Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T14:21:28.969Z Has data issue: false hasContentIssue false
  • English
  • Français

Ion-acoustic double layers 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 April 2008

JAYASREE DAS ,
ANUP BANDYOPADHYAY  and
K. P. DAS
JAYASREE DAS
Affiliation:
Department of Mathematics, Chittaranjan College, 8A Beniatola Lane, Kolkata – 700 009, 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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

A combined Schamel's modified Korteweg–de Vries–Zakharov– Kuznetsov (S–KdV–ZK) equation efficiently describes the nonlinear behaviour of ion-acoustic waves in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons as prescribed by Cairns et al. (1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712), i.e. when the contribution of trapped electrons tends to zero. This combined S–KdV–ZK equation admits a double-layer solution propagating obliquely to the external uniform and static magnetic field. The condition for the existence of this double-layer solution has been derived. The three-dimensional stabilities of the double-layer solutions propagating obliquely to the external uniform and static magnetic field have been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands (1993 Determination of growth rate for linearized Zakharov–Kuznetsov equation. J. Plasma Phys. 50, 413–424; 1995 Stability obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73). It is found that the double-layer solutions of the combined S–KdV–ZK equation are stable at the lowest order, i.e. up to the order k, where k is the wave number of perturbation.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 2 , April 2008 , pp. 163 - 186
Copyright
Copyright © Cambridge University Press 2007

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

[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.Google 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 T 63, 80–86.Google 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.Google 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. 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
[9]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.Google 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.Google 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.Google 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.Google 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.Google 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]Allen, M. A. and Rowlands, G. 1993 Determination of growth rate for linearized Zakharov–Kuznetsov equation. J. Plasma Phys. 50, 413–424.CrossRefGoogle Scholar
[19]Allen, M. A. and Rowlands, G. 1995 Stability obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73.CrossRefGoogle Scholar
[20]Munro, S. and Parkes, E. J. 2000 Stability of solitary-wave solutions to a modified Zakharov–Kuznetsov equation. J. Plasma Phys. 64, 411–426.Google Scholar
[21]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
[22]Munro, S. and Parkes, E. J. 2005 The stability of obliquely-propagating solitary-wave solutions to a Zakharov–Kuznetsov-type equations. J. Plasma Phys. 71, 695–708.Google Scholar
[23]Schamel, H. 1971 Stationary solutions of the electrostatic Vlasov equation. Plasma Phys. 13, 491–505.CrossRefGoogle Scholar
[24]Schamel, H. 1972 Stationary solitary, snoidal and sinusoidal ion acoustic waves. Plasma Phys. 14, 905–924.Google Scholar
[25]Schamel, H. 1973 A modified Korteweg–de Varies equation for ion acoustic waves due to resonant electrons. J. Plasma Phys. 9, 377–387.Google Scholar
[26]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
[27]Schamel, H. 2000 Hole equlibria in Vlasov–Poisson systems: a challenge to wave theories of ideal plasmas. Phys. Plasmas 7, 4831–4844.Google Scholar
[28]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
[29]Schamel, H. 1982 Stability of electron vortex structures in phase space. Phys. Rev. Lett. 48, 481–483.CrossRefGoogle Scholar
[30]Schamel, H. 1987 On the stability of localized electrostatic structures. Z. Naturforsch. 42a, 1167–1174.CrossRefGoogle Scholar
[31]Jovanović, D. and Schamel, H. 2002 The stability of propagating slab electron holes in a magnetized plasma. Phys. Plasmas 9, 5079–5087.Google Scholar
[32]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
[33]Coffey, M. W. 1991 On the integrability of Schamel's modified Korteweg–de Vries equation. J. Phys. A: Math. Gen. 24, L1345–L1352.Google Scholar
[34]Verheest, F. and Hereman, W. 1994 Conservations laws and solitary wave solutions for generalized Schamel equations. Phys. Scripta 50, 611–614.Google Scholar
[35]Das, J., Bandyopadhyay, A. and Das, K. P. 2007 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. J. Plasma Phys. (to appear).Google Scholar
[36]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
[37]Sato, T. and Okuda, H. 1980 Ion-acoustic double layers. Phys. Rev. Lett. 44, 740–743.CrossRefGoogle Scholar
[38]Temerin, M., Cerny, K., Lotko, W. and Mozer, F. S. 1982 Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 1175–1179.Google Scholar
[39]Kim, K. Y. 1987 Theory of nonmonotonic double layers. Phys. Fluids 30, 3686–3694.CrossRefGoogle Scholar
[40]Böstrom, R., Gustafsson, G., Holback, B., Holmgren, G., Koskinen, H. and Kintner, P. 1988 Characteristics of solitary waves and weak double layers in the magnetospheric plasma. Phys. Rev. Lett. 61, 82–85.Google Scholar
[41]Böstrom, R. 1992 Observations of weak double layers on auroral field lines. IEEE Trans. Plasma Sci. 20, 756–763.CrossRefGoogle Scholar
[42]Vago, J. L., Kintner, P. M., Chesney, S. W., Arnoldy, R. L., Lynch, K. A.Moore, T. E. and Pollock, C. J. 1992 Transverse ion acceleration by localized lower-hybrid waves in the topside auroral ionosphere. J. Geophys. Res. 97, 16935–16957.CrossRefGoogle Scholar
[43]Han, J. M. and Kim, K. Y. 1994 Weak nonmonotonic double layers and sock-like structures in multispecies plasma. Plasma Phys. Control. Fusion 36, 1141–1157.Google Scholar
[44]Kim, S. S. and Kim, K. Y. 1998 Ion mass effects on sock-like structures in multi-species plasma. Plasma Phys. Control. Fusion 40, 1313–1325.Google Scholar
[45]Kim, T. H., Kim, S. S., Kim, H. Y. and Hwang, J. H. 2007 Modified Korteweg–de Vries theory of non-monotonic double layers in multi-species plasma. J. Plasma Phys. 73, 485–493.Google Scholar
[46]Bharuthram, R. and Shukla, P. K. 1986 Large amplitude ion-acoustic double layer in double Maxwellian electron plasma. Phys. Fluids 29, 3214–3218.Google Scholar
[47]Shukla, P. K. and Yu, M. Y. 1978 Exact solitary ion acoustic waves in a magnetoplasma. J. Math. Phys. 19, 2506–2508.Google Scholar
[48]Yu, M. Y., Shukla, P. K. and Bujarbarua, S. 1980 Fully nonlinear ion-acoustic solitary waves in a magnetized plasma. Phys. Fluids 23, 2146–2147.CrossRefGoogle Scholar
[49]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
[50]Wolfram, S. 1996 The Mathemetica Book, 3rd edn.Cambridge: Wolfram Media/Cambridge University Press.Google Scholar