Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

Di Qi, Andrew J. Majda

Research output: Contribution to journalArticlepeer-review


A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima (MHM for short) model, which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima (CHM for short) model for both plasma and geophysical flows. The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state. Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model, while stabilizing damping effect is shown with a zonal flow base state. Together with the selective decay effect from the dissipation, the secondary instability offers a complete characterization of the convergence process to the purely zonal structure. Direct numerical simulations with and without dissipation are carried out to confirm the instability theory. It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration. In comparison, the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

Original languageEnglish (US)
Pages (from-to)869-890
Number of pages22
JournalChinese Annals of Mathematics. Series B
Issue number6
StatePublished - Nov 1 2019


  • 35Q60
  • 76E25
  • 76F06
  • Drift wave turbulence
  • Modified Hasegawa-Mima model
  • Secondary instability
  • Zonal flow generation

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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