Rowlands, G. (George) and Allen, M. A.. (2007) Nonlinear magnetoacoustic waves in a cold plasma. Journal of Plasma Physics, Vol.73 (No.4). pp. 543-554. ISSN 0022-3778

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Abstract

The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Nonlinear acoustics, Nonlinear theories, Plasma electrodynamics, Nonlinear waves -- Mathematics
Journal or Publication Title:	Journal of Plasma Physics
Publisher:	Cambridge University Press
ISSN:	0022-3778
Official Date:	August 2007
Dates:	Date Event August 2007 Published
Volume:	Vol.73
Number:	No.4
Page Range:	pp. 543-554
Identification Number:	10.1017/S0022377806004818
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	Bakholdin, I. and Il'ichev, A. 1998 J. Plasma Phys. 60, 569. Bakholdin, I., Il'ichev, A. and Zharkov, A. 2002 J. Plasma Phys. 67, 1. Haken, H. 1983 Synergetics, 3rd edn. Berlin: Springer. Il'ichev, A. 1996 J. Plasma Phys. 55, 181. Infeld, E. and Rowlands, G. 2000 Nonlinear Waves, Solitons and Chaos, 2nd edn. Cambridge: Cambridge University Press. Jackson, E. A. 1960 Phys. Fluids 3, 831. Kakutani, T., Kawahara, T. and Taniuti, T. 1967 J. Phys. Soc. Japan 23, 1138. Kakutani, T., Ono, H., Taniuti, T. and Wei, C.-C. 1968 J. Phys. Soc. Japan 24, 1159. Nayfeh, A. H. and Mook, D. T. 1979 Nonlinear Oscillations. New York: Wiley. Rowlands, G. 1990 Non-Linear Phenomena in Science and Engineering. London: Ellis Horwood.
URI:	http://wrap.warwick.ac.uk/id/eprint/672

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