Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T08:15:07.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 1. Stability of solitary waves

Published online by Cambridge University Press:  01 April 2007

M.A. ALLEN ,
S. PHIBANCHON  and
G. ROWLANDS
M.A. ALLEN
Affiliation:
Physics Department, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand
S. PHIBANCHON
Affiliation:
Faculty of Sciences and Liberal Arts, Burapha University, 57 Moo 1, Thamai, Chanthaburi 22170, Thailand
G. ROWLANDS
Affiliation:
Department of Physics, University of Warwick, Coventry CV4 7AL, UK ([email protected]; [email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

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.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 2 , April 2007 , pp. 215 - 229
Copyright
Copyright © Cambridge University Press 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, M. A. 1994 The Evolution of Plane Solitons PhD Thesis, University of Warwick.Google Scholar
Allen, M. A. 2007 Amer. Math. Monthly (in press).Google Scholar
Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413.CrossRefGoogle Scholar
Bernstein, I. B., Greene, J. M. and Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Das, G. C., Sarma, J., Gao, Y. -T. and Uberoi, C. 2000 Phys. Plasmas 7, 2374.CrossRefGoogle Scholar
Das, G. C. and Sen, K. M. 1991 Contrib. Plasma Phys. 31, 647.CrossRefGoogle Scholar
El-Labany, S. K. and El-Taibany, W. F. 2004 J. Plasma Phys. 70, 69.CrossRefGoogle Scholar
Ghosh, G. and Das, K. P. 1998 J. Plasma Phys. 59, 333.CrossRefGoogle Scholar
Infeld, E. and Rowlands, G. 2000 Nonlinear Waves, Solitons and Chaos, 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Laedke, E. W. and Spatschek, K. H. 1982 J. Plasma Phys. 28, 469.CrossRefGoogle Scholar
Munro, S. and Parkes, E. J. 1999 J. Plasma Phys. 62, 305.CrossRefGoogle Scholar
Munro, S. and Parkes, E. J. 2000 J. Plasma Phys. 64, 411.CrossRefGoogle Scholar
Ono, H. 1976 J. Phys. Soc. Japan 41, 1817.CrossRefGoogle Scholar
Pelinovsky, D. E. and Grimshaw, R. H. J. 1997 Phys. Lett. A 229, 165.CrossRefGoogle Scholar
Ramani, A. and Grammaticos, B. 1991 J. Phys. A: Math. Gen. 24, 1969.CrossRefGoogle Scholar
Schamel, H. 1972 Plasma Phys. 14, 905.CrossRefGoogle Scholar
Schamel, H. 1973 J. Plasma Phys. 9, 377.CrossRefGoogle Scholar
Schamel, H. 1982 Phys. Rev. Lett. 48, 481.CrossRefGoogle Scholar
Schamel, H. 1986 Phys. Rep. 140, 161.CrossRefGoogle Scholar
Schamel, H. and Fedele, R. 2000 Phys. Plasmas 7, 3421.CrossRefGoogle Scholar
Shukla, P. K. and Bharuthram, R. 1986 Phys. Rev. A 34, 4457.CrossRefGoogle Scholar
Verheest, F., Mace, R. L., Pillay, S. R. and Hellberg, M. A. 2002 J. Phys. A: Math. Gen. 35, 795.CrossRefGoogle Scholar
Washimi, H. and Taniuti, T. 1966 Phys. Rev. Lett. 17, 996.CrossRefGoogle Scholar
Zakharov, V. E. and Kuznetsov, E. A. 1974 Sov. Phys. JETP 39, 285.Google Scholar