[Table of Contents]

Plasma and Fusion Research

Volume 3, 011 (2008)

Rapid Communications

Spectral Effect of Zonal Flows and Enhanced Growth Rate
Ken UZAWA, Jiquan LI and Yasuaki KISHIMOTO
Graduate School of Energy Science, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan
(Received 28 December 2007 / Accepted 18 January 2008 / Published 28 February 2008)


The effect of the spectrum of the radial wave number of zonal flows on zonal flow generation is theoretically investigated using the Hasegawa-Mima turbulence model by representing the spectrum by means of two monochromatic waves. Based on this method, we explored a ten-wave coupling model of modulational instability. We found that the zonal flow generation is qualitatively different in cases with and without such a spectral effect, exhibiting the enhancement of the growth rate. This originates from the coupling property of the new zonal flow eigenmode equation system. We refer to this state as a coupled zonal flows eigenmode, which leads to a spatial modulation of zonal flows affected by the turbulence structure.


drift wave turbulence, zonal flow, modulational instability, electron temperature gradient (ETG) mode

DOI: 10.1585/pfr.3.011


  • [1] A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 59, 1581 (1987).
  • [2] P.H. Diamond et al., Plasma Phys. Control. Fusion 47, R35 (2005).
  • [3] L. Chen et al., Phys. Plasmas 7, 3129 (2000).
  • [4] J.Q. Li and Y. Kishimoto, Phys. Plasmas 9, 1241 (2002).
  • [5] K. Uzawa et al., Plasma Fusion Res. 1, 024 (2006).
  • [6] A.I. Smolyakov et al., Phys. Plasmas 7, 1349 (2000).
  • [7] J. Anderson and Y. Kishimoto, Phys. Plasmas 14, 012308 (2007).
  • [8] M.A. Malkov et al., Phys. Plasmas 8, 1553 (2001).

This paper may be cited as follows:

Ken UZAWA, Jiquan LI and Yasuaki KISHIMOTO, Plasma Fusion Res. 3, 011 (2008).