skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfven waves

Abstract

The generation of zonal flows by drift-Alfven waves is studied with allowance for magnetic curvature effects. The basic plasmadynamic equations relating the electrostatic potential, vector potential, and perturbed plasma density are the vorticity equation, longitudinal Ohm's law, and continuity equation. The basic equations are analyzed by applying a parametric formalism similar to that used in the theory of the generation of convective cells. In contrast to most previous investigations on the subject, consideration is given to primary modes having an arbitrary spectrum rather than to an individual monochromatic wave packet. The parametric approach so modified makes it possible to reveal a new class of instabilities of zonal flows that are analogous to two-stream instabilities in linear theory. It is shown that, in the standard theory of zonal flows, the zonal components of the vector potential and perturbed density are not excited. It is pointed out that zonal flows can be generated both in the case of a magnetic hill and in the case of a magnetic well. In the first case, the instabilities of zonal flows are analogous to negative-mass instabilities in linear theory, and, in the second case, they are analogous to two-stream instabilities.

Authors:
; ; ;  [1];  [2]
  1. Russian Research Centre Kurchatov Institute, Nuclear Fusion Institute (Russian Federation)
  2. University of Sao Paulo, Institute of Physics (Brazil)
Publication Date:
OSTI Identifier:
21100174
Resource Type:
Journal Article
Resource Relation:
Journal Name: Plasma Physics Reports; Journal Volume: 33; Journal Issue: 5; Other Information: DOI: 10.1134/S1063780X07050066; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; CONTINUITY EQUATIONS; MAGNETIC FIELDS; MINIMUM-B CONFIGURATIONS; MONOCHROMATIC RADIATION; NEGATIVE MASS INSTABILITY; PLASMA DENSITY; SPECTRA; TWO-STREAM INSTABILITY; WAVE PACKETS

Citation Formats

Mikhailovskii, A. B., Kovalishen, E. A., Shirokov, M. S., Tsypin, V. S., and Galvao, R. M. O.. Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfven waves. United States: N. p., 2007. Web. doi:10.1134/S1063780X07050066.
Mikhailovskii, A. B., Kovalishen, E. A., Shirokov, M. S., Tsypin, V. S., & Galvao, R. M. O.. Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfven waves. United States. doi:10.1134/S1063780X07050066.
Mikhailovskii, A. B., Kovalishen, E. A., Shirokov, M. S., Tsypin, V. S., and Galvao, R. M. O.. Tue . "Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfven waves". United States. doi:10.1134/S1063780X07050066.
@article{osti_21100174,
title = {Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfven waves},
author = {Mikhailovskii, A. B. and Kovalishen, E. A. and Shirokov, M. S. and Tsypin, V. S. and Galvao, R. M. O.},
abstractNote = {The generation of zonal flows by drift-Alfven waves is studied with allowance for magnetic curvature effects. The basic plasmadynamic equations relating the electrostatic potential, vector potential, and perturbed plasma density are the vorticity equation, longitudinal Ohm's law, and continuity equation. The basic equations are analyzed by applying a parametric formalism similar to that used in the theory of the generation of convective cells. In contrast to most previous investigations on the subject, consideration is given to primary modes having an arbitrary spectrum rather than to an individual monochromatic wave packet. The parametric approach so modified makes it possible to reveal a new class of instabilities of zonal flows that are analogous to two-stream instabilities in linear theory. It is shown that, in the standard theory of zonal flows, the zonal components of the vector potential and perturbed density are not excited. It is pointed out that zonal flows can be generated both in the case of a magnetic hill and in the case of a magnetic well. In the first case, the instabilities of zonal flows are analogous to negative-mass instabilities in linear theory, and, in the second case, they are analogous to two-stream instabilities.},
doi = {10.1134/S1063780X07050066},
journal = {Plasma Physics Reports},
number = 5,
volume = 33,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • The understanding of low to high (L-H) transition in tokamaks has been an important area of investigation for more than a decade. Recent 3D finite {beta} simulations of drift-resistive ballooning modes in a flux tube geometry by Rogers et al.[Phys.Rev.Lett.81, 4396 (1998)] have provided a unique parametrization of the transition in a two-dimensional phase space. Comparison of the threshold curve in this phase space with data from ASDEX and C-MOD has shown very good agreement. In this Letter we provide a simple theory, based on the generation of zonal flow and zonal magnetic field in a finite-beta plasma, which explainsmore » this threshold curve for L-H transition in tokamaks.« less
  • Analytical theory of nonlinear generation of magnetoacoustic zonal flows in a rotating plasma is developed. As the primary modes causing such a generation, a totality of the Alfven waves are considered, along with the kinetic, inertial, and rotational. It is shown that in all these cases of the Alfven waves the generation is possible if the double plasma rotation frequency exceeds the zonal flow frequency.
  • The generation of zonal flows by kinetic Alfven waves is analyzed. It is noted that the basic approach underlying the existing theory of this phenomenon is too simplified because it attributes the generation of zonal flows to instabilities of an individual monochromatic wave packet of kinetic Alfven waves. It is shown that, when a monochromatic wave packet is stable, it is necessary to analyze a more complicated situation with a double-peak packet (or, in the simplest case, with two pump waves). It is found that, for a double-peak packet of kinetic Alfven waves, there is a new class of instabilitiesmore » of zonal flows and that these instabilities are analogous to two-stream instabilities in linear theory. The main types of such instabilities are investigated.« less
  • Generation of large-scale zonal flows by comparatively small-scale electrostatic drift waves in electron-positron-ion plasmas is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves having arbitrary wavelengths (as compared with the ion Larmor radius of plasma ions at the plasma electron temperature). Temperature inhomogeneity of electrons and positrons is taken into account assuming ions to be cold. To describe the generation of zonal flow generalized Hasegawa-Mima equation containing both vector and two scalar (of different nature) nonlinearities is used. A set of coupled equations describing the nonlinear interaction of drift wavesmore » and zonal flows is deduced. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. Enriched possibilities of zonal flow generation with different growth rates are revealed. The present theory can be used for interpretations of drift wave observations in laboratory and astrophysical plasmas.« less
  • The generation of zonal flows by small-scale drift-Alfven (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 standardmore » drift modes.« less