Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-27T23:48:23.354Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Arons, J. & Scharlemann, E. 1979 Astrophys. J. 231, 854.CrossRefGoogle Scholar
Chian, A. & Kennel, C. 1983 Astrophys. Space Sci. 97, 9.Google Scholar
Gil, J. 1986 Astrophys. J. 308, 691.Google Scholar
Karpman, V. & Krushkal, E. 1969 Soviet Phys. JETP, 28, 277.Google Scholar
Kates, R. 1981 Ann. Phys. (NY), 132, 1.CrossRefGoogle Scholar
Kates, R. & Kaup, D. 1989 J. Plasma Phys. 42, 521.CrossRefGoogle Scholar
Kozlov, V., Litvak, A. & Suvarov, E. 1979 Soviet Phys. JETP, 49, 75.Google Scholar
Luenow, W. 1968 Plasma Phys. 10, 973.CrossRefGoogle Scholar
Manakov, S. V. 1973 Soviet Phys. JETP, 38, 248.Google Scholar
Max, C. 1973 a Phys. Fluids, 16, 1277.Google Scholar
Max, C. 1973 b Phys. Fluids, 16, 1480.Google Scholar
Mofiz, U. A., DeAngelis, U. & Forlani, A. 1984 Plasma Phys. Contr. Fusion, 26, 1099.CrossRefGoogle Scholar
Mofiz, U. A., DeAngelis, U. & Forlani, A. 1985 Phys. Rev., A 31, 951.Google Scholar
Mofiz, U. A. & Podder, J. 1987 Phys. Rev., A 36, 1811.Google Scholar
Nayfeh, A. 1981 Introduction to Perturbation Techniques. Wiley.Google Scholar
Rickett, B. 1975 Astrophys. J. 197, 185.Google Scholar
Ruderman, M. & Sutherland, P. 1975 Astorophys. J. 196, 51.Google Scholar
Smirnova, T. V. 1988 Soviet Astron. Lett. 14, 20.Google Scholar
Smirnova, T. V., Soglasnov, V. A., Popov, M. V. & Novikov, A. Yu. 1986 Soviet Astron. 30, 51.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.Google Scholar
Whitham, G. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar