How nonlinear spectral back transfer limits the temporal coherency of zonal modes?

TL;DR

This paper shows that nonlinear spectral back-transfer limits the persistence of zonal flows in plasma turbulence, with negative triangularity reducing back-transfer and enhancing turbulence regulation.

Contribution

It demonstrates that spectral back-transfer is a key nonlinear damping mechanism affecting zonal flow coherence, with implications for modeling plasma turbulence.

Findings

Back-transfer occurs intermittently in bursts co-existing with zonal flow generation.

Negative triangularity reduces back-transfer, increasing shear auto-coherence time.

Reduced back-transfer enhances turbulence regulation despite lower zonal kinetic energy.

Abstract

Zonal modes are central to magnetic confinement because their radial shears regulate turbulence and transport. While the generation of these flows is well understood, the mechanisms limiting their persistence in collisionless regimes remain unresolved. In this Letter, we demonstrate that nonlinear spectral back-transfer of free energy from zonal modes to turbulence sets the fundamental limit on the temporal coherency of the shearing field. Using gyrokinetic GENE simulations, we show that back-transfer is highly intermittent and occurs in bursts that co-exist with the zonal flow generation process. We find that negative triangularity (NT) plasmas exhibit significantly reduced back-transfer compared to positive triangularity (PT). This suppression increases the shear auto-coherence time $\tau_{E}$ and the shearing Kubo number $K_{u}$, leading to more resilient and effective turbulence regulation despite lower absolute zonal kinetic energy. These results identify back-transfer as a key nonlinear damping mechanism and suggest that it must be explicitly treated in reduced models of drift-wave zonal-flow turbulence.