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Title: Basic physics of Alfven instabilities driven by energetic particles in toroidally confined plasmas

Abstract

Superthermal energetic particles (EP) often drive shear Alfven waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfven instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfven waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfven eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfven eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfven instabilities of all three types occur in every toroidal magnetic confinement devicemore » with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum P{sub {zeta}} is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.« less

Authors:
 [1]
  1. Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697 (United States)
Publication Date:
OSTI Identifier:
21120337
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 15; Journal Issue: 5; Other Information: DOI: 10.1063/1.2838239; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; IONS; MAGNETIC CONFINEMENT; NONLINEAR PROBLEMS; PHASE SPACE; PHASE VELOCITY; PLASMA; PLASMA INSTABILITY; PLASMA WAVES; REFRACTIVE INDEX; TOKAMAK DEVICES

Citation Formats

Heidbrink, W W. Basic physics of Alfven instabilities driven by energetic particles in toroidally confined plasmas. United States: N. p., 2008. Web. doi:10.1063/1.2838239.
Heidbrink, W W. Basic physics of Alfven instabilities driven by energetic particles in toroidally confined plasmas. United States. doi:10.1063/1.2838239.
Heidbrink, W W. Thu . "Basic physics of Alfven instabilities driven by energetic particles in toroidally confined plasmas". United States. doi:10.1063/1.2838239.
@article{osti_21120337,
title = {Basic physics of Alfven instabilities driven by energetic particles in toroidally confined plasmas},
author = {Heidbrink, W W},
abstractNote = {Superthermal energetic particles (EP) often drive shear Alfven waves unstable in magnetically confined plasmas. These instabilities constitute a fascinating nonlinear system where fluid and kinetic nonlinearities can appear on an equal footing. In addition to basic science, Alfven instabilities are of practical importance, as the expulsion of energetic particles can damage the walls of a confinement device. Because of rapid dispersion, shear Alfven waves that are part of the continuous spectrum are rarely destabilized. However, because the index of refraction is periodic in toroidally confined plasmas, gaps appear in the continuous spectrum. At spatial locations where the radial group velocity vanishes, weakly damped discrete modes appear in these gaps. These eigenmodes are of two types. One type is associated with frequency crossings of counterpropagating waves; the toroidal Alfven eigenmode is a prominent example. The second type is associated with an extremum of the continuous spectrum; the reversed shear Alfven eigenmode is an example of this type. In addition to these normal modes of the background plasma, when the energetic particle pressure is very large, energetic particle modes that adopt the frequency of the energetic particle population occur. Alfven instabilities of all three types occur in every toroidal magnetic confinement device with an intense energetic particle population. The energetic particles are most conveniently described by their constants of motion. Resonances occur between the orbital frequencies of the energetic particles and the wave phase velocity. If the wave resonance with the energetic particle population occurs where the gradient with respect to a constant of motion is inverted, the particles transfer energy to the wave, promoting instability. In a tokamak, the spatial gradient drive associated with inversion of the toroidal canonical angular momentum P{sub {zeta}} is most important. Once a mode is driven unstable, a wide variety of nonlinear dynamics is observed, ranging from steady modes that gradually saturate, to bursting behavior reminiscent of relaxation oscillations, to rapid frequency chirping. An analogy to the classic one-dimensional problem of electrostatic plasma waves explains much of this phenomenology. EP transport can be convective, as when the wave scatters the particle across a topological boundary into a loss cone, or diffusive, which occurs when islands overlap in the orbital phase space. Despite a solid qualitative understanding of possible transport mechanisms, quantitative calculations using measured mode amplitudes currently underestimate the observed fast-ion transport. Experimentally, detailed identification of nonlinear mechanisms is in its infancy. Beyond validation of theoretical models, the future of the field lies in the development of control tools. These may exploit EP instabilities for beneficial purposes, such as favorably modifying the current profile, or use modest amounts of power to govern the nonlinear dynamics in order to avoid catastrophic bursts.},
doi = {10.1063/1.2838239},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 5,
volume = 15,
place = {United States},
year = {2008},
month = {5}
}