Allen, M. A., Phibanchon, S. and Rowlands, G. (George). (2007) Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 1, Stability of solitary waves. Journal of Plasma Physics, Vol.73 (No.2). pp. 215-229. ISSN 0022-3778

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Abstract

Weakly nonlinear waves in strongly magnetized plasma with slightly non-isothermal electrons are governed by a modified Zakharov–Kuznetsov (ZK) equation, containing both quadratic and half-order nonlinear terms, which we refer to as the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation. We present a method to obtain an approximation for the growth rate, γ, of sinusoidal perpendicular perturbations of wavenumber, k, to SKdVZK solitary waves over the entire range of instability. Unlike for (modified) ZK equations with one nonlinear term, in this method there is no analytical expression for kc, the cut-off wavenumber (at which the growth rate is zero) or its corresponding eigenfunction. We therefore obtain approximate expressions for these using an expansion parameter, a, related to the ratio of the nonlinear terms. The expressions are then used to find γ for k near kc as a function of a. The approximant derived from combining these analytical results with the ones for small k agrees very well with the values of γ obtained numerically. It is found that both kc and the maximum growth rate decrease as the electron distribution becomes progressively less peaked than the Maxwellian. We also present new algebraic and rarefactive solitary wave solutions to the equation.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Maxwell equations -- Numerical solutions, Electromagnetic theory -- Mathematics, Nonlinear waves -- Mathematics, Nonlinear theories
Journal or Publication Title:	Journal of Plasma Physics
Publisher:	Cambridge University Press
ISSN:	0022-3778
Date:	April 2007
Volume:	Vol.73
Number:	No.2
Page Range:	pp. 215-229
Identification Number:	10.1017/S0022377806004508
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	Allen, M. A. 1994 The Evolution of Plane Solitons PhD Thesis, University of Warwick. Allen, M. A. 2007 Amer. Math. Monthly (in press). Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413. Bernstein, I. B., Greene, J. M. and Kruskal, M. D. 1957 Phys. Rev. 108, 546. Das, G. C., Sarma, J., Gao, Y. -T. and Uberoi, C. 2000 Phys. Plasmas 7, 2374. Das, G. C. and Sen, K. M. 1991 Contrib. Plasma Phys. 31, 647. El-Labany, S. K. and El-Taibany, W. F. 2004 J. Plasma Phys. 70, 69. Ghosh, G. and Das, K. P. 1998 J. Plasma Phys. 59, 333. Infeld, E. and Rowlands, G. 2000 Nonlinear Waves, Solitons and Chaos, 2nd edn. Cambridge: Cambridge University Press. Laedke, E. W. and Spatschek, K. H. 1982 J. Plasma Phys. 28, 469. Munro, S. and Parkes, E. J. 1999 J. Plasma Phys. 62, 305. Munro, S. and Parkes, E. J. 2000 J. Plasma Phys. 64, 411. Ono, H. 1976 J. Phys. Soc. Japan 41, 1817. Pelinovsky, D. E. and Grimshaw, R. H. J. 1997 Phys. Lett. A 229, 165. Ramani, A. and Grammaticos, B. 1991 J. Phys. A: Math. Gen. 24, 1969. Schamel, H. 1972 Plasma Phys. 14, 905. Schamel, H. 1973 J. Plasma Phys. 9, 377. Schamel, H. 1982 Phys. Rev. Lett. 48, 481. Schamel, H. 1986 Phys. Rep. 140, 161. Schamel, H. and Fedele, R. 2000 Phys. Plasmas 7, 3421. Shukla, P. K. and Bharuthram, R. 1986 Phys. Rev. A 34, 4457. Verheest, F., Mace, R. L., Pillay, S. R. and Hellberg, M. A. 2002 J. Phys. A: Math. Gen. 35, 795. Washimi, H. and Taniuti, T. 1966 Phys. Rev. Lett. 17, 996. Zakharov, V. E. and Kuznetsov, E. A. 1974 Sov. Phys. JETP 39, 285.
URI:	http://wrap.warwick.ac.uk/id/eprint/677

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