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Nonlinear modulational stability and propagation of an electromagnetic pulse in a two-component neutral plasma

Published online by Cambridge University Press:  13 March 2009

Ronald E. Kates  and
D. J. Kaup
Ronald E. Kates
Affiliation:
Max-Planck-Institut für Astrophysik, 8046 Garching, Federal Republic of Germany
D. J. Kaup
Affiliation:
Clarkson University, Potsdam, New York 13676, U.S.A.
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Abstract

We study nonlinear effects including possible modulational instability of an intense electromagnetic pulse propagating through a fully ionized unmag-netized plasma. (The pulse is assumed to be sufficiently strong to accelerate particles to weakly, but not fully, relativistic velocities.) The envelope is shown to evolve over long time scales in general according to a vector form of the well-known cubic nonlinear Schrödinger (NLS) equation. Three distinct nonlinear effects contribute terms cubic in the amplitude and thus can be of comparable magnitude: ponderomotive forces, relativistic corrections and harmonic generation. In contrast with previous work, our calculation takes all three effects into account. Integrability and modulational stability of any given system are shown to depend on polarization, frequency, composition and temperature, and these dependences are given. We first carry out the calculation in detail for the case of zero temperature. In the special case of a cold positron-electron plasma, in contrast with the predictions of Chian & Kennel (1983), the model is strictly modulationally stable for both linear and circular polarization. We then generalize our result by giving the dependence of the nonlinear coefficients on temperature. As it turns out, finite-temperature effects are qualitatively important only near a critical frequency (<3/2ωp) just above the plasma frequency for which the group velocity is comparable to either (or both) of the sound velocities. The results have important implications for pulsar micropulse observations and possible technological applications.

Type
Research Article
Information
Journal of Plasma Physics , Volume 42 , Issue 3 , December 1989 , pp. 507 - 519
Copyright
Copyright © Cambridge University Press 1989

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