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  • 1
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    Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions (1983)
    In:  Other Sources
    Details
    Publication Date: 2011-08-18
    Description: A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.
    Keywords: PLASMA PHYSICS
    Type: Radio Science (ISSN 0048-6604); 18; 1369-137
    Format: text
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  • 2
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    Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation (1983)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.
    Keywords: PLASMA PHYSICS
    Type: Radio Science; 18; Mar
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  • 3
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    Simplified theory of large-amplitude wave propagation (1976)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: An orbit perturbation procedure was applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest order approximation, untrapped electrons were assumed to follow constant-velocity orbits and trapped electrons were assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits were regarded as perturbations. The nonlinear damping rate and frequency shift were then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses.
    Keywords: PLASMA PHYSICS
    Type: NASA-CR-147229 , SU-IPR-582
    Format: application/pdf
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  • 4
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    Approximate theory of large-amplitude wave propagation (1977)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.
    Keywords: PLASMA PHYSICS
    Type: Journal of Plasma Physics; 17; June 197
    Format: text
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  • 5
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    Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions (1977)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.
    Keywords: PLASMA PHYSICS
    Type: Radio Science; 12; Nov
    Format: text
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