Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-29T05:04:14.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Critical densities for Korteweg–de Vries-like acoustic solitons in multi-ion plasmas

Published online by Cambridge University Press:  20 November 2015

Frank Verheest
Frank Verheest*
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000, South Africa
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A generic proof has been given that, for the acoustic mode with the highest velocity in a plasma comprising a number of fluid species and one kind of inertialess electrons, even though there can be critical densities (making the coefficient of the quadratic nonlinearity in a Korteweg–de Vries equation vanish), no supercritical densities exist (requiring the simultaneous annulment of both the quadratic and cubic nonlinearities in a reductive perturbation treatment). Similar conclusions hold upon expansion of the corresponding Sagdeev pseudopotential treatment. When there is only one (hot) electron species, the highest-velocity mode is an ion-acoustic one, but if there is an additional cool electron species, with its inertia taken into account, the highest-velocity mode is an electron-acoustic mode in a two-temperature plasma. The cool fluid species can have various polytropic pressure–density relations, including adiabatic and/or isothermal variations, whereas the hot inertialess electrons are modelled by extensions of the usual Boltzmann description that include non-thermal effects through Cairns, kappa or Tsallis distributions. Together, in this way quite a number of plasma models are covered. Unfortunately, there seems to be no equivalent generic statement for the slow modes, so that these have to be studied on a case-by-case basis, which for models with more than three species is far from straightforward, given the parameter ranges to be discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810605
Copyright
© Cambridge University Press 2015 

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

Baluku, T. K., Hellberg, M. A. & Verheest, F. 2010 New light on ion acoustic solitary waves in a plasma with two-temperature electrons. Europhys. Lett. 91, 15001.Google Scholar
Buti, B. 1980 Ion-acoustic holes in a two-electron-temperature plasma. Phys. Lett. A 76, 251–254.Google Scholar
Cairns, R. A., Mamun, A. A., Bingham, R., Boström, R., Dendy, R. O., Nairn, C. M. C. & Shukla, P. K. 1995 Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712.Google Scholar
Das, G. C. 1975 Ion-acoustic solitary waves in multicomponent plasmas with negative-ions. IEEE Trans. Plasma Sci. 3, 168–173.Google Scholar
Das, G. C. & Sarma, J. 1998 A new mathematical approach for finding the solitary waves in dusty plasma. Phys. Plasmas 5, 3918–3923.Google Scholar
Das, G. C. & Tagare, S. G. 1975 Propagation of ion-acoustic waves in a multi-component plasma. Plasma Phys. 17, 1025–1032.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2000 Tables of Integrals, Series, and Products, 6th edn., p. 1054. Academic.Google Scholar
Hellberg, M. A., Mace, R. L., Baluku, T. K., Kourakis, I. & Saini, N. S. 2009 Comment on ‘Mathematical and physical aspects of kappa velocity distribution’ [Phys. Plasmas, 14, 110702 (2007)]. Phys. Plasmas 16, 094701.Google Scholar
Korteweg, D. J. & de Vries, G. 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39, 422–443.Google Scholar
Lima, J. A. S., Silva, R. Jr & Santos, J. 2000 Plasma oscillations and nonextensive statistics. Phys. Rev. E 61, 3260–3263.Google Scholar
Nishihara, K. & Tajiri, M. 1981 Rarefaction ion-acoustic solitons in two-electron-temperature plasma. J. Phys. Soc. Japan 50, 4047–4053.Google Scholar
Olivier, C. P., Maharaj, S. K. & Bharuthram, R. 2015 Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion and two electron species. Phys. Plasmas 22, 082312.Google Scholar
Saberian, E. & Esfandyari-Kalejahi, A. 2013 Langmuir oscillations in a non-extensive electron–positron plasma. Phys. Rev. E 87, 053112.Google Scholar
Sagdeev, R. Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 4, p. 23. Consultants Bureau.Google Scholar
Tagare, S. G. 1986 Effect of ion-temperature on ion-acoustic solitons in a two-ion warm plasma with adiabatic positive and negative ions and isothermal electrons. J. Plasma Phys. 36, 301–312.Google Scholar
Tsallis, C. 1988 Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487.Google Scholar
Vasyliunas, V. M. 1968 A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73, 2839–2884.CrossRefGoogle Scholar
Verheest, F. 1988 Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities. J. Plasma Phys. 39, 71–79.Google Scholar
Verheest, F. 2000 Waves in Dusty Space Plasmas, pp. 109–112. Kluwer.Google Scholar
Verheest, F. 2013 Ambiguities in the Tsallis description of non-thermal plasma species. J. Plasma Phys. 79, 1031–1034.Google Scholar
Verheest, F., Cattaert, T., Hellberg, M. A. & Mace, R. L. 2006 On the existence of ion-acoustic double layers in two-electron temperature plasmas. Phys. Plasmas 13, 042301.Google Scholar
Verheest, F., Cattaert, T., Lakhina, G. S. & Singh, S. V. 2004 Gas-dynamic description of electrostatic solitons. J. Plasma Phys. 70, 237–250.Google Scholar
Verheest, F., Hereman, W. & Malfliet, W. 1999 Comment on ‘A new mathematical approach for finding the solitary waves in dusty plasma’ [Phys. Plasmas, 5, 3918 (1998)]. Phys. Plasmas 6, 4392–4393.Google Scholar
Verheest, F. & Pillay, S. R. 2008 Large amplitude dust-acoustic solitary waves and double layers in nonthermal plasmas. Phys. Plasmas 15, 013703.Google Scholar
Washimi, H. & Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998.Google Scholar
Watanabe, S. 1984 Ion acoustic soliton in plasma with negative ions. J. Phys. Soc. Japan 53, 950–956.Google Scholar
Watanabe, K. & Taniuti, T. 1977 Electron-acoustic mode in a plasma of two-temperature electrons. J. Phys. Soc. Japan 43, 1819–1820.Google Scholar