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. doi:10.1017/S0022377806004508 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, Engineering and Medicine > 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
Official Date:	April 2007
Dates:	Date Event April 2007 Published
Volume:	Vol.73
Number:	No.2
Page Range:	pp. 215-229
DOI:	10.1017/S0022377806004508
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)

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