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Title: Drift-Alfven eigenmodes in inhomogeneous plasma

Abstract

A set of three nonlinear equations describing drift-Alfven waves in a nonuniform magnetized plasma is derived and discussed both in linear and nonlinear limits. In the case of a cylindric radially bounded plasma with a Gaussian density distribution in the radial direction the linearized equations are solved exactly yielding general solutions for modes with quantized frequencies and with radially dependent amplitudes. The full set of nonlinear equations is also solved yielding particular solutions in the form of rotating radially limited structures. The results should be applicable to the description of electromagnetic perturbations in solar magnetic structures and in astrophysical column-like objects including cosmic tornados.

Authors:
;  [1]
  1. Centre for Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium)
Publication Date:
OSTI Identifier:
20782542
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 3; Other Information: DOI: 10.1063/1.2181436; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; AMPLITUDES; DISTRIBUTION; DISTURBANCES; DRIFT INSTABILITY; GAUSS FUNCTION; INHOMOGENEOUS PLASMA; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PLASMA DENSITY; PLASMA DRIFT

Citation Formats

Vranjes, J., and Poedts, S.. Drift-Alfven eigenmodes in inhomogeneous plasma. United States: N. p., 2006. Web. doi:10.1063/1.2181436.
Vranjes, J., & Poedts, S.. Drift-Alfven eigenmodes in inhomogeneous plasma. United States. doi:10.1063/1.2181436.
Vranjes, J., and Poedts, S.. 2006. "Drift-Alfven eigenmodes in inhomogeneous plasma". United States. doi:10.1063/1.2181436.
@article{osti_20782542,
title = {Drift-Alfven eigenmodes in inhomogeneous plasma},
author = {Vranjes, J. and Poedts, S.},
abstractNote = {A set of three nonlinear equations describing drift-Alfven waves in a nonuniform magnetized plasma is derived and discussed both in linear and nonlinear limits. In the case of a cylindric radially bounded plasma with a Gaussian density distribution in the radial direction the linearized equations are solved exactly yielding general solutions for modes with quantized frequencies and with radially dependent amplitudes. The full set of nonlinear equations is also solved yielding particular solutions in the form of rotating radially limited structures. The results should be applicable to the description of electromagnetic perturbations in solar magnetic structures and in astrophysical column-like objects including cosmic tornados.},
doi = {10.1063/1.2181436},
journal = {Physics of Plasmas},
number = 3,
volume = 13,
place = {United States},
year = 2006,
month = 3
}
  • The spectrum of the compressional Alfven eigenmodes in a magnetohydrodynamic (MHD) current-carrying inhomogeneous plasma column is obtained analytically. A MHD model that is adequate for calculating the compressional Alfven spectra in large tokamaks like the Joint European Torus (JET) [[ital Plasma] [ital Physics] [ital and] [ital Controlled] [ital Fusion] [ital Research] 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] and Tokamak Fusion Test Reactor (TFTR) [[ital Plasma] [ital Physics] [ital and] [ital Controlled] [ital Fusion] [ital Research] 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 9] is employed. It is shown that the radial nonuniformitiesmore » of the plasma density give rise to various types of localization of the eigenmodes. Thus, the global, near-axis, near-wall, and annulus spectra are identified and studied. The eigenfrequencies and domains of localization of the various eigenmodes, as well as their range of existence in parameter and wavelength space, are determined and investigated. The effects of finite ion gyrofrequency on the MHD eigenmodes are examined, and a perturbation scheme for calculating the modified eigenfrequencies and localization domains is presented. Numerical calculations of a set of near-axis eigenmodes for the JET parameters is given as an example for the applicability of the MHD model. Finally, the relevancy of the eigenmodes to plasma heating in large tokamaks is discussed.« less
  • The uniform cylindrical plasma model of Litwin and Hershkowitz (Phys. Fluids {bold 30}, 1323 (1987)) is shown to predict mode conversion between the lowest radial order {ital m}=+1 fast magnetosonic surface and slow ion-cyclotron global eigenmodes of the Alfven wave at the light-ion species Alfven resonance of a cold two-ion plasma. A hydrogen ({ital h})--deuterium ({ital d}) plasma is examined in experiments. The fast mode is efficiently excited by a rotating field antenna array at {omega}{similar to}{Omega}{sub {ital h}} in the central cell of the Phaedrus-B tandem mirror (Phys. Rev. Lett. {bold 51}, 1955(1983)). Radially scanned magnetic probes observe themore » propagating eigenmode wave fields within a shallow central cell magnetic gradient in which the conversion zone is axially localized according to {ital n}{sub {ital d}}/{ital n}{sub {ital h}}. A low radial-order slow ion-cyclotron mode, observed in the vicinity of the conversion zone, gives evidence for the predicted mode conversion.« less
  • Global Alfven eigenmodes are studied using two different models for the plasma and the results compared with the instability threshold measured experimentally. Fluid-resistive models predict that continuum damped toroidicity induced Alfven modes (TAE) are formed in the frequency range of the experimental instabilities, but using realistic values of the resistivity makes a stability analysis impossible for computational reasons. The kinetic plasma model solves this problem by taking into account the ion Larmor radius and the resonant Landau interactions between the particles and the wavefield. As a consequence drift-kinetic Alfven eigenmodes (DKAE) are created by toroidal coupling between the global TAEmore » wavefield, the mode converted kinetic Alfven, ion-acoustic and drift waves. The power transfers between the wave and the particles show that the drift character of the wavefield in the core destabilizes DKAE modes through resonant interactions with the fast beam ions. The predicted beam pressure instability threshold is in agreement with the one measured experimentally. {copyright} {ital 1997 American Institute of Physics.}« less
  • Alfven wave instabilities in a reacting tokamak plasma are calculated both analytically and numerically. Two distinct classes of eigenmodes are considered, global Alfven eigenmodes and kinetic Alfven waves, each driven unstable by the free energy associated with the alpha particle density gradient. The growth rates of the global Alfven eigenmodes are given for the first time. These are basically magnetohydrodynamic (MHD) modes, whose resonances with electrons and alpha particles are calculated using kinetic theory. The calculation of kinetic Alfven wave growth rates is improved from earlier treatments. These modes depend on electron inertia and finite ion gyroradius for their existencemore » and have no counterpart in MHD theory. In both sets of calculations toroidal coupling of the alpha particle response to sidebands in the poloidal mode number is fully taken into account. Global modes with small parallel phase velocity are identified as the most dangerous, both because of their substantial growth rates and the expected ineffectiveness of quasilinear stabilization. The kinetic waves, on the other hand, are likely to be stabilized easily by quasilinear flattening of the alpha particle profile. Calculations using both Maxwellian and slowing-down alpha distributions are performed, showing that, for the same alpha density and energy density, the slowing-down distribution yields somewhat larger growth rates.« less
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