On Nonlocal Energy Transfer via Zonal Flow in the Dimits Shift

Abstract

The two-dimensional Terry-Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\mathbf{E}\times \mathbf{B}$ nonlinearity that can efficiently transfer energy nonlocally to length scales on the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This nonlocal mechanism of energy transfer is argued to be generically important even for more physically complete systems.

28 pages, 7 figures, 4 movies

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Cited by in corpus (18)

• Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence
• Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
• On the Rayleigh--Kuo criterion for the tertiary instability of zonal flows
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• Wave-kinetic approach to zonal-flow dynamics: recent advances
• On the structure of the drifton phase space and its relation to the Rayleigh--Kuo criterion of the zonal-flow stability
• Dimits transition in three-dimensional ion-temperature-gradient turbulence
• Theory of the tertiary instability and the Dimits shift within a scalar model
• Nonlinear saturation and oscillations of collisionless zonal flows
• Dimits shift, avalanche-like bursts, and Solitary propagating structures in the two-field Flux-Balanced Hasegawa-Wakatani model for plasma edge turbulence
• A Flux-Balanced Fluid Model for Collisional Plasma Edge Turbulence: Numerical Simulations with Different Aspect Ratios
• The residual flow in well-optimized stellarators
• Solitary zonal structures in subcritical drift waves: a minimum model
• Predicting the Z-pinch Dimits shift through gyrokinetic tertiary instability analysis of the entropy mode
• Nearly integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence
• Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics
• Wave kinetic equation in a nonstationary and inhomogeneous medium with a weak quadratic nonlinearity
• Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit