Zonal flows generated by small-scale drift-Alfvén modes

Abstract

The generation of zonal flows by small-scale drift-Alfvén (SSDA) modes is investigated. It is shown that these zonal flows can be generated by a monochromatic wave packet of SSDA modes propagating in the ion diamagnetic drift direction. The corresponding zonal-flow instability resembles a hydrodynamic one. Its growth rate depends on the spectrum purity of the wave packet; it decreases for relatively weak spectrum broadening and the instability turns into a resonant one, and eventually is suppressed, as the broadening increases. A general conclusion of this work is that the SSDA modes are less effective for driving zonal flows than standard drift modes.

Small-scale drift-Alfven wave driven zonal flows in plasmas

“…13 is connected only with the spectral analysis of investigation and we retain the main approach to the solving of the problem and all initial equations as in Ref. 13.…”

“…Electronic mail: tamazគkaladze@yahoo.com was shown that the wave vector of the fastest growing zonalflow mode is perpendicular to that of the electrostatic drift pump wave. Thus the given paper may be considered as a generalization of the previous investigations and, for details, we refer the reader to Mikhailovskii et al 13 The paper is organized as follows: In Sec. II the spectral analysis of the problem is carried out and zonal-flow evolution equations in terms of electrostatic and vector potentials are obtained introducing the variables characterizing the zonal flows, the primary modes generating the flows, and the sideband amplitudes which depend on both the primary modes and zonal flows.…”

“…26 The generation of zonal flows by the iontemperature-gradient and related modes, in the presence of neoclassical viscosity, was investigated by Mikhailovskii et al employing an approach similar to the parametric one. 12 In the given paper the question of zonal-flow generation by SSDA waves is continued on the basis of parametric instability using the methodical achievements developed recently by Mikhailovskii et al 13 But the latter investigation was restricted by the consideration of the case k x 2 ӷ k y 2 , where k x and k y are the "radial" and "poloidal" components of the wave vector, respectively. Owing to this restriction obtained by Mikhailovskii et al, 13 growth rates of the zonal-flow generation turn out to be proportional to the small parameter k y 2 / k x 2 .…”

“…12 In the given paper the question of zonal-flow generation by SSDA waves is continued on the basis of parametric instability using the methodical achievements developed recently by Mikhailovskii et al 13 But the latter investigation was restricted by the consideration of the case k x 2 ӷ k y 2 , where k x and k y are the "radial" and "poloidal" components of the wave vector, respectively. Owing to this restriction obtained by Mikhailovskii et al, 13 growth rates of the zonal-flow generation turn out to be proportional to the small parameter k y 2 / k x 2 . In the given paper we remove that restriction and obtain general expressions describing the zonal-flow generation by SSDA modes for arbitrary relations between k x and k y .…”

“…This is the reason that zonal flows driven by drift-type turbulence have been intensively investigated theoretically in recent years. [2][3][4][5][6][7][8][9][10][11][12][13] Most of these theoretical investigations are focused on the regime of large-scale turbulence, i.e., turbulence generated by drifttype waves for which the characteristic perpendicular scale length is larger than the ion Larmor radius. However, in inhomogeneous plasmas with ␤ Ͼ m e / m i , small-scale driftAlfven ͑SSDA͒ modes, with a characteristic perpendicular scale length smaller than the ion Larmor radius, also play an important role in driving the ubiquitous turbulence.…”