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Title: Saturation of the fan instability: Nonlinear merging of resonances

Abstract

A Hamiltonian self-consistent wave-particle model has been built in order to study the nonlinear interaction of a packet of waves with a nonequilibrium electron distribution in a magnetized background plasma. In particular, this model and the corresponding numerical code allow us to study in detail the excitation by the fan instability of lower hybrid waves interacting resonantly with a strongly anisotropic electron velocity distribution. This paper points out the essential role played by the process of ''dynamical merging of resonances,'' which results from an instability of the trapped particles' motion, leading, in its explosive stage, to the amplification of the waves' amplitudes. Moreover the relaxation phase of the fan instability is shown to lead to a universal distribution of the particles' velocities, which does not depend on the number of waves and on their distribution in the k space.

Authors:
; ;  [1];  [2];  [3]
  1. Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, 91405 Orsay Cedex (France)
  2. (Russian Federation)
  3. (France)
Publication Date:
OSTI Identifier:
20782338
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 11; Other Information: DOI: 10.1063/1.2118727; (c) 2005 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; AMPLIFICATION; AMPLITUDES; ANISOTROPY; DISTRIBUTION; ELECTRONS; EXCITATION; HAMILTONIANS; LOWER HYBRID CURRENT DRIVE; LOWER HYBRID HEATING; NONLINEAR PROBLEMS; PLASMA; PLASMA INSTABILITY; RELAXATION; RESONANCE; TRAPPING; VELOCITY

Citation Formats

Krafft, C., Volokitin, A., Zaslavsky, A., Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, 142190, and Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, 91405 Orsay Cedex. Saturation of the fan instability: Nonlinear merging of resonances. United States: N. p., 2005. Web. doi:10.1063/1.2118727.
Krafft, C., Volokitin, A., Zaslavsky, A., Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, 142190, & Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, 91405 Orsay Cedex. Saturation of the fan instability: Nonlinear merging of resonances. United States. doi:10.1063/1.2118727.
Krafft, C., Volokitin, A., Zaslavsky, A., Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, 142190, and Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, 91405 Orsay Cedex. Tue . "Saturation of the fan instability: Nonlinear merging of resonances". United States. doi:10.1063/1.2118727.
@article{osti_20782338,
title = {Saturation of the fan instability: Nonlinear merging of resonances},
author = {Krafft, C. and Volokitin, A. and Zaslavsky, A. and Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, 142190 and Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, 91405 Orsay Cedex},
abstractNote = {A Hamiltonian self-consistent wave-particle model has been built in order to study the nonlinear interaction of a packet of waves with a nonequilibrium electron distribution in a magnetized background plasma. In particular, this model and the corresponding numerical code allow us to study in detail the excitation by the fan instability of lower hybrid waves interacting resonantly with a strongly anisotropic electron velocity distribution. This paper points out the essential role played by the process of ''dynamical merging of resonances,'' which results from an instability of the trapped particles' motion, leading, in its explosive stage, to the amplification of the waves' amplitudes. Moreover the relaxation phase of the fan instability is shown to lead to a universal distribution of the particles' velocities, which does not depend on the number of waves and on their distribution in the k space.},
doi = {10.1063/1.2118727},
journal = {Physics of Plasmas},
number = 11,
volume = 12,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • This paper studies the linear and nonlinear stages of the fan instability, considering electromagnetic waves of the whistler frequency range interacting resonantly with energetic electron fluxes in magnetized plasmas. The main attention is paid to determine the wave-particle interaction processes that can lead to the excitation of intense electromagnetic waves by nonequilibrium particle distributions involving suprathermal tails, and to explain under what conditions and through what mechanisms they can occur, develop, and saturate. This paper presents and discusses two main processes: (i) the linear fan instability and (ii) the nonlinear process of dynamical resonance merging, which can significantly amplify themore » energy carried by linearly destabilized waves after they saturate due to particle trapping. This study consists of (i) determining analytically and numerically, for parameters typical of space and laboratory plasmas, the linear growth rates of whistlers excited by suprathermal particle fluxes through the fan instability, as well as the corresponding thresholds and the physical conditions at which the instability can appear, (ii) building a theoretical self-consistent 3D model and a related numerical code for describing the nonlinear evolution of the wave-particle system, and (iii) performing numerical simulations to reveal and characterize the nonlinear amplification process at work, its conditions of development, and its consequences, notably in terms of electromagnetic wave radiation. The simulations show that when the waves have reached sufficient energy levels owing to the linear fan instability, they saturate by trapping particles and due to the complex dynamics of these particles in the electromagnetic fields, the resonant velocities' domains of the waves overlap and merge, meanwhile a strong increase of the wave energy occurs.« less
  • The nonlinear saturation amplitude of the dissipative trapped electron instability is calculated. Comparison is made with an experiment carried out in linear mirror geometry and near threshold, with only a single mode predominating. A model in which the untrapped electrons respond in a Boltzmann fashion yields good agreement. A model in which Landau damping is included predicts saturation amplitudes much smaller than observed. The first model seems appropriate for linear geometries while the second may apply to closed devices.
  • Analytical analysis of the nonlinear saturation of the Rayleigh--Taylor (R--T) instability has been carried out and an appropriate physical model has been proposed for the saturation mechanism. Stationary wave formalism and initial value approach have been applied for the analysis. In the former case, a linear superposition model has been forwarded to understand the nonlinear saturation process, whereas in the latter, the mode--mode coupling model. Parallel friction due to shear effect and ion polarization drift are identified as the basic sources of the nonlinearity. Utility of the results in laboratory plasmas are highlighted.