The Maintenance of Coherent Vortices by Lagrangian Chaos in the Dimits Shift Regime of Plasma Edge Turbulence*

Understanding mechanisms for turbulence drive and saturation in the tokamak edge and scrape-off-layer is vital for predictive models of plasma confinement. These regions can experience large-amplitude, intermittent fluctuations that challenge assumptions of quasi-linearity and statistical homogeneity. Motivated by this, we study the Dimits shift regime of the flux-balanced Hasegawa-Wakatani (BHW) equations, which model a transitional regime of resistive drift-wave turbulence in the plasma edge. We show that turbulence in this regime is dominated by strong zonal flows and coherent drift-wave vortices which exhibit a form of "near-integrability" that qualitatively organizes the turbulent flows. Using an exact stochastic Lagrangian representation of vorticity transport based on the Feynman-Kac formula, we demonstrate how these flows influence ion polarization charge accumulation within the vortices through partial Lagrangian transport barriers linked to near-integrability. Drawing parallels with pattern formation in zonal flows, we argue that the resulting inhomogeneous mixing reinforces, rather than destroys, the large-amplitude vortex structures. Finally, we discuss possible broader implications of this mechanism, dubbed the "potential vorticity bucket brigade", for structure formation in fluid and plasma systems beyond the studied model.