Bifurcation in electrostatic resistive drift wave turbulence

Abstract

The Hasegawa-Wakatani equations, coupling plasma density and electrostatic potential through an approximation to the physics of parallel electron motions, are a simple model that describes resistive drift wave turbulence. We present numerical analyses of bifurcation phenomena in the model that provide new insights into the interactions between turbulence and zonal flows in the tokamak plasma edge region. The simulation results show a regime where, after an initial transient, drift wave turbulence is suppressed through zonal flow generation. As a parameter controlling the strength of the turbulence is tuned, this zonal flow dominated state is rapidly destroyed and a turbulence-dominated state re-emerges. The transition is explained in terms of the KelvinHelmholtz stability of zonal flows. This is the first observation of an upshift of turbulence onset in the resistive drift wave system, which is analogous to the well-known Dimits shift in turbulence driven by ion temperature gradients. * Electronic address: ryusuke.numata@anu.edu.au

Nonadiabatic electron response in the Hasegawa-Wakatani equations

“…For 2D equations, substitute ∇ 2 → −k 2 for nonzonal components and ∇ 2 → 0 for zonal components, with the constant k nominally unity. 38 Although wellmotivated by geometrical constraints, 16 the 2D model of course misses modal resonances with rational surfaces as well as the nonlinear cascade in k . For a realistic 3D model, some form of magnetic shear must be incorporated: The simplest shearless model, ∇ → ∂ z with simply periodic boundary conditions in z, admits a k = 0 mode for each and every k ⊥ , which is grossly inconsistent with toroidal and poloidal periodicity for nonvanishing rotational transform.…”

Shear-flow trapped-ion-mode interaction revisited. I. Influence of low-frequency zonal flow on ion-temperature-gradient driven turbulence

“…are, respectively, defined by relations (13) and (14) by substituting f j;E by f j;E ¼ J 0 f j;E . The smoothed ion density n and ion pressure P ðnÞ are defined by Eqs.…”

Hasegawa–Wakatani and Modified Hasegawa–Wakatani Turbulence Induced by Ion-Temperature-Gradient Instabilities

“…This model aims to capture the essential physics while involving the least number of scalar fields as possible, in order to get a deeper physical insight and in the attempt to unravel the complexity of the phenomena under investigation. In this context, great interest has been recently attracted by the two-field descriptions (involving ion density and vorticity) provided by the Hasegawa-Wakatani [15] (HW) and Modified Hasegawa-Wakatani [16,17] (MHW) models for drift-wave turbulence. They consist in a more complex formulation of the earlier and somehow simpler Charney-Hasegawa-Mima (CHM) model, successful in describing a wide variety of turbulent process, both in atmospheric fluids [13] and in plasmas [14].…”

“…These corrections to the HW model have been included in Ref. [16] because it was mentioned that, without these terms, the original HW model was otherwise incapable of describing the zonal flow generation. This assertion, mentioned in Ref.…”