Publication: Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves
Issued Date
2007-12-01
Resource Type
ISSN
14697807
00223778
00223778
Other identifier(s)
2-s2.0-36248992992
Rights
Mahidol University
Rights Holder(s)
SCOPUS
Bibliographic Citation
Journal of Plasma Physics. Vol.73, No.6 (2007), 933-946
Suggested Citation
S. Phibanchon, M. A. Allen, G. Rowlands Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves. Journal of Plasma Physics. Vol.73, No.6 (2007), 933-946. doi:10.1017/S002237780700640X Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/25123
Research Projects
Organizational Units
Authors
Journal Issue
Thesis
Title
Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves
Author(s)
Other Contributor(s)
Abstract
We determine the growth rate of linear instabilities resulting from long-wavelength 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 cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial 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 6 increases as the electron distribution becomes increasingly flat-topped. As 6 and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle 6 at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of 6 for which the first-order growth rate is not zero. © 2007 Cambridge University Press.