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Weakly nonlinear waves in magnetized plasma with a slightly nonMaxwellian electron distribution. Part 2, Stability of cnoidal waves
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Phibanchon, S., Allen, M. A. and Rowlands, G. (George). (2007) Weakly nonlinear waves in magnetized plasma with a slightly nonMaxwellian electron distribution. Part 2, Stability of cnoidal waves. Journal of Plasma Physics, Vol.73 (No.6). pp. 933946. ISSN 00223778

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Official URL: http://dx.doi.org/10.1017/S002237780700640X
Abstract
We determine the growth rate of linear instabilities resulting from longwavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized coldion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate nontrivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flattopped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than longwavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than longwavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the firstorder growth rate is not zero.
Item Type:  Journal Article 

Subjects:  Q Science > QC Physics 
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:  00223778 
Official Date:  21 February 2007 
Volume:  Vol.73 
Number:  No.6 
Page Range:  pp. 933946 
Identification Number:  10.1017/S002237780700640X 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Allen, M. A., Phibanchon, S. and Rowlands, G. 2006 J. Plasma Phys. Published online 23 May 2006, doi:10.1017/S0022377806004508. 
URI:  http://wrap.warwick.ac.uk/id/eprint/663 
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