# Plasma and Fusion Research

## Volume 1, 024 (2006)

# Letters

- 1)
- Graduate School of Energy Science, Kyoto University
- 2)
- Naka Fusion Research Establishment
- 3)
- Southwestern Institute of Physics

### Abstract

The effects of an external mean flow on the generation of zonal flow in drift wave turbulence are theoretically studied in terms of a modulational instability analysis.
A dispersion relation for the zonal flow instability having complex frequency ω_{q} = Ω_{q} + iγ_{q} is derived, which depends on the external mean flow's amplitude |φ_{f}| and radial wave number k_{f}.
As an example, we chose an ion temperature gradient (ITG) turbulence-driven zonal flow as the mean flow acting on an electron temperature gradient (ETG) turbulence-zonal flow system.
The growth rate of the zonal flow γ_{q} is found to be suppressed, showing a relation γ_{q} = γ_{q0}(1-α|φ_{f}|^{2}k_{f}^{2} ), where γ_{q0} is the growth rate in the absence of mean flow and α is a positive numerical constant.
This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized at α|φ_{f}^{2}|k_{f}^{2} ≈ 1.
Meanwhile, the suppression is accompanied by an increase of the real frequency |Ω_{q}|.
The underlying physical mechanism of the suppression is discussed.

### Keywords

drift wave turbulence, zonal flow, mean plasma flow, modulational instability

### Full Text

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This paper may be cited as follows:

Ken UZAWA, Yasuaki KISHIMOTO and Jiquan LI, Plasma Fusion Res. 1, 024 (2006).