Inhomogeneous mixing: From microscopic dynamics to mesoscopic staircases

TL;DR

The paper addresses how inhomogeneous mixing in magnetized plasmas, driven by intermittent blobs/voids and modulated by $E \times B$ shear, gives rise to mesoscopic transport barriers known as the $E \times B$ staircase. It synthesizes experimental progress across multiple machines, detailing turbulence spreading by blobs/voids, layer broadening of the turbulent envelope, and the interaction with zonal flows, alongside observations and metrics of the staircase (lifetime, barrier strength, tread width). It reviews theoretical models (bistable mixing, homogenization, phase separation) and compares them with analogies from classical layer-formation phenomena, aiming to bridge micro- and mesoscopic transport physics. The findings illuminate how coherent structures and turbulence spreading shape transport barriers, with implications for core–boundary coupling and predictive modeling in ITER-like devices. overall, the work advances a coherent picture of layering in confined magnetized plasmas and outlines directions for unified modeling and multi-machine validation.

Abstract

Inhomogeneous mixing and the consequent mesoscopic layered structure have been observed in many physical systems, including magnetically confined fusion plasmas. Especially, in plasmas, mixing can be enhanced through turbulence spreading by intermittent coherent structures (blobs/voids), or suppressed due to the formation of transport barriers (sheared zonal flows). Interestingly, blobs/voids and zonal flows are not independent, and they can co-exist in a state of inhomogeneous mixing, often called the E x B staircase. In this paper, we first introduce recent experimental progress on the physics of blobs/voids: how turbulence spreading by blobs/voids occurs, the consequences of enhanced turbulence spreading for the power decay length, and the interaction between blobs/voids and zonal flows. Then, we provide a brief review of experimental results on staircases, or more generally layered mesoscopic transport barriers. Staircases are often elusive and different complementary methods have been utilized to identify them, but our understanding is still incomplete. This paper serves as an initial step toward applying insights gained from inhomogeneous mixing due to blobs/voids to the understanding of a staircase.

Figures (10)

• Figure 1: Schematic diagram of (a) homogeneous mixing and (b) inhomogeneous mixing.
• Figure 2: Schematic diagram of birth of a blob-void pair due to local relaxation of gradients of a conserved order parameter (density $n$ or temperature $T$).
• Figure 3: Blob and void structures in the linear device LAPD carter2006. In (a) and (b) are cross-conditional averages of ion saturation current $\tilde{I}_{sat}$ (representative of density fluctuations) for blob and void events respectively, showing propagation of blobs out of the plasma and voids back into the plasma. In (c) and (d) are two-dimensional cross-conditional averages to show the blob and void structures respectively. Here, a negative $\Delta x$ indicates closer to the outer wall, and a positive $\Delta x$ indicates closer to the core of plasma. Reprinted from Carter et al. carter2006. Copyright 2006 AIP.
• Figure 4: (a) Turbulence spreading "lip" curves: distribution of turbulence spreading flux $P_{spreading}(A)$ relative to the density fluctuation amplitude $A = | \tilde{n} |/\sigma_{\tilde{n}}$; (b) contribution of blobs and voids to the total turbulence spreading $\langle {\tilde{v}}_{r}{\tilde{n}}^{2} \rangle/2$ in the plasma edge. Reprinted from Long et al. long2024_structures. Copyright 2024 IOP.
• Figure 5: (a) Time series of the relative density fluctuations $\delta n/n$ (top) and of the perpendicular velocity (bottom); (b) wavelet power of $\delta n/n$ (black solid line) and of the poloidal-velocity fluctuations near the GAM frequency (green dashed line) in the plasma edge. Vertical red lines denote the times when voids are present. Reprinted from Sladkomedova et al. sladkomedova2023. Copyright 2023 Cambridge University Press.