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Title: Modulation instability of waves in a magnetized plasma

Abstract

Modulation instability of finite-amplitude transverse waves in an ideal magnetized plasma with a non-zero sound speed has been investigated theoretically by use of an isentropic two-fluid model. In the first part of this thesis, a perturbation expansion is performed on a circularly polarized, transverse Alfven wave propagating parallel to the constant ambient magnetic field with arbitrary amplitude and with arbitrary frequency {omega}{sub 0}. The result of the perturbation expansion is a sixth-order algebraic dispersion relation in terms of the frequency and wave number perturbations, w and k. The analysis is then limited to the case where {omega}{much lt} {omega}{sub 0} {much lt} {omega}{sub ce}, {omega}{sub ce} being the electron-cyclotron frequency. The resulting fourth-order dispersion relation is examined analytically and numerically and a surface is found that separates modulationally stable and unstable regions in parameter space. In the second part of this thesis, a reductive perturbation expansion of the two-fluid equations is used to derive a nonlinear Schrodinger equation, which describes the time evolution of a modulated, weakly nonlinear, elliptically polarized carrier wave propagating obliquely to the constant ambient magnetic field with frequency wo. Here, the author assumes that wo is negligible compared with {omega}{sub ce} but nonnegligible with {omega}{sub ci},more » the ion-cyclotron frequency.« less

Authors:
Publication Date:
Research Org.:
Dartmouth Coll., Hanover, NH (United States)
OSTI Identifier:
5595843
Resource Type:
Miscellaneous
Resource Relation:
Other Information: Thesis (Ph. D.)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EARTH MAGNETOSPHERE; WAVE PACKETS; WAVE PROPAGATION; ALFVEN WAVES; ANALYTICAL SOLUTION; COMPARATIVE EVALUATIONS; CYCLOTRON FREQUENCY; DISPERSION RELATIONS; EARTH ATMOSPHERE; INTERACTIONS; ISOTROPY; MAGNETIC FIELDS; MATHEMATICAL MODELS; MODULATION; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PERTURBATION THEORY; PLASMA; PLASMA WAVES; SCHROEDINGER EQUATION; SOLAR WIND; DIFFERENTIAL EQUATIONS; EQUATIONS; HYDROMAGNETIC WAVES; PARTIAL DIFFERENTIAL EQUATIONS; SOLAR ACTIVITY; WAVE EQUATIONS; 640201* - Atmospheric Physics- Auroral, Ionospheric, & Magetospheric Phenomena

Citation Formats

Longtin, M C. Modulation instability of waves in a magnetized plasma. United States: N. p., 1988. Web.
Longtin, M C. Modulation instability of waves in a magnetized plasma. United States.
Longtin, M C. 1988. "Modulation instability of waves in a magnetized plasma". United States.
@article{osti_5595843,
title = {Modulation instability of waves in a magnetized plasma},
author = {Longtin, M C},
abstractNote = {Modulation instability of finite-amplitude transverse waves in an ideal magnetized plasma with a non-zero sound speed has been investigated theoretically by use of an isentropic two-fluid model. In the first part of this thesis, a perturbation expansion is performed on a circularly polarized, transverse Alfven wave propagating parallel to the constant ambient magnetic field with arbitrary amplitude and with arbitrary frequency {omega}{sub 0}. The result of the perturbation expansion is a sixth-order algebraic dispersion relation in terms of the frequency and wave number perturbations, w and k. The analysis is then limited to the case where {omega}{much lt} {omega}{sub 0} {much lt} {omega}{sub ce}, {omega}{sub ce} being the electron-cyclotron frequency. The resulting fourth-order dispersion relation is examined analytically and numerically and a surface is found that separates modulationally stable and unstable regions in parameter space. In the second part of this thesis, a reductive perturbation expansion of the two-fluid equations is used to derive a nonlinear Schrodinger equation, which describes the time evolution of a modulated, weakly nonlinear, elliptically polarized carrier wave propagating obliquely to the constant ambient magnetic field with frequency wo. Here, the author assumes that wo is negligible compared with {omega}{sub ce} but nonnegligible with {omega}{sub ci}, the ion-cyclotron frequency.},
doi = {},
url = {https://www.osti.gov/biblio/5595843}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1988},
month = {Fri Jan 01 00:00:00 EST 1988}
}

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