, various self-organized phenomena have been reported, and two of them, coexisting in the near-marginal (interaction dominant) regime, are avalanches and the $E \times B$ staircase. Avalanches mean the ballistic flux propagation event through successive interactions as it propagates, and the $E \times B$ staircase means a globally ordered pattern of self-organized zonal flow layers. Various models have been suggested to understand their characteristics and relation, but experimental researches have been mostly limited to the demonstration of their existence. Here we report detailed analyses of their dynamics and statistics and explain their relation. Avalanches influence the formation and the width distribution of the $E \times B$ staircase, while the $E \times B$ staircase confines avalanches within its mesoscopic width until dissipated or penetrated. Our perspective to consider them the self-organization phenomena enhances our fundamental understanding of them as well as links our findings with the self-organization of mesoscopic structures in various complex systems.

Figures (12)

• Figure 1: (a) The channel distance $\Delta R$ versus the maximum correlation time lag $\Delta t$. (b) The average avalanche propagation speed versus $\eta_i \equiv L_n/L_{T_\mathrm{i}}$. (c) The avalanche rate versus the magnetic shear. (d) The average avalanche amplitude versus the magnetic shear.
• Figure 2: (a) The normalized density fluctuation ($\tilde{n}_\mathrm{e} = \delta n_\mathrm{e} / \langle n_\mathrm{e} \rangle$) power spectrum. (b) The local wavenumber frequency spectrum. The cross correlation coefficient ($C_\mathrm{coef}$) images of density fluctuation (50--100 kHz) at the zero time lag in (c) the near-large-avalanche phases and (d) the far-from-large-avalanche phases. The white X indicates the reference channel for the $C_\mathrm{coef}$ calculation. The length of the black arrows means the strength of the local laboratory phase velocity $v^\mathrm{ph}_\mathrm{lab}$.
• Figure 3: (a) The normalized electron temperature fluctuation power spectrum. (b) The local wavenumber frequency spectrum.
• Figure 4: (a) The $T_\mathrm{e}$ time trace at $R \approx R_\mathrm{av}$. Measurement times of $\delta T_\mathrm{e} / \langle T_\mathrm{e} \rangle$ images shown in (b) and (c) are indicated by red lines and letters ‘b’s and ‘c’s, respectively. $\delta T_\mathrm{e} / \langle T_\mathrm{e} \rangle$ images along time ($t$) during the large avalanche (b) without and (c) with the $E \times B$ staircase.
• Figure 5: (a) The initial formation of the $E \times B$ staircase (class A). (b) Transformation of the smaller scale ($\Delta_z \approx 10$ cm) staircase to the larger scale ($\Delta_z \approx 20$ cm) staircase. (c) Transformation of the larger scale ($\Delta_z \approx 25$ cm) staircase to the smaller scale ($\Delta_z \approx 12$ cm) staircase.