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Intense propagation in a magnetized cold plasma: modulational instabilities of fully relativistic electromagnetic waves

Published online by Cambridge University Press:  13 March 2009

Ronald E. Kates  and
D. J. Kaup
Ronald E. Kates
Affiliation:
Institut für Theoretische Physik und Sternwarte, Universität Kiel, 2300 Kiel, Germany
D. J. Kaup
Affiliation:
Clarkson University, Potsdam, New York 13676, U.S.A.
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Abstract

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 1 , August 1992 , pp. 119 - 137
Copyright
Copyright © Cambridge University Press 1992

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References

Arons, J. & Scharlemann, E. 1979 Astrophys. J. 231, 854.CrossRefGoogle Scholar
Chian, A. & Kennel, C. 1983 Astrophys. Space Sci. 97, 9.CrossRefGoogle Scholar
Gil, J. 1986 Astrophys. J. 308, 691.CrossRefGoogle Scholar
Karpman, V. & Krushkal, E. 1969 Soviet Phys. JETP 28, 277.Google Scholar
Kates, R. & Kaup, D. 1989 J. Plasma Phys. 42, 507 (paper I).CrossRefGoogle Scholar
Kates, R. & Kaup, D. 1989 J. Plasma Phys. 42, 521 (paper II).CrossRefGoogle Scholar
Kates, R. & Kaup, D. 1991 J. Plasma Phys. 46, 85 (paper III).CrossRefGoogle Scholar
Mikhailovskii, A., Onishchenko, O. & Smolyakov, A. 1985 Soviet Astron. Lett. 11, 1985.Google Scholar
Mjolhus, E. 1976 J. Plasma Phys. 16, 321.CrossRefGoogle Scholar
Mofiz, U., Deangelis, U. & Forlani, A. 1984 Plasma Phys. Contr. Fusion 26, 1099.CrossRefGoogle Scholar
Mofiz, U., Deangelis, U. & Forlani, A. 1985 Phys. Rev. A 31, 951.CrossRefGoogle Scholar
Mofiz, U. & Podder, J. 1987 Phys. Rev. A 36, 1811.CrossRefGoogle Scholar
Rickett, B. 1975 Astrophys. J. 197, 185.CrossRefGoogle Scholar
Ruderman, M. & Sutherland, P. 1975 Astrophys. J. 196, 51.CrossRefGoogle Scholar
Shukla, P. & Stenflo, L. 1984 Phys. Rev. A 30, 2110.CrossRefGoogle Scholar
Smirnova, T. 1988 Soviet Astron. Lett. 14, 20.Google Scholar
Smirnova, T., Soglasnov, V., Popov, V. & Novikov, A. 1986 Soviet Astron. 30, 51.Google Scholar
Stenflo, L., Shukla, P. K. & Yu, M. Y. 1985 Astrophys. Space Sci. 117, 303.CrossRefGoogle Scholar