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Alternative ion-acoustic solitary waves in magnetized plasma consisting of warm adiabatic ions and non-thermal electrons having vortex-like velocity distribution: existence and stability

Published online by Cambridge University Press:  01 December 2007

JAYASREE DAS ,
ANUP BANDYOPADHYAY  and
K.P. DAS
JAYASREE DAS
Affiliation:
Dum Dum Prachya Bani Mandir High School for Girls, 4, Seth Bagan Road, Kolkata – 700 030, India
ANUP BANDYOPADHYAY
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata – 700 032, India
K.P. DAS
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92-Acharya Prfulla Chandra Road, Kolkata – 700 009, India
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Abstract

The solitary structures of the ion-acoustic waves have been considered in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having a vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is governed by the Schamel's modified Korteweg–de Vries–Zakharov–Kuznetsov (S-ZK) equation. This equation admits solitary wave solutions having a profile sech4. When the coefficient of the nonlinear term of this equation vanishes, the vortex-like velocity distribution function of electrons simply becomes the non-thermal velocity distribution function of electrons and the nonlinear behaviour of the same ion-acoustic wave is described by a Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. This equation admits solitary wave solutions having a profile sech2. A combined S–KdV–ZK equation more efficiently describes the nonlinear behaviour of an ion-acoustic wave when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons, i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having a profile different from either sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been derived. It is found that this alternative solitary wave solution approaches the solitary wave solution (the sech2 profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero. The three-dimensional stability of these solitary waves propagating obliquely to the external uniform and static magnetic field has been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of the instability have been derived at the lowest order. It is also found that the instability condition and growth rate of instability of the alternative solitary waves are exactly the same as those of the solitary waves as determined from the KdV-ZK equation (the sech2 profile) when the contribution of trapped electrons tends to zero.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 6 , December 2007 , pp. 869 - 899
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Dovner, P. O., Eriksson, A. I., Böstrom, R. and Holback, B. 1994 Freja multiprobe observations of electrostatic solitary structures. Geophys. Res. Lett. 21, 1827–1830.CrossRefGoogle Scholar
[2]Cairns, R. A., Mamun, A. A., Bingham, R., Dendy, R. O., Böstrom, R., Shukla, P. K. and Nairn, C. M. C. 1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712.CrossRefGoogle Scholar
[3]Cairns, R. A., Bingham, R., Dendy, R. O., Nairn, C. M. C., Shukla, P. K. and Mamun, A. A. 1995 Ion sound solitary waves with density depressions. J. Physique 5 (C6)43–48.Google Scholar
[4]Cairns, R. A., Mamun, A. A., Bingham, R. and Shukla, P. K. 1995 Ion-acoustic solitons in a magnetized plasma with nonthermal electrons. Phys. Scripta T63, 80–86.CrossRefGoogle Scholar
[5]Mamun, A. A. and Cairns, R. A. 1996 Stability of solitary waves in a magnetized non-thermal plasma. J. Plasma Phys. 56, 175–185.CrossRefGoogle Scholar
[6]Bandyopadhyay, A. and Das, K. P. 1999 Stability of solitary waves in a magnetized non-thermal plasma with warm ions. J. Plasma Phys. 62, 255–267.CrossRefGoogle Scholar
[7]Bandyopadhyay, A. and Das, K. P. 2000 Ion-acoustic double layers and solitary waves in a magnetized plasma consisting of warm ions and non-thermal electrons. Phys. Scripta 61, 92–96.CrossRefGoogle Scholar
[8]Bandyopadhyay, A. and Das, K. P. 2000 Stability of solitary kinetic alfvén waves and ion-acoustic waves in a nonthermal plasma. Phys. Plasmas 7, 3227–3237.CrossRefGoogle Scholar
[9]Bandyopadhyay, A. and Das, K. P. 2001 Stability of ion-acoustic double layers in a magnetized plasma consisting of warm ions and nonthermal electrons. Phys. Scripta 63, 145–149.CrossRefGoogle Scholar
[10]Bandyopadhyay, A. and Das, K. P. 2001 Growth rate of instability of obliquely propagating ion-acoustic solitons in a magnetized nonthermal plasma. J. Plasma Phys. 65, 131–150.CrossRefGoogle Scholar
[11]Bandyopadhyay, A. and Das, K. P. 2002 Higher order growth rate of instability of obliquely propagating kinetic alfvén and ion-acoustic solitons in a magnetized nonthermal plasma. J. Plasma Phys. 68, 285–303.CrossRefGoogle Scholar
[12]Mamun, A. A. 1997 Effect of ion-temperature on electrostatic solitary structures in non-thermal plasmas. Phys. Rev. E 55, 1852–1857.Google Scholar
[13]Mamun, A. A. 1998 Instability of obliquely propagating electrostatic solitary waves in magnetized nonthermal dusty plasma. Phys. Scripta 58, 505–509.CrossRefGoogle Scholar
[14]Mamun, A. A., Russell, S. M., Mendoza-Briceño, César. A., Alam, M. N., Datta, T. K. and Das, A. K. 2000 Multi-dimensional instability of electrostatic solitary structures in magnetized nonthermal dusty plasmas. Planet. Space Sci. 48, 163–173.CrossRefGoogle Scholar
[15]Pillay, S. R. and Verheest, F. 2005 Effect of non-thermal ion distributions on the Jeans instability in dusty plasmas. J. Plasma Phys. 71, 177–184.CrossRefGoogle Scholar
[16]Kourakis, I. and Shukla, P. K. 2005 Modulated dust-acoustic wave packets in a plasma with non-isothermal electrons and ions. J. Plasma Phys. 71, 185–201.CrossRefGoogle Scholar
[17]Das, J., Bandyopadhyay, A. and Das, K. P. 2006 Stability of an alternative solitary wave solution of an ion-acoustic wave obtained from MKdV-KdV-ZK equation in magnetized non-thermal plasma consisting of warm adiabatic ions. J. Plasma Phys. 72, 587–604.CrossRefGoogle Scholar
[18]Schamel, H. 1971. Stationary solutions of the electrostatic Vlasov equation. Plasma Phys. 13, 491–505.CrossRefGoogle Scholar
[19]Schamel, H. 1972. Stationary solitary, snoidal and sinusoidal ion acoustic waves. Plasma Phys. 14, 905–924.CrossRefGoogle Scholar
[20]Schamel, H. 1973. A modified Korteweg–de Vries equation for ion acoustic waves due to resonant electrons. J. Plasma Phys. 9, 377–387.CrossRefGoogle Scholar
[21]Mamun, A. A. 1997 Nonlinear propagation of ion-acoustic waves in a hot magnetized plasma with vortexlike electron distribution. Phys. Plasmas 5, 322–324.CrossRefGoogle Scholar
[22]Coffey, M. W. 1991 On the integrability of Schamel's modified Korteweg–de Vries equation. J. Phys. A: Math Gen. 24, L1345–L1352.CrossRefGoogle Scholar
[23]Verheest, F. and Hereman, W. 1994 Conservations laws and solitary wave solutions for generalized schamel equations. Phys. Scripta 50, 611–614.CrossRefGoogle Scholar
[24]Nejoh, Y. 1992 Double layers, spiky solitary waves, and explosive modes of relativistic ion-acoustic waves propagating in a plasma. Phys. Plasmas 5, 2830–2840.Google Scholar
[25]Allen, M. A. and Rowlands, G. 1993. Determination of the growth rate for the linearized Zakharov–Kuznetsov equation. J. Plasma Phys. 50, 413–424.CrossRefGoogle Scholar
[26]Allen, M. A. and Rowlands, G. 1995 Stability of obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73.CrossRefGoogle Scholar
[27]Munro, S. and Parkes, E. J., 2000 Stability of solitary-wave solutions to a modified Zakharov–Kuznetsov equation. J. Plasma Phys. 64, 411–426.CrossRefGoogle Scholar
[28]Munro, S. and Parkes, E. J. 2004 The stability of obliquely propagating solitary-wave solutions to a modified Zakharov–Kuznetsov equation. J. Plasma Phys. 70, 543–552.CrossRefGoogle Scholar
[29]Munro, S. and Parkes, E. J. 2005 The stability of obliquely-propagating solitary-wave solutions to Zakharov–Kuznetsov-type equations. J. Plasma Phys. 71, 695–708.Google Scholar
[30]Das, K. P. and Verheest, F. 1989 Ion-acoustic solitons in magnetized multi-component plasmas including negative ions. J. Plasma Phys. 41, 139–155.CrossRefGoogle Scholar
[31]Munro, S. and Parkes, E. J. 1999 The derivation of a modified Zakharov–Kuznetsov equation and the stability of its solution. J. Plasma Phys. 62, 305–317.CrossRefGoogle Scholar
[32]Wolfram, S. 1996 The Mathematica Book, 3rd edn.Cambridge, Wolfram Media/Cambridge University Press.Google Scholar
[33]Schamel, H. 1986 Electron holes, ion holes and double layers: electrostatic phase space structures in theory and experiment. Phys. Rep. 140, 161–191.CrossRefGoogle Scholar
[34]Schamel, H. 2000 Hole equlibria in Vlasov–Poisson systems: a challenge to wave theories of ideal plasmas. Phys. Plasmas 7, 4831–4844.CrossRefGoogle Scholar
[35]Luque, A. and Schamel, H. 2005 Electrostatic trapping as a key to the dynamics of plasmas, fluids and other collective systems. Phys. Rep. 415, 261–359.CrossRefGoogle Scholar
[36]Schamel, H. 1982 Stability of electron vortex structures in phase space. Phys. Rev. Lett. 48, 481–483.CrossRefGoogle Scholar
[37]Schamel, H. 1987 On the stability of localized electrostatic structures. Z. Naturf. a42, 1167–1174.CrossRefGoogle Scholar
[38]Jovanović, D. and Schamel, H. 2002 The stability of propagating slab electron holes in a magnetized plasma. Phys. Plasmas 9, 5079–5087.CrossRefGoogle Scholar